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Introduction to the Philosophy of

Reginald Adrián Slavkovský · Michal Kutáš Edition Cognitive Studies Introduction to the

Reginald Adrián Slavkovský · Michal Kutáš Edition Cognitive Studies Peer reviewers Table of Contents

Prof. Silvia Gáliková, Ph.D. PhDr. Dezider Kamhal, Ph.D.

Editorial Board

Doc. Andrej Démuth ∙ Trnavská univerzita Prof. Josef Dolista ∙ Trnavská univerzita Prof. Silvia Gáliková ∙ Trnavská univerzita Prof. Peter Gärdenfors ∙ Lunds Universitet Dr. Richard Gray ∙ Cardiff University Doc. Marek Petrů ∙ Univerzita Palackého ∙ Olomouc 1. Introduction to the Philosophy of Language ..... 11 Dr. Adrián Slavkovský ∙ Trnavská univerzita 1.1 What is the Philosophy of Language Concerned with? What is Language? ...... 11 1.2 Why Get Interested in the Philosophy of Language? 13 1.3 Who and how Studies the Language? ...... 15 1.4 The Role of Philosophy and Cognitive Sciences in Studying Language ...... 16

2. Insight to the History ...... 19 2.1 Master Chuang ...... 19 2.2 Nagarjuna: Borders of Rationality ...... 20 2.3 John Locke ...... 22

3. Frege I: ( Script) ...... 24 3.1 Mathematical Proofs and Logic ...... 24 3.2 Schemes of ...... 26

The publication of this book is part of the project Innovative Forms of Education in Transform- 3.3 To Understand the Language of Nature ...... 27 ing University Education (code 26110230028) — preparation of a study program Cognitive Stud- 3.4 Predicate Logic System ...... 29 ies, which was supported by the European Union via its European Social Fund and by the Slovak Ministry of Education within the Operating Program Education. The text was prepared in the Centre of Cognitive Studies at the Department of Philosophy, Faculty of Philosophy in Trnava. 4. Frege II: (Bedeutung) ...... 31 4.1 The Reference of Proper and Single–argument Predicates ...... 31 © Reginald Adrián Slavkovský · Michal Kutáš ∙ 2013 4.2 The Reference of Multi–argument Predicates © Towarzystwo Słowaków w Polsce ∙ Kraków ∙ 2013 and Logical Operators ...... 36 © Filozofická fakulta Trnavskej univerzity v Trnave ∙ 2013 ISBN 978–83–7490–614–2 4.3 Principle of Compositionality ...... 39

5 4.4 Quantifiers and Their Importance ...... 40 11. of Speech Acts ...... 93 11.1 Ordinary Language Philosophy ...... 93 5. Frege III: Sense (Sinn) ...... 46 11.2 Importance of Social Context for ...... 94 5.1 The Relation between according to Frege ...... 46 12. ...... 99 5.2 Thought according to Frege ...... 49 12.1 Analytic and Synthetic ...... 99 12.2 Analyticity and Meaning ...... 102 6. Russell I: Definite ...... 51 12.3 Analyticity and ...... 105 6.1 Denoting ...... 51 12.4 Dogma of Analyticity and Syntheticity: Conclusion 107 6.2 Logical Analysis ...... 55 12.5 Dogma of Reductionism ...... 108 12.6 Pragmatism and Naturalisation of Epistemology . . 112 7. Russell II: Proper Names and ... 62 7.1 Proper Names ...... 62 ...... 115 7.2 Logical Atomism: Language Should Represent the World ...... 66

8. Russell III: by Acquaintance and Real Proper Names ...... 69 8.1 Knowledge by Acquaintance ...... 69 8.2 The Only Real Proper Names (Expressions Used in Pointing at an Object) ...... 71 8.3 Non–existent Subjects ...... 76

9. Russell and Frege: Russell’s and Type Theory ...... 78 9.1 Russell’s Paradox ...... 78 9.2 Type Theory ...... 80

10. ...... 83 10.1 Verifiability Criterion ...... 83 10.2 State ...... 87 10.3 Meaningfulness ...... 89

6 7 Introduction

In today globalized world, more than before people are being con- fronted with situations of foreign language environment or com- munication with people speaking different . The lan- guage of science has evolved to such form that a common person will comprehend a highly scientific article to a limited extent only. Information technology, whose software part is based on artificial programming languages, is infiltrating the ever growing number of areas of our life. As if even more pressingly than before, question from these and other areas can be heard, : What is language? What is sense? How do words carry sense? Many fields of study are concerned with language. This text- book is focusing on one line of language study only, for which the philosophy of language became common. It is intended pri- marily for students of the Master’s level of the Cognitive studies field of study, but everyone who wants to become familiar with this topic is invited to reach for it. As for the teaching method used in the textbook, we would like to point out that we have focused on certain important thoughts of selected philosophers only (mainly Frege and Russell, because they are virtually the “founders of the philosophy of language”). At least in case of some partial problems, we wanted to go in more details, because we hope that these more detailed analyses can be inspiring for the reader to the effect that he will become interested in more detailed and precise solution of problems that also impor- tant thinkers of were concerned with. We also

9 hope that this detailed will motivate him to immerse 1. Introduction to the Philosophy of Language in the study of original texts. Many works that are part of the ana- lytic traditions are not only some vague discussions about big top- ics, but they are attempts for very precise solution of certain, albeit partial, problems. Mainly due to this fact, certain analytic philoso- phers contributed significantly to the understanding in such fields as logic, , mathematics, , artificial intelligence and others. In chapters concerned in more detail with certain specific is- sues, we expect some knowledge of (propositional and predicate) Keywords: linguistic turn, analysis, language, philosophy of lan- logic, which is the content of basic university courses on logic. Be- guage, sense cause we think that without this basic knowledge many works of analytic philosophy (although not all) will remain closed off to per- 1.1 What is the Philosophy of Language Concerned with? son and the beauty of their ideas will not be visible. What is Language?

In Trnava, July 31, 2012 Adrián Slavkovský and Michal Kutáš One of the most prominent movement in contemporary phi- losophy is the philosophy of language. It is a broad movement, not quite unified, but connected through such approach to phi- losophising that emphasises the role of language as a medium of our thought and our relation to the reality. In the history of philosophy, individual thinkers who thematised the role of language have been emerging since ancient history, but only at the turn of 19th and 20th century such approach became widespread, therefore this shift is usually called the linguistic turn. The new emphasis on language was accompanied also by the conviction that the analysis of language, which can either help solving the problem or reveal that it is a pseudo–problem emerging from the misunderstanding of the functioning of lan- guage, is the road to solving traditional philosophical problems.

Apart from the emphasis on the role of language, science be- came another impulse and challenge for philosophy. For ones, the

10 11 enchantment with science and its exactness became an ideal the road , human gestures and facial expressions, formal languag- philosophy too should fulfil, whereas for others it became a warn- es in mathematics and logic, artificial computer languages, etc., can ing against the danger of narrower perception detached from re- be considered a language. Language is associated with the human ality in its complexity. The movement emerging from the effort ability to acquire certain system of and use it for commu- for scientific approach in philosophy is usually calledanalytical nication, i.e. for exchange of information. philosophy. It is mainly understood as broader movement, more or less also including the philosophy of language. 1.2 Why Get Interested in the Philosophy of Language? The same thinkers are considered inspirers of both movements: , , , G. E. Moore When people started to use language and communicate with it, de- and also logical positivists concentrated in the Vienna Circle. For scribe the world and ask questions, it was only a matter of time this , certain authors also use the terms “philosophy of lan- when the language itself becomes the subject of interest. There is guage” and “analytical philosophy” as synonyms. Said thinkers nothing left that we would not continuously try to grasp with lan- played an important role in forming modern logic too. Due to that, guage, therefore we ask with the language about the language it- philosophy of language is being sometimes taught within the stud- self too. What sort of special phenomenon is it, seemingly infinites- ies in logic as well. imal, demonstrating no notably distinctive differences from other Mainly in the English language area, a selected circle of topics animals, but playing an important role in changing the surface of and authors is understood under the philosophy of language, al- our planet and even its close surrounding? The language is like an though the topic of language is much broader. We will take this us- eminence grise of these changes. What is its essence? How does it age into account in this text, but we will cross it in part. Therefore facilitate communication, mutual understanding, but also the feel- also our usage of the term “philosophy of language” will be broader. ing that we understand the reality? The nature of meaning, use of language, knowledge of language If it is not too exaggerated, then we could also talk in case of and relation between language and reality are mainly stated as animals about at least the fact that certain objects, events, relation- the central topics of the philosophy of language. Also other top- ships are important to them through the fact that they need them ics are added in broader understanding of philosophy: how is the for living, they are fulfilling their certain needs. A cat does not hold language made and how are we learning it, the issue of translation, the meaning of milk in it as we are picturing the meaning of milk, understanding, metaphorical nature of language, the role of lan- for example, within the semantic triangle. When we speak about guage in forming social reality, impact on interpersonal relations the meaning of milk for a cat, it is more the way how we describe and even on understanding of self–identity. the of cat’s approaches to different realities: from total Language, like other important essential terms, cannot be easily indifference to necessity. But a cat has no mobile phones, air planes defined. Aslanguage in general, a complex system of symbols used nor institutionalized health care network up to teeth filling. Neither for communication is understood. The main and the most usual it has political parties and religions. But it has quite decent flexible representative are the human languages, which at first had acous- system of environmental adaptation, mainly due to emotional- tic shape in the form of speech and later also visual (or today also ity. This system enables it to adapt to outer and inner changes so haptic) shape of script. In the generalized form, also the system of the organism survives and remains in dynamic balance, which the

12 13 body perceives as something pleasant. Even despite rationality, this type of emotional significance is still an important moving agent of that is significantly contributing to our difference from oth- human behaviour. Life can therefore exist also without language. er beings. The most profound language–related questions What is language good for? Or is our language foreshadowing to us surpass facts perceived by senses, thus being philosophical that communication and mainly information exchange were here questions, aiming at the substance. Therefore every try for in some form in all times, that they form a basis of existence, but we knowledge needs the philosophy of language too. are able to realize it only thanks to language? The origin of our human communication can be anticipated just in connection with satisfying basic needs, therefore meanings of 1.3 Who and how Studies the Language? first sounds, words and sentences related probably to such situa- tions, as was the need to notify about danger or, to the contrary, We can find thoughts about languages already with the ancient about the source of food. When the language was created, the real- thinkers. Some of their observations deserve admiration even to- ity became as if doubled. Our finality forced and still forces us to day. Nowadays, there are several approaches to language. They fulfil our basic needs, but due to language, thoughts and , partially overlap, although each of it otherwise focuses its atten- the image of world is here as well and this image can stir us in simi- tion on slightly different aspect of language or studies it with dif- lar way as the reality itself. Our image of world should help us to ferent method. orientate ourselves in the real world so there should be a certain re- Linguistics studies the language as a relatively independent lationship of correspondence between them. The occurrence of phi- phenomenon and system. As founder of this approach is consid- losophy is connected with period in which humans had been using ered Ferdinand de Sausssure (1857 — 1913). He analysed the lan- quite complex language. Among expressions of wonder were also guage as a formal system of symbols. The function of a is questions: How can we keep putting our experience, tradition, the given through relations to other symbols. best of knowledge into fragile and passing sounds? But language Cognitive linguistics is one of the fields of cognitive sciences, also brought the possibility to use it to one’s benefit at the expense deals with explanation of mental structures and processes con- of others. Thus emerged the need to protect, defend, control the op- nected with linguistic knowledge. It studies the possibilities of eration of language. To understand each other, we need to define modelling the process of acquisition, reception and production the word. But that already brings us to . According to him, of language, whereas its main effort is to create a complex theory we can approach the meaning of word if we classify it correctly into on the interconnectedness of structural and procedural aspects a tidy structure of language, in which 10 main branches stem from of linguistic knowledge. Mária Bednáriková pursues cognitive lin- the trunk and which branch further into genders and classes. guistic in more detail in the textbook dedicated to this topic (Bed- náriková, 2013). Among other specialized areas of research are the neurolinguis- If we want to better understand ourselves, we cannot bypass tics, psycholinguistics, evolutionary linguistics, comparative lin- the language, because we would have bypassed something guistics, sociolinguistics, computer linguistics, and others.

14 15 language into another, the question of meaning emerges in full. Jaroslav Peregrin characterizes the main line of the phi- And this question is sublimely philosophical. There are various losophy of language as “... an attempt to think about tradi- of meaning. Come put emphasis on experience, others on tional philosophical issues with the “mathematical” of innateness, on the position of concept in the structure of concepts, the twentieth century.” The boundaries of this approach are on conditions of , on the method of usage, on implications rather vague. Its features (whereas some of them define the and practical use. Each theory exposes certain aspect of meaning. method) include: analysis, anti–psychologism in logic, logical We made first steps on the path of machine translation and we also analysis, philosophical interpretation of thought through created programmes that are able to lead a discussion. However, in philosophical interpretation of language, linguistic turn, pri- both cases we can find mistakes quite fast, pointing out that our macy of the philosophy of language and rejection of meta- understanding of meaning is still rather partial and little complex. physics (Peregrin, 2005, 17–22). None of these features are necessary. Besides that, nowadays a discussion across origi- nally divided approaches is under way. Said problems are among those that inspire thinkers today to questions about language and meaning. A good aid for us to understand what led different thinkers to their under- 1.4 The Role of Philosophy and Cognitive Sciences standing of language and meaning is to put these question in Studying Language into the context of work and efforts of given author and into the context of given period. Frege, who inspired many with Many impulses for deeper understanding of language, but also his interest in meaning, was concerned with thoroughness many applications come from the area of cognitive fields. As I am and objectiveness of proving in mathematics. writing this text, a computer programme is checking my spelling in a quite simple way. Should I make a mistake and write a word that absolutely does not belong to the lexicon of Slovak language, Many proofs were indeed thorough enough, but Frege did not like the programme will underline it. The functioning principle of such the argumentation for this thoroughness, therefore he was looking check is very simple: it is enough for the programme to contain all for new foundations. His understanding of meaning is thus marked words of given language and all their correctly created forms and by his direction. He himself was aware that he is engaged with only it just finds out if the word is on the list. Far more difficult is to cre- a narrow slice of knowledge and science and had no aspirations for ate programmes that are able to read written texts in a way that is creation of an universal theory of meaning, which would apply to getting very close to how a human reads text. Such programmes all areas of life and reality. The effort for accuracy down to the level are already available. Even more difficult is to programme the re- of concepts helps the science to be a better science. But when we verse process: to record the acoustic form of speech, analyse it and start to ask: What is science? Where is it heading? Can we develop transcribe into text. it without negative side consequences? etc., we open up to broader In case of previous applications it rather poses a technical understanding of meaning. problem. But during attempts for machine translation from one

16 17 Recommended Literature 2. Insight to the History

MARVAN, T.: Otázka významu. Cesty analytické filosofie jazyka. Praha : Togga, 2010, pp. 7 — 29. MARVAN, T. — HVORECKÝ, J. (eds.): Základní pojmy filosofie jazyka a mysli. Nym- burk : OPS, 2007. PEREGRIN, J.: Kapitoly z analytické filosofie. Praha : Filosofia, 2005, pp. 13 — 29. THAGARD, P.: Úvod do kognitivní vědy. Mysl a myšlení. Praha : Portál, 2001, pp. 76 — 94. WOLF, M. P.: Philosophy of Language. In: Internet Encyclopedia of Philosophy. [on- line]. 2009. [cit. 12. 7. 2012]. Available on the internet: . ISSN 2161–0002. Keywords: relativity of language, meaning behind words, identity and difference, language and thinking

2.1 Master Chuang

From the down of philosophical reflection, many thinkers realised that language is an amazing communication tool, yet it forms cer- tain threats. Neither words, nor sentences can completely express the meaning; meaning transcendents them. In ancient China, the fact was probably the most realised by master Chuang (around 4th–3rd century BC), a representative of Daoism in its early form. For one thing, Master Chuang makes the role of language topical, for another in his way of philosophising; it clearly reflects how he understands the role of language for thinking and recognition. Ac- cording to him, language is an obstacle in following the Dao way and names (ming) are just an artificial and disobedient viewport of reality. He mocks rational philosophising. Humour is an important tool for him to look in whereby the first object of irony and humour is he himself. In master Chuang’s opinion, wisdom the second to language. He says on the intermediating role of words: “The role of the net is to catch fish; when it is caught, we think about the net no more. The function of the rabbit trap is to catch the rabbit. When it is caught, we think about the trap no more. The role of words is to express the meaning. When the meaning is expressed, we forget about the

18 19 words. Where should I search for a man that can forget about the words so that I can talk with him?” (Cheng, 2006, p.112) itself. Our deepest emotional and existential problems rise Words are an instrument for master Chuang. Without them, it from the fact that we stick to cognitive approaches and as- would be more difficult to communicate and all our cognitive func- sumptions. tions would be weakened. Behind the last sigh, there is probably an experience of incomprehension, taking at words, and stress in communication. One can anticipates that if we want to understand Illusions created by language can be explained by the following other person, it is not enough to listen to their words, as though it example in Nagarjuna’s teaching. The “Milan is walking” were self–standing semantic units. It is necessary to listen to what creates an illusion of mutual separateness of Milan and the walk- does not fit into words, what is behind them. ing. Without Milan, there would not be any walking, and without In his opinion, a confrontation of opinions is a non–sense, as walking, it would be a different Milan. “Milan” and “is walking” are there is no standpoint from which it could be possible to consider, inseparable, but under the language influence we can imagine that how the things “really” are. Recognition is ability to hit the reality. someone named Milan exists independently on the walking and A wise man cannot be taken in by language and a prideful idea that the walking can exist independently on Milan. Linguistic differ- they can “claim something”. ences hide the real inseparability of factors of happening. Language also creates an illusion of unchanged Milan. Even though Milan is not walking, he is still considered Milan, so his basic Master Chuang’s approach means a reflection of language, but identity stays unchanged and untouched by various activities ex- the one leading to language usage so that language could be pressed by verbs. But in fact, we are changed by our actions (karma). transcended to show fullness of life. In this, he is a predeces- Assignment of language role of unchanged Milan whose identity sor of the attitude emphasising the pragmatic aspect of life. is not changing considering time and actions, leads to postulation of an unchanged “me” (atman); substance remaining permanent from life to life (this argumentation belongs to Buddhist critics of 2.2 Nagarjuna: Borders of Rationality traditional Brahma philosophical schools). Metaphysics rises from linguistic constructions. “Milan” and “the walking” are neither any- thing separate nor identical; the middle way should be kept. According to Nagarjuna, an ancient Indian Buddhist thinker This leads to correlative perception. Understanding of the (aprox. 2nd — 3rd century), at closer look, even the most ra- “game of black and white” means that explicit contrasts are always tional theories are incoherent and irrational (drishti). Think- implicit allies. Such relation between identity and difference is ing expects the category of identity and difference, but these later called by Shankara, another Indian thinker, non–duality. Lan- are not coherent, they refer to nothing (absolute difference guage cannot get over duality, like a picture cannot overcome its would mean total separateness, gap, and a loss of any coher- two dimensions. But as thank to perspective we can see depth in ence). Therefore language does not refer to things, but to the picture, understanding of non–duality opens up a new perspec- tive of reality.

20 21 2.3 John Locke Recommended Literature

M. Morris begins its book on philosophy of language by the BONDY, E.: Indická filosofie. Praha : Vokno, 1997, pp. 126 — 149. introduction of eight thesis summarising the most important CHENG, A.: Dějiny čínského myšlení. Praha : DharmaGaia, 2006, pp. 101 — 128. MORRIS, M.: An Introduction to the Philosophy of Language. New York : Cambridge features of Lock’s comprehension of language. When John Locke University Press, 2007, pp. 5 — 20. (1632 — 1704) started to examine the content of mind — the idea in human mind — it brought him to a certain conception of lan- guage. Some features of his concept were accepted by later think- ers led by mathematician and logician Gottlob Frege (1848 — 1925) and they continued with them, whereas others were rejected. Let’s introduce the abovementioned thesis: (L1) Nature of language is determined by its function. (L2) The function of language is to enable communication. (L3) Thinking is considered to be what is communicated by means of language. (L4) Words mark components of what is communicated by means of language. (L5) Components of thinking are ideas. (L6) Ideas of one person cannot be perceived by a different person. (L7) A relation between words and what they indicate is accidental. (L8) Words in their essence do not carry a meaning. As M. Morris shows, thesis (L1), (L2), (L7) and (L8) were taken to the analytical tradition, whereas others were not.

Gottlob Frege was troubled by the idea that at the end, math- ematic proofs should be based on something as subjective and omissible as thoughts in heads. Therefore he radically changed some aspects of long accepted and relatively natu- ral Lock’s conception of language.

22 23 3. Frege I: Logic (Concept Script) geometry from five postulates (axioms). Such approach to con- struction of certain theory is therefore called axiomatic approach. For a mathematical to be valid, it cannot be done ran- domly, but certain rules must be observed. These rules must be included in proving by implication, as Euclid did. In that case we are observing them, but we have not recorded them anywhere. But if we have not explicitly expressed them, how do we know, if we followed them in a specific proof? To be able to clearly determine at all times whether we followed these rules of proof, it would be Keywords: predicate logic, proof, axiom, concept script good to create their list, to make an inventory of them. And exactly this was one of Gottlobe Frege’s goals. 3.1 Mathematical Proofs and Logic His motivation was to ensure validity of proofs in mathematics. For us to be able to clearly verify if the proof was valid, it would be good to decompose it to such steps, which would be evident to be Gottlobe Frege can be considered the “father” of analytical valid. If, however, some step was not evident to be valid, it would philosophy. But his original intent was not to answer phil- not be certain, if the proof as a whole is valid either. Again, to de- osophical questions. He rather wanted to strengthen the termine whether given step of the proof is valid, we would look at foundations of mathematics: to elaborate proofs and to cre- whether it has the valid form, i.e. we would compare its form with ate an inventory of proper logic steps in inference. For us to the list of valid forms (schemes) of derivation, and if we found this understand the motivation behind his theoretical work and scheme in this list, it would be clear that this step is valid. how is this related to philosophy of language, it will be good So Frege wanted to find such schemes for individual possible to think for a moment about what a proof really is. steps of proof, for which their validity would be evident. Never- theless, the obviousness of validity of these forms in case of all of them cannot have the form, which would consist of being on a list. In logic, proof is understood as inference of some assertion, called To avoid an infinite regress, it is necessary to announce at least one conclusion, from other assertions, which are . These prem- of these lists of schemes of inference as the list of valid schemes of ises can be sentences we have proven earlier or they can be the so– inference without deriving it from another list. Such list is called called axioms — sentences considered as true without the need to the list of essential rules of valid inference. Of course, it would be prove them. Proof is therefore a sequence of steps through which good if schemes on this list would be as “self–evident” as possible, we get from premises to the conclusion. obvious for all or for at least most of people. But we will not dis- The approach, used for the first time by Greek mathematician cuss here the problem how and if something can be evident in this Euclid (he lived in 4th century BC) in his Elements for creation of direct way. the system of geometry, got gradually established in mathemat- ics. With the help of proofs, he inferred all known statements of

24 25 3.2 Schemes of Inference His system of propositional logic included, apart from these ba- sic elements, also the rule of substitutions (Gahér, 2004, p. 95). With the help of said basic elements, we can infer all other valid It is a huge progress to have a list of essential valid schemes rules of inference and all necessarily true forms of statements (the- of inference. Because if they are really valid, we can deter- orems of propositional logic). If we succeed in decomposing given mine validity of any proof with the help of this list. proof into steps, which all will be done according to these rules or will contain such necessarily true forms of statements (axioms or forms purely derived from axioms — ), it will be certain It is known that at the level of propositional logic, it is possible that given proof is valid. to define the propositional logic system so that there is only one We could ask, however, why should we concern ourselves with axiom defined through one logical operator and one inference rule. logic, if we want to find validity in mathematics? The answer is, Such system was created by French logician J. G. P. Nicod (Gahér, that if we want to ensure validity of proving in any field of sci- 2003, p. 94). This system is created artificially with the goal of hav- ence, we have to turn to the field that is concerned with what true ing minimum premises, however, his creator achieved it at the ex- proving is, and exactly such field is logic. Although it might not be pense of great complexity. The obviousness of his axiom is out of obvious at the first glance, we use rules and laws of logic in math- question. ematics too. If, for example, one assertion follows from another, Frege in his system 6 axioms and one inference rule. We will and this first assertion is valid, then the second assertion must be show it through notation used in today propositional logic (Gahér, valid as well. This is, however, description of the rule called modus 2003, p. 95): ponens, which, as we have already seen, Frege included as basic one in his system. Whenever we think like this (in any science, includ- (q i (p i q)) ing natural sciences), we are using this rule. Naturally, we can use (p i (q i r)) i ((p i q) i (q i r)) it as if “intuitively” and its abstract scheme does not have to tell (p i (q i r)) i (q i (p i r)) us anything, unless we have some training in more abstract logical (p i q) i (¬q i ¬p) thinking. Even in mathematics we can do inference according to (¬¬p i p) this rules without being aware that we are using something, that (p i ¬¬p) was define by logicians as one of valid schemes of inference.

Frege set as the inference rule: 3.3 To Understand the Language of Nature

p i q Because there are many logical systems, with certain amount of p simplification we could say that logic is in certain (implicit) way q included in mathematics (but obviously also in every contempo- rary scientific system, including the theory of natural sciences), because it is necessary to use also logical rules and logical axioms

26 27 or theorems in mathematical inference. Let’s also consider that 3.4 Predicate Logic System mathematics and are necessary also in empiri- cal sciences, for example in physics, which practically would not In the previous text we mentioned Frege’s formalisation of propo- do without mathematics. Galileo’s statement should be mentioned sitional logic. With regard to this type of logic, we have to give Frege in this regard, that the book of nature is written in mathematical credit for its re–discovery. Although this logic was being developed language. With this assumption, one of the basic feature of incred- already by Stoics, however, in Frege’s period it was in fact forgotten. ibly broad and fruitful research programme that successfully con- Moreover the logic, whose formal and symbolic form Frege creat- tinues already for three centuries and which we call modern sci- ed, was broader and richer than propositional logic. Frege created ences, is established. theoretical system that formally grasps what we call predicate logic today. This logic contains whole classical propositional logic. We can thus conclude that in his effort to ensure validity of math- We could say that our successes in the study of world we live ematical proofs, Frege re–discovered the propositional logic and in are very powerful support for assertion that our universe discovered predicate logic, whereas he grasped them also formally speaks certain language. However, this language is neither with a symbolic notation. Just this fact alone is enough, according Slovak, nor English, nor Chinese, but the language of math- to many, to secure him a permanent place in the , ematics. But if the language of mathematics is so important, mathematics, but also philosophy. this fact is partially transferred to logic as well. Frege did not record statements, and proofs in the same way as we do it in predicate logic today. He named his nota- tion method concept script. Frege’s notation method and the mod- Why only partially? Although the founders of analytical philoso- ern notation method are in fact positively mutually convertible. phy on the turn of 19th and 20th century cherished the hope for that The modern notation is simpler and clearer, therefore we will use it would be possible to derive the whole mathematics from logic, it in the following text. Reader interested in Frege’s notation can later it turned out it is not possible. Also the is needed become familiar with it also in detailed monograph dedicated to for it. But as notices one of the most important philosophers of an- G. Frege’s logic (Kolman, 2002). But we can in fact say that Frege’s alytical tradition, Willard van Orman Quine (Quine, 2004), this fact concept script is actually modern predicate logic. does not create a problem from epistemological standpoint. How- We can assemble all necessary schemes of inferences in predicate ever, not all axioms of the set theory are as obvious as we would logic with the help of operators of , conjunction, disjunc- desired (at first sight, they do not seem any obvious to us). But as tion, implication and equivalence (which correspond to commonly we already mentioned before, Frege wanted to find such very foun- used principles of our thought) and with the help of quantifiers dations of mathematics, which would be obvious. “for all” (this quantifier is called universal quantifier and today it’s denoted with the symbol “∀”) and “there is at least one” (this quan- tifier is called existential quantified and today it’s denoted with the symbol “∃”). Also in case of quantifiers, just one would be enough, because to say that something holds true for all items is the same

28 29 as say there is no item for which it would not hold true. In the same 4. Frege II: Reference (Bedeutung) way it is possible in Frege’s system to record predicates and indi- viduals. With the help of Frege’s notation it it therefore possible to express all valid schemes of inference in predicate logic.

In conclusion, let’s summarise in brief how does this all relate to philosophy of language. Frege wanted to elaborate math- ematical proofs even more. Work on this task brought him not only to creation of modern logic, but also to think deeper Keywords: denotation, meaning, individual, predicate, function, do- about basic terms of mathematics, which is a number, for ex- main of definition, concept ample. When he began to ask: What is the meaning of the word “number”? and How are we using this word?, he initi- 4.1 The Reference of Proper Names and Single–argument ated a line of thought typical for the philosophy of language. Predicates

Frege assigns to language expression something he calls reference Recommended Literature (Bedeutung in German). But it should be noted that Frege used dif- ferent terminology than it is used today. Frege uses this expression KOLMAN, V.: Logika Gottloba Frega. Praha : Filosofia, 2002. to describe something we would call denotation today. We would MILLER, A.: Philosophy of Language. London: Routledge, 2007, pp. 1 — 22. also say that the language expression refers to what Frege calls MORRIS, M.: An Introduction to the Philosophy of Language. New York: Cambridge university press, 2007, pp. 21 — 48. reference. PEREGRIN, J.: Kapitoly z analytické filosofie. Praha: Filosofia, 2005, pp. 31 — 67. PRIEST, G.: Logika. Praha : Dokořán, 2007, pp. 10 — 28. According to Frege, individual types of expressions corre- spond with respective types of references. For Frege, the ref- erence of proper name is the object described by this proper name. For example, the reference of the expression “Socrates” is, according to Frege, the specific person, who is called like this and lived in the times of ancient Greece in Athens. Similarly it applies to definite descriptions too, in this case: “Greek philosopher who was a teacher of , husband of Xanthippe, and was sentenced to death in Athens”.

30 31 For Frege, the reference of such expression is also one spe- We can take x as a variable, as something, instead of which cer- cific object, which is again the mentioned Greek philosopher. It tain element from certain set, called domain of definition of our would hold true also if someone in Athens, in the period when predicate, can be substituted. Such use of predicates is similar to Socrates lived, would have pointed at him and had used for it, using functions in mathematics. And Frege really came with the for example, the expression “this man”. The specific separate idea to understand predicates as functions. For example in math- things, which is the reference of expressions “Socrates” and ematics, the function f(x) = 2x has certain domain of definition (let “Greek philosopher who was a teacher of Plato, husband of Xan- us choose the set of natural numbers) and certain range (it will also thippe, and was sentenced to death in Athens”, is reference of this be a set of natural numbers). Any element from the domain of defi- expression as well. nition can be substituted for the variable x. The variable x is also We would record these expressions in the language of modern usually called the argument of function f. If for I we substitute, for symbolic logic, founded right by Frege, with the help of individual example, the number 3, the value of said function will be the num- constant, e.g. “a” (we will use lower case letters from the beginning ber 6. We usually record it as follows of the alphabet “a”, “b”, “c”, “d”, etc. for individual constants). However, in language we often express also properties of things f(3) = 6 or relations between things. Frege calls such language expressions predicates. If we take, for example, the following sentence: but for the purposes of further explanation, we can express it like this: Socrates is mortal. f(3) –––> 6 then we understand the expression “... is mortal” as predicate that expresses the to be mortal. As we can notice, in this The symbol “–––>” expresses the fact that the function with expression is an empty space, marked with three dots “...”, in which given argument on the left side of this symbol has the value which we could put some other expression, referring to specific object. is written on its right side. The set of things to which it is reasonable to assign the property We can also understand our predicate x is mortal as a func- of mortality, is the maximum possible domain of definition of our tion, whose domain of definition can be, for example, all living predicate. It is a set of elements whose names we can put into the being (that means that we could substitute the proper names of empty place in the expression “... is mortal”. To define this place, living beings or certain descriptions referring to a living being or we do not have to necessarily use the expression “...”, but we can expressions as “this” and “this dog”, etc. for the expression “x”). We use also another expression, e.g. “x”, which would have the same described the argument of this function as x. We use the letters “F”, function for us. Then we could record the considered predicate for “G”, “H”, etc. to denote predicates in modern denotation. Because it example like this: is an analogy to use of functions in mathematics, we can record the expression “x is mortal” as follows: x is mortal F(x)

32 33 where “F” denotes the predicate to be mortal. Socrates is also In this denotation it is clear that the function, corresponding a living being, he is therefore an element of the domain of defini- with the predicate, actually becomes a statement, should we sub- tion of our function F. So the expression “Socrates” can be substi- stitute the variable with a suitable individual (a suitable individual tuted for the expression “x”, which corresponds with substituting x is an individual from its domain of definition). So the fact that it re- with Socrates. If we describe Socrates within the language of mod- fers to –value is quite understandable. We can express it also ern symbolic logic with the individual constant “a”, we can record in the following way: because in logic we call that what can assume the expression Socrates is mortal in this language as follows: the truth–value as statement, therefore for Frege the meaning of statements is one of the truth–value True or . For example, the F(a) meaning of specific statement “Socrates is mortal” or its formal de- notation “F(a)”, is the truth–value True. Our function should, however, gives us certain value, which However, the expression “x is mortal” (or, if we wanted to em- depends on its argument. In this case Socrates was the argument phasize that “x” actually refers to an empty space, we can write “... of the function, but what was its value? Frege proposed that we is mortal”) is not a statement. Unless we put in the place marked considered as values of functions, which correspond to predicates, with the expression “x” a name of some entity out of the domain always one of the truth–value True or False. The value of function of definition, we cannot say, if this expression is true or false. This F is in case that its argument is Socrates, the value True. We can expression therefore cannot be a statement and its meaning prob- record it as follows: ably would not be one of the truth–values. According to Frege, the meaning of such expression is just the function from the domain F(a) –––> True of definition to the range, about which we we said it corresponds with the predicate. The meaning of predicate is therefore the func- If we want to express it less formally, for clarification, we can tion that always returns as value one of the member of set {True, write also False}. Frege also calls that what has a meaning such functions, concepts. We can understand it like this that, for example, the pred- F(Socrates) –––> True icate expressing certain property defines which objects fall under the concept, which corresponds with given expression. The reason or: is that given predicate assigns to individuals having this property the value True and those not having the property, value False. So Mortal(Socrates) –––> True for example the predicate x is mortal assigns the value True right to those objects in the world, which fall under the concept mortal, or: i.e. those, which are mortal; on the other hands, to objects for which it is not true that they are mortal, it assigns the value False. Thus in Socrates is mortal –––> True fact, we can translate the label “concept script”, given certain free- dom, as “predicate script”, or “formal and symbolic language to talk about predicates”; or else: “predicate logic”.

34 35 4.2 The Reference of Multi–argument Predicates This is already a statement, i.e. an entity, for which it worth to and Logical Operators ask about the truth–value. In our case, this statement acquires the truth–value False: However, not only one–argument predicates exist (those that have only one argument, such as the predicate x is mortal) but also V(b, c) –––> False multi–argument (those having 2, 3 or more arguments). One–argu- ment (or also unary) predicates express properties, such as mor- Because by meaning according to Frege we understand today what tal, red, big, etc. But with certain level of abstraction, as a property we usually describe as denotation, then we can say that the (Frege’s) can be understood not only what we express by adjectives in the meaning or the denotation of this sentence is the entity False. language, but also what we express in it by nouns (a predicate can Frege thus understands adjectives, nouns and verbs as possible then be, e.g., x is mammal) or what we express with verbs (e.g. pred- predicates. But in language, there are also,e.g. conjunctions, such as icate x is running). Multi–argument (binary, trinary, etc.) predicate “if ..., then ...”, “..., or ...”, “... and ...” etc. Some of them have a prominent express relations between things, e.g. x is taller than y, or x gave z to position in propositional logic, we call them logical operators and y, etc. We could transcribe such predicates into the formal language write them with the symbols such as material implication (“i”), dis- of predicate logic as follows: junction (“˅”), conjunction (“˄”), etc. We can understand logical operators as functions, however in Predicate Predicate notation in formal language this case they are functions, for which the set of truth–values {True, x is taller than y V(x, y) False} is not only their range but also their domain of definition. x gave z to y D(x, y, z) In predicate logic, apart from individual variables (which we recorded with letters from the end of alphabet “x”, “y”, “z”, etc., i.e. Also in this case the predicate can correspond with the verb, as variables, which can be substituted with individuals, specifically for example the predicate x is lying to y, and so on. The meaning separate things such as Socrates, Bratislava, Atlantic ocean, etc.) of such expressions are also functions of sets, from which we se- we have also propositional variables, which can assume one of the lect elements, which we will substituted for given variables into truth–values True or False and which we will record with lower a binary set {True, False}. In case we substitute all variables with case letters “p”, “q”, “r”, etc. We can then formally rewrite the follow- some singular expressions (i.e. such, corresponding to individual ing expressions like this: constants in predicate logic), we will get statements. E.g. if we label the Gerlachovský Peak with the individual constant “b” and Mount “It is not true, that p” ¬p Everest with the individual constant “c”, then we can record the fol- “If p, then q” p i q lowing sentence like this: “p or q” p ˄ q “p and q” p ˅ q The Gerlachovský Peak is taller than Mount Everest V(b, c) “p if and only if q” p cd q

36 37 With regard to expressions from ordinary language (left side), from the domain of definition of the implication function (i.e. some the expressions “p” and “q” mark places, which we can substitute statements), this expression too becomes a statement. with some language expression, whose meaning is some element from the domain of definition of given function. The elements 4.3 Principle of Compositionality of domain of definition of logical functions are the truth–values, so we can substitute “p” and “q” with certain statements (because statements are language expressions whose meaning are truth– Frege strived for the so–called principle of compositionality values). With regard to formal notation (right side), here too are that says the meaning of expression is fully determined by the expressions “p” and “q” expressions whose meaning are truth– the meaning of its parts, to hold true in his system. values. Therefore the expressions “p” and “q” “represent” the state- ments. Because, according to Frege, the meaning of statements are truth–values, then we can substitute variables p and q with just According to this principle, the meaning of statement we get af- the truth–values. Let us further note, that we choose different ex- ter substituting “p” and “q” in the expression “If p, then q” must de- pressions (“p” and “q”) instead of one expression (“...”) also because pend on meanings of all elements of this composed statement. The in case of logical operators, the order of arguments in general mat- meaning of statements substituted for “p” and “q” will be truth–val- ters. Specifically, the order of arguments is important in case of ues, the meaning of expression “if p, then q” is the function called implication. implication, which after substituting p and q with truth–values re- If we substitute propositional variables with any of truth–val- turns one of the values True and False. If we substituted “p” with ues, logical functions, to which we will apply these propositional the statement “Socrates is human” and “q” with the statement “So- variables, will return to us as value one of the truth–values. For us crates is mortal”, we get this statement: to see more clearly the similarity to predicates, which are also func- tions for Frege, we recorded the statements in the second column If Socrates is human, then Socrates is mortal. by putting the truth–values into the given function with prefix notation: The meaning of the statement “Socrates is human” is, in Frege’s con- cept, the truth–value True. The meaning of the statement “Socrates ¬True –––> False ¬(True) –––> False is mortal” is also True. The meaning of the statement “If p, then True d False –––> False d(True, False) –––> False q” is the function called implication, which assigns truth–values to True ˅ False –––> True ˅(True, False) –––> True truth–values as follows: True ˄ False –––> False ˄(True, False) –––> False True cd True –––> True cd(True, True) –––> True p q p ® q False False True Like in the case of predicate functions, if we put in the expression True False False “If p, then q” language expressions whose meaning are elements False True True True True True

38 39 Because the statement is composed of three parts, “p”, “q”, and not exclude that we can substitute x and y with also with the same “...d...”, which are interconnected like this: p d q, it will have the object, i.e. that in some cases x = y. But we do not have to mind this truth–value True, which for Frege is the meaning of said statement. in case of our statement, as long as we do not mind that each thing As we see, this meaning was fully determined by its elements (“p”, is related to itself as well. “q” and “...d...”) and their arrangement (p d q). Likewise, we could formally record the sentence “Some things relate to each other” with the help of symbol called existential 4.4 Quantifiers and Their Importance quantifier: ∃“ ” which we use in noting the expression “For certain x holds true that α(x)”. Such expression can be formally recorded In language, we can also find expressions like “all”, “everyone”, as “(∃x)α(x)”. Then we can record the sentence “Some things are re- “some”, etc. Let us take, for example, the following sentence: lated to each other” like this:

Everything is related to everything. (∃x)(∃y)S(x, y)

According to what we have already said, we can see the predicate But what is the meaning of expressions “(“x)α(x)” and “(∃x)α(x)”? Let x is related to y in it. We can record it as “S(x, y)”. Today, when not- us not forget that the expression “α(x)” actually means to us the ing the expression “For all x holds true, that...” we use the symbol place, where we can put some grammatically correctly created ex- called universal quantifier: ∀“ ”. Then we can formally record the ex- pression of predicate logic, which contains at least one free varia- pression “For all x holds true, that ...” e.g. like this: “(∀x)...”. However, ble x, i.e. at least one place, where we can again put a name of some there is one problem here. In the part of expression marked with certain separate thing. That means that by adding the expression “...”, it is predicated of the same, of which it is predicated in the part “(∀x)” or the expression “(∃x)” before the expression ”α(x)”, we still marked with “(∀x)”. Therefore, from now on we will use the expres- do not get a statement. We get it only in the case, when we substi- sion “α(x)” instead of the expression “...”. This will represent for us tute “α(x)” with some grammatically correctly created expression a certain grammatically correctly created expression of predicate of predicate logic, which contains at least one free variable x, i.e. logic, in which is at least one free occurrence of the variable x. We which contains by itself at least one place, where we can again put could also say that we have placed the symbol “x” in the expression a name of some certain separate thing. If we do not make such sub- “α(x)” because we wanted to note that this expression refers to the stitution, we have to regard the place marked with the expression same to which the expression “For all x holds true, that...” refers “α(x)” as a variable, but not as an individual variable (because we — therefore in both expressions the symbol “x” occurs. cannot put any individual there), but as a variable, which can be Then we can record the previous sentence as follows: substituted with some expression containing at least one predicate and at least one free occurrence of the variable x. (∀x)(∀y)S(x, y) Let us assume, for simplicity, that “α(x)” will have the form “F(x)”. That means that we could substitute the variable α(x) with We can read this notation like this: for all pairs of things (x and y) some unary predicate containing the variable x. α(x) is now practi- it holds true that they are related. Of course, such notation does cally a “predicate variable”, whose domain of definition are unary

40 41 predicates). We can then understand the expression “(∀x)α(x)” as {(False, False, True), (False, True, True), (True, False, False), (True, the name of function that returns as value one of the truth–val- True, True)} ues and its argument must be some unary predicate containing the variable x. We can express it also when we say that it is a second– What is then the extension of the function (∀x)α(x)? Because order function. we understand α(x) as a variable which can be substituted with We can explain this with the help of the term extension of func- one–argument predicates with the variable x, we can substitute tion, as used by, e.g. A. Miller (Miller, 2007, p. 14). Under the exten- it with, e.g. predicates H(x) (x is human), M(x) (x is mortal), D(x) (x sion of function with n–1 arguments, we have in mind the set of n– is dog), etc. The quantifier, because it is a second–order function, tuples, whereas each n–tuple is created so that some possible value then should assign truth–values to these predicates. The universal of k–th argument of given function always corresponds with its quantifies assigns them to individual predicates in the following k–th element (1 < k < n–1) and the value of this function for given way: if the given predicate assigns to all elements of universe of combination of arguments corresponds with its n–th element. E.g. consideration the value True, then the universal quantifies assigns the mathematical function f(x) = 2x, which we shown above, has to this predicate the value True as well; otherwise the universal then this extension: quantifier assigns to this predicate the value False. If for us the universe of consideration are living beings, then the extension of {(1, 2), (2, 4), (3, 6), (4, 8), ...} universal quantifier is this:

Because Frege understands predicates as functions too, also {(H, False), (M, True), (D, False), ...} they have extension in our defined sense. E.g. the predicate x is hu- man, which we note with the expression “H(x)”, has the following Why? The universal quantifier assigned to the predicate H(x) extension: the value False because the predicate H(x) does not assign to all elements of the universe of consideration the value True. Not all {(Socrates, True), (Plate, True), (Sandy, False), ....} living beings are in fact humans. For example, the dog called Sandy is not a human and therefore the predicate H(x) assigned to this Then the predicate x is taller than y (T(x,y)) has the extension: dog the value False. But from this results that the predicate H(x) as- signs the value True not to all elements of the universe. And there- {(Gerlachovský Peak, Mount Everest, False), (Gerlachovský Peak, fore the universal quantifier assigned to the predicate H(x) the Empire State Building, True), (Mount Everest, Gerlachovský Peak, value False. But as all living beings are mortal, the predicate M(x) True), ...} assigns to all values from the universe of consideration the value True. Therefore the universal quantifies assigned to this predicate But also implication, for example, has extension, because it is the value True. And under the same rule it assigned the universal function, according to Frege: quantifier to the predicateD(x) the value False. This predicate in- deed assigns the dog called Sandy the value True, but there are ele- ments of the universe of consideration, to which it assigns False, e.g. to the separate things Socrates and Plato.

42 43 The existential quantifier is also a second–order function, but it assigns to individual predicates the values True or False in oth- cates and their meanings are, according to Frege, functions of er way than the universal quantifier. It assigns True to them only sets of individuals into the sets of truth–values. when if given predicate is assigning to at least one element of the (2) Proper names and numerals, but also expressions con- universe the value True. Failing that, the existential quantifier as- taining word like “this...”, “that...”, etc. can be understood as signs to given predicate the value False. singular terms and their meanings are objects, to which we So also the meanings of quantifiers are functions, but functions refer with the help of these terms (i.e. such objects we call of predicates into truth–values. Naturally, the expression with their denotations today). quantifier is a function only if we do not substitute the “predicate (3) Conjunctions can be understood also like names of func- variable” with a specific predicate. Like in case of other functions, if tions out of the set of truth–values into the same set. Their we substitute this variable with a specific predicate, the expression meanings are therefore such functions. with quantifier becomes a statement. Let us note that this holds (4) The meaning of expressions like “all ... are ...” or “some ... true only if the resulting expression does not contain any free are ...” are functions of predicates into the domain of truth– variable, which in our simplified case is always met, because we al- values. lowed to substitute a(x) only with unitary predicates with the vari- (5) The meaning of whole statements is, according to Frege, able x only. The meaning of the resulting statement will of course one of the truth–values (the one concerning in the specific be again one of the truth–values. case is fully determined by the significant elements of that Frege’s objective was to find a formal language for the notation statement). of logical relations in ordinary language, whereas he was interest- ed mainly in such logical relations, through which we could check if the proofs (mainly mathematical proofs) are valid. Therefore in Recommended Literature case of language, he was interested in what was substantial with regard to his objective. Due to that in his analysis he is not pro- GAHÉR, F.: Logika pre každého. Bratislava : Iris, 2003, pp. 159 — 217. posing the transcription of imperative or interrogative sentences, MARVAN, T.: Otázka významu. Cesty analytické filosofie jazyka. Praha : Togga, 2010, pp. 13 — 29. but declarative sentences only. He also does not propose a formal MILLER, A.: Philosophy of Language. London : Routledge, 2007, pp. 1 — 22. transcription for all types of expressions that can be found in sen- MORRIS, M.: An Introduction to the Philosophy of Language. New York : Cambridge tences (he does not propose e.g. transcriptions of interjections). University Press, 2007, pp. 21 — 48. PEREGRIN, J.: Kapitoly z analytické filosofie. Praha : Filosofia, 2005, pp. 31 — 67.

We can summarize the way Frege is assigning to types of ex- pressions in language important to him, types of meanings, as follows: (1) Nouns, adjective and verbs can be understood as predi-

44 45 5. Frege III: Sense (Sinn) expression, the expression “Morning Star”. This term too refers to the planet Venus. But if we substitute the former expression with the latter, we get this sentence:

Jana thinks that the Morning Star is shining in the sky.

Yet it is possible that Jana does not know that both of these terms refer to the same object, to the planet Venus. In this case, however, the statements will have a different truth–value, different Keywords: sense, semantics, idea, two–level semantics meaning. But this is violating the mentioned principle that should naturally be valid at all times, therefore also when Jana does not 5.1 The Relation Between Sense and Reference know, that both expressions refers to the same object. according to Frege Moreover, the informativeness problem arises. Let us imagine that Jana does not know that “Evening Star” is the name of the But with regard to semantics, Frege was not satisfied with describ- same object we call “Venus” too. But Jana knows several things ing in just with the term “reference”. For some , he felt com- about Venus, e.g. that it is a planet of our Solar System. If we tell pelled to introduce also another term concerning semantics — the Jana the sentence: term of sense (Sinn in German). We will try to explain in following lines what he had in mind with this term and what motivation led The Evening Star is the planet Venus. him to its introduction. Frege postulated a principle that says if we substitute one ex- Jana will learn something. But if we tell her the sentence: pression with another expression with the same meaning, then the meaning of the statement, whose part was the original expres- The Evening Star is the Evening Star. sion, should be the same as the meaning of statement that was cre- ated from the first expression by substituting the first expression she will not learn anything new. Nevertheless, all these expres- with the second one. But it seems that some such substitutions are sions (“Evening Star”, “Morning Star”, “Venus”) have, according to problematic. Frege, the same meaning, they refer to the same object. However, Let us take the following sentence as an example: this is problematic, if we assume that Jana thinks about meanings of these expressions, because in this case she would be thinking Jana thinks that the Evening Star is shining in the sky. always about the same thing. If the object of Jana’s conclusion or thinking was in case of these expressions their meaning, she would According to Frege’s theory, the meaning of the expression have to be thinking about Evening Star, Morning Star and Venus “Evening Star” is indeed an object to which it refers, i.e. the planet always at the same time, she would have to be thinking about the Venus. But this object is, at the same time, the meaning of another one object, because according to Frege it is the shared meaning of

46 47 all these expressions. Moreover, in such case, the previous two sen- have to find the brightest object of morning sky. The ways of choos- tences would have to be equally uninformative for Jana. Yet this is ing denotation are different, i.e. the senses of these expressions are not true. different. But the referent, the meaning of these expressions is, by The informativeness problem manifests itself also in that we coincidence, the same: it is the planet we call “Venus”. are able to understand also the expression whose denotation, i.e. Similar thing applies to, e.g. mathematical expressions. Both the what Frege calls reference, we do not know. In the same way, we are expression “3 + 3” and expression “2 + 4” refer to the same abstract able to understand a sentence whose meaning, i.e. the truth–value, object, to the number 6. Therefore they have the same reference, we do not know. Let us consider, for example, the sentence: which is exactly the number 6. But they refer to it in different way, so they have different sense. The oldest human on Earth is having a walk at the moment. 5.2 Thought according to Frege Because we do not know the meaning of the expression “the oldest human on Earth” (i.e. we do not know to which specific hu- The sense of whole statements is, according to Frege, the thought. man it applies at this point) and because the meaning of the whole But by thought he does not have something subjective in mind, but sentence depends also on the meaning of this expression, we nei- he understands it objectively. This objectivity of that, what is the ther now the meaning of this sentence, i.e. its truth–value. Despite sense of sentences we are saying, lets us understand each other. that, we understand this sentence. So can semantics be reduced to With a sentence, we are expression a thought (which is its sense), talking about reference (in Frege’s sense) only? but the meaning of the sentence is its truth–value. Therefore we do not have to know the meaning of the sentence (its truth–value) in order to understand it. To understand a sentence, we just need Frege therefore introduces another term — sense. Therefore to know its sense. In case of the sentence “The oldest human on all expressions will have not only meaning, but also sense. Earth is having a walk at the moment” we need then to know the The meaning of the expression will be the method how is its sense of the expression “The oldest human on Earth” and the sense meaning given, or more precisely the method, by which we of the expression “... is having a walk”. The sense of the expression are determining the denotation of given expression. “the oldest human on Earth” is the way how we assign this expres- sion its meaning, i.e. the way how we define, which individual it de- scribes. The sense of the expression “... is having a walk” is also the So for example the sense of the expression “Evening Star” will be way how we assign this expression its meaning, i.e. the way how we the brightest object of evening sky. The sense of the expression assign this predicate the function that assigns separate things the “Morning Star” will be the brightest object of morning sky. There- truth–value Truth when these individuals are having a walk right fore we will select the denotation (the reference for Frege) of the now and assigns them the value False, if they are not having a walk expression “Evening Star” in such way, that we find the brightest right now. object of evening sky. However, the way how we choose the denota- tion of the expression “Morning Star” is different: in this case, we

48 49 6. Russell I: Definite Descriptions Frege’s semantics is therefore two–level, Frege assigns each ex- pression both the reference (what is usually called denotation today) and the sense (what is usually called meaning today).

Frege made ​​a tremendous job in the field of semantics. While build- ing his theory, he himself was finding weak spots, questions, he did not know answers to. Otherwise, other thinkers were gradu- ally finding such spots. Uncertainties concerned mainly the sense Keywords: , denotation, , logical of proper names, the sense of expressions in indirect context and analysis. criteria of the identity of thoughts (Marvan, 2010, p. 26 — 29). In following text, we will have a look on some attempts for solution of 6.1 Denoting these uncertainties. But another important analytical philosopher, Bertrand Russell Recommended Literature (1872 — 1970) perceived Frege’s two–level semantics as problem- atic. Why should be words assigned two different semantic enti- KOLMAN, V.: Logika Gottloba Frega. Praha : Filosofia, 2002, pp. 64 — 79. ties, reference and sense? He found the concept of sense unclear MILLER, A.: Philosophy of Language. London : Routledge, 2007, pp. 1 — 22. and so he tried to avoid its introduction when describing semantic MORRIS, M.: An Introduction to the Philosophy of Language. New York : Cambridge university press, 2007, pp. 21 — 48. properties of language expressions. PEREGRIN, J.: Kapitoly z analytické filosofie. Praha : Filosofia, 2005, pp. 31 — 67. WIGGINS, D.: Meaning and truth conditions: from Frege’s grand design to David- son’s. In: HALE, B. — WRIGHT, C. (eds.): A Companion to the Philosophy of Lan- Russell is proposing a view on semantics that is different guage. Oxford : Blackwell Publishers, 1997, pp. 3 — 28. from Frege’s. (Russell, 1903, 1905) Although he, like Frege, considers names as indication of things (the meaning of names are, according to him, objects to which these names refer), but he does not take predicate expressions as names of functions, but as names of concepts (the meaning of given predicate expression is therefore the respective concept). The meaning of statements are, according to him, not the truth–values, but , which he sees as conglomer- ates of entities that refer to individual words, from which is the statement made up.

50 51 However, Russell is later again approaching the two–level se- cannot say about the previous sentence that it is true. But if on mantics. Concepts can actually relate not only to other concept or the other hand this sentence should have the truth–value False, names of things, but also to objects themselves. Russell calls this its negation should be true. It also seems that its negation is the relation of concepts to objects denoting. That is, any concept can sentence: be devised so that it refers to some object. Moreover, different con- cepts can in some cases refer to the same object. Predicate language The current French king is not bald. expressions therefore relate not only to concepts, but through them they can relate to objects, i.e. in fact, two types of entities be- which can be recorded, according to Frege, as: long to them: concepts and things (if they denote anything). To clarify it, it will be good to start with the analysis of how ¬H(a) is Russell logically analysing one special type of expressions, the so–called definite descriptions. According to Russell, this type of But this sentence should be true, if the original sentence was express actually does not behave as proper names. For example, false and this sentence is truly its negation. But it seems that we according to him, the expression “the current French king” as if are not able to say that. would not be a proper name, referring to one object, to one specific In case of Frege, we can still understand this sentence, even person. Let us consider the sentence: though we are not assigning any meaning to it, because this sen- tence has still one entity of another semantic category assigned, The current French king is bald. namely its sense. For Frege, the expression “current French king” has a sense too, although it has no meaning, i.e. it does not refer to If we have understood the expression “the current French king” any object. But according to Russell, the meaning of any previous so that it refers to some object, then we should mark it, accord- sentences is none of the truth–values, however it is a proposition, ing to Frege’s concept, with an individual constant, e.g. “a”. On the some sort of compound of two entities, which refer to expressions other hand, we should understand the expression “x is bald” as the “the current French king” and “... is bald”. The expression “the cur- marking of the predicate x is bald and we could mark it with the rent French king” should have some object as its meaning, namely expression “B(x)” in formal language. Then it would be necessary to the current French king. The expression “... is bald” has the concept transcribe the selected statement as follows: of baldness as meaning. As the statement “The current French king is bald” is like an image of proposition, which is its meaning, then H(a) the connection between expressions “the current French king” and “... is bald” should be the same as the connection between the cur- Is this statement true or false? There is no French king at the rent French king and the concept of baldness. moment after all. According to Frege, if some element of the sen- However, there is no French king at the moment. The expression tence has no meaning, the sentence as a whole has no meaning as “the current French king” does not refer to any object, therefore well; i.e. that sentence has no truth–value. If it had a truth–value, it should have no meaning. Should the isomorphism between the then it should be either true or false. But it seems obvious that we statement and proposition be valid and the sequence of symbols

52 53 “The current French king is bald” truly be a statement, then this the negation of this statement). What if our ordinary language sen- statement cannot have any truth–value today. tence does not represent any possible proposition well (an there- This, however, is a problem for Russell, because he insists on fore it does not represent even the given hypothetical proposition, the principle of the excluded third, which he describes as that for which we thought it represented), i.e. what if the proposition it every meaningful statement it should hold, that either it is valid would represent well, is not possible? or its negation. Yet M. Morris remarks in this regards (Morris, 2007, It seems that this statement represents well the proposition p. 51) that maybe we should be talking rather about the principle B(a). But if the individual a does not exist, then it is not possible of bivalence in this case. Actually, today a distinction between the that B(a) is true, but it is not possible that ¬B(a) is true. The se- principle of bivalence, which says that each meaningful sentence quences of symbols “B(a)” and “¬B(a)” of the formal language are should have just one of two truth–values and the principle of the not possible proposition given the world in which the individual excluded third, which says that each statement being in form of a does not exist, because in such world neither the proposition B(a) A ∨¬A is (i.e. it always is a true expression, regardless of nor ¬B(a) is possible. what expression we substitute A for and regardless of the truth– value of expression A) is made. He also remarks that it is possible 6.2 Logical Analysis to devise a logical system also in such way, that on one hand, the law of the excluded third is valid in it, but the principle of bivalence We can take another path, though. Let us assume that our sentence is not. On the basis of that he claims that it is possible to argue in does not represent well some suitable proposition. Let us assume favour of the opinion, that what Russell is talking about in this re- that the logical structure of what we wanted to express in ordinary gard, concerns rather the principle of bivalence than the law of the language is not clearly visible in the ordinary language sentence. excluded third. Let us explore the possibility that this logical structure is different Anyway, for Russell is important that both above mentioned from F(a), i.e. let us try to explore some other transcription of our statements have the truth–value, if they even are meaningful sen- statement, one that would represent some proposition that would tences. This assumption is sound, because we can understand these be possible (that would be some possible relation between things sentences and we normally use sentences of similar type (contain- wouldor some be possible possible (thatpertaining would of be some some properties possible torelation some things)between things or some possible ing expression not referring to any existing object). pertainingand at the of samesome time properties suitable to (i.e. some such, things) about whichand at it the could same be astime- suitable (i.e. such, about However, as we have already said, if the sentence “The current whichserted, it couldas good be as asserted,possible, thatas good it has as such possible, ,that whichit has wassuch logical form, which was French king is bald” is to be an image of a proposition, we have trou- vaguelyvaguely "meant" “meant” by by our our senten sentencece in in ordinary ordinary language). language). ble with determining what corresponds to the element marked Let usLet have us ahave look a lookthen thenon the on fo thellowing following logical logical analysis analysis of ofthe the sentence "The current French with the expression “the current French king”. But is our assump- kingsentence is bald", “The as proposedcurrent French by Russell: king is bald”, as proposed by Russell: tion correct that this ordinary language sentence truly represents some preposition well? The proposition is in fact some possible (∃x)(K(x)x)(K(x) ˄ H(x)  H(x) ˄ (∀ y)(K(y) (y)(K(y) d (x = y))) (x = y))) element of reality, some possible arrangement of things, which if exists, then the statement representing it is true, and if not, then wherewhere we mark we markwith thewith expression the expression "K(x)" “K(x)” the thepredicate predicate x is x the is current French king. The the statement representing is if false (the opposite is then true for quitethe complicated current French transcription king. The quite into formalcomplicated language, transcription shown above, into expresses that there is at least one such thing that is the current French king and is at the same time bald, and it 54 concurrently asserts that all things, which are the current French55 king, are identical with this thing; i.e. this expression asserts that there is just one such thing, which is a French king and that this thing is bald. So Russell's record is not acting as designation of certain object that has to exist. If there is no French king, then this expression neither looses meaning, nor it becomes false. This example of formal transcription of statement shows well also why Russell in fact speaks about logical analysis. The form this expression has in ordinary language, does not have even to resemble its logical form. Thus, the transcription of the statement from ordinary language into formal language is not always a trivial task. An expression in ordinary language can in fact hide its logical form, as we can just see on our example. The logical form of this statement is hidden, it hardly shows in ordinary language. Therefore effort has to be exerted to acquire this logical form. We need to, so to speak, think about what does the expression "mean" (in terms of its logical structure) and we should get mislead by its form in ordinary language. But the fact that the logical form of the previous statement is so different from its form in ordinary language contains also additional consequences, not obvious at the first sight. Ono of them is that its negation is not a statement.

The current French king is not bald.

We can discover this, when we negate our formal record:

(x)(K(x)  H(x)  (y)(K(y)  (x = y)))

This expression means, that

It is not true that there is just one current French king, which is bald at the same time.

As we have seen, this statement is not identical with the statement "The current French king is not bald", we can adjust this expression:

(x)(K(x)  H(x)  (y)(K(y)  (x = y))) (x)(K(x)  H(x)  (y)(K(y)  (x = y))) (x)(K(x)  H(x)  (y)(K(y)  (x = y))) (x)(K(x)  H(x)  (y)(K(y)  (x = y))) (x)(K(x)  H(x)  (y)(K(y)  (x  y)))

Statement written in this way means, that for all things, at least one of these three assertions would be possible (that would be some possible relation between things or some possible pertaining of some properties to some things) and at the same time suitable (i.e. such, about whichwould itbe couldpossible be asserted,(that would as goodbe some as possible,possible relationthat it has between such logicalthings orform, some which possible was vaguelypertaining "meant" of some by propertiesour senten toce somein ordinary things) language). and at the same time suitable (i.e. such, about whichLet us haveit could a look be thenasserted, on the as fo goodllowing as possible,logical analysis that it ofhas the such sentence logical "The form, current which French was kingvaguely is bald", "meant" as proposed by our senten by Russell:ce in ordinary language). Let us have a look then on the following logical analysis of the sentence "The current French king is( bald",x)(K(x) as proposed H(x)  (byy)(K(y) Russell: (x = y)))

where( wex)(K(x) mark with H(x) the  (expressiony)(K(y)  "K(x)" (x = y))) the predicate x is the current French king. The quite complicated transcription into formal language, shown above, expresses that there is at leastwhere one we suchmark thingwith thethat expressionis the current "K(x)" Fren thech predicateking and xis is atthe the current same Frenchtime bald, king and. The it concurrentlyquite complicated asserts transcription that all things, into whichformal are language, the current shown French above, king, expresses are identi thatcal there with isthis at leastthing; one i.e. thissuch expression thing that assertsis the thatcurrent there Fren is justch kingone suchand thing,is at thewhich same is atime French bald, king and and it concurrentlythat this thing asserts is bald. that So allRussell's things, record which is are not the acting current as designation French king, of arecertain identi objectcal with that thishas thing;to exist. i.e. Ifthis there expression is no Frenchasserts thatking, there then is thisjust expressionone such thing, neither which looses is a Frenchmeaning, king nor and it becomesthat this thing false. is bald. So Russell's record is not acting as designation of certain object that has Thisto exist. example If there of formal is no transcriptionFrench king, of thenstatem thisent expressionshows well neitheralso why looses Russell meaning, in fact speaksnor it aboutbecomeslogical false. analysis . The form this expression has in ordinary language, does not have even toThis resemble example its of logical formal form. transcription Thus, the of transcriptionstatement shows of the well statement also why from Ru ssellordinary in fact language speaks intoabout formallogical language analysis is. Thenot alwaysform this a trivial expression task. has in ordinary language, does not have even Anto resemble expression its inlogical ordinary form. languag Thus,e thecan transcription in fact hide itsof logicalthe statement form, as from we canordinary just see language on our example.into formal The language logical is form not alwaysof this astatement trivial task. is hidden, it hardly shows in ordinary language. ThereforeAn expression effort in has ordinary to be exertedlanguag eto can acquire in fact th ishide logical its logical form. form,We need as we to, can so tojust speak, see on think our example.about what The does logical the expressionform of this "mean" statement (in termsis hidden, of its it logical hardly structure)shows in ordinaryand we should language. get misleadTherefore by effort its form has in to ordinary be exerted language. to acquire this logical form. We need to, so to speak, think Butabout the what fact does that thethe expressionlogical form "mean" of the (in previo termsus ofstatement its logical is sostructure) different and from we itsshould form get in ordinarymislead by language its form contains in ordinary also language. additional consequences, not obvious at the first sight. Ono of themBut the is thatfact itsthat negation the logical is not form a statement. of the previo us statement is so different from its form in ordinary language contains also additional consequences, not obvious at the first sight. Ono of them isThe that current its negation French is king not ais statement. not bald.

We canThe discover current this, French when king we is negate not bald. our formal record: formal language, shown above, expresses that there is at least one We can¬(∃x)(K(x) (discoverx)(K(x) ˄ this, H(x) H(x) when ˄ ( ∀y)(K(y) (wey)(K(y) negate → (x =our y))) (x formal = y))) record: such thing that is the current French king and is at the same time bald, and it concurrently asserts that all things, which are the cur- This expressionThis(x)(K(x) expression means, H(x) means, that  ( thaty)(K(y)  (x = y))) rent French king, are identical with this thing; i.e. this expression asserts that there is just one such thing, which is a French king and This expressionIt is notnot truetrue means, thatthat there that is justjust oneone current current French French king, king, which which is is bald at the same time. that this thing is bald. So Russell’s record is not acting as designa- bald at the same time. tion of certain object that has to exist. If there is no French king, As weIt have is not seen, true thisthat statement there is just is notone identica current lFrench with the king, statement which "Theis bald current at the Frenchsame time. king is then this expression neither looses meaning, nor it becomes false. not bald",As we we have can seen, adjust this this statement expression: is not identical with the state- As mentwe have “The seen, current this statementFrench king is notis not identica bald”,l withwe can the adjust statement this "The current French king is notexpression: bald",(x) we(K(x) can adjust H(x) this  ( expression:y)(K(y)  (x = y))) This example of formal transcription of statement shows (x)(K(x)  H(x)  (y)(K(y)  (x = y))) well also why Russell in fact speaks about logical analysis. ((“x)Ø(K(x)x)x)((K(x)K(x) Ù H(x) H(x) ÙH(x) (“y)(K(y)  ( (y)(K(y)y) ® (x (K(y)= y))) (x =(x y))) = y))) The form this expression has in ordinary language, does not ((“x)(ØK(x)x)(K(x) Ú ØH(x) H(x) Ú Ø(“y)(K(y) ((y)(K(y)y)(K(y) ® (x = y))) (x (x = = y))) y))) have even to resemble its logical form. Thus, the transcrip- ((“x)(ØK(x)x)(K(x) Ú ØH(x) H(x) Ú ($y)Ø(K(y) (y)y)(K(y) (K(y)® (x = y))) (x (x y))) = y))) tion of the statement from ordinary language into formal ((“x)(ØK(x)x)(K(x) Ú ØH(x) H(x) Ú ($y)(K(y) (y)(K(y) Ù Ø(x = y)))(x = y))) language is not always a trivial task. Statement((“x)(ØK(x)x)( writtenK(x) Ú ØH(x) in thisH(x) Ú way ($y)(K(y) (means,y)(K(y) Ù (x that ¹ y))) (xfor  all y))) things, at least one of these three assertions

Statement written in this way means, that for all things, at least one of these three assertions An expression in ordinary language can in fact hide its logical form, Statement written in this way means, that for all things,at least as we can just see on our example. The logical form of this state- one of these three assertions holds true: ment is hidden, it hardly shows in ordinary language. Therefore ef- fort has to be exerted to acquire this logical form. We need to, so to (1) given thing is not the current French king speak, think about what does the expression “mean” (in terms of its (2) given thing is not bald logical structure) and we should get mislead by its form in ordinary (3) there is a thing that is the current French king, but which is language. different from the given thing (i.e. there is some other thing that is But the fact that the logical form of the previous statement is the current French king). so different from its form in ordinary language contains also addi- tional consequences, not obvious at the first sight. Ono of them is Such situations allow many options, however it does not allow that its negation is not a statement. that neither (1) nor (2) nor (3) held true about some thing. It thus does not allow that it is true, at the same time, that some thing is The current French king is not bald. the current French king, that it is bald and that it was just one. If there is more than one current French king, this sentence is true. It We can discover this, when we negate our formal record: is also true, if there is none. And if there is just one current French king, but not bald, it is true as well.

56 57 holds true: holds true: holds true(1) :given thing is not the current French king (2)(1) given thing is not baldthe current French king (1)(3)(2) given giventhere thing isthing a thing is is not not that the bald iscurrent the current French French king king, but which is different from the given (2)thing(3) given there (i.e. thing is there a thing is is not some that bald isother the thicurrentng that French is the king,current but French which king). is different from the given (3)thing there (i.e. is therea thing is somethat is other the current thing that French is the king, current but Frenchwhich isking). different from the given Suchthing situations (i.e. there allow is many some options,other thi nghowever that is itthe does current not allowFrench that king). neit her (1) nor (2) nor (3) Suchheld truesituations about allowsome thing.many options,It thus does however not allo it doesw that not it allowis true, that at neitthe hersame (1) time, nor (2)that nor some (3) Suchthingheld situationstrue is the about current allow some French many thing. options,king, It thus th athoweverdoes it is not bald itallo doesandw that thatnot itallowit iswas true, that just at neit one.theher sameIf (1) there nortime, is (2) morethat nor some than(3) heldonething truecurrent is theabout currentFrench some king,French thing. this Itking, thussent th encedoesat it isnotis true.bald allo Itwand isthat alsothat it ittrue,is wastrue, if just thereat theone. is same none.If there time, And is that moreif there some than is thingjustone onecurrentisLet the current us current Frenchhave French aFrench king,closer king, thislookking, but sent on thnot enceatone bald,it ofisis thesebald true.it is trueandItoptions, is thatas also well. iton true, was the ifjustone there one. is If none. there And is more if there than is But let us notice that it does not follow from Russell’s logical oneLetjust validcurrent usone have currentat Frenchthis a closer moment.French king, look king, thisAt on this sentbut one moment, encenot of bald, theseis true.the it opti is empirical Ittrueons, is alsoas on well. situationtrue,the one if there validin is at none. this moment.And if there At analysis thisis of the expression “the current French king” that this ex- justmoment,Let oneour us realcurrenthave the world aempirical closerFrench is such, look king, situation that on but there one notin is of ourbald, no these Frenchreal it isworldopti true king.ons, asis In such,onwell. that the case,that one therethe valid is at no this French moment. king. AtIn pressionthatthis is description of some object. For no such object has to Letcase,moment, ussentence thehave sentencethe a empiricalcloser look situation on one in of our these real opti worldons, is on such, the thatone therevalid isat nothis French moment. king. At In this exist.that The meaning (denotation) of such expression is thus not any moment,case, the the sentence empirical situation in our real world is such, that there is no French king. In thatobject. case, the(($x)(K(x) sentencex)(K(x) Ù  H(x) H(x) Ù (“y)(K(y) (y)(K(y) ® (x = y))) (x = y))) Let us examine this expression closer: To get its formal record, (x)(K(x)  H(x)  (y)(K(y)  (x = y))) we will use the formal record of the expression “The current French is false,(isx)(K(x) false,because because  itH(x) is true it  is ( thattruey)(K(y) therethat there is no (x is current= no y))) current French French king: king: king is bald”. Yet if we remove the expression “x is bald” from this is false, because it is true that there is no current French king: statement, we should be left with this expression: is false,Ø($x)K(x) because(x)K(x) it is true that there is no current French king: (x)K(x) “The current French king ...”. from thisfrom(x)K(x) assertions this assertions follows follows also the also validity the validity of that of therethat there is no is current no bald French king fromcurrent this assertions bald French follows king also the validity of that there is no current bald French king i.e. an expression with some kind of empty space for something from this( assertionsx)(K(x)  follows H(x)) also the validity of that there is no current bald French king we want to say about the current French king. Let us make a re- Ø($x)(K(x)(x)(K(x) Ù H(x)) H(x)) currentmoval French in our formalking. Let language. us make In thata removal case, we in removeour formal the expres language.- In that case, we remove As long( x)(K(x)as there is H(x))nothing that would be the current French king and bald at the samecurrentthe time,sion expression “ B(x)French” that "B(x)"king. is the Let thatname us is make ofthe the name apredicate removal of the x inpredicate is baldour formal in formalx is baldlanguage. lan in- formal In that language. case, we By remove doing Asneither longAs it as longis theretrue as that thereis nothing there is nothing would that would thatbe just would be one the besuch cu therrent thing. current French Hence French king the andfollo baldwing at assertion the same issothe time,true, guage.we expression get: By doing "B(x)" so we that get: is the name of the predicate x is bald in formal language. By doing Aswhichneither longking already asitand is there truebald is is thatatthe nothing the negationthere same wouldthat time, of would the beneither originaljust be one itthe is statement: such cutruerrent thatthing. French there Hence wouldking the and follo baldwing at assertionthe same issotime, true, we get: neitherwhichbe just italready is one true such is that the thing. there negation Hencewould of the bethe followingjust original one such assertionstatement: thing. is Hencetrue, which the follo wing assertion is true, ($x)(K(x)(x)(K(x) Ù ... Ù ... (“y)(K(y)  (y)(K(y) ® (x = y))) (x = y))) whichalready already( isx)(K(x) the is the negation negation H(x) of  the of( theoriginaly)(K(y) original statement: (xstatement: = y))) (x)(K(x)  ...  (y)(K(y)  (x = y))) (x)(K(x)  H(x)  (y)(K(y)  (x = y))) However,However, if we if wantwe want to mark to mark the the place place from from which which we we have have removed re- the expression "B(x)", This sentenceØ($x)(K(x)(x)(K(x) is Ùthus H(x) H(x) really Ù (“y)(K(y)  true,(y)(K(y) as® (x long = y))) as (x there = y))) is no French king, while its negation (i.e.However,like movedour we did the if it weexpression above, want we to “B(x)”, canmark write likethe wethisplace did formal fromit above, expressionwhich we canwe writehavelike this thisremoved as well: the expression "B(x)", originalThis sentence statement) is thus is reallyon the true, othe ras hand long true, as there under is thisno French condition. king, while its negation (i.e.like formalour we did expression it above, like we thiscan aswrite well: this formal expression like this as well: ThisInoriginal general sentenceThis statement) wesentence is can thus say, is isreally onthus that the true, reallyin othe case asr true, handlong of theas astrue, long analysedthere under as is there no thisRussell's French is condition. no French trking,anscription while its andnegation its negation, (i.e. our the ( x)(N(x)  (x)  (y)(N(y)  (x = y))) originalproblemIn generalking, statement) while does we itscannot negation issay,lie on in thatthe that(i.e. othein ourcasetheser hand original of sentences, thetrue, statement)analysed under expressed this Russell's is condition.on the in tr otherformalanscription language, and its would negation, violate the($x)(N(x)( x)(N(x) Ù a(x)  (x)Ù (“y)(N(y) (y)(N(y) ® (x = y))) (x = y))) Inrequirementsproblem generalhand true, doeswe canunderthat not say, (1)lie this eachthatin condition. that instatement case these of sentences,thehad analysed a truth- expressedvalue Russell's and inthattr anscriptionformal (2) negation language, and ofits eachnegation,would statement violateThis the formulation has the advantage that the expression "(x)" preserves the information that problemhadrequirements theIn opposite doesgeneral thatnot we truth-value lie(1) can ineach say, that thatstatement asthese thisin case sentences,statement. had of the a truth- analysed Neitherexpressedvalue Russell’s theand in violation that formal tran (2)- negationoflanguage, the law of ofwouldeach the statement excludedviolateThiswhat formulationThiswe areformulation saying has in thehas this advantage the place advantage of that our thethat expression, expression the expression we " are(x)" “a(x)” inpreserves fact saying the informationabout the same that requirementsthirdhadscription the nor opposite the andthat situation its(1)truth-value negation, each that statement as thewe this problemare statement.had forced a doestruth- to Neithernot valuesay lie that and inthe that thatgivenviolation these (2) sentences negation of the law ofhave eachof theno statement excludedmeaningwhatobjectpreserves we, about are the sayingwhich information wein thisare that placesaying what of that weour isare expression, the saying only in current thiswe placeare French in of fact king. saying This about connection the same is hadoccurred.third thesentences, nor opposite the expressedsituation truth-value inthat formalas wethis are statement.language, forced would Neitherto say violate thatthe violation givenrequire sentences- of the law have of the no excluded meaningobjectsecuredour ,expression, aboutin such which way, we arewe that inare therefact saying saying is th thate about same is the thesymbol onlysame "x"currentobject in, theabout French expression king. This"(x)" connection as is in the is thirdButoccurred.ments letnor us thethat notice situation (1) eachthat itstatement thatdoes we not hadare follow aforced truth–value from to Russell's say and that that logical given (2) nega ansentencesalysis- of havethe expression no meaningsecuredremaining "thewhich inwe partsuch are sayingof way, expression that isthere the on onlyisthose th currente placessame French symbolof its, king.wh "x"ere Thisin is the itcon beingexpression- said about "(x)" the as object is in thewe occurred.Butcurrenttion let ofusFrench eachnotice statementking" that thatit does hadthis not theexpression followopposite from is truth–value desc Russell'sription as oflogical this some state an object.alysis- Forof the no expressionsuch objectremainingare "the nectionhas substituting ispart secured ofthe expression variable in such way,x on with, tthathose that there places it is is the ofthe its,current same wh eresymbol French is it “x”being king andsaid thatabout there the isobject just onewe Buttocurrent exist.ment.let us French The Neithernotice meaning king" that the it thatviolation (denotation)does this not expression of follow the of lawsuch from isof expression desc theRussell's riptionexcluded islogical of thus thirdsome not an nor object. alysisany object. ofFor the no expression such objectaresuch "the inhas substituting the object. expression But the the variable“a(x)” expression as isx with,in the" (x)"that remaining itthus is thedescribes part current of expression theFrench variab king le thatand thatcan therebe, in is predicate just one currentLetto exist.the us Frenchsituationexamine The meaning king" thisthat thatexpression we (denotation) arethis forced expression closer: toof saysuch To is that descgetexpression givenitsription formal sentences isof thusrecord,some not have object. weany will object. For use no the such formal object recordsuchlogic, hason thoseobject. substituted places But withtheof its,expression grammatically where is "it being(x)" correctly thus said describesabout created the expressions theobject variab we le contai that ningcan be,at least in predicate one free toofLet exist. theno us meaning expressionexamineThe meaning occurred. this "The expression(denotation) current closer:French of such Toking expression get is its ba formalld". is Yetthus record, if not we anywe remove object.will use the the expression formal recordlogic,occurrence "xare is substitutingsubstituted of the with variablethe variablegrammatically x. x with, correctlythat it is createdthe current expressions French containing at least one free Letofbald" usthe examinefrom expression this this statement, "The expression current we shoulcloser: Frenchd be To kingleft get with itsis baformal thisld". expression: Yet record, if we we remove will use the the expression formal recordoccurrenceLike "x is in the ofprevious the variable part, xlet. us simplify the situation at this point in such way, that we will ofbald" the expressionfrom this statement, "The current we shoul Frenchd be king left withis ba ld".this expression:Yet if we remove the expression "x is  58 Likeassume in thatthe previouswe could part, substitute let us thesimplify expression the situation " (x)" onlyat this with point59 expres in suchsions way, describing that we unary will bald" from"The this current statement, French we king shoul ...".d be left with this expression: assumepredicates, that as we is could the case substitute, e.g. withthe expression the predicate "(x)" B(x) only. Then with the expres (x)sions is in describingfact a predicate unary "The current French king ...". predicates,variable, which as is can the be case substituted, e.g. with with the predicates predicate expressing B(x). Then some the property.(x) is in fact a predicate i.e. an"The expression current French with some king ...".kind of empty space for something we want to say aboutvariable,The the expression which can"the be current substituted French with king predicates ..." is theref expressingore an unsaturatedsome property. expression, which is i.e. an expression with some kind of empty space for something we want to say aboutThenot the aexpression statement "theby itself. current This Fren canch be king clearly ..." isseen theref onore its anformal unsaturated record. Unlessexpression, we substitute which is i.e. an expression with some kind of empty space for something we want to say aboutnotthe the apredicate statement variable by itself. (x) This with can any be specificclearly seenpredicate, on its theformal previous record. formal Unless record we substitute is not a thestatement, predicate thus variable it is not  (x)an imagewith any of somespecific proposition. predicate, If,the however, previous we formal substitute record  (x)is notwith a statement,some predicate, thus ita isstatement not an imagewill be of create somed. proposition.Although, his If, truth-valuehowever, wewill substitute depend on  (x)various with somethings. predicate, If, for example, a statement there will is no be object, create d.whic Although,h is the hiscurrent truth-value French willking, depend a false on statement various things.will be If,created for example, after the there placement is no object, of any whic predhicate is the into current the expression French king, "the a falsecurrent statement French willking". be If created there are after more the current placement French of kings,any pred thenicate it is into true the again expression that the statement"the current we French get by king".substituting If there(x) are with more any current predicate, French will kings, be false. then If it thereis true is againjust one that current the statement French king,we get then by substitutingthis statement(x) will with be any true, predicate, if at the will same be false. time If this there king is just has one the current property French expressed king, then by thisrespective statement predicate will bewe true,are substituting if at the same (x) with,time andthis willking be has false, the ifproperty it does notexpressed have such by respectiveproperty. predicate we are substituting (x) with, and will be false, if it does not have such property.Lastly, let us still mention that we should not get fooled by the form of the expression "the Lastly,current letFrench us still king" mention in ordinary that we shouldlanguage not. Thisget fooled expression by the doesform notof thecontain expression space "thefor currentplacement French of predicate king" in thisordinary form, butlanguage this can. This be explained expression in suchdoes way, not thatcontain in case space of such for placementexpression, of the predicate ordinary in languagethis form, failsbut thisto expresscan be explainedthe logical in stsuchructure way, of that given in case expression of such expression,well, similarly the as ordinary in the case language of the wholefails to sentence express "The the logicalcurrent stFrenchructure king of isgiven bald". expression well,Differences similarly in asconstructing in the case semanticsof the whole between sentence Frege "The and current Russell French arise king to certain is bald". extent also Differencesfrom their different in constructing motivation. semantics Logical between analysis Fr forege Frege and wasRussell mostly arise the to tool certain to visualize extent also the fromphenomenon their different of implication motivation. and Logical the process analysis of proving. for Frege He was was mostly interested the tool in moreto visualize strictness the phenomenonof mathematical of implicationproofs, mainly and inthe that process their ofinterpretation proving. He is was not interestedbased on factualin more process strictness of ofhuman mathematical thought, whichproofs, is mainly too subjective in that their and interpretationelusive for solid is not knowledge based on tofactual be based process on ofit. humanRussell's thought, motive, which on the isother too hand,subjective was toand engage elusive logic for in solid our discoveryknowledge of to outer be basedworld. on That it. Russell'sis why he motive, abandons on the Frege's other hand,strict wasantipsychol to engageogism, logic i.e. in ourstrict discovery differentiation of outer between world. That the isexamination why he abandons of implication Frege's (basedstrict antipsychol on the analysisogism, i.e.of language,strict differentiation not thought) between and the examination ofof processes implication of thought(based (whichon the can analysis be the subjectof language, of psyc nothology, thought) neurosciences, and the examination of processes of thought (which can be the subject of psychology, neurosciences, king and that there is just one such object. But the expression “α(x)” Differences in constructing semantics between Frege and Rus- thus describes the variable that can be, in predicate logic, substi- sell arise to certain extent also from their different motivation. tuted with grammatically correctly created expressions containing Logical analysis for Frege was mostly the tool to visualize the at least one free occurrence of the variable x. phenomenon of implication and the process of proving. He was Like in the previous part, let us simplify the situation at this interested in more strictness of mathematical proofs, mainly in point in such way, that we will assume that we could substitute that their interpretation is not based on factual process of human the expression “α(x)” only with expressions describing unary predi- thought, which is too subjective and elusive for solid knowledge cates, as is the case, e.g. with the predicate B(x). Then the α(x) is in to be based on it. Russell’s motive, on the other hand, was to en- fact a predicate variable, which can be substituted with predicates gage logic in our discovery of outer world. That is why he abandons expressing some property. Frege’s strict antipsychologism, i.e. strict differentiation between The expression “the current French king ...” is therefore an un- the examination of implication (based on the analysis of language, saturated expression, which is not a statement by itself. This can not thought) and the examination of processes of thought (which be clearly seen on its formal record. Unless we substitute the predi- can be the subject of psychology, neurosciences, cognitive sciences) cate variable α(x) with any specific predicate, the previous formal (Peregring, 2005, p. 84). record is not a statement, thus it is not an image of some proposi- tion. If, however, we substitute α(x) with some predicate, a state- Recommended Literature ment will be created. Although, his truth–value will depend on var- ious things. If, for example, there is no object, which is the current MARVAN, T.: Otázka významu. Cesty analytické filosofie jazyka. Praha : Togga, 2010, French king, a false statement will be created after the placement pp. 31 — 45. MILLER, A.: Philosophy of Language. London : Routledge, 2007, pp. 23 — 89. of any predicate into the expression “the current French king”. MORRIS, M.: An Introduction to the Philosophy of Language. New York : Cambridge If there are more current French kings, then it is true again that university press, 2007, pp. 49 — 73. the statement we get by substituting α(x) with any predicate, will PEREGRIN, J.: Kapitoly z analytické filosofie. Praha : Filosofia, 2005, pp. 69 — 93. be false. If there is just one current French king, then this state- PRIEST, G.: Logika. Praha : Dokořán, 2007, pp. 37 — 44. ment will be true, if at the same time this king has the property ex- pressed by respective predicate we are substituting a(x) with, and will be false, if it does not have such property. Lastly, let us still mention that we should not get fooled by the form of the expression “the current French king” in ordinary lan- guage. This expression does not contain space for placement of predicate in this form, but this can be explained in such way, that in case of such expression, the ordinary language fails to express the logical structure of given expression well, similarly as in the case of the whole sentence “The current French king is bald”.

60 61 7. Russell II: Proper Names and Logical Atomism

Keywords: proper names, representationism, logical atomism, language, world

7.1 Proper Names

Russell, however, expands his understanding of certain descriptions also to proper names. These are for him actually hidden certain descriptions, so that also in their case it in fact concerns unsaturated expressions of this type, such as the expression "the current French king". For this reason is for him, for example, the name "Socrates" just a hidden certain description. We can understand it, e.g., as an expression, which is equivalent to, e.g. the certain description "Greek philosopher who was a teacher of Plato, husband of Xanthippe, and was sentenced to death in Athens". So the formal shape of this expression will have the same form as had the expression "the current French king". Its logical analysis could therefore look like this:

(x)(So(x)  (x)  (y)(So(y)  (x = y)))

7. Russell II: Proper Names and Logical Atomism Whereand wasthe expressionsentenced to "So(x) death marks in Athens the . predicateAlso in this x is case a Greek the state philosopher- who was a teacher of Plato,ment, whichhusband is createdof Xanthippe, through and was sentenced of the to variable death ina(x) Athens . Also in this case the statement,with some which predicate, is created is false, through as long substitution as the predicate of the So(x) variable cannot  (x) with some predicate, is false,be truthfullyas long as said the about predicate any object.So(x) cannotIf we take be istruthfully like that saidSocrates about any object. If we take is likeis thatno longer Socrates alive, is thenno longer this individual alive, then exists this no individual more, then exists all sen no- more, then all sentences of thetences type of the type

Socrates α(x)(x)

Keywords: proper names, representationism, logical atomism, lan- are false,are false, regardless regardless of ofwhat what predicate predicate wewe substitute substitute the the variable variable (x) with. If we thus guage, world substitutea(x) with. it Ifwit weh, thuse.g. substitutethe predicate it with, x is e.g.a man the predicate(formally, x weis a willman mark it with the expression "M(x)")(formally, the sentencewe will mark it with the expression “M(x)”) the sentence 7.1 Proper Names 7. Russell II: Proper Names and Logical Atomism Socrates is is a a man. man.

Keywords:Russell,proper however, names, expands representationism, his understanding logical of certainatomism, de -language, world will bewill false. be false. In formal In formal record record we wouldwe would express express it like it like this: this: scriptions also to proper names. These are for him actually 7.1 Properhidden Names certain descriptions, so that also in their case it in ($x)(So(x)(x)(So(x) Ù M(x) M(x) Ù (“y)(So(y)  (y)(So(y) ® (x = y))) (x = y))) fact concerns unsaturated expressions of this type, such as Russell,the however,expression expands “the current his Frenchunderstanding king”. of certain descriptions also to proper Thisnames. resultsBut let also us imagine, in that we that cannot we are write: living in the age when Socrates These are for him actually hidden certain descriptions, so that also in their case it in lived,fact or that we are assigning existence as if in terms of timeless- concerns unsaturated expressions of this type, such as the expression "the current Frenchness to( alla) things that existed at least once. Then the sentence “So- king".For this reason is for him, for example, the name “Socrates” just crates is a man” is true. But it really depends on various things, as Fora thishidden reason certain is for description. him, for example, We can understand the name "Socrates" it, e.g., as an just ex a- hidden certain description.if thewe logical want analysisto write of something this statement grammatically shows. The factcorrect that withinthe in- the predicate logic. Such Wepression, can understand which is equivalent it, e.g., to,as e.g.an theexpressio certain n,description which is “Greek equivalent to, e.g. the expressioncertaindividual —is notwhich allowed should in have it at theall, propertyit is not createdto be a Greekproperly philoso according- to rules of expression descriptionphilosopher "Greek who philosopherwas a teacher who of Plato,was a husbandteacher ofof Plato,Xanthippe, husband of Xanthippe, andcreation pherwas who in predicate was a teacher logic. ofBut Plato, how husband can we thenof Xanthippe, express, e.g.and the was following sentence? sentencedand was to sentenced death in toAthens". death in So Athens”. the formal So the shape formal of shapethis expression of this will have the same formsentenced to death in Athens, if it existed — would at the same time as expressionhad the expression will have "thethe same current form French as had king" the expression. Its logical “the analysis cur- could therefore look havelikeSanta the propertyClaus does to benot a exist.man, is just one of them. Other assump- this:rent French king”. Its logical analysis could therefore look like this: tions (which must be all valid at the same time for the sentence If we“Socrates marked is aSanta man” Claus to be true) e.g. withare: the individual constant "a", it seems that for transcription ($x)(So(x)(x)(So(x) Ù a(x)(x) Ù (“y)(So(y) (y)(So(y) ® (x = y))) (x = y))) we should use precisely the above mentioned formal record, which is, however, not — there is at least one individual, which has the property to be WhereWhere the expression the expression "So(x) “So(x) marks marks the predicate the predicate x is ax Greekis a Greek philosopher who was a teachera Greek philosopher who was a teacher of Plato, husband of of Plato,philosopher husband who of was Xanthippe, a teacher and of Plato,was sentenced husband ofto Xanthippe,death in Athens . Also in this case theXanthippe, and was sentenced to death in Athens statement, which is created through substitution of the variable (x) with some predicate, is false,62 as long as the predicate So(x) cannot be truthfully said about any object. If we take is 63 like that Socrates is no longer alive, then this individual exists no more, then all sentences of the type

Socrates (x) are false, regardless of what predicate we substitute the variable (x) with. If we thus substitute it with, e.g. the predicate x is a man (formally, we will mark it with the expression "M(x)") the sentence

Socrates is a man. will be false. In formal record we would express it like this:

(x)(So(x)  M(x)  (y)(So(y)  (x = y)))

This results also in that we cannot write:

(a) if we want to write something grammatically correct within the predicate logic. Such expression is not allowed in it at all, it is not created properly according to rules of expression creation in predicate logic. But how can we then express, e.g. the following sentence?

Santa Claus does not exist.

If we marked Santa Claus e.g. with the individual constant "a", it seems that for transcription we should use precisely the above mentioned formal record, which is, however, not 7. Russell II: Proper Names and Logical Atomism

Keywords: proper names, representationism, logical atomism, language, world

7.1 Proper Names

Russell, however, expands his understanding of certain descriptions also to proper names. These are for him actually hidden certain descriptions, so that also in their case it in fact concerns unsaturated expressions of this type, such as the expression "the current French king". For this reason is for him, for example, the name "Socrates" just a hidden certain description. We can understand it, e.g., as an expression, which is equivalent to, e.g. the certain description "Greek philosopher who was a teacher of Plato, husband of Xanthippe, and was sentenced to death in Athens". So the formal shape of this expression will have the same form as had the expression "the current French king". Its logical analysis could therefore look like this:

(x)(So(x)  (x)  (y)(So(y)  (x = y)))

Where the expression "So(x) marks the predicate x is a Greek philosopher who was a teacher of Plato, husband of Xanthippe, and was sentenced to death in Athens. Also in this case the statement, which is created through substitution of the variable (x) with some predicate, is false, as long as the predicate So(x) cannot be truthfully said about any object. If we take is grammatically correct in terms of predicate logic. like that Socrates is no longer alive, then this individual exists no more, thengrammatically all sentences correct of in terms of predicate logic. — each thing, for which it is true that it is a Greek philosopher who In Frege's concept,object, the sentencewhich would "Santa have Cl ausbeen does its meaning,not exist" is hasassigned no meaning, to it. Then for the the typewas a teacher of Plato, husband of Xanthippe, and was senten- expression "Santa theClaus" whole has sentenceno meaning. cannot It is that have this any expre meaning,ssion does i.e. truth–value.not refer to any object ced to death in Athens, is identical with the thing, about which and therefore no object,Because, which wouldhowever, have Russell been its requires meaning, observance is assigned ofto theit. Then principle the whole Socratesthe rest is(x) being said sentence cannot haveof theany excluded meaning, third,i.e. truth-value. also the statement “Santa Claus does not ex- Because, however,ist” Russell should requires be either observance true or of false. the principle That Santa of the Claus excluded does third, not alsoex- the are false,But regardless let us have of a lookwhat also predicate on the otherwe substitute problem, theconcerning variable (x)statement with. If "Santa we thus Clausist can does be notsaid ex withist" shouldthe predicate be either x trueis Santa or false. Claus That. We Santa can Clausmake does not exist can be said with the predicate x is Santa Claus. We can make transcription on the substituteproper it nouns. with, e.g.What the if predicatea name that x is refers a man to (formally,some fictional we will entity, mark it withnot exist the expressioncan be saidtranscription with the predicate on the xbasis is Santa of these Claus relations. We can between make transcription expressions on the basis of these relations between expressions of ordinary language and symbolic language of "M(x)")e.g. tothe the sentence name “Santa Claus”, occurs in the expression? From the of ordinary language and symbolic language of logic: logic: point of view of Frege’s approach, we have to assume — if we want thatSocrates sentences, is a man.in which it occurs, had meaning, i.e. the truth–value Ordinary language Ordinary language FormalFormal symbolic symbolic language language of of logic logic according to Frege — that given individual, which we mark with ... is Santa Claus S(x) will besome false. individual In formal constant, record exists,we would at least express in some it like sense: this: maybe it ... is Santa Claus ((or:or: x xis is Santa Santa Claus) Claus) S(x) exists within some theory, some discourse, some book, some my- Santa Claus (...) Santa Claus (...) (or: Santa Claus (x)) ($x)(S(x)(x)(S(x) Ù a(x)(x) Ù (“y)(S(y) (y)(S(y) ® (x = y))) (x = y))) thology,(x)(So(x) etc. but M(x) it has  to ( existy)(So(y) in some (xway. = y)))We can say it also like (or: Santa Claus a(x)) this, that individuals must have pre–theoretic existence. This re- Santa Claus does notSanta exist. Claus does not exist. Ø($x)S(x)(x)S(x) This sultsresults also also in thatin that we wecannot cannot write: write: It is appropriate toIt make is appropriate two remarks. to Firstly:make two we remarks.do not have Firstly: to use we the do transcription not have toof the Ø($a)(a) expression "Santa useClaus" the in transcription this case because of the the expressionsituation gets “Santa simpler Claus” by that in we this just case need to say that there is nobecause such thi theng, situation which would gets besimpler a Santa by Claus.that we Nevertheless, just need to we say present that its if we wantif we wantto write to writesomething something grammatically grammatically correct correct within within the predicatetranscription logic. for Such comparison.there is no such thing, which would be a Santa Claus. Nevertheless, Secondly: in these transcriptions, "x" marks an empty space, where a name of some individual expressionthe predicate is not allowedlogic. Such in itexpression at all, it is is not not created allowed properly in it at all, according it is to rules of expressionwe present its transcription for comparison. can be put and "(x)" marks a space, where we can put name of some term, written in the creationnot createdin predicate properly logic. according But how to can rules we ofthen expression express, creatione.g. the following in sentence? Secondly: in these transcriptions, “x” marks an empty space, formal language of logic. Here we can see again that individual empty spaces are not of the predicate logic. But how can we then express, e.g. the following same type, but theywhere are specific a name also of bysome names individual of what thingscan be they put can and be “a(x)” substituted marks with. sentence?Santa Claus does not exist. Apart from that, theya space, are also where specific we bycan what put positionname of they some take term, within written the whole in theexpression. for- That is why, e.g. malGahér language says that of logic."a variable Here we... canis not see only again an that unspecified individual empty empty space. " If we markedSanta Claus Santa does Claus not e.g. exist. with the individual constant "a", it seems that(Gahér, for transcription 2003, p. 178)spaces We are could not ofsee the the same situation type, butalso theylike arethat specific the variable also isby anames specified we should use precisely the above mentioned formal record, which emptyis, however, space. This notof space what is things specified they by can where be substituted it is located with. in givenApart expression, from that, theyin which If we marked Santa Claus e.g. with the individual constant “a”, expression it is locatedare also and namesspecific of whicby whath objects position can be they put takeinto thiswithin place. the whole ex- it seems that for transcription we should use precisely the above pression. That is why, e.g. Gahér says that “a variable ... is not only 7.2 Logical Atomism: Language Should Represent the World mentioned formal record, which is, however, not grammatically an unspecified empty space.” (Gahér, 2003, p. 178) We could see correct in terms of predicate logic. We can call Russell'sthe viewsituation on the also relation like that between the variablelanguage is and a specified world representationalistic empty space. . In Frege’s concept, the sentence “Santa Claus does not exist” has Also the term logicalThis atomism space is is specified used to describe by where Russell's it is located concept, in whichgiven shouldexpression, express in the no meaning, for the expression “Santa Claus” has no meaning. It is fact that because thewhich language expression of logic it consistsis located of andnames names of objects of which and objectsconcepts can (names be of that this expression does not refer to any object and therefore no concepts are namesput of into properties this place. and relations) and because between it and the world some kind of isomorphism (language represents the world, or at least it should) exists, then the world too consists of, in a sense, objects, relations and properties. 64 Of course, we should not forget that which objects have which properties and which relations65 are between which objects, is an element of the world, i.e. we should not forget about something that could be called "relations" of objects and properties and "relations" of objects and relations. These "relations" are expressed on the language level by that, which names occur together with which predicates in statements describing the world. Let us try to illustrate this view on the relation between language and world with this example. Let us imagine a very simple world, consisting only from several objects, properties and relations. In the picture, we will mark individuals with individual constants, because for simplicity, we will firstly describe this world with proper names of individuals. We will have It is appropriate to make two remarks. Firstly: we do not have to use the transcription of the expression "Santa Claus" in this case because the situation gets simpler by that we just need to say that there is no such thing, which would be a Santa Claus. Nevertheless, we present its transcription for comparison. Secondly: in these transcriptions, "x" marks an empty space, where a name of some individual can be put and "(x)" marks a space, where we can put name of some term, written in the formal language of logic. Here we can see again that individual empty spaces are not of the same type, but they are specific also by names of what things they can be substituted with. Apart from that, they are also specific by what position they take within the whole expression. That is why, e.g. Gahér says that "a variable ... is not only an unspecified empty space." (Gahér, 2003, p. 178) We could see the situation also like that the variable is a specified empty space. This space is specified by where it is located in given expression, in which expression it is located and names of which objects can be put into this place.

7.2 Logical Atomism: Language Should Represent the World

We can call Russell's view on the relation between language and world representationalistic. Also the term logical atomism is used to describe Russell's concept, which should express the fact that because the language of logic consists of names of objects and concepts (names of concepts are names of properties and relations) and because between it and the world some kind of isomorphism (language represents the world, or at least it should) exists, then the world too consists of, in a sense, objects, relations and properties. Of course, we should not forget that which objects have which properties and which relations are between which objects, is an element of the world, i.e. we should not forget about something that could be called "relations" of objects and properties and "relations" of objects and relations. These "relations" are expressed on the language level by that, which names occur together with which predicates in statements describing the world. Let us try to illustrate this view on the relation between language and world with this example. Let us imagine a very simple world, consisting only from several objects, properties and relations. In the picture, we will mark individuals with individual constants, because for simplicity, we will firstly describe this world with proper names of individuals. We will have four objects in our universe, a, b, c, d; three properties F,G, H; and two relations between two possible objects R, S. We can depict our simple world, marked as World1, for example with the following picture:

7.2 Logical Atomism: Language Should Represent the World World1: World1: S aF, G bF, G We can call Russell’s view on the relation between language S and world representationalistic. Also the term logical atom- R R ism is used to describe Russell’s concept, which should ex- press the fact that because the language of logic consists of S H H names of objects and concepts (names of concepts are names c d S of properties and relations) and because between it and the world some kind of isomorphism (language represents the world, or at least it should) exists, then the world too consists If we do notIf use we any do variablesnot use anyto record variables all facts to record of this alluniverse, facts of this universe, but only predicated and of, in a sense, objects, relations and properties. but only predicatedindividual and constants, individual weconstants, can record we can these record fact these as follows, as elements of the sent, which fact as follows,expresses as elements all basic of the("atomic", sent, which so to expresses say) facts all about basic this universe: (“atomic”, so to say) facts about this universe: Of course, we should not forget that which objects have which properties and which relations are between which objects, is an el- M1 = {F(a), G(a), ¬H(a), F(b), G(b), ¬H(b), ¬F(c), ¬G(c), H(c), ¬F(d), ¬G(d), ement of the world, i.e. we should not forget about something that H(d), R(a, c), ¬R(c, a), R(b, d), ¬R(d, b), ¬R(a, b), ¬R(b, a), ¬R(c, d), ¬R(d, could be called “relations” of objects and properties and “relations” c), ¬R(b, c), ¬R(c, b), ¬R(a, d), ¬R(d, a), ¬R(a, a), ¬R(b, b), ¬R(c, c), ¬R(d, d), of objects and relations. These “relations” are expressed on the lan- ¬S(a, c), ¬S(c, a), ¬S(b, d), ¬S(d, b), S(a, b), S(b, a), S(c, d), S(d, c), ¬S(b, c), guage level by that, which names occur together with which predi- ¬S(c, b), ¬S(a, d), ¬S(d, a), ¬S(a, a), ¬S(b, b), ¬S(c, c), ¬S(d, d)} cates in statements describing the world. Let us try to illustrate this view on the relation between lan- As atomic statements we understand now all statements that con- guage and world with this example. Let us imagine a very simple tain exactly one predicate and at the same time do not contain any world, consisting only from several objects, properties and rela- variables or logical operators. Then we can say that the set M1 is tions. In the picture, we will mark individuals with individual con- a set, in which for each possible atomic statement, either it itself stants, because for simplicity, we will firstly describe this world or its negation can be found. This set unambiguously represents with proper names of individuals. We will have four objects in one possible distribution of properties and relations over individu- our universe, a, b, c, d; three properties F,G, H; and two relations als of that world. We can understand it also as a set, which assigns between two possible objects R, S. We can depict our simple world, every atomic statement a truth–value in the following way: it as- marked as World1, for example with the following picture: signs the truth–value Truth to the statement, if it belongs to ele- ments of the set and the truth–value False, is its negation belongs to elements of the set. The fact that it assigns truth–value to every atomic statement means, that for every atomic statement it is true that either it or its negation has to be the element of the set.

66 67 The set M1 is the set of statements, which represent atomic 8. Russell III: Knowledge by Acquaintance proposition of our world. These statements are images of these and Real Proper Names propositions in formal language and there should be isomorphism between them and propositions of our world1. It is one of maximum consistent set of atomic statements and their negation, which can be assembled for the world of four individuals, three properties and two relations between two possible things. A conflict would be the result of addition of any additional atomic statement or its negation would. If, for example, we added the statement S(b, c), a conflict would occur between it and the statement ØS(b, c), which Keywords: knowledge by acquaintance, non–existence, proper already is in the set M1. names, sense perceptions Let us notice too that our description of universe contains all information. It contains also statements that say that some indi- 8.1 Knowledge by Acquaintance vidual does not have certain property, or that there is no relation be- tween certain individuals. Thus, it represents also propositions of But what is the situation of a hypothetical individual that does not this type: propositions, that some individual does not have certain exist? However, what is an individual without features and rela- property; propositions, that there is no relation between two ob- tions to other individuals? If they are nothing without them, to un- jects. These are also facts that create that world. We could therefore ambiguously determine the specific individual, would it be enough say that they are “conglomerates” of objects and properties or rela- to have the description that would univocally determine them, tions that do not belong to these objects. But the fact, that certain i.e. a specific description? And ultimately, do we need any proper object does not have certain property, is a fact, which comprises that names to describe individuals; if the individual is nothing without world in the very same way as the fact, that certain object has cer- their features and relations to other individuals? Or, could names tain property. Or, if we want to consider as conglomerates of some of individuals be just definitional abbreviations of appropriately objects and some properties and relations only such compounds of selected descriptions specifying the very individual we want to call objects and properties or relations that exist in that world, then we by the expression? could derive the set M1 from these facts about these conglomerates Nevertheless, let’s take note of the fact that in our world1 it can and from that they are all facts about such conglomerates. be selected no specific description that would define any of indi- viduals making them. We can distinguish in it between two types Recommended Literature: of individuals; one type consists of individuals initially called a and b, and the other type is made by individuals originally called MILLER, A.: Philosophy of Language. London : Routledge, 2007, pp. 23 — 89. c and d. The reason is symmetry. Because of that we cannot distin- MORRIS, M.: An Introduction to the Philosophy of Language. New York : Cambridge guish between the abovementioned pairs of individuals as far as University Press, 2007, pp. 49 — 73. PEREGRIN, J.: Kapitoly z analytické filosofie. Praha : Filosofia, 2005, pp. 69 — 93. we want to specify them by a description. Seeing that World1 is not

68 69 symmetric in the vertical direction, we can distinguish between 8.2 The Only Real Proper Names two types of individuals. (Expressions Used in Pointing at an Object) If we were part of this world, then we could distinguish individu- als, as long as being part of the world would necessarily mean that As long as we can indicate at least one individual (that does not lie we can directly perceive some individuals. Strictly speaking, the nec- on the axis of symmetry of the world) by an expression owing to we essary condition of the possibility to define all other individuals of can point at it, the situation is getting better. According to Russell, it the world by some descriptions is that we could refer to at least one is the only case when we can use the subject indication strategy that by pointing at them. However, this statement has one more condi- is used with proper names. In this case only it is guaranteed that tion; the individual we pointing at cannot be on the axis of symme- the object exists. In other situations the proper name could have no try of this world (if there is no individual lying on the axis of symme- referent. As long as by proper name we indicate something we are try — which would be caused by non–existence of the axis, because pointing at, i.e. what we perceive, this problem can never emerge. the world is not symmetric — this cannot come about for sure). The reason for the need to directly refer to an individual we have described is not Russell’s motif for allowing the only ones to It is necessary to say that sole perception is a certain de- behave as proper names with expressions by which we refer to sub- signing of a conception not necessarily corresponding to re- jects by pointing at (such as expression “this”, “this man” etc.). We ality. It is not an entirely direct and errorless contact with think though that the previous description can help understand subjects, therefore the situation in which the constructions why at least in this case allowing of proper names is the right step. refer to nothing real, is in perception yet possible. This is In some cases, anyway, it is an inevitable step on the way to deter- why Russell considers real subjects of pointing for subjects mine all other individuals by some descriptions. we can refer to by the “this” expression. According to him, in existence and nature of the entities we cannot be wrong, therefore with these objects we can safely use the reference In Russell’s terminology, it could be said that we have to be strategy used with proper names. directly acquainted or confronted (the latter is used by Per- egrin (Peregrin, 2005, p. 83.) with some subjects. Russell uses for this type of knowledge of the subject the knowledge by In order to avoid epistemological questions we do not want to deal acquaintance expression. The motif for introduction of this with now, let’s not to be engaged in the nature of individuals in our kind of knowledge was, among others, the fact that he was world1. Let’s not deal with the question, whether it’s sense percep- an empiricist, and all knowledge had to come out from the tions, or some fundamental elements of the world that could also experience. This experience has to be processed by our cogni- be outside us. Let’s presume that we are able to point at an object tive apparatus, whereby Russell considered being part of the world by the expression “this”. It can be the object originally of the apparatus as well, because, from the experience with labelled by the expression “a”. In this case the object has the name the world, it is necessary to get more general knowledge. but as it is getting it now based on pointing, let its name be the expression “this”. The original names of the subject (“a”, “b”, “c”, “d”)

70 71 (x)(N(x)  (x)  (y)(N(x)  (x = y)))

where (x) is a certain grammatically correctly created expression of predicate logics that could be forgotten and the features of the individual (which has containsonly( thex)(N(x) at leastindividual one(x) occurrence originally (y)(N(x) labelled of the variable (xby =the y))) expression x; it is the “b”? expr Whatession we want to say about the the “this” name) can be written down as follows: object.else shouldIf we wantwe substitute to say about instead the of individual “N(x)”? originally labelled by the “b" expression, we wouldwhereWe like(x) can first is use a to certain anysay featureabout grammatically it that that hasit has the correctly features individual createdF, Goriginally and expression has lanot- feature of predicate H. So, welogics want that to F(this) containscreatebelled three atby least statements,the “b”one expression occurrence which and will of only thegradually variablethis individual contain x; it is expressions hasthe it.expr In essionthis F(x), we G(x) want and to sayH(x) about in the G(this) object.placevery of Ifpoint we(x). itwant willWhat tohelp issay usindeed about that by inthe pointing thisindividual case we a could originallyunique label feature thelabelled indi that- by has the only“b" expression,the individual we ¬H(this) wouldoriginallyvidual like originally labelled first to bysay labelled the about expression by it the that expression it “b”? has featuresWhat “a”. Theelse F individual ,shouldG and wehas orig substitute not- feature instead H. So, of we “N(x)”? want to createWeinally can three usenamed statements,any b feature is the only whichthat one has will individual the gradually individual relation contain originally to theexpressions individual labelled F(x), by the G(x) “b” and expression H(x) in andthe Obviously it is the same transcription strategy as in the previ- onlyplacethat this of we individual point(x). Whatat, the has isS(this, it.indeed In b) this relation. in very this point We case could it awill alsouni helpque use usotherfeature that rela by that- pointing has only we couldthe individual label the ous records of the facts on the world1. The strategy can be used in originallyindividualtion, e.g.: labelledoriginally S(b, this) by. Even labelledthe expression though by thethe “b”?expresrelation Whatsion of theelse“a”. same shouldThe type individual we (type substitute originally instead named of “N(x)”? b is the the transcription of all expressions telling on subject labelled by WeonlyS )can oneis concerned, use individual any feature it relatiis not thaton the to hassame the the individual relation. individual that originally we point labelledat, the S(this, by the b) “b” relation. expression We could and the expression “this”. We can use it in the transcription of state- alsoonly usethisAs weotherindividual would relation, like has to e.g.:it. avoid In S(b,this proper verythis) names. pointEven ofit though objectswill help the in usthe relation that world by 1of , pointing the same we type could (type label S )the is ments telling about its relations. We have to say about this subject concerned,individualwe have originallyit(besides is not thethe labelled sameindividual relation. by the we expres have pointedsion “a”. at), The to useindividual varia- originally named b is the that it toward itself has none of the relations R and S. Expressions Asonly bles.we one Wewould individual have like selected relatito avoid (arbitrary)on to proper the individualthe names x variable, ofth at objectsso we we point have in toat,the use the world it S(this, 1, we b) relation.have (besides We could the originally as ØR(a, a) and ØS(a,a) can be written down as follows: individualalsoat use determination other we haverelation, pointedof the e.g.: individual at), S(b, to this)use by va. meansEvenriables. thoughof Wea unique have the relationfactselected valid of (arbitrary) the same the type x variable, (type S) sois weconcerned, abouthave it.to itThereforeuse is notit at the determination we same have relation. to use of the the expression individual “S(toto, by means x)”. After of -a unique fact valid about it. ¬R(this, this) ThereforeAs wardswe would we we get have like the to expression:to use avoid the expressionproper names “S(tot ofo, objects x)”. Afterwards in the world we get1, we the haveexpression: (besides the ¬S(this, this) individual we have pointed at), to use variables. We have selected (arbitrary) the x variable, so we have(($x)(S(this,x)(S(this, to use it x) x)at Ù determinationa(x)(x) Ù (“y)(S(this, (y)(S(this, of x) the ® (x indi x) = y)))vidual (x = byy))) means of a unique fact valid about it. However, we cannot use this strategy when recording facts re- Therefore we have to use the expression “S(toto, x)”. Afterwards we get the expression: garding other individuals. How should we record the other facts? This isThis not is a notstatement, a statement, but an but incomplete an incomplete expr expressionession used used to tellto about the individual. It is We can use Russell’s analysis of the sentences containing certain incomplete,tell( aboutx)(S(this, becausethe individual. x) it contains(x) It (is incomplete, y)(S(this,the variable x) because   (x).(x = it Asy))) contains a consequence, the it is not possible to descriptions. If N is the feature with the only one individual, we determinevariable its a(x). truth As valuea consequence, (as it depends it is not on possiblewhat is substitutedto determine for its the variable). That is why it can say about the individual through the feature as follows: cannotThistruth is benot value a astatement. statement, (as it depends but onan whatincomplete is substituted expression for the used variable). to tell about the individual. It is Inincomplete, orderThat isto why get because ita cannotstatement, it becontains a westatement. have the tovariable substitute (x). for Asthe avariable consequence, some grammatically it is not possible correct to (($x)(N(x)x)(N(x) Ù  a(x)(x) Ù (“y)(N(x) (y)(N(x) ® (x = y))) (x = y))) createddetermineIn expressionsorder its truth to get value aof statement, the (as predit dependsicate we have logics. on to what substitute If iswe substituted want for theto record varifor -the that variable). individual That havingis why ita relationcannotable besome S(this, a statement. grammatically x) with the individualcorrect created labelled expressions by the expression of the predi “this”,- has the feature F, we wherewhere(x) isa(x) a iscertain a certain grammatically grammatically correctly correctly created created expression expres- of predicate logicshaveIn ordercatethat to logics.substitute to get If a westatement, the want expression to werecord have “F(x)” that to individualsubstifor (x),tute andforhaving get:the a variable relation so me grammatically correct containssion of at predicate least one logics occurrence that contains of the atvariable least one x; occurrenceit is the expr ofession the we want to say aboutcreatedS(this, the expressions x) with the individualof the pred labelledicate logics. by the Ifexpression we want “this”, to record has that individual having a object.variable If we x; itwant is the to expressionsay about wethe want individual to say aboutoriginally the object.labelled If by the “b" expression,relationthe we( feature x)(S(this,S(this, F x), we x)with have F(x)the to individual substitute (y)(S(this, labelledthe expressionx)  by (x th =e y))) “F(x)”expression for a(x), “this”, has the feature F, we wouldwe wantlike first to say to aboutsay about the individualit that it has originally features labelled F, G and by hasthe “b”not feature H. So, we wanthaveand to get:substitute the expression “F(x)” for (x), and get: createexpression, three statements, we would whichlike first will to gradually say about contain it that itexpressions has features F(x), G(x) and H(x)The in thesimilar thing is valid even though we would like to express that the individual has feature placeF, G of and  (x).has notWhat feature is indeed H. So, wein wantthis tocase create a uni threeque statements, feature that has only the individualG(x) and(($x)(S(this, x)(S(this, has feature x) x) Ù H(x)F(x) F(x) Ù: (“y)(S(this, (y)(S(this, x) ® (x x) = y))) (x = y))) originallywhich will labelled gradually by the contain expression expressions “b”? WhatF(x), G(x) else and should ¬H(x) we in substitutethe instead of “N(x)”? Weplace can useof α (x).any What feature is indeed that has in thisthe caseindividual a unique originally feature thatlabelled has by the “b” expressionThe and similar (x)(S(this, thing is x) valid  G(x)) even  though (y)(S(this, we would x)  like (x =to y)))express that the individual has feature only this individual has it. In this very point it will help us that by pointing we could labelG(x) the and ( hasx)(S(this, feature x) H(x)  :H(x)  (y)(S(this, x)  (x = y))) individual72 originally labelled by the expression “a”. The individual originally named b is the 73 only one individual relation to the individual that we point at, the S(this, b) relation. WeIn could case (wex)(S(this, would like x) to G(x)) talk about  (y)(S(this, the individual x)  that(x = has y))) originally been labelled c, we have also use other relation, e.g.: S(b, this). Even though the relation of the same type (typeto Sfind) is (a featurex)(S(this, unique x)  forH(x) this individual. (y)(S(this, It x)could  (x be = feature y))) R(this, x). Then we record the concerned, it is not the same relation. facts that this individual has not features F and G, and has feature H, as follows: As we would like to avoid proper names of objects in the world1, we have (besidesIn case the we would like to talk about the individual that has originally been labelled c, we have individual we have pointed at), to use variables. We have selected (arbitrary) the x variable,to find so( ax)(R(this, feature unique x)   forF(x) this (individual.y)(R(this, Itx) could  (x be= y)))feature R(this, x). Then we record the we have to use it at determination of the individual by means of a unique fact valid aboutfacts it.that( x)(R(this, this indivi x)dual   hasG(x) not (featuresy)(R(this, F and x) G , and (x = has y))) feature H, as follows: Therefore we have to use the expression “S(toto, x)”. Afterwards we get the expression: (x)(R(this, x)  H(x)  (y)(R(this, x)  (x = y))) (x)(R(this, x)  F(x)  (y)(R(this, x)  (x = y))) (x)(S(this, x)  (x)  (y)(S(this, x)  (x = y))) A little( x)(R(this,more complicated x)  G(x) it is ( withy)(R(this, the individual x)  (x = originallyy))) labelled as d, because the individual(x)(R(this, has no x)direct  H(x) relati  on( y)(R(this,to the individual x)  (x we= y))) refer to by the expression “this”. We This is not a statement, but an incomplete expression used to tell about the individual. It is incomplete, because it contains the variable (x). As a consequence, it is not possibleA little to more complicated it is with the individual originally labelled as d, because the determine its truth value (as it depends on what is substituted for the variable). That isindividual why it has no direct relation to the individual we refer to by the expression “this”. We cannot be a statement. In order to get a statement, we have to substitute for the variable some grammatically correct created expressions of the predicate logics. If we want to record that individual having a relation S(this, x) with the individual labelled by the expression “this”, has the feature F, we have to substitute the expression “F(x)” for (x), and get:

(x)(S(this, x)  F(x)  (y)(S(this, x)  (x = y)))

The similar thing is valid even though we would like to express that the individual has feature G(x) and has feature H(x):

(x)(S(this, x)  G(x))  (y)(S(this, x)  (x = y))) (x)(S(this, x)  H(x)  (y)(S(this, x)  (x = y)))

In case we would like to talk about the individual that has originally been labelled c, we have to find a feature unique for this individual. It could be feature R(this, x). Then we record the facts that this individual has not features F and G, and has feature H, as follows:

(x)(R(this, x)  F(x)  (y)(R(this, x)  (x = y))) (x)(R(this, x)  G(x)  (y)(R(this, x)  (x = y))) (x)(R(this, x)  H(x)  (y)(R(this, x)  (x = y)))

A little more complicated it is with the individual originally labelled as d, because the individual has no direct relation to the individual we refer to by the expression “this”. We (x)(N(x)  (x)  (y)(N(x)  (x = y))) where ((x)x)(N(x) is a certain (x) grammatically (y)(N(x)  correctly(x = y))) created expression of predicate logics that contains at least one occurrence of the variable x; it is the expression we want to say about the object.where If (x)we iswant a certain to say grammaticallyabout the individual correctly originally created la expressionbelled by theof predicate“b" expression, logics wethat wouldcontains like at first least to one say occurrenceabout it that of it the has variable features x; F it, Gis theand expr has essionnot feature we want H. So, to saywe aboutwant tothe createobject. three If we statements, want to saywhich about will the gradually individual contain originally expressions labelled F(x), by G(x)the “b" and expression, H(x) in the we placewould of like (x). first What to say is aboutindeed it thatin this it has case features a uni Fque, G featureand has that not featurehas only H . theSo, individualwe want to originallycreate three labelled statements, by the whichexpression will “b”?gradually What contain else should expressions we substitute F(x), G(x)instead and of  “N(x)”?H(x) in the Weplace can ofuse  (x).any featureWhat is that indeed has thein individualthis case aoriginally unique feature labelled that by thehas “b”only expression the individual and onlyoriginally this individual labelled byhas the it. Inexpression this very “b”? point What it will else help should us that we by substitute pointing instead we could of “N(x)”?label the individualWe can use originally any feature labelled that byhas the the expres individualsion “a”. originally The individual labelled originallyby the “b” named expression b is theand onlyonly one this individual individual relati has onit. Into thisthe individualvery point th itat will we help point us at, that the by S(this, pointing b) relation. we could We label could the alsoindividual use other originally relation, labelled e.g.: S(b, by this)the .expres Even sionthough “a”. the The relation individual of the originally same type named (type b Sis) theis concerned,only one individual it is not the relati sameon relation. to the individual that we point at, the S(this, b) relation. We could Asalso we use would other like relation, to avoid e.g.: properS(b, this) names. Even of thoughobjects the in relationthe world of 1the, we same have type (besides (type Sthe) is individualconcerned, we it haveis not pointed the same at), relation. to use va riables. We have selected (arbitrary) the x variable, so weAs have we towould use itlike at determinationto avoid proper of thenames indi vidualof objects by means in the of world a uniqu1, wee fact have valid (besides about it.the Thereforeindividual we we have have to pointed use the at),expression to use va “S(totriables.o, x)”.We Afterwardshave selected we (arbitrary) get the expression: the x variable, so we have to use it at determination of the individual by means of a unique fact valid about it. Therefore(x)(S(this, we have x) to use(x) the ( expressiony)(S(this, “S(totx)  o,(x x)”.= y))) Afterwards we get the expression:could introduce it through the relation with some individuals labelled before, or in this case, wecould can useintroduce a little itmore throu compligh thecated relation facts with valid some in the individuals world1. Regarding labelled before,the individual or in this we case,are This is (notx)(S(this, a statement, x)  but(x) an (incompletey)(S(this, x)expr ession (x = y))) used to tell about the individual.talkingwecould It canis aboutintroduce use a is little valid it morethrou that ghcompliit isthe the relationcated only facts one with havingvalid some in no theindividuals relation world1 to. Regardinglabelled the individual before, the individual labelled or in this by we case,the are incomplete, because it contains the variable (x). As a consequence, it is not possibleexpressiontalkingwe canto aboutuse “this”, a littleis valid ne moreither that compli theit is relation thecated only facts R(this, one valid having x) ,in nor theno therelationworld relation1. Regardingto the S(this, individual thex). individualSo labelled a searched, weby arethe determineThis is not its atruth statement, value (as but it andepends incomplete on what expr isession substituted used forto tell the aboutvariable). the individual.That isunique whytalkingexpression It it isfeature about “this”, couldis valid ne be itherthat e.g. it the( is R(this, therelation only x) oneR(this,  havingS(tjis, x), x))nonor. relation Thenthe relation we to can the S(this,talkindividual about x). itsSolabelled featuresa searched, by asthe cannotincomplete, be a statement. because it contains the variable (x). As a consequence, it is not possiblefollows:uniqueexpression to feature “this”, could ne beither e.g. the ( relationR(this, x) R(this,  S(tjis, x), nor x)) . theThen relation we can S(this, talk a boutx). So its a features searched, as Indetermine order to getits trutha statement, value (as we it have depends to substi on whattute foris substituted the variable for so theme variable). grammatically That iscorrectfollows:unique why it feature could be e.g. (R(this, x)  S(tjis, x)). Then we can talk about its features as createdcannot expressionsbe a statement. of the predicate logics. If we want to record that individual havingfollows: (a x)( R(this, x)  S(this, x)  F(x)  (y)((R(this, x)  S(this, x)  (x = y))) relationIn order S(this, to get x) a withstatement, the individual we have labelledto substi tuteby th fore expression the variable “this”, some has grammatically the feature Fcorrect, we(( x)( x)(R(this,R(this, x) x)  S(this,S(this, x) x)  G(x)F(x)  ( (y)((y)((R(this,R(this, x) x)  S(this,S(this, x) x)   (x (x = = y))) y))) havecreated to substitute expressions the expressionof the pred “F(x)”icate logics.for (x), If andwe get:want to record that individual having( (ax)( x)(R(this,R(this, x) x)  S(this,S(this, x) x)   H(x)F(x)G(x)  (  y)(( ((y)((y)((R(this,R(this,R(this, x) x)x) S(this,S(this,S(this, x) x)x) (x =(x(x y))) == y)))y))) relation S(this, x) with the individual labelled by the expression “this”, has the feature F, we( x)(R(this, x)  S(this, x)  H(x)G(x)  ( (y)((y)((R(this,R(this, x) x)  S(this,S(this, x) x)   (x (x = =y))) y))) have( tox)(S(this, substitute x) the  F(x)expression  (y)(S(this, “F(x)” for x) (x), (x and= y))) get: However,(x)( formulationR(this, x) of  theS(this, relation x)  will H(x) be  more(y)(( complicatedR(this, x) in general.S(this, x) The  (xsituation = y))) is relativelyHowever,could introduce simpler, formulation it throu ifgh we the oftalkrelation the about withrela sometiona relation individualswill be of labelledmorean individual complicatedbefore, or inwith this incase,th egeneral. individual The we situation refer to is we can use a little more complicated facts valid in the world1. Regarding the individual we are The similarThe(x)(S(this, similar thing is thing x) valid  F(x)is even valid  though(eveny)(S(this, though we would x)we  would like(x = to likey))) express to express that the individual has byfeatureHowever,relativelytalking theexpression aboutexpression simpler, formulationis valid “this”. that “this”.if itFor weis theof example, talk onlytheFor aboutone relaex havingwithample,tion a relation nothewill relation withtranscription be of tomorethe thean individualtranscriptionindividual complicated of the labelled relawith byof-in the thgeneral.the e individual relation The situationoriginallywe refer tois G(x)that and thehas individual feature H(x) has: feature G(x) and has feature H(x): recordedrelativelybyexpression tionthe asoriginallyexpression “this”, simpler,R(a, ne c)ither ,recorded ifwe “this”. thewe substitute relation talk asFor about R(this,R(a, exthe c) ample,x)a , expres, relationwenor substitutethe withsion relation of “R(toto,anthe S(this, individual thetranscription expressionx) x)”. So afor withsearched, “  ofth(x)” ethe individual expression, relation we originally and refer we to The similar thing is valid even though we would like to express that the individual has byrecordedfeatureunique the feature expression as couldR(a, bec) e.g. , “this”.we ( R(this,substitute For x)  ex S(tjis,theample, expresx)). Thenwithsion we canthe “R(toto, talk transcription about x)” its features for “of as (x)” the expression,relation originally and we get:follows:“R(toto, x)” for “a(x)” expression, and we get: G(x) and($x)(S(this,(x)(S(this, has feature x) x) Ù G(x))H(x) G(x)): Ù (“y)(S(this,  (y)(S(this, x) ® (x x)= y)))  (x = y))) get:recorded as R(a, c), we substitute the expression “R(toto, x)” for “(x)” expression, and we ($x)(S(this,(x)(S(this, x) x) Ù ØH(x)H(x) Ù (“y)(S(this, (y)(S(this, x) ® (x x) = y))) (x = y))) get: ((($x)(R(this,x)(x)(R(this,R(this, x) x)  x) Ù S(this, R(this, R(this, x) x) Ùx)F(x) (“y)(R(this,   ( (y)((y)(R(this,R(this, x) ® (x x) x) = y)))S(this, (x = x) y)))  (x = y))) (x)(S(this, x)  G(x))  (y)(S(this, x)  (x = y))) (x)((x)(R(this,R(this, x)  x)S(this,  R(this, x)  G(x) x)  ( (y)((y)(R(this,R(this, x) x) S(this, (x x)= y))) (x = y))) (x)(R(this, x)  S(this, x)  H(x)  (y)((R(this, x)  S(this, x)  (x = y))) In case Inwe( case x)(S(this,would we likewould x) to  talklikeH(x) aboutto talk ( the y)(S(this,about individual the x) individual that (x has = y))) originallythat has been labelled c, weAs havein this As( caseinx)(R(this, this we case coincidentally x) we  coincidentallyR(this, x)express  ( expressy)(R(this, the ve thery factx) very  used fact(x = in usedy))) the in definition of the individual to findoriginally a feature been unique labelled for c, this we haveindividual. to find It a featurecould be unique feature for R(this,this x). Then we recordoriginallyAsHowever, thethein this definition formulationlabelled case we asof coincidentally thec, relaweindividualtion used will thebe expressoriginally moreexpression complicated the labelled ve “R(this,ry in fact general.asc , weused x)” Theused twoin situation thethe times definition is in a conjunction. of the individual So, In case we would like to talk about the individual that has originally been labelled c, werelatively have simpler, if we talk about a relation of an individual with the individual we refer to factsindividual. that this indivi It coulddual be has feature not features R(this, x)F. andThen G we, and record has feature the facts H , as follows: theAsoriginallyby overall expressioninthe thisexpression expressioncaselabelled “R(this, we“this”. coincidentallyas coul Forx)”c, wetwoexd ample,be used timeseven with expressthe simpler:in the expressiona conjunction.transcription the very “R(this, offact So,the used therelation x)” overallin two originallythe times definition in a ofconjunction. the individual So, to findthat athis feature individual unique has for not this features individual. F and GIt, andcould has be feature feature H ,R(this, as x). Then we recordoriginallytherecorded expression overallthe as R(a,labelled expression c) could, we substituteas be ccouleven, we thed simpler: usedbe expres even thesion simpler: “R(toto,expression x)” for “R(this, “(x)” expression, x)” two and times we in a conjunction. So, factsfollows:( thatx)(R(this, this indivi x) dualF(x) has not ( featuresy)(R(this, F andx)  G ,(x and = y)))has feature H, as follows: theget: overall(x)(R(this, expression x)  ( couly)(R(this,d be even x) simpler: (x = y)))     (x)(R(this, x)  G(x)  (y)(R(this, x)  (x = y))) (($x)(R(this,(x)(R(this, x) x) x) R(this,Ù (“y)(R(this, ( x)y)(R(this,  (y)(R(this, x) ® (xx) x)= y))) (x = = y))) y))) (($x)(R(this,(x)(R(this,x)(R(this, x)x) x) Ù  ØF(x) H(x)F(x) Ù (“y)(R(this,( y)(R(this,(y)(R(this, x) ®x) (x x)= y))) (x (x= y))) = y))) However,(x)(R(this, in the case x)  of ( y)(R(this,the record x) of  relation (x = y))) previously recorded as R(c, a) a similar ($x)(R(this,(x)(R(this, x) x) Ù ØG(x)G(x) Ù (“y)(R(this, (y)(R(this, x) ® (x x)= y)))  (x = y))) simplificationHowever,As in thisHowever, case in we willthe coincidentally in not thecase becase ofpossible, express ofthe the record therecord so ve rywe fact ofof have relationusedrelation toin theuse previously definition previouslythe following of recordthe individualrecorded expression:- as R(c, a) a similar originally labelled as c, we used the expression “R(this, x)” two times in a conjunction. So, A little($x)(R(this,( morex)(R(this, complicated x) x) Ù H(x) H(x) Ù it(“y)(R(this,  is ( withy)(R(this, x)the ® (xindividual x) = y))) (x = y)))originally labelled as d, becauseHowever,simplificationthe the edoverall as R(c, expression in a) the willa similar coul casenotd be be simplification ofeven possible, the simpler: record so wewillof haverelationnot beto possible,use previously the followingso we recordedhave expression: as R(c, a) a similar individual has no direct relation to the individual we refer to by the expression “this”.simplification Weto( use x)(R(this, the following will x) not  expression:beR(x, possible, this)  so( wey)(R(this, have to x) use  the (x =following y))) expression: A littleA littlemore morecomplicated complicated it isit iswith with the the individualindividual originallyoriginally la -labelled as d, because the((x)(R(this, x)(R(this, x)  (x)y)(R(this,  R(x, x) this) (x = y))) ( y)(R(this, x)  (x = y))) individualbelled as has d, because no direct the relati individualon to hasthe noindividual direct relation we refer to the to inby- the expression “this”.TheHowever, transcriptionWe(($x)(R(this, x)(R(this,in the case ofx) x)of Ùthe the ØR(x,  relarecordR(x, this)tion ofthis) Ùrelationpreviously (“y)(R(this,  ( previouslyy)(R(this, recorded x) ®recorded (x x)= y))) as as (x R(c, R(b,= y)))a) c)a similarwill be more complicated, dividual we refer to by the expression “this”. We could introduce becauseThesimplification transcription for talkingwill not be ofabout possible, the relaboth so wetion respective have previously to use the subjects following recorded weexpression: needas  R(b,to use c) variableswill be more and atcomplicated, the same it through the relation with some individuals labelled before, or timebecause it hasThe for to transcription betalking told aboutabout of both theboth relationof respective them previouslyby meanssubjects ofrecorded itswe uniqueneed as toØR(b, characteristics: use variables and at the same The transcription(x)(R(this, x)  ofR(x, the this) rela  (tiony)(R(this, previously x)  (x = recordedy))) as R(b, c) will be more complicated, in this case, we can use a little more complicated facts valid in the becausetimec) itwill has for be to moretalking be told complicated, about about bothboth because respectiveof them for by talking subjects means about of we its bothneed unique respec to characteristics:use- variables and at the same world1. Regarding the individual we are talking about is valid that timeThetive transcription (it x, hassubjects y)(S(this, to be of we thetold need x)rela about tion toR(this, previously use both variables y) of recorded themR(x, and byas at y)meansR(b, the (c) same willofz)(S(this, itsbe time uniquemore it z) complicated,has characteristics: to (x = z))  ( w)(R(this, w) couldit isintroduce the only it throu onegh having the relation no relationwith some toindividuals the individual labelled before, labelled or in by this case, becausebe (told  for(yx, talking=abouty)(S(this, w))) about both bothx) of  themrespective R(this, by meanssubjectsy)   weofR(x, itsneed uniquey) to  use ( variables characteristics:z)(S(this, and atz) the  same (x = z))  (w)(R(this, w) we can use a little more complicated facts valid in the world . Regarding the individual we are time it has to be told about both of them by means of its unique characteristics: the expression “this”, neither the relation R(this,1 x), nor the relation talking about is valid that it is the only one having no relation to the individual labelled by the (x, (y y)(S(this, = w))) x)  R(this, y)  R(x, y)  (z)(S(this, z)  (x = z))  (w)(R(this, w) expressionS(this, x)“this”,. So ane searched,ither the relation unique R(this, feature x), nor could the relation be e.g. S(this, (¬R(this, x). So x) a Ùsearched, (x, y)(S(this,(y = w))) x)  R(this, y)  R(x, y)  (z)(S(this, z)  (x = z))  (w)(R(this, w)  (y = w))) unique¬S(tjis, feature x)) .could Then be we e.g. can (R(this, talk aboutx)  S(tjis, its features x)). Then aswe follows: can talk about its features as (($x,x)(F(x) y)(S(this,  H(x) x)  (x)  (y)((F(x)  H(x))  (x = y))) follows: (x)(F(x)  H(x)  (x)  (y)((F(x)  H(x))  (x = y))) (($x)(ØR(this,x)(R(this, x) “y)((ØR(this,S(this, x)  x)F(x) Ù ØS(this, (y)(( x)R(this, ® (x x)= y))) S(this, x)  (x = y))) where ((Byx)(F(x)(x)x)(F(x) using is part H(x) this ofH(x) strategy (x)the  expression(y)((F(x)(x) it is (possible  H(x))y)((F(x), where  to(x =wetranscribe y))) H(x)) would  allsubstitute (x the= y))) state what- we want to say about (($x)(ØR(this,x)(R(this, x) )((ØR(this,S(this, x) x)  ÙG(x) ØS(this, (y)(( x) ®R(this, (x = y)))x)  S(this, x)  (x = y))) ments from the set M1. If we can determine by pointing at least thewherewhere only (x)individual(x) is partis partof the that of expression thewe expressioncan, where substitute we ,would where for substitute thewe wouldvariable what we substitute want x so to thatsay aboutwhat the createdwe want expression to say about is (x)(R(this, x)  S(this, x)  H(x)  (y)((R(this, x)  S(this, x)  (x = y))) ($x)(ØR(thiy)((ØR(this, x) Ù ØS(this, x) ® (x = y))) true.wherethethe oneonlyonlyThe objectindividual (x)expression,individual is not part that lying we ofthat as can theon wewesubstitute the expression mentioned,can axis forsubstitute of thesymmetry, variablewhere is forinco xwe ofsothemplete. thatthewould variable the world, created Itsubstitute meansthen x expression so the that thatwhat isthe we wecreated cannot want expression tosay say that about it is true.new The canexpression, completely as we mentioned,determine is theinco mplete.world Itby means some that descriptions, we cannot say in that it However, formulation of the relation will be more complicated in general. The situation is referstrue. toThe an expression,object. We canas wesay mentioned,this only: it isis incoan expressionmplete. It whichmeans wouldthat we refer cannot to an say object that if it therefers only to an individual object. We can that say thiswe only: can it substitute is an expression for which the variablewould refer xto soan objectthat theif created expression is relativelyHowever, simpler, ifformulation we talk about aof relation the relation of an individual will be with more the individual complicat we- refer to which we use the only real proper name. theretrue.refersthere is isThe tojustjust an one expression,one object. object object with We featureswithas can we features sayF andmentioned, this G. IfF only:  and(x) is Gisitvalid .is incoIf withan (x) mplete.expression refere is ncevalid Itto the means withwhich object, refere thatthiswould ncewe refer tocannot the to object, ansay object that this ifit by the expression “this”. For example, with the transcription of the relation originally ed in general. The situation is relatively simpler, if we talk about expressionIf the would world be true, is otherwis asymmetric,e it would then be false. this But only if ther onee is not proper just one name object, the  expressionthererefers is to just an would object.one objectbe Wetrue, withcan otherwis sayfeatures thise itonly: F would and it G is .be Ifan false. expression(x) isBut valid if whichther withe isrefere would not ncejust refer to one theto object, anobject, object the this if recordeda relation as R(a, of c) ,an we individualsubstitute the with expres thesion individual“R(toto, x)” wefor “refer(x)” toexpression, by the and we entirewould expression not betalking even on necessary,object (x) butwill beit wouldfalse regardless be enough what weto specificallyhave get: entirethereexpression isexpression just would one object talkingbe true, with onotherwis features objecte Fit and(x)would Gwill. Ifbe  befalse.(x) false is Butvalid regardless if withther erefere is whatnotnce just weto onethe specifically object,object, thisthe substitute for (x). substituteexpressionentireNote that expression iffor we would want(x). to be talktalking true,about non-exisotherwison objecttinge object it would(x) by meanswill be offalse.be its properfalse But name, ifregardless ther it woulde is notwhat just we one specifically object, the (x)(R(this, x)  R(this, x)  (y)(R(this, x)  (x = y))) 74 Notesubstituteentire that expression if forwe  want(x). talking to talk abouton object non-exis (x)ting will object be byfalse means regardless of75 its proper what name,we specifically it would As in this case we coincidentally express the very fact used in the definition of the individual Notesubstitute that iffor we (x). want to talk about non-existing object by means of its proper name, it would originally labelled as c, we used the expression “R(this, x)” two times in a conjunction. So, Note that if we want to talk about non-existing object by means of its proper name, it would the overall expression could be even simpler:

(x)(R(this, x)  (y)(R(this, x)  (x = y)))

However, in the case of the record of relation previously recorded as R(c, a) a similar simplification will not be possible, so we have to use the following expression:

(x)(R(this, x)  R(x, this)  (y)(R(this, x)  (x = y)))

The transcription of the relation previously recorded as R(b, c) will be more complicated, because for talking about both respective subjects we need to use variables and at the same time it has to be told about both of them by means of its unique characteristics:

(x, y)(S(this, x)  R(this, y)  R(x, y)  (z)(S(this, z)  (x = z))  (w)(R(this, w)  (y = w)))

(x)(F(x)  H(x)  (x)  (y)((F(x)  H(x))  (x = y)))

where (x) is part of the expression, where we would substitute what we want to say about the only individual that we can substitute for the variable x so that the created expression is true. The expression, as we mentioned, is incomplete. It means that we cannot say that it refers to an object. We can say this only: it is an expression which would refer to an object if there is just one object with features F and G. If (x) is valid with reference to the object, this expression would be true, otherwise it would be false. But if there is not just one object, the entire expression talking on object (x) will be false regardless what we specifically substitute for (x). Note that if we want to talk about non-existing object by means of its proper name, it would could introduce it through the relation with some individuals labelled before, or in this case, we can use a little more complicated facts valid in the world1. Regarding the individual we are talking about is valid that it is the only one having no relation to the individual labelled by the expression “this”, neither the relation R(this, x), nor the relation S(this, x). So a searched, unique feature could be e.g. (R(this, x)  S(tjis, x)). Then we can talk about its features as follows:

(x)(R(this, x)  S(this, x)  F(x)  (y)((R(this, x)  S(this, x)  (x = y))) (x)(R(this, x)  S(this, x)  G(x)  (y)((R(this, x)  S(this, x)  (x = y))) (x)(R(this, x)  S(this, x)  H(x)  (y)((R(this, x)  S(this, x)  (x = y)))

However, formulation of the relation will be more complicated in general. The situation is relatively simpler, if we talk about a relation of an individual with the individual we refer to by the expression “this”. For example, with the transcription of the relation originally recorded as R(a, c), we substitute the expression “R(toto, x)” for “(x)” expression, and we get: predicates, quantifiers and logical connections for entire descrip- Note that if we want to talk about non–existing object by means tion (ofx)(R(this, this world. x) Every  R(this, subject x)  of ( they)(R(this, world is x) thanks  (x =to y))) asym - of its proper name, it would not be possible. We cannot point at metry really unique (even if we suppose that subjects are nothing it, because it does not exist, and therefore we cannot use an ex- As withoutin this case its features we coincidentally and relations express to other the subject)very fact and used therefore in the definition of the individualpression like “this”, etc. But we cannot even use the proper name in originallyit can be labelled defined as by c ,an we utterance used the thatexpression is true about “R(this, itself x)” only. two This times in a conjunction. aSo, typical meaning, which substitute in the formal language would the worldoverall could expression be created, coul ford example,be even simpler: if we exclude individual d from be an individual invariable, such as “e”, because, as said before, in the world1 and therefore all the relations and features it exists in. this language it cannot be said for example ¬(∃e), if we want to keep Thinking(x)(R(this, over the x) way ( y)(R(this,we could record x)  all(x =the y))) facts regarding the its grammatical rules. world without using proper names (individual constants), could be However,left for inthe thereader. case of the record of relation previously recorded as R(c, a) a similar simplification will not be possible, so we have to use the following expression: Based on our simple model world, we hope, is well seen some 8.3 Non–existing Subjects of substantial points of Russell’s teaching. We can also see (x)(R(this, x)  R(x, this)  (y)(R(this, x)  (x = y))) that between these worlds and their descriptions (e.g. world1 What would be the situation of subject that does not exist? and set M1) are like a perfect “equivalence” of a certain type TheHow transcription could we recordof the arela statementtion previously that talks recorded on this non–existingas R(b, c) will be more complicated,we called isomorphism. The language of symbolic logics de- becauseindividual? for talking We can about use Russell’s both respective logical analyses subjects of certainwe need descrip to use- variables and at the samescribes (represents) this world in a perfect way. So, as every timetions, it has while to be as told a supposed about both unique of them feature by means we introduce of its unique a feature characteristics: single world like this consists of subjects, features and re- that no individual of the universe does not fulfil. For example, in lations, and possibilities how these basic entities are “con- the( worldx, y)(S(this,1 there is x) no  individual R(this, y) that   couldR(x, y)have  ( concurrentlyz)(S(this, z) fea - (x = z))  (w)(R(this, w)nected”, also the symbolic language consists of the subject tures F(y and = w))) H. The expression referring to the individual typical by names, feature names and relations and possibilities how to this feature would seem to be like: connect the names into the statements. The formal language consists of certain logical atoms. This fact corresponds to the (($x)(F(x)x)(F(x) Ù  H(x) H(x) Ù a(x)  (x)Ù (“y)((F(x) (y)((F(x) Ù H(x))  ® H(x)) (x = y)))  (x = y))) picture of the world made from some analogical atoms. wherewhere(x) isα (x)part is ofpart the of expression the expression,, where where we wouldwe would substitute substi -what we want to say about the tuteonly what individual we want that to we say can about substitute the only for individual the variable that xwe so can that the created expressionRecommended is Literature true.substitute The expression, for the variable as we xmentioned, so that the createdis inco mplete.expression It meansis true. that we cannot say that it refersThe to expression, an object. asWe we can mentioned, say this only:is incomplete. it is an expression It means that which we would refer to an objectMILLER, if A.: Philosophy of Language. London : Routledge, 2007, pp. 23 — 89. cannot say that it refers to an object. We can say this only: it is an MORRIS, M.: An Introduction to the Philosophy of Language. New York : Cambridge there is just one object with features F and G. If (x) is valid with reference to the object, thisUniversity Press, 2007, pp. 49 — 73. expressionexpression would which be would true, referotherwis to ane objectit would if there be false. is just But one if object there is not just one object, PEREGRIN,the J.: Kapitoly z analytické filosofie. Praha : Filosofia, 2005, pp. 69 — 93. entirewith expression features F andtalking G. If onα(x) objectis valid with(x) referencewill be tofalse the regardlessobject, what we specifically substitutethis expression for (x). would be true, otherwise it would be false. But if Notethere that is if not we just want one to object, talk about the entire non-exis expressionting object talking by onmeans object of its proper name, it would α(x) will be false regardless what we specifically substitute for α(x).

76 77 9. Russell and Frege: Russell’s Paradox becomes a paradox. The statement means that 1) if we presume and Type Theory that it is true, we can prove that it is false; and 2) if we assume that it is false, we can prove that it is true. Therefore we say it is a paradox. Let’s show why. First of all, let’s presume that the statement is true, i.e. m ∈ m is valid. The statement says that m is an element of m, i.e. m belongs to the set m. However, with each set belonging to the set m, it is valid that it is not an element of itself. So, it is valid with the set m. The fact we could write down as Keywords: self reference, paradox statement, paradox of a liar, Rus- sell’s paradox, set theory, type theory m ∉ m

9.1 Russell’s Paradox is contrary to our presumption m ∈ m. Nevertheless, if we presume that our presumption is not valid Russell is along with N. A. Whitehead also an author of the signifi- it means that the set m is not an element of itself. However, each masterpiece (Russell — Whitehead, set that is not an element of itself, belongs by definition of the set 1910–1913), in which they used modern symbolic logics in order to m to the set. So, even the set m should belong to the set. It means establish mathematics systematically, formally, and symbolically. though that m ∈ m is valid, which is contrary to our presumption In the piece of work they strived to avoid a problem discovered by that m ∈ m is not valid. So, again we come to a dispute. So, regard- Russell in Frege’s system, and which is commonly called Russell’s less of whether we presume that statement m ∈ m is true or not, it paradox. always raises a dispute. This statement is really a paradox. We can outline the paradox in its modern version, because the In Frege’s system, there is a mistake of the same type. It was version is simpler and more elegant, than its version in Frege’s sys- just Russell who drew Frege’s attention. Frege tried to dispose of tem. A reader interested in the exact form of the Frege’s paradox the mistake, but didn’t manage to come to solution satisfying him. can take a look at Kolman’s monograph on Frege (Kolman, 2002, But as Peregrin says (Peregrin, 2005, s. 64), in principle the mistake p. 229 — 234). is not non–removable when creating the type of system built by Let’s define set m as the set which all sets that are not elements Frege, and its presence in Frege’s system does not deteriorate all of themselves belong in. Mathematically, we can define the set asm Frege’s theoretical results. = {x ½ x ⊄ x}. The problem lies in the fact that if set m is defined this As Russell and Whitehead were aware of the paradox, they way, the statement strived to avoid it in their own system. Russell considered the source of the problem certain characteristics present also in the m ∈ m following paradox statement:

78 79 This statement is false Russell wanted to prevent the situation that a statement It is a paradox statement, similar to the above mentioned state- could state about itself by means of so–called type theory. ment „m ∈ m“. He proposed to distinguish between statements of various If we presume that it is true then what it says should be true. orders. If a statement states about other statements, the But what it says is that it is false, so it should be false. But if we, statements have to be the statements of the lower order by contrast, presume that it is false, than what it says is not true. than the statement itself. We can imagine that statements of Subsequently, it is not true that it is false which means it is true. order 0 are statements that can state about anything, except We can see that similarly as statement “m ∈ m”, statement “This for statements. Statements of order 0 can never state about statement is false” is paradox. Both statements have, beside para- themselves. If we want to state anything, we have to do it doxicality, also something else in common; they contain self refer- by means of statement of order 1 that are statements about ence. By self reference of a statement we mean that the statement statements of order 0. If we want to state about statements of refers to itself; or “it says about itself”. order 1, we have to continue with one order higher, and our statement has to be comprehended as the statement of the higher order, statement of order 2. This way it arises a certain Russell’s paradox begins when a notion can belong or not hierarchy of statements which provides for that any state- to itself, i.e. if it is allowed to assign or deny the notion to it- ment would state about itself. This way a creation of the self in the symbolic language. Similarly, with functions, the abovementioned paradox is avoided. analogous problem would emerge if a function could have itself as an argument, i.e. if one of elements of its domain of definition could be itself. In case of sets the problem would An analogical hierarchy can by created for functions. In predicate emerge when in the system it would be allowed to construct logics the hierarchy could have the following form: Let the func- a statement stating that a specific set belongs, or does not tions of the first orderbe the functions which argument could only belong to itself. be individuals, but never any functions. Let the functions of the sec- ond order be the functions which arguments can only be the func- tions of the first order etc. In case of this hierarchy of functions 9.2 Type Theory there cannot be a function that is an element of its own domain of definition. There cannot be a notion that could be stated about Just this was a problem according to Russell and in his work Math- itself (i.e. attribute it to itself, or deny to itself). ematical logics based on type theory (Russell, 1908) he proposed his As one of versions of the abovementioned paradox concerns solution of the problem. He and Whitehead elaborated on that in sets, modern attempts on axiomatization of the set theory had to detail in the introduction to work Principia Mathematica,. figure out the problem. We can see that Frege’s and Russell’s theo- retical work also touched mathematics except for philosophy and logics. As it was led by the requirement of exactness and accuracy

80 81 (which they mainly tried to ensure by the formalization of the 10. Logical Positivism problems they dealt with), it brought permanent and firm results, which either stayed in a form until now or, in case of errors, were rectifiable many times. In any case, it was possible to build on their work not only in philosophy, but also in the fields like logics or mathematics.

Recommended literature

KOLMAN, V.: Logika Gottloba Frega. Praha : Filosofia, 2002, pp. 209 — 234. Keywords: logical positivism, pseudo–problem, state–description, PEREGRIN, J.: Kapitoly z analytické filosofie. Praha : Filosofia, 2005, pp. 32 — 93. meaningfulness PRIEST, G.: Logika. Praha : Dokořán, 2007, pp. 45 — 52. SVOBODA, V. — PEREGRIN, J.: Od jazyka k logice. Filozofický úvod do moderní logi- ky. Praha : Academia, 2009, pp. 315 — 370. 10.1 Verifiability Criterion

The movement, usually called logical positivism or logical empiri- cism, was inspired, apart from older empiricists and positivists, mainly by Russell and Frege. Several prominent philosophers who can be included in this philosophical movement, established in 1920 the so–called Vienna circle. , Otto Neurath, Moritz Schlick, Kurt Gödel, Alfred J. Ayer, Hans Hahn, Karl Menger and others were its members. Also for example Ludwig Wittgen- stein, whose Tractatus logico–philosophicus was revered by the members and used to read from it for a certain period, was in con- tact with them. One of the most important philosopher of this movement, Ru- dolf Carnap (1891 — 1970), ventured even further, than Russell, in his stands concerning the critique of traditional philosophy. In his opinion, we can divide all traditional philosophical questions into two types: 1) to those, that can be in principle solved by science (so they could be assumed by science, as soon as it will dispose of resources for their solution) and 2) to those, which in reality are no problems at all. We can call problems that fall under this category, pseudo–problems.

82 83 But how can we tell pseudo–problems from real problems? We empiricists, they did not want to admit any other source of our cog- can reformulate this question like this: how will we distinguish, nition and our science than empirical experience. Of course, they which questions are meaningful and which are not? For this rea- acknowledged also the status of mathematics and logic, but we will son, the criterion of meaningfulness of statements became impor- get later to this point. tant for logical empiricists. That is, certain statements as possible The notion of logical positivists about the cognition was such, answers correspond to questions. If it is not possible fundamen- that on the basis of sentences, capturing our observations, we are tally determine the truth–value of possible answers to given ques- creating more general sentences, hypotheses and theories, which tion, it means, that it is not possible to answer such question. become part of science. It would be ideal if we could derive our theories from our observations. Then all our scientific knowledge would be based on such foundation, which is the least dubious The so–called verifiability criterion of meaningfulness of from all possible foundations, in the following sense. The fact that statements is characteristic for logical positivists. It can be something like sensory perception and sensory experience exists, expressed like this: the sense of statement is the method of its is much less dubious than the fact that there is, for example, some verification. Because verification is in fact the determination purely rational cognition or perception of some realm of ideas etc. of truth–value of the statement, then the sense of statement The majority of non–empiricists too acknowledge that senses real- is in fact the method, how to determine its truth–value. That ly exist and provide some (although maybe imperfect) knowledge. meant that if there is no way how (at least in principle) to de- First, let us then imagine some very idealized model of our cog- termine the truth–value of some statement, this statement nition, based on the above described world1. Let us notice, that fol- has no sense. lowing sentences about this model world are true:

(“x)(F(x)(x)(F(x) ® G(x)) G(x)) According to positivists, science is concerned with whether is given ($x)F(x)(x)F(x) statement true. Philosophy is concerned, whether it is meaningful ($x)G(x)(x)G(x) at all, i.e. if its truthfulness can be determined (at least in princi- ($x)H(x)(x)H(x) ple) at all. It analyses language and statements in it to find out, if Ø($x)(F(x)(x)(F(x) Ù H(x)) H(x)) they have absolutely any sense. Only after this analysis can science Ø($x)(G(x)(x)(G(x) Ù H(x)) H(x)) proceed to studying whether is given statement true or false. This Ø($x)(F(x)(x)(F(x) Ù G(x) G(x) Ù H(x))  H(x)) is then vicariously applied to whole theories, for they are actually (“x,(x, y)((F(x) y)((F(x) Ù F(y))  F(y)) « (G(x)  Ù (G(x) G(y)))  G(y))) sets of statements. (“x, y)((F(x) Ù F(y)) ® S(x, y)) (x, y)((F(x)  F(y))  S(x, y)) This is also related to how logical positivists understood the (“x, y)((G(x) Ù G(y)) ® S(x, y)) (x, y)((G(x)  G(y))  S(x, y)) nature of cognition. The basic idea of their approach can again (“x, y)((H(x) Ù H(y)) ® S(x, y))    be represented with our simple model world1. Logical positiv- ( x, y)((H(x) H(y)) S(x, y)) ists imagined that the foundation of our cognition are sentences, and so on.on. which capture our observations or experience. Because they were We could call statements, such as (x)(F(x)  G(x)) some sort of "physical laws" of the world1. They are not logical laws, they are not valid on the basis of axioms and rules of our 84 logical system (predicate logic). But they predicate something general85 , so they are some sort Of course, in predicate logic the assertion (x)F(x) cannot be derived from the assertion F(a). Neither there is any such rule among rules of predicate logic:

F(a1)  F(a2)  ... F(an) (x)F(x)

However, if we knew that all individuals have the property F, we could deservedly derive the assertion (x)F(x) from the assertion F(a1)  F(a2)  ... F(an) (of course, if a1, a2, ... an are all individuals in that world). It would be true also vice versa, which could be written, for example, as follows:

((a1, a2, ... an are all individuals of universe)  F(a1)  F(a2)  ... F(an))  (x)F(x)

F(a) G(a) R(b, c) (x)G(x) (x)H(x) (x)(F(x)  H(x)) (x)(F(x)  G(x))

are meaningful statement with respect to the world W and the language of predicate logic. We can equally determine also that following sentences are not meaningful statements with respect to the world W and the language of predicate logic (with respect to both at once):

F(e) T(a, b, c) (x) (x)(F(x)G(x)) E(g) a F(a (x, y)((A(x)  B(y))  C(x, y)) (x)(F(x)  G(x)) (x)F(x) (x)G(x) (x)H(x) (x)(F(x)  G(x)) (x)(F(x)  H(x)) (x)F(x) (x)(G(x)  H(x)) (x)G(x) We could call statements, such as (∀x)(F(x) i G(x)) some sort of (in cases when is the given atomic assertion false). And     (x)H(x)“physical( x)(F(x) laws” of theG(x) world H(x))1. They are not logical laws, they are not this is exactly in essence the idea of logical positivists. (x)(F(x)valid( onx, H(x)) y)((F(x)the basis  of F(y)) axioms  and(G(x) rules  G(y))) of our logical system (predi- (x)(G(x)cate( logic).x, H(x)) y)((F(x) But they  F(y))predicate  S(x, something y)) general, so they are some 10.2 State Description (x)(F(x)sort( ofx, G(x)laws y)((G(x) after H(x)) all. G(y)) They are S(x, such y)) laws that are valid forall items (x, y)((F(x)in the(x, world y)((H(x)F(y))1, they (G(x) are H(y)) not G(y))) necessarily S(x, y)) valid in every world, which (x, y)((F(x)canand be exhaustinglyso F(y)) on.  S(x, describedy)) with the means of predicate logic. Carnap introduced in his work Meaning and Necessity the    ( x, y)((G(x)They are G(y))not even S(x,valid y)) in a specific subset of worlds describable in term state–description. “A state description in a semantical    ( x,We y)((H(x)predicate could call H(y)) logic, statements, which S(x, y))is defined such as by( thatx)(F(x) every  worldG(x)) in someit consists sort of "physical laws" of thesystem denoted S1, is a of sentences in S1 which contains and so on. worldof four1. They individuals, are not threelogical properties laws, th eyand are two not relations. valid on the basis of axioms and rules of ourfor every either the sentence or its negation logicalOf system course, (predicate in predicate logic) logic. Butthe assertionthey predicate (∀x)F(x) something cannot be general de- , so they are some sort but not both. Such a sentence is called a state description, be- We could call statements, such as (x)(F(x)  G(x)) some sort of "physical laws" of the Of rivedcourse, from in thepredicate assertion logic F(a). the Neither assertion there ( isx)F(x) any such cannot rule be among derived from the assertion F(a).cause it gives a complete description of a possible state of the world1. They are not logical laws, they are not valid on the basis of axioms and rules of our logical systemNeitherrules (predicate thereof predicate is logic) any .logic:such But theyrule predicateamong rules something of predicate general logic:, so they are some sort universe of individuals with respect to all the properties and Of course, in predicate logic the assertion (x)F(x) cannot be derived from the assertion F(a). relations expressed by the predicates of the system. It thus Neither there is F(aany11 )such )Ù F(a F(a rule2) 2Ù) among ... F(a... F(an )rulesn) of predicate logic: represents one of Leibniz’s possible worlds or Wittgenstein’s (“x)F(x)(x)F(x) possible states of affairs.” (Carnap, 2005, p. 26). F(a1)  F(a2)  ... F(an) (x)F(x)However,However, if we if knew we knew that allthatindividuals all individuals have have the property the property F, we F , could deservedly derive the assertionwe could( x)F(x)deservedly from derive the assertion the assertion F(a1) (∀ x)F(x)F(a2) from ... F(a then )asser (of course,- if a1, a2, ... an areAccording all to this definition, our set M1 is in fact a state–descrip- However,individuals if wetion knew F(a1) that∧in F(a thatall2) individuals∧ world). ... F(an) (ofIt have course,would the propertyifbe a1 , truea2, ... F aalso,n we are couldvice all individuals versdeservedlya, which derive could the be written,tion for. But it would be good to perceive what we called world1 from assertion example,(x)F(x)in that from asworld). follows: the Itassertion would beF(a true1)  alsoF(a2 vice)  ... versa, F(an )which (of course, could if be a 1writ, a2,- ... an are all a new perspective. World1 is in fact just one of big number of pos- individuals inten, that for world).example, It aswould follows: be true also vice versa, which could be written, for sible distribution of three properties and two relations over four example, as follows: ((a1, a2, ... an are all individuals of universe)  F(a1)  F(a2)  ... F(an))  (x)F(x) individuals. If we now perceive these four individuals as certain ((a1, a2, ... an are all individuals of universe) Ù F(a1) Ù F(a2) Ù ... universe of individuals (set of individuals), we can understand the ((a1, a2, ... an are all individuals of universe)  F(a1)  F(a2)  ... F(an))  (x)F(x) F(an)) « (“x)F(x) world1 as one of its possible states, which may or may not occur in F(a) our universe. F(a) UnderG(a) the condition that we knew the truth–value of all atomic Naturally, each such world (which can now assume different G(a) statementsR(b, c) about that world, we could execute a programme, in states) is defined not only by the number of individuals but also R(b, c)which ( wex)G(x) would derive all other possible assertions (of course, to by the number of properties and numbers and sort (by sort, we (x)G(x)derive(x)H(x) all true assertions, we would need an infinite amount of have in mind the “arity” of respective predicate, i.e. how many argu- (x)H(x)time,( x)(F(x)because  the H(x)) number of statements, that can be derived in ments it has) of relations in it. So what we are going to call world   ( x)(F(x)propositional ( H(x))x)(F(x) and G(x)) predicate logic from even finite set of certain from our new perspective, could be defined like this: (x)(F(x)other statements,G(x)) is infinite) from these atomic assertions or their are meaningfulare meaningful statement with statement respect with to the respect world Wto andthe wothe rldlanguage W and of the predicate language logic. of Wepredicate logic. We can equallycan determineequally determinealso that following also that sent followingences are sent notences meaningful are not statements meaningful with statements with respect torespect the86 world to Wthe and world the languageW and the of predicatelanguage logic of predicate (with respect logic to (w bothith atrespect once): to both at once): 87

F(e) F(e) T(a, b, c) T(a, b, c) (x) (x) (x)(F(x)G(x))(x)(F(x)G(x)) E(g) E(g)  a F(a a F(a (x, y)((A(x)  B(y))  C(x, y)) (x, y)((A(x)  B(y))  C(x, y)) (x)(F(x)  G(x)) (x)F(x) (x)G(x) (x)H(x) (x)(F(x)  H(x)) (x)(G(x)  H(x)) (x)(F(x)  G(x)  H(x)) (x, y)((F(x)  F(y))  (G(x)  G(y))) (x, y)((F(x)  F(y))  S(x, y)) (x, y)((G(x)  G(y))  S(x, y)) (x, y)((H(x)  H(y))  S(x, y)) and so on.

We could call statements, such as (x)(F(x)  G(x)) some sort of "physical laws" of the world1. They are not logical laws, they are not valid on the basis of axioms and rules of our logical system (predicate logic). But they predicate something general, so they are some sort Of course, in predicate logic the assertion (x)F(x) cannot be derived from the assertion F(a). Neither there is any such rule among rules of predicate logic:

F(a1)  F(a2)  ... F(an) (x)F(x)

However, if we knew that all individuals have the property F, we could deservedly derive the assertion (x)F(x) from the assertion F(a1)  F(a2)  ... F(an) (of course, if a1, a2, ... an are all individuals in that world). It would be true also vice versa, which could be written, for example, as follows:

((a1, a2, ... an are all individuals of universe)  F(a1)  F(a2)  ... F(an))  (x)F(x)

F(a) (x)(F(x)  G(x)) G(a) (x)F(x) R(b, c) (x)G(x) (x)G(x) (x)H(x) (x)H(x) (x)(F(x)  H(x)) (x)(F(x)  H(x)) (x)(G(x)  H(x)) (x)(F(x)  G(x)) (x)(F(x)  G(x)  H(x)) (x, y)((F(x)  F(y))  (G(x)  G(y))) are meaningful statement with respect to the world W and the language of predicate logic. We SV = {a, b, c, d, F1, G1, H1, R2, S2} canthe equally world Wdetermine and the languagealso that of following predicate logicsentences (with arerespect not tomeaningful statements with (x, y)((F(x)  F(y))  S(x, y)) Therefore the world for us will be the set of individuals and respectboth toat theonce): world W and the language of predicate logic (with respect to both at once): (x, y)((G(x)  G(y))  S(x, y)) predicates (the superscript expresses the “arity” of respective (x, y)((H(x)  H(y))  S(x, y)) predicate). F(e) and so on. The set M1 is one possible state–description of the world W. The T(a, b, b, c) c) world1 is one possible state of the world W. Let us notice though, Ø($x)(x) We could call statements, such as (x)(F(x)  G(x)) some sort of "physical laws" of the that we can derive from M1 all possible statements, true for the (“x)(F(x)G(x))(x)(F(x)G(x)) world . They are not logical laws, they are not valid on the basis of axioms and rules of our state1 world1, as long as we know that M1 really contains all atomic E(g) logical system (predicate logic). But they predicate something general, so they are some sort statements (or their negations). The state–description contains all {{a aF(a F(a Of course, in predicate logic the assertion (x)F(x) cannot be derived from the assertion F(a). information about given state of the world. We can derive from (“x,(x, y)((A(x) y)((A(x) Ù B(y))  B(y)) ® C(x,  y)) C(x, y)) Neitherit the there truth–value is any such of any rule statement, among rules which of predicateis meaningful logic: for the world W. Sentences “¬(∃x)”, “(∀x)(F(x)G(x))” and “{{a F(a” were not mean- SoF(a we1) came F(a 2to)  the ... termF(an )of meaningfulness. What does this term ingful with respect to the world W, because they were not gram- mean( x)F(x)within our very idealized model for description of relation matically correctly created expressions of predicate logic (formulas between the language and the world and also for the description of the language of predicate logic). The remaining expressions con- However,of cognition? if we Theknew list that of meaningfulall individuals statements have the “for property the world F, we W” could deservedly derivetained the names of objects not existing in the world W (∀F(e)”, “E(g)”), assertionis determined(x)F(x) by from two thethings: assertion F(a 1rules)  F(a of2 )formal ... F(a language,n) (of course, if a1, a2, ... an areor all names of properties that are not possible in W (∀E(g)”, “(“x, y) individualswhich we in use that to world).describe Itthe would world be W, trueand thealso worldvice itself,versa, i.e.which could be written,((A(x) for ∧ B(y)) i C(x, y))”), or names of relations that are not possible example,the set asW. follows: So it has to be said that meaningfulness is determined in W (∀T(a, b, c)”, “(“x, y)((A(x) ∧ B(y)) i C(x, y))”). with respect to the pair of things: 1) certain language and 2) cer- Let us notice that all sentences, which were meaningless with tain((a world.1, a2, On... a then are basis all individualsof this fact we of canuniverse) derive,  that F(a for1)  example F(a2)  ... F(an))  (x)F(x) respect to the pair (predicate logic, world W) are sentences, whose sentences truth–value cannot be determined. They are sequences of symbols, for which the way to determine their truth–value with respect to F(a) the pair (predicate logic, world W) is not possible. On the other G(a) hand, it is possible for all meaningful statements. R(b, c) c) Ø($x)G(x)(x)G(x) 10.3 Meaningfulness ($x)H(x)(x)H(x) ($x)(F(x)(x)(F(x) Ù H(x)) H(x)) Let us now understand by meaningfulness, with respect to certain (“x)(F(x)(x)(F(x) ® G(x)) G(x)) pair of some language and some world, the property, that there is an unambiguous way to define the truth–value of this statement, are meaningfulare meaningful statement statement with respect with respect to the to wo therld world W and W theand language the of predicate logic.if We we know that language, that world and state–description of canlanguage equally ofdetermine predicate logic.also Wethat can following equally determine sentences also are that not fol meaningful- statements withthat world; by meaninglessness of certain statement we under- respectlowing to sentencesthe world Ware and not themeaningful language statements of predicate with logic respect (with torespect to both at once): stand the property that the truth–value of that statement cannot

F(e) 88 89 T(a, b, c) (x) (x)(F(x)G(x)) E(g) a F(a (x, y)((A(x)  B(y))  C(x, y)) be determined even with full description of that language, world This brings us to the importance of non–empirical disciplines, and state–description. This property is, so to say, “fundamental”. such as logic and mathematics. We are finding out that thing we By this we have in mind that certain statement could be meaning- can perceive on one hand purely as constructs (languages, math- ful with respect to the pair (predicate logic, W) also if we did not ematical and logical systems), are at the same time necessary for know full state–description of that world, i.e. if we did not know cognition of the world (for empirical cognition). Of course, it can be such basic set of information, from which everything about this objected, that other animals do not have any language, or at least world could be derived. In other words, even if we did not know language of the time, as have we, humans, but still are discovery everything about the state of that world. Also under these circum- (they discover, for example, their surroundings). We can therefore stances it could be true that if we knew the state–description of say at least that languages or symbolic system are necessary for this world, then we could unambiguously define the truth–value scientific cognition of the world. So that even an empiricists has of that statement. good reason to acknowledge mathematics and logic, if he thinks Let us notice, that in our simple idealized model of the relation that scientific cognition of the world is possible and valuable. between language and world, we were forced to include some lan- guage as well into our description. We had to describe meaning- fulness as a property no only with respect to certain world, but Because our cognition is relative also to language, it seem with respect to world + certain language. If we were talking only that we can create many languages, many systems, which about meaningfulness with respect to some world, someone could could serve us to describe the world. Carnap admits that we rightfully object: “But what if the expression “{{a F(a” has meaning can choose the language and even the logic we can use to in some language, whereas this statement has truth–value, if we describe the world. In this sense his attitude appears to be an take is as a description of something in the world W?” We would attitude of a relativist. On the other hand, he is of course an have to answer: “Yet it predicate logic, it has no meaning”. However, empiricists too. by saying this we would actually admit that the meaningfulness is relative not only to the world, but also to the language. Hence language too is important for the cognition of the world, Let us notice, that if we chose a language, the truth of statements not only how the things are in terms of experience. Language as in it will be determined not only by this language, but also by the a construct we use to grasp the world is therefore some kind of world. Thus the relativeness of our description of the world with second substantial element of cognition. Let us recall Russell in respect to the languages does by no means mean that this descrip- this connection, according to which we use not only our experi- tion would be determined by the world itself. If we take a good look ence, but also logic in our cognition. We can draw an analogy with on how thing are in our model example, we will find out, that al- our simple model of relation between language and world and say: though our description of the world depended on the chosen lan- in cognition, we need to find out not only what things exists and guage, the world itself did not depend on it at all. However, can we what properties they have and what relations between them they ask the following questions: is any language suitable for descrip- have, but we need to find out also some kind of language (which tion of a certain world? What if that language is not complex and will have to apparently include some logic). rich enough? And if we can use multiple languages to describe

90 91 certain world, are they not in fact same or unambiguously convert- 11. Theory of Speech Acts ible from one to another?

Recommended Literature

CARNAP, R.: Význam a nevyhnutnosť. Bratislava : Kalligram, 2005. FIALA, J. (ed.): Analytická filosofie. První čítanka. I Plzeň : Fakulta humanitních studií, Západočeská univerzita, 1999, s. XIX — LI, 14 — 58. MILLER, A.: Philosophy of Language. London : Routledge, 2007, pp. 90 — 125. PEREGRIN, J.: Kapitoly z analytické filosofie. Praha: Filosofia, 2005, pp. 95 — 122. Keywords: philosophy of ordinary language, , status function, symbolization

11.1 Ordinary Language Philosophy

Richard Rorty divided the philosophers of the linguistic turn into two big groups, according to what conclusions they drew from the discovery that the structure of the world and the structure of the language do not correspond. He called the way of philosophising of the first group the ideal language philosophy. It meant, in respect to language, that language must be improved, repaired, or a new language of science must be created. In this group we can put B. Russell, R. Carnap or earl Wittgenstein, the logical positivists move- ment. The centres of this approach were mainly Cambridge and Vienna of the first half of 20th century. He called the way of philosophising of the second group the or- dinary language philosophy.

This group emphasized that it is necessary to understand the functioning of the ordinary language. Late Wittgenstein, G. Ryle, J. L. Austin, P. Grice, J. R. Searle can be considered as their representatives and its centre was Oxford.

92 93 (1900 — 1976) wrote in 1932 an article “System- knowledge, but on the study of its actual use. He paid attention to atically misleading expressions”, in which he analyses, similar to language not as an abstract system, but rather as specific ways logical positivists, the relation between language and reality and how we use the language, in which contexts, situations, because points out to situation, when the language is misleading us. Unlike without that, in his opinion, we cannot understand the meaning. logical positivists, he sees no reason why should we change lan- Peter F. Strawson pointed out to the importance of context al- guage because of that. To analyse it is enough. ready before him. Austin considered as important to classify the Let us show an example of a misleading expression: speech acts. If entomologists take pains with the of bugs, philosophers should, in his opinion, resolve to categorize the There are no flying dogs. speech acts. We can see utterances from various viewpoints. Each means Ryle calls this type of misleading expression quasi–ontologi- emphasis on another aspect of the utterance. Utterance as a pho- cal. In his opinion, we say nothing about flying dogs in this way. netic act means that by uttering the sentence we make certain To better understand the state of thing, we can express the same sounds. We can analyse and record these sounds, study their physi- sentence in another form, which is more suitable to this state: cal properties. When we speak about the phatic act, we emphasize that the uttered sounds have the form of words and sentences of Nothing is a dog and a flying being at the same time. certain language, in which they mean something. Today, we can create programmes that recognize in the sound the words of a lan- In this case, his analysis practically does not differ from Rus- guage. Finally, with the rhetic act we emphasise that we are stating sell’s in this case. Ryle became know through application of his something. approach to human mind. Frege and his followers avoided it. Ryle More famous is Austin’s classification of rhetic speech acts. thinks, that talking about human mind is also misleading, in his A perlocutionary speech act means the utterance of a meaningful opinion it is a category mistake. The relation between mind and sentence, with which we are saying something. By reserving a illo- body is, in his opinion, similar to the relation between university cutionary speech act, we emphasise the way how we utter the sen- and its buildings. Let us imagine that someone comes to Oxford tence with the same content. The same idea can be used in speech and wants to see the university. He will be shown all departments, as a question, order, reply, information, decision, description, judge- libraries, dormitories and laboratories. He sees all that with inter- ment, critique, challenge, provision... In language, the necessary est but in the end he asks: Good, but where is the university? context is sometimes substituted with punctuation marks, which attach at least the most common contexts to the idea. Let us show 11.2 Importance of Social Context for Meaning these simple examples:

Probably the most known manifestation and result of the ordinary Did they convict him? language philosophy became the theory of speech acts by John They convicted him. L. Austin (1911 — 1960). He focused in it not on the study of lan- Convict him! guage as a tool of expression and preservation of (mainly scientific) The court convicts you...

94 95 To express other illocutionary acts, it would be necessary to ex- will collapse, cease to exist. The status function has the following press the context in more detail. In a specific situation, the context form: X counts as Y in context C. Let us have an example: is usually obvious to those present. Finally, under perlocutionary speech act, Austin has in mind This piece of paper counts as a 10 Euro bill in the Slovak Repub- such speech act, through which something is done, for example, we lic (and everywhere money are used). persuade someone, we convict someone, we oblige someone, etc. It can be successful or unsuccessful, according to what the act was Simply said: human social reality is constituted by what people aiming at succeeds or not. think and what they has has, on the other hand, origin in how they Austin’s thoughts on speech acts were further developed by the talk with each other and how the interact. Therefore language, ac- American philosopher John Rogers Searle (born on 1932). Searle cording to Searle, plays extremely important role in creating hu- has a broad scope in the philosophy, he contributed significantly man social reality. to the philosophy of language, philosophy of mind and social phi- Searle notices another important social role of the language, losophy. He became known with his “Chinese room” argument, fo- which he calls symbolization. As humans, we have the ability to cused against “strong” version of artificial intelligence. He proceeds use one thing for substitution, representation or symbolising an- from the assumption that we live in one world and that within the other thing. The symbolising property of language is an important boundaries given by our evolutionary equipment, this world is condition of institutional facts. Knife’s ability to perform the func- comprehensible to us even though the sceptical approach in mod- tion of a knife proceeds from its physical properties but human ern philosophy is still quite popular. cannot hold the office of a president just on the basis of physical Searle tried to explain with methods of analytical philosophy properties. Behind this lies the collective recognition of a status the relations between mental states, language and social real- function represented with words: “This gentleman is president”. ity. We can notice a difference with respect to Frege’s approach. To recognize an object as an object with status function serve the With respect to his motives, Frege strictly separated mental states indicators of status (a ring, a badge, an identity card...) In Searle’s (thinking) from language and he was absolutely not interested in opinion, they are of language nature, the symbolize even though the social reality represented by institutions. they do not need to use words for that. Let us go back to Searle and his more complex view on language. As philosopher, he was not interested in specific questions, but questions of the whole, which he calls frame questions. Accord- Ordinary language philosophy disrupted with its approach ing to Searle, many social realities (money, property, government, the traditional division into semantics and of lan- courts, university, marriage) exist only thanks to our conviction guage. Semantics should have studied relations between lan- that they exist. He asks: What maintains the institutions? guage expressions and the relation between signifier — sig- In his opinion, we are creating and maintaining the institution- nified, pragmatics again studied relations between language al reality through collective assignment of status functions, their expressions and those using or interpreting them. However, long–term acknowledgement and acceptance. If the society ceases to understand the meaning of the sentence, it is often neces- to acknowledge the status functions, the respective institutions

96 97 12. Willard van Orman Quine sary to include something from the context and the context is not considered a factor of semantics factor (apart from the case of context of other sentences in the text), but mostly of pragmatics (for example, the role of language in creation and maintaining institutions). So while the ordinary language philosophy contributed significantly to understanding the role of the language wherever the interpersonal relations are important, the ideal language philosophy made possible the development logic, mathematicisation of science, com- Keywords: analyticity, syntheticity, , meaning, pragma- puter science and artificial intelligence. tism, naturalisation of epistemology

12.1 Analytic and Synthetic Recommended Literature

AUSTIN, J. L.: Ako niečo robiť slovami. Bratislava : Kalligram, 2004. The American philosopher Willard van Orman Quine (1908 MARVAN, T.: Otázka významu. Cesty analytické filosofie jazyka. Praha : Togga, 2010, — 2000) can also be placed among the most important phi- pp. 165 — 180. MORRIS, M.: An Introduction to the Philosophy of Language. New York : Cambridge losophers of the philosophy of language. Despite that he was University Press, 2007, pp. 231 — 270. an empiricist (like logical positivists), he took a critical stand PEREGRIN, J.: Kapitoly z analytické filosofie. Praha : Filosofia, 2005, pp. 167 — 180. towards the traditional empiricism. In his paper Two Dog- SEARLE, J. R.: Myseľ, jazyk, spoločnosť. Bratislava : Kalligram, 2007. mas of Empiricism he called two of the central aspects of tra- ditional empiricism dogmas and tried to disprove them. As the first dogma he called the conviction that statements can be divided into analytic and synthetic. The notion that state- ments can be divided like that, was traditionally accepted as accurate, however, according to Quine it is not valid, because the line between analytic and synthetic statements cannot be clearly defined. The second dogma of empiricism is, ac- cording to him, “”reductionism: the that each mean- ingful statement is equivalent to some logical construct upon terms which refer to immediate experience” (Quine, 2005, p. 36).

98 99 The distinction between analytic and synthetic statements is part the terms true and false as well. So it appears that philosophy too of the philosophical tradition since the times of Immanuel Kant. In could reveal , but only those, which are valid regardless the the mentioned paper, Quine analyses in his opinion the most im- empirical situation, because the study of world is surely a neces- portant proposals for division of statements into these two catego- sary prerequisite for discovery of empirical truths. Then even the ries. Because in the analysis of each of these proposals he comes to metaphysics may be possible, unless we would say that statements that it is not functional, he concludes that statements cannot be that are true on the basis of logical relations, in fact say nothing divided in the mentioned way. and have no content. Of course, this does not have to mean that To explain Quine’s thinking, we will have a closer look on first they are useless, they can in fact be necessary so that others, not two parts of his paper Two Dogmas of Empiricism. We will just necessarily true statements, could even create some system of logi- mention other proposals for defining analyticity, which Quine cally connected statements. analyses. We would like to recommend to the reader, interested Because logical positivists did not revere metaphysics, they also in the analysis of these remaining proposals, to immerse di- could have always said that statements, whose truth cannot be rectly in the Quine’s text. There he will find also a more elegant de- determined (not even in principle), have no sense; and the could scription of what follows; we hope, however, that our analysis will have said about statements, which are necessarily true, that they aid the reader in understanding the part of Quine’s text, to which are true only in such sense that they are derivable from the axioms we are now going to pay closer attention. of system, through the defined rules of system, what still does not Kant defined analytic statement as a statement that does not as- imply that we are acquiring some knowledge through pure reason to the subject anything more than what the subject already con- or by examining some realm of non–empirical truths. Even in case ceptually contains. Quine does not find this way of defining analy- we consider Gödel’s incompleteness theorems, we can say that the ticity satisfying, because 1) it can be applied only to statements that expressions “true” and “false” have other meaning, if we use them have subject–predicate form and also because 2) the term containing purely in description of symbolic language (which we take as a con- is not precisely defined, so it is not clear, what it actually means. So struct), than if we use them in making statements about the world. to be able to study the issue of analyticity, he reformulated Kant’s We can say that a true statement is such, with the help of which, definition of analyticity as follows: “a statement is analytic when it is assuming it is true, we can never derive, with the help of other true true by virtue of meanings and independently of fact” (Quine, 2005, statement and system’s rules of inference, any statement, which p. 37). Now we see that this division is present in logical positivism would not be true. However, according to Quine, it is not possible to too, which we described above. We talked there about that the study distinguish between analytic and synthetic statements, therefore of meaning and potential determination of truth and falsehood of the boundary between science and metaphysics collapses. State- those statements, whose truth depends only on axioms and rules of ments cannot be in fact divided into meaningful and meaningless inference of given system, belongs to philosophy. in absolute sense, because the statements that would not make any Certain statements indeed seem to be true on the basis of mean- sense in one system of statements, could make sense in some other ings: logic and mathematics contain statements that are true re- system. We will see that according to Quine, it is possible to modify gardless to empirical facts. Or at least it seems as first glance, be- the system in order to maintain the truth of some statement (and cause when describing logical and mathematical systems, we use therefore also its meaningfulness) in various ways and thus it is

100 101 possible, in principle, to save the truth and meaningfulness of any denotations of expression or elements of their extensions. So it could seem that meaning is an expression. This, however, does not mean, that it will really happen entity butof completelyreformulate differen talkingt abouttype than meanings entities to creating talking theabout physical world. But Quine does with every statement, for in fact we dispose of various willingness not likelanguage the concept formations. that meanings should be some entities creating some kind of other, non- to give up statements. We can cling to some statements so much, physical realm of meanings. How to grasp meanings, grasping of which seems to be an that they seem analytic. inevitable condition for grasping the analyticity? QuineWe defineproposes the to term solve of meaning the whole only problem through of termsmeaning of synonymy at the level of language. Let us not 12.2 Analyticity and Meaning graspand meanings analyticity as asobjects, follows: but let reformulate us assume talkthating some about two meanings expres- to talking about language formations.sions have the same meaning only when they are synonymous; we Quine is in Two Dogmas of Empiricism concerned mainly with Wethen define define the term analyticity of meaning with onlythe helpthrough of the terms term of synonymy synonymy andand analyticity as follows: let the issue of meaning. He reminds Frege’s distinction between the us assumesome other that terms,some twowhich expressions should be haveclearly the defined same meaning as follows: only let when they are synonymous; meaning (sense in Frege’s terminology) and denotation (reference we analyticthen define statements analyticity be such with statements the help thatof the are term one ofsynonymy the two fol and- some other terms, which for Frege). This distinction can be applied not only to singular ex- shouldlowing be types:clearly defined as follows: let analytic statements be such statements that are one of pressions, but to predicates as well, because also in their case it can the two1) followinglogical truths types: (such as the sentence “No unmarried man is be distinguished between extension and . The extension married”, that are true due to their structure and due to the fact of expression is the set of objects for which is the given statement that1) we logical understand truths certain(such as expressions the sentence as logical "No unm constants,arried manwhich is married", that are true due true. For example, the expression “x is human” is true for all hu- haveto firmlytheir structure defined and properties due to the determining fact that wethe understand dependence certain of expressions as logical mans. Its extension is thus the set of all humans. Therefore, the theirconstants, truth–value which on truth–valueshave firmly ofdefined their components. properties determining the dependence of their extension of general expression is analogous to the denotation truth-value2) statements on wetruth-values can make of from their analytic components. statements of the of singular expression. The intension of general statement is its first time in such way, that we substitute some expression with meaning. It is obvious that two predicates can differ in meaning, its 2)synonym statements (such we as canin the make sentence from “Noanalytic bachelor statements is married”, of the in first time in such way, that yet they can have the same extension. whichwe wesubstitute substituted some the expression term “unmarried with its man” synonym with its (such synonym as in the sentence "No bachelor Meanings are thus different from objects of the world, for the “bachelor”).is married", in which we substituted the term "unmarried man" with its synonym objects of the world are either denotations of expression or ele- "bachelor").But if we want to clearly define the analyticity, we should clearly ments of their extensions. So it could seem that meaning is an en- define the term of synonymy, to which we are now trying to reduce tity of completely different type than entities creating the physical Butthe if termwe wantof meaning. to clearly In this define context, the Quineanalyt isicity, responding we should to the clearly define the term of world. But Quine does not like the concept that meanings should synonymy,views of toR. Carnap,which we who are was now his trying teacher. to reduceCarnap thactuallye term definedof meaning. In this context, Quine be some entities creating some kind of other, non–physical realm is respondinganalytic statements to the viewsas such of that R. are Carnap, true in wallho state–descriptions was his teacher.. Carnap actually defined of meanings. How to grasp meanings, grasping of which seems to analyticIn case statements of our world as W,su wech couldthat are then true show in all as examplesstate-descriptions of analytic. In case of our world W, we be an inevitable condition for grasping the analyticity? couldstatements then show these: as examples of analytic statements these:

((“x)(F(x)x)(F(x) Ú ØF(x)) F(x)) Quine proposes to solve the whole problem of meaning at (($x)(G(x)x)(G(x) ® G(x)) G(x)) the level of language. Let us not grasp meanings as objects, ((“x)((F(x)x)((F(x) Ù (F(x) (F(x) ® G(x)))  G(x)))® G(x))  G(x)) and so on.on.

These statements are true in every possible state-description, not only in M . However, let us 102 103 1 remark that our world W, because it is defined as a world with four individuals, three properties and two binary relations, it not the only describable in predicate logic. It is also true that all statements, which are always true in predicate logic, will be true also in any possible world that could be defined in the way as we define the world W, i.e. by stating all individuals and predicates and their arity. This definition of analyticity is good, however it does not suit all languages. In the case of synonymous expressions, there are predicates, which are not mutually independent. But if the own set of some atomic statements should correspond to every predicate, several atomic statements would not be mutually independent. This would lead to the following issue. Let us imagine we have predicates "x is an unmarried man" and "x is a bachelor". If we assume that these predicates are mutually independent, then there has to be a state-description, in which the statement "Peter is an unmarried man" is true and the statement "Peter is a bachelor", is false. Then the statements "unmarried man" and "bachelor" should not be synonyms, though. These statements are true in every possible state–description, should look like this: not only in M1. However, let us remark that our world W, because it is defined as a world with four individuals, three properties and Peter is an unmarried man U(a) two binary relations, it not the only possible world describable in Peter is a bachelor B(a) predicate logic. It is also true that all statements, which are always true in predicate logic, will be true also in any possible world that These sentences, however, look like atomic sentences. As long could be defined in the way as we define the world W, i.e. by stating as we are recording both predicates in the above mentioned way, all individuals and predicates and their arity. there is no dependency between the transcribed sentences in This definition of analyticity is good, however it does not suit all terms of predicate logic itself. Nevertheless, we consider these ex- languages. In the case of synonymous expressions, there are predi- pressions as synonymous (we can take this as the assumption of cates, which are not mutually independent. But if the own set of our consideration), therefore there should be some dependency some atomic statements should correspond to every predicate, sev- between them. eral atomic statements would not be mutually independent. This So the mentioned Carnap’s definition of analyticity is suitable would lead to the following issue. only for the language, in which are atomic sentences mutually inde- Let us imagine we have predicates “x is an unmarried man” and pendent and in which different sentences with identical meaning “x is a bachelor”. If we assume that these predicates are mutually are not transcribed as different atomic sentences. Yet in a language independent, then there has to be a state–description, in which the where synonymy exists, some atomic expressions would have to statement “Peter is an unmarried man” is true and the statement be either mutually dependent or the synonymous sentences would “Peter is a bachelor”, is false. Then the statements “unmarried man” have to be formally transcribed with only one expression, so that and “bachelor” should not be synonyms, though. only one atomic statement corresponds to synonymous sentences. But if we want to assume that these expressions are synonyms, But such language would not represent synonymy by itself. Nev- given predicates should not be independent. Then these sentences, ertheless, then we could not model and clearly grasp the term of however, should not be both atomic sentences, because in case of synonymy through it, so our main problem would not get solved. atomic sentences it is assumed that they are mutually independ- The problem is in fact the very analytic sentences of second type, ent. Yet both sentences, in case we would like to record them for- which are based on synonymy. To define analyticity of these sen- mally and mark individual expression in a different way, for exam- tences, it is therefore necessary to define the term synonymy. Lan- ple like this: guages that do not model synonymy, will not actually help us.

x is an unmarried man U(x) 12.3 Analyticity and Definition x is a bachelor B(x) Peter a Quine examines also another possibility, how to define analyticity: let us try to reduce analytic statements of second type to analytic statements of first type withdefinition ; let us try to understand synonym in such way, that it is created through definition. This

104 105 method is, according to Quine, unproblematic only if the definition A lexicographer only records, between which expressions of the is actually a full introduction of synonymy. If we simply introduce language exists synonymy, but he does not specify criteria, by a new term into the language or if we simple establish that certain which we could define it. So he does not even provide us with cri- expression will be synonymous with some other, everything is all teria to be subsequently able to define analyticity, which could right. This is happening also in artificial languages, where we can, emerge through this synonymy. for example, introduce certain expression as an abbreviation for another expression. However, synonymy in natural languages has other sources too, According to Quine, the reduction of the term synonymy it cannot be fully reconstructed as a definition in such sense, in with the term definition is not possible. The sameness of which is this term used in artificial languages. It is, for example, meaning cannot be explained in the way that the expres- possible to understand the definition asexplication as well. In this sions are synonymous due to being connected through defi- case too, the expressions are synonymous, but their synonymy is nition , i.e. due to fact that one of them is a definiendum and not purely a creation of who defines one of these expressions with the second a definiens in some definition. the second one. Synonymy, created as a result of explication, is al- ready based on certain previous synonymy, that existed in the lan- guage already before the explication and which was therefore not 12.4 Dogma of Analyticity and Syntheticity: Conclusion created by this explication. Let as take as an example the definition “Human is a social animal”. The definiendum “human” becomes, Quine therefore turns to another possible understanding of syn- thanks to this definition, the synonym of the expression “social onymy: synonymous are expressions that can be mutually inter- animal”, which is the definiens of this definiendum. However, we changed within certain statement without changing the truth con- did not introduce some completely new connection between this ditions of this statement. But not even this solution is satisfactory. definiendum and definiens, but we only refined the meaning of Eventually, he turns back to Carnap and comes to the conclusion definiendum, i.e. the meaning of the expression “human”. But this that the analyticity cannot be defined even with semantic rules, expression has even before had some partially unclear meaning, which we can use for the definition of analyticity in individual ar- which overlapped in part with the meaning it acquired through tificial languages (in which these semantic rules can be different), explication. So there was some synonymy already before explica- as Carnap did. On the basis of that none of the previous proposals tion. Therefore in this case, synonymy cannot be explained in full for distinguishing analytic from synthetic worked, Quine declares with explication. the conviction that such distinction exists, as metaphysical part of There is also a synonymy, existing in natural languages, but the faith of empiricists. which is not created neither through definition in the sense, in So if we do not want our philosophy to contain this dogma, we which this term is used in artificial languages, nor is it shaped should give up this distinction, although it looks reasonable at first through explication. An empirical researcher of given language glance. It seems, after all, that the truth of given statement does can notice this synonymy e.g. in a monolingual dictionary. Nev- not depend only on the way things are in the world, but also on the ertheless, this does not explain what this synonymy really is. meaning individual expressions, comprising a sentence, have; so it

106 107 seems that sentences have some factual and some language com- 12.5 Dogma of Reductionism ponent. Some statements will then, it seems, should have zero fac- tual component, such as statements of logic or mathematics. They The second dogma is the dogma of reductionism. It survives, ac- should be true purely on the basis of axioms of logic or mathematics cording to Quine, in the assumption that “each statement, taken in and on the basis of their rules of inference. These should be analytic isolation from its fellows, can admit of confirmation or infirmation statement — however, we failed to define them in a reasonable way. at all. My countersuggestion ... is that our statements about the ex- ternal world face the tribunal of sense experience not individually but only as a corporate body. (Quine, 2005, p. 61). As we have seen, Quine therefore claims, that no statement is in reality resist- the verification criterion of meaning, respected by logical positiv- ant to revision; no statement is necessarily true. On the other ists, considered the statement as the unit of meaningfulness — and hand, it is theoretically possible to maintain every statement it should be decided just about individual statements, whether as true, if we make changes somewhere else in our system of they are meaningful. But Quine claims that units of meaningful- statements. ness should not be statements but some bigger systems or sets consisting of statements. Now it shows, that both dogmas are very closely related, because if it is true, that we can save the truth and That is to say that Quine understands a certain system of state- also meaningfulness of each statement by chaining the truth or ments as a network, whose connections are created by logical rela- meaningfulness of other statements, then we cannot understand tions between statements. We can illuminate this network meta- a statement as an unit of meaning, as long as we perceive it by it- phor with the following example. We are studying some physical self. To maintain the truth or meaningfulness of this statement, phenomenon, but our measurements lead to sentences that are we would have to change the truth or meaningfulness of other inconsistent; there is no way to describe in theory we have at the possible statements (other sequences of symbols), whereas at least moment, what we are observing without producing a contradic- some of them must contain also those expression, which contained tion. Should we give up this theory or, e.g. the logical principle of the statement we want to save. This means we are changing its ? It seems to be easier to give up that theory, because meaning. But if it is possible to do this, it means, that some part it would be more difficult to create some other logic, in which we of experience or some meaning cannot correspond to some state- could retell our whole other knowledge and at the same time to ment (as a sequence of symbols in language), unless we take into describe this new studied phenomenon as well. But in principle, we account the whole system of statements, whose part is the given could give some logical principles up too and recreate other parts statement. But by it the epistemological programme that wanted of that network, which would contain statements we believe in. to show, how it is possible to assemble meaningful sentences from Then we could keep the original theory and sentences, in which we some basic expressions according to certain rules that would refer have expressed the results of our experiments; and these sentenc- to some meanings or experience, collapses. No certain expression es would not have to be inconsistent any more, if our new system or certain meaning can, in fact, correspond to any statement, per- of logic could not contain the contradiction of the type as in the ceived by itself. classic logic. In principle, this possibility seems to be present.

108 109 We could therefore say that not statements have factual and lan- rules or derivation rules of the language, with which we are sci- guage component, but only big sets of statements have factual and entifically describing these phenomena? Is should be allowed, in language component. The language component can be understood principle, if we do not want to artificially thwart the path to bet- as a language, consisting of vocabulary and grammar and derivation ter understanding of the reality. Of course, now we have primar- rules and eventually logical axioms. The factual component can be ily in mind the language created by science in order to understand understood as a certain set of statements, to which we are assign- the reality. But, after all, neither natural languages are resistant to ing the truth on the basis of experience, i.e. some empirical theory changes to their vocabulary or grammar rules (or derivation rules, expressed in given language. Statements by themselves, regardless to the extent in which such rules can be considered in connection of any theory, thus have no meaning. By theory we understand some with natural languages at all). pair, consisting of language and a set of statements, formulated in Quine therefore says that “total science is like a field of force this language — those we consider true, but not purely on the basis whose boundary conditions are experience. A conflict with experi- of eventual logical axioms or logical rules. Therefore, theory is not ence at the periphery occasions readjustments in the interior of only a set of statements, but a set of some sequence of symbols. This the field.” (Quine, 2005, p. 63). But what does the term “at the pe- set of statements would have no meaning without certain language. riphery” mean? Is it not again a reference to empirical statements But language itself, regardless of whether we consider some of its as opposed to analytic ones? Quine, however, explains this term in statements true, also does not tells about any reality. To be able to more detail as well: the statements at the periphery are those, for tell with the help of it something about the reality, we need to assign which it is likely, that we will adjust their truth–value, if we have truth to some of its statements. And this is the creation of theory. just certain experience. Let us notice that this is actually as if “natu- The unit of meaningfulness can therefore be only a theory, some- ralistic” understanding of syntheticity and analyticity. These prop- thing that is created on one hand on the basis of language, and as- erties are now not understood absolutely, but they express only signment of truth to some statements of this language on the other the willingness of us, humans, to adjust the truth of some of our hand. Therefore Quine says that “the unit of empirical significance is assertions on the basis of some of our experience. This so–called the whole of science.” (Quine, 2005, p. 62). If we imagine that all sci- “naturalized” analyticity is in fact only an empirically detectable entific truths are exactly those statements, to which we are assigning relation of us, humans, to certain statement: our tendency to not truth, and that at the same time we have a language that contains change its truth–value under any circumstances. And as “natural- a vocabulary and grammar and derivation rules and in which these ized” syntheticity we could understand, on the other hand, as such scientific rules are expressed, the science will in fact be a theory in empirically detectable relations of humans to certain statement: the above described way. Let us leave the problem, that assertions of the tendency to change the truth–value of this statement, if they the modern science are not unified in one theory, aside for now. have just the specific experience. But not even this distinction into language and factual compo- nent is absolute. Why, as a matter of fact, we could not change also the language itself, apart from the truth–value of some assertions, So it cannot be said that some statements are in principle if we want to build the understanding of some new phenomena in synthetic, in principle bound to experience. But then it the science? Why could we not change the vocabulary or grammar

110 111 certain theoretical constructs or their components, but introduction should be said that experience is not in principle bound to of anything as what we are going to insist on (as if it was analytic), is these statements. That means that it does not fully define its a thing of pragmatic decision depending on which conceptual tools truth–value. Nonetheless, because the truth–value of state- are suitable for reaching the goals, we have set in the science. ments creating our science is related to these only “natural- This all strikes also the epistemology, which should become natu- ized” empirical statement, it too is finally undefinedby expe- ralized, according to Quine. As we have seen, the way how we create rience. our description of the world, our science, is in fact dependent, apart from our experience, also on our willingness to give up rather the for- mer, than the latter assertions. So if we want to find out how our cog- Another consequence of these considerations is that there are no nition works, we have to study empirical things, such as, for example, fundamentally necessarily true sentences, there is no area in which this willingness (or lack thereof). We need to study in general, how we metaphysics as acquisition of a priori valid knowledge could ex- are building our description of the world in reality. It is not possible to ists. On the other hand, metaphysics as the activity of acquisition study the process of our cognition without using empirical research. of thematically defined knowledge(such as acquisition of knowl- We need to study real human beings and real cognitive processes, edge about God, freedom and immortality; Kant called the solving which are running in them. Otherwise we will not recognize the cog- of these issues as its final purpose) cannot be separated from sci- nition. Because there are no fundamentally analytical judgements, ence, because its area of study cannot be separated from the area, there are also not a priori truths per se. Therefore we cannot rely on which is studied by sciences. So our scientific study invaded this some a priori knowledge, not even in epistemology, but we have to use area and we can decide about the existence of metaphysical and the best empirical knowledge we have. And because the best empiri- mythical entities. However, not with the help of finding truth of cal understanding is the understanding of sciences, this understand- individual statements about them, taken individually, but with the ing should be used. So, for example, in understanding of our science help of assessment of whole theories, in which these entities are and how it works, we have to use the knowledge of exactly the same postulated. We can ask: does that system help us, postulating such science, because 1) we do not have better empirical knowledge and 2) and such entities, in predicating our experience and in coping with there is no non–empirical knowledge in absolute sense, because there the stream of these sensual experiences, in handling them? Yet to- is no fundamental boundary between analytic and synthetic. gether with given theory, also the entities postulated by it collapse (like gods of Olympus, Centaur, ether, phlogiston, etc.) or they ac- quire gravity, even though we could not see them directly (such as Therefore Quine in his next influential articleEpistemol - quarks, neutrinos, etc.). ogy naturalized (Quine, 2004) proposes such scientific pro- gramme for epistemology that will make it part of scientific 12.6 Pragmatism and Naturalisation of Epistemology research of cognition, mainly part of psychology, but also linguistics; it can be said, in general, that it will make it part According to Quine, as a result of abandoning these empiricist dog- of cognitive science. mas, we come to pragmatism as well. Not only the introduction of

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AUSTIN, J. L.: Ako niečo robiť slovami. Bratislava : Kalligram, 2004. BEDNÁRIKOVÁ, M.: Úvod do kognitívnej lingvistiky. Trnava : Filozofická fakulta TU, 2013. BONDY, E.: Indická filosofie. Praha : Vokno, 1997. CARNAP, R.: Význam a nevyhnutnosť. Bratislava : Kalligram, 2005. FIALA, J. (ed.): Analytická filosofie. První čítanka. I Plzeň : Fakulta humanitních studií, Západočeská univerzita, 1999. GAHÉR, F.: Logika pre každého. 3. doplnené vydanie. Bratislava : Iris, 2003. HALE, B. — WRIGHT, C. (eds.): A Companion to the Philosophy of Language. Oxford : Blackwell Publishers, 1997. CHENG, A.: Dějiny čínského myšlení. Praha : DharmaGaia, 2006. KOLMAN, V.: Logika Gottloba Frega. Praha : Filosofia, 2002. MARVAN, T.: Otázka významu. Cesty analytické filosofie jazyka. Praha : Togga, 2010. MARVAN, T. — HVORECKÝ, J. (eds.): Základní pojmy filosofie jazyka a mysli. Nym- burk : OPS, 2007. MILLER, A.: Philosophy of Language. London : Routledge, 2007. MORRIS, M.: An Introduction to the Philosophy of Language. New York : Cambridge University Press, 2007. PEREGRIN, J.: Kapitoly z analytické filosofie. Praha : Filosofia, 2005. PRIEST, G.: Logika. Praha : Dokořán, 2007. QUINE, W. V. O.: Epistemology naturalized. In: QUINE, W. V. O.: Quintessence. Basic Readings from the Philosophy of W. V. Quine. London : The Belknap Press of Harvard University Press, 2004, pp. 259 — 274. QUINE, W. V. O.: Dve dogmy empiricizmu. In: QUINE, W. V. O.: Z logického hľadiska. Bratislava : Kalligram, 2005, pp. 36 — 67. RUSSELL, B.: The Principles of Mathematics. Cambridge : Cambridge University Press, 1903. RUSSELL, B.: On denoting. In: Mind. ISSN 0026–4423, Vol. 14, 1905, No. 56, pp. 479 — 493.

114 115 RUSSELL, B.: as based on theory of types. In: American Journal of Mathematics. ISSN 0002–9327, 1908, Vol. 30, No. 3, pp. 222 — 262. RUSSELL, B. — WHITEHEAD, A. N.: Principia Mathematica I, II, III. Cambridge : Cambridge University Press, 1910; 1912; 1913. SEARLE, J. R.: Myseľ, jazyk, spoločnosť. Bratislava : Kalligram, 2007. SVOBODA, V. — PEREGRIN, J.: Od jazyka k logice. Filozofický úvod do moderní logiky. Praha : Academia, 2009. THAGARD, P.: Úvod do kognitivní vědy. Mysl a myšlení. Praha : Portál, 2001, pp. 76 — 94. WOLF, M. P.: Philosophy of Language. In: Internet Encyclopedia of Philosophy. [on- line]. 2009. [cit. 12. 7. 2012]. Available on the internet: . ISSN 2161–0002.

116 RNDr. Mgr. Reginald Adrián Slavkovský, Ph.D. Mgr. Ing. Michal Kutáš, Ph.D.

Introduction to Philosophy of Language

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Publisher Faculty of Philosophy and Arts ∙ Trnava University in Trnava Hornopotočná 23 ∙ 918 43 Trnava [email protected] ∙ Http://fff.truni.sk in cooperation with

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© Reginald Adrián Slavkovský ∙ Michal Kutáš ∙ 2013 © Towarzystwo Słowaków w Polsce ∙ Kraków ∙ 2013 © Filozofická fakulta Trnavskej univerzity v Trnave ∙ 2013 ISBN 978-83-7490-614-2