DOCSLIB.ORG

Philosophical Journey: Bridging the Gap ______

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Philosophical Journey: Bridging the Gap ______ Journal of World Philosophies Intellectual Journeys/161 Philosophical Journey: Bridging the Gap _________________________________________ J. L. SHAW Victoria University of Wellington, New Zealand ([email protected]) Throughout my philosophical journey, I have tried to bridge the gap between contemporary western philosophy and the analytical traditions of the Indian philosophical systems, especially Navya-Nyāya. Hence my aim has been to promote a dialogue between these two traditions where each can derive insights from the other. I have focused on new or better solutions to some contemporary problems of epistemology, philosophy of language, philosophy of mind, as well as global issues, and think Indian philosophy can be integrated with current western philosophy, adding a new dimension to global culture and understanding. Key words: Indian philosophy; Navya-Nyāya; Buddhism; Sāṃkhya; sources of knowledge; philosophy of language My philosophical development goes back to my childhood in Kolkata, where I had teachers such as Mr. Shyamapada Sen, who were well-versed in Indian literature and scriptures, including the Bhagavad-Gītā. I read Indian scriptures and engaged with philosophers and writers such as Swami Vivekananda, Rabindranath Tagore, and Sri Aurobindo. Through them, I had questions such as, “What is the nature of ultimate reality? What is the meaning of life? What are the goals of life? Is there any afterlife or God? What is the nature of Brahman?” Both at postgraduate and undergraduate levels, I used to discuss philosophical problems—such as the momentariness of Buddhism, the nature of Brahman, causation, perception, theories of truth and error, Kant’s conception of self or categories—with teachers such as Gopinath Bhattacharya, Pravas Jiban Choudhury, Naresh Chandra Chakraborty, Pranab Kumar Sen, Bimal Krishna Matilal, and Jitendra Nath Mohanty. They encouraged me to develop my thoughts to incorporate the views of western philosophers, such as Kant, Hegel, and Bradley, and the Indian philosophers such as Saṃkara and the followers of the Nyāya. I was also interested in the meanings of metaphysical utterances, such as “God exists” or “God does not exist.” In this context I would like to mention that my father passed away when I was a high school student in Kolkata. During this time, it was a struggle for both my family and myself. We were passing through abject poverty, sometimes without food or electricity, but my spirit was guided by the beacon light of masters like Vivekananda and the hope of words from the poet P.S. Shelly, “If the winter comes, can spring be far behind?” For the basic necessities of life, I used to teach children. While I was teaching at Jadavpur University (Kolkata) in 1962, I attended the classes of Professor Sibajiban Bhattacharya on symbolic logic at the Indian Academy of Philosophy and studied with him the views of analytic philosophers and semanticists such as Alfred Tarski. I was asked to write a paper on Bertrand Russell’s theory of definite descriptions for Journal of the Philosophical Association in 1964. A critique of a paper published in the same journal, it set the stage for my dissertation topic “Some Logical Problems Concerning Existence,” which included not only a long section on definite descriptions, but also sections on the nature of existence, subject and predicate, and whether existence is a predicate. All the problems discussed in my dissertation, directly and indirectly, related to the questions of existence. Hence some of my earlier questions were discussed from the perspective of western analytical tradition. I am _______________ Journal of World Philosophies 4 (Summer 2019): 161-172 Copyright © 2019 Jay Shaw. e-ISSN: 2474-1795 • http://scholarworks.iu.edu/iupjournals/index.php/jwp • doi: 10.2979/jourworlphil.4.1.09 Journal of World Philosophies Intellectual Journeys/162 grateful to my late supervisor Professor Carlo Giannoni for his continual support and encouragement. My dissertation created a forum for the development of my thoughts on comparative and Indian philosophy, which were not familiar to western academics at that time, although there was a continuity in my thought with the metaphysical questions that originated from within the framework of Anglo-American philosophy. My dissertation focused on logic or systems of logic, philosophy of language, epistemology, as well as ontology. Moreover, it tried to resolve some of the conflicting views through a range of levels or uses of terms or propositions in different contexts. Hence, from the dawn of my philosophical journey the aim was not to side with a particular view, but to look for the solutions to conflicting views, and thereby restore different perspectives in diverse traditions of philosophy. Hence, I introduced several definitions of existence, uses of terms or propositions, and levels or types of subject and predicate in my discussion. I completed my PhD at Rice University, Houston, in two years with a lot of hard work and dedication. I was then asked to take a job teaching in the United States, as my scholarship was for three years at Rice University, in addition to the Fulbright travel grant. I am very grateful to my French Professor Hodges, who taught me French every day for about an hour and a half, so that I could take the exam in two months. My background in German also helped me in passing the German exam, another requirement for the PhD in philosophy. My teaching at both undergraduate and postgraduate levels at Jadavpur University aided me in the courses I had, as well as the comprehensive exam required for the PhD program. When I applied for a job, I received three offers and accepted the one from the University of Alabama, although it was for only one year. I taught several courses, including logic, philosophical logic, and contemporary philosophy. I was requested to offer a course on Indian philosophy in 1970 after my dissertation at Rice University, in order to remove the misconception that Indian philosophy is not distinct from religion. During my teaching period in India, the USA, and New Zealand—at Victoria University of Wellington, where I taught for more than 42 years—I focused on the consequences of a view on our life, society, or the world at large. I also focused on contemporary problems, such as pragmatism and its application to morality. At the University of Alabama, students approached the president of the university for the continuation of my teaching. The then chairperson Irdell Jenkins offered me a tenure-track position, which I could not accept as I had a Fulbright grant. He was kind enough to approach a senator and a congressman to see if the restrictions on Fulbright scholarships could be waived. Since my work was not related to physics or US defence, he found that the restrictions could not be waived. Hence, I was advised to look for a job in Canada so that I could take up a position at Alabama after two years. In the meantime, I got a permanent position from Victoria University of Wellington in New Zealand, which I was advised to accept. I joined Victoria University in the September of 1970. In December 1971, I visited India and got married to Shipra Bhattacharya, a nursing tutor, whose family migrated from East Pakistan (currently called “Bangladesh”) and was known to my teachers Shyamapada Sen and Professor Pranab Kumar Sen. Our daughter Natalie, who is now a lawyer, was born in 1975. Here at Victoria University of Wellington Professor Max Creswell and the then chairperson, Professor George Hughes, encouraged me to publish in the area of comparative philosophy and logic. I presented several papers both in the seminar of the philosophy department and the logic group, in addition to conferences in New Zealand and overseas. My peer-reviewed or editor-reviewed papers, “Empty Terms: the Nyāya and the Buddhist,” “Subject and Predicate,” “The Nyāya on Existence,” “Knowability and Nameability,” “Negation and the Buddhist Theory of Meaning,” were published in the Journal of Indian Philosophy.1 I also presented _______________ Journal of World Philosophies 4 (Summer 2019): 161-172 Copyright © 2019 Jay Shaw. e-ISSN: 2474-1795 • http://scholarworks.iu.edu/iupjournals/index.php/jwp • doi: 10.2979/jourworlphil.4.1.09 Journal of World Philosophies Intellectual Journeys/163 papers at logic conferences. My paper “Number: From Frege-Russell to Nyāya”2 was published in Studia Logica, Poland, and several abstracts in the Journal of Symbolic Logic.3 Through a range of activities, I tried to remove misunderstandings about Indian philosophy and logic. Towards the end of the seventies, I invited Professor S. Bhattacharya and Professor B. K. Matilal to give a few lectures in my course on contemporary philosophy at Victoria University, as our department had a visiting position. My journey took a concrete shape as I pointed out that it is not enough to translate the texts of Indian philosophers with commentaries into English, or to compare an Indian philosopher, such as Saṃkara, with Hegel or Bradley. We have to demonstrate the relevance of Indian philosophy to certain problems or questions, especially the contemporary discussion on epistemology and philosophy of language, so that it could be integrated with contemporary western analytical philosophy. With this end in view, Professor Matilal and I submitted the proposal for the volume Analytical Philosophy in Comparative Perspective.4 My paper “Some Reflections on Kripke,” published in Logique et Analyse,5 set the scene for contemporary discussion on the problems of philosophy of language, including proper names, definite descriptions, and dichotomies such as necessary-contingent. In this paper, I focussed on Kripke’s criticism of philosophers such as Frege, Russell, Wittgenstein, Searle, and Strawson, as well as on other scholars’ views of Kripke. As time went on, my mind was occupied with contemporary problems, which were later discussed using the perspective of Indian systems, especially the Nyāya, for better solutions.
Load more

Recommended publications
  • Poznań Studies in the Philosophy of the Sciences and the Humanities), 21Pp
    Forthcoming in: Uncovering Facts and Values, ed. A. Kuzniar and J. Odrowąż-Sypniewska (Poznań Studies in the Philosophy of the Sciences and the Humanities), 21pp. Abstract Alfred Tarski seems to endorse a partial conception of truth, the T-schema, which he believes might be clarified by the application of empirical methods, specifically citing the experimental results of Arne Næss (1938a). The aim of this paper is to argue that Næss’ empirical work confirmed Tarski’s semantic conception of truth, among others. In the first part, I lay out the case for believing that Tarski’s T-schema, while not the formal and generalizable Convention-T, provides a partial account of truth that may be buttressed by an examination of the ordinary person’s views of truth. Then, I address a concern raised by Tarski’s contemporaries who saw Næss’ results as refuting Tarski’s semantic conception. Following that, I summarize Næss’ results. Finally, I will contend with a few objections that suggest a strict interpretation of Næss’ results might recommend an overturning of Tarski’s theory. Keywords: truth, Alfred Tarski, Arne Næss, Vienna Circle, experimental philosophy Joseph Ulatowski ORDINARY TRUTH IN TARSKI AND NÆSS 1. Introduction Many of Alfred Tarski's better known papers on truth (e.g. 1944; 1983b), logical consequence (1983c), semantic concepts in general (1983a), or definability (1948) identify two conditions that successful definitions of “truth,” “logical consequence,” or “definition” require: formal correctness and material (or intuitive) adequacy.1 The first condition Tarski calls “formal correctness” because a definition of truth (for a given formal language) is formally correct when it is constructed in a manner that allows us to avoid both circular definition and semantic paradoxes.
    [Show full text]
  • An Understanding of Maya: the Philosophies of Sankara, Ramanuja and Madhva
    An understanding of Maya: The philosophies of Sankara, Ramanuja and Madhva Department of Religion studies Theology University of Pretoria By: John Whitehead 12083802 Supervisor: Dr M Sukdaven 2019 Declaration Declaration of Plagiarism 1. I understand what plagiarism means and I am aware of the university’s policy in this regard. 2. I declare that this Dissertation is my own work. 3. I did not make use of another student’s previous work and I submit this as my own words. 4. I did not allow anyone to copy this work with the intention of presenting it as their own work. I, John Derrick Whitehead hereby declare that the following Dissertation is my own work and that I duly recognized and listed all sources for this study. Date: 3 December 2019 Student number: u12083802 __________________________ 2 Foreword I started my MTh and was unsure of a topic to cover. I knew that Hinduism was the religion I was interested in. Dr. Sukdaven suggested that I embark on the study of the concept of Maya. Although this concept provided a challenge for me and my faith, I wish to thank Dr. Sukdaven for giving me the opportunity to cover such a deep philosophical concept in Hinduism. This concept Maya is deeper than one expects and has broaden and enlightened my mind. Even though this was a difficult theme to cover it did however, give me a clearer understanding of how the world is seen in Hinduism. 3 List of Abbreviations AD Anno Domini BC Before Christ BCE Before Common Era BS Brahmasutra Upanishad BSB Brahmasutra Upanishad with commentary of Sankara BU Brhadaranyaka Upanishad with commentary of Sankara CE Common Era EW Emperical World GB Gitabhasya of Shankara GK Gaudapada Karikas Rg Rig Veda SBH Sribhasya of Ramanuja Svet.
    [Show full text]
  • 9. Brahman, Separate from the Jagat
    Chapter 9: Brahman, Separate from the Jagat ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Question 1: Why does a human being see only towards the external vishayas? ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Answer: Katha Upanishad states in 2.1.1 that Paramatma has carved out the indriyas only outwards and ​ ​ therefore human beings see only towards external vishayas. ​परािच खान यतणृ वयभूतमापरा पयत नातरामन .् Question 2: What is the meaning of Visheshana? What are the two types of Visheshanas of Brahman? ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Answer: That guna of an object which separates it from other objects of same jati (=category) is known as ​ ​ Visheshana. For example, the ‘blue color’ is guna of blue lotus. This blue color separates this blue lotus from all other lotuses (lotus is a jati). Therefore, blue color is a Visheshana. The hanging hide of a cow separates it from all four-legged animals. Thus, this hanging hide is a Visheshana of cow among the jati of four-legged animals. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ The two types of Visheshanas of Brahman which are mentioned in Shruti are as follows:- ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ● Bhava-roopa Visheshana (Those Visheshanas which have existence) ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ● Abhava-roopa Visheshana (Those Visheshanas which do not exist) ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Question 3: Describe the bhava-roopa Visheshanas of Brahman? ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Answer: Visheshana refers to that guna of object which separates it from all other objects of same jati. Now jati ​ ​ of human beings is same as that of Brahman. Here, by Brahman, Ishvara is meant who is the nimitta karan of jagat. Both human being as well as Brahman (=Ishvara) has jnana and hence both are of same jati. However, there is great difference between both of them and thus Brahman (=Ishvara) is separated due to the following bhava-roopa Visheshanas:- ​ ​ ● Human beings have limited power, but Brahman is omnipotent.
    [Show full text]
  • Alfred Tarski His:Bio:Tar: Sec Alfred Tarski Was Born on January 14, 1901 in Warsaw, Poland (Then Part of the Russian Empire)
    bio.1 Alfred Tarski his:bio:tar: sec Alfred Tarski was born on January 14, 1901 in Warsaw, Poland (then part of the Russian Empire). Described as \Napoleonic," Tarski was boisterous, talkative, and intense. His energy was often reflected in his lectures|he once set fire to a wastebasket while disposing of a cigarette during a lecture, and was forbidden from lecturing in that building again. Tarski had a thirst for knowledge from a young age. Although later in life he would tell students that he stud- ied logic because it was the only class in which he got a B, his high school records show that he got A's across the board| even in logic. He studied at the Univer- sity of Warsaw from 1918 to 1924. Tarski Figure 1: Alfred Tarski first intended to study biology, but be- came interested in mathematics, philosophy, and logic, as the university was the center of the Warsaw School of Logic and Philosophy. Tarski earned his doctorate in 1924 under the supervision of Stanislaw Le´sniewski. Before emigrating to the United States in 1939, Tarski completed some of his most important work while working as a secondary school teacher in Warsaw. His work on logical consequence and logical truth were written during this time. In 1939, Tarski was visiting the United States for a lecture tour. During his visit, Germany invaded Poland, and because of his Jewish heritage, Tarski could not return. His wife and children remained in Poland until the end of the war, but were then able to emigrate to the United States as well.
    [Show full text]
  • Alfred Tarski and a Watershed Meeting in Logic: Cornell, 1957 Solomon Feferman1
    Alfred Tarski and a watershed meeting in logic: Cornell, 1957 Solomon Feferman1 For Jan Wolenski, on the occasion of his 60th birthday2 In the summer of 1957 at Cornell University the first of a cavalcade of large-scale meetings partially or completely devoted to logic took place--the five-week long Summer Institute for Symbolic Logic. That meeting turned out to be a watershed event in the development of logic: it was unique in bringing together for such an extended period researchers at every level in all parts of the subject, and the synergetic connections established there would thenceforth change the face of mathematical logic both qualitatively and quantitatively. Prior to the Cornell meeting there had been nothing remotely like it for logicians. Previously, with the growing importance in the twentieth century of their subject both in mathematics and philosophy, it had been natural for many of the broadly representative meetings of mathematicians and of philosophers to include lectures by logicians or even have special sections devoted to logic. Only with the establishment of the Association for Symbolic Logic in 1936 did logicians begin to meet regularly by themselves, but until the 1950s these occasions were usually relatively short in duration, never more than a day or two. Alfred Tarski was one of the principal organizers of the Cornell institute and of some of the major meetings to follow on its heels. Before the outbreak of World War II, outside of Poland Tarski had primarily been involved in several Unity of Science Congresses, including the first, in Paris in 1935, and the fifth, at Harvard in September, 1939.
    [Show full text]
  • Alfred Tarski, Friend and Daemon Benjamin Wells
    Alfred Tarski, Friend and Daemon Benjamin Wells Engaging Tarski When I had passed doctoral exams in 1963 and Alfred Tarski’s name stayed with me after I read sounded Bob Vaught and John Addison on their about the Banach-Tarski paradox in [3] during availability for supervising my research, both said high school. I then discovered logic (and Tarski’s that the department recognized me as Tarski’s definition of truth) in the last year of college but student. News to me, despite the second opinion. still considered myself to be a topologist, not from So I called him to learn more about my fate. He love but from intimate contact in four courses as acknowledged the claim, “Good,” and invited me an undergraduate. So before arriving at UC Berke- for the first serious nighttime talk. ley in fall 1962 for graduate work, I thought only Source of the Title vaguely about taking a course with him. But my inclinations were shifting: dutifully registering Throughout cooperation and separation, Alfred for fall classes in topological groups and algebraic and I were friends, cordial and personable, but geometry, I added metamathematics and Tarski’s not really personal. He also established another general algebraic systems. The next fall, Tarski of- role, that of daemon in the sense of [4]: a leonine fered set theory. These two courses were my only externalized conscience, at least. The scope of Tarski lectures, but there were numerous seminars. this conscience was foremost mathematical, with a hope for political, a goal of cultural, a reserva- Visitors to Berkeley constantly identified Tarski tion on philosophical and moral, and a hint of with whatever topic occupied him so fruitfully and spiritual.
    [Show full text]
  • Issues in Indian Philosophy and Its History
    4 ISSUESININDIAN PHILOSOPHY AND ITS HISTORY 4.1 DOXOGRAPHY AND CATEGORIZATION Gerdi Gerschheimer Les Six doctrines de spéculation (ṣaṭtarkī) Sur la catégorisation variable des systèmes philosophiques dans lInde classique* ayam eva tarkasyālaņkāro yad apratişţhitatvaņ nāma (Śaģkaraad Brahmasūtra II.1.11, cité par W. Halbfass, India and Europe, p. 280) Les sixaines de darśana During the last centuries, the six-fold group of Vaiśeşika, Nyāya, Sāņkhya, Yoga, Mīmāņ- sā, and Vedānta ( ) hasgained increasing recognition in presentations of Indian philosophy, and this scheme of the systems is generally accepted today.1 Cest en effet cette liste de sys- tèmes philosophiques (darśana) quévoque le plus souvent, pour lindianiste, le terme şađ- darśana. Il est cependant bien connu, également, que le regroupement sous cette étiquette de ces six systèmes brahmaniques orthodoxes est relativement récent, sans doute postérieur au XIIe siècle;2 un survol de la littérature doxographique sanskrite fait apparaître quil nest du reste pas le plus fréquent parmi les configurations censées comprendre lensemble des sys- tèmes.3 La plupart des doxographies incluent en effet des descriptions des trois grands sys- tèmes non brahmaniques, cest-à-dire le matérialisme,4 le bouddhisme et le jaïnisme. Le Yoga en tant que tel et le Vedānta,par contre, sont souvent absents de la liste des systèmes, en particulier avant les XIIIe-XIVe siècles. Il nen reste pas moins que les darśana sont souvent considérés comme étant au nombre de six, quelle quen soit la liste. La prégnance de cette association, qui apparaît dès la première doxographie, le fameux Şađdarśanasamuccaya (Compendium des six systèmes) du jaina Haribhadra (VIIIe s.
    [Show full text]
  • Brahman, Atman and Maya
    Sanatana Dharma The Eternal Way of Life (Hinduism) Brahman, Atman and Maya The Hindu Way of Comprehending Reality and Life Brahman, Atman and Maya u These three terms are essential in understanding the Hindu view of reality. v Brahman—that which gives rise to maya v Atman—what each maya truly is v Maya—appearances of Brahman (all the phenomena in the cosmos) Early Vedic Deities u The Aryan people worship many deities through sacrificial rituals: v Agni—the god of fire v Indra—the god of thunder, a warrior god v Varuna—the god of cosmic order (rita) v Surya—the sun god v Ushas—the goddess of dawn v Rudra—the storm god v Yama—the first mortal to die and become the ruler of the afterworld The Meaning of Sacrificial Rituals u Why worship deities? u During the period of Upanishads, Hindus began to search for the deeper meaning of sacrificial rituals. u Hindus came to realize that presenting offerings to deities and asking favors in return are self-serving. u The focus gradually shifted to the offerings (the sacrificed). u The sacrificed symbolizes forgoing one’s well-being for the sake of the well- being of others. This understanding became the foundation of Hindu spirituality. In the old rites, the patron had passed the burden of death on to others. By accepting his invitation to the sacrificial banquet, the guests had to take responsibility for the death of the animal victim. In the new rite, the sacrificer made himself accountable for the death of the beast.
    [Show full text]
  • The Development of Mathematical Logic from Russell to Tarski: 1900–1935
    The Development of Mathematical Logic from Russell to Tarski: 1900–1935 Paolo Mancosu Richard Zach Calixto Badesa The Development of Mathematical Logic from Russell to Tarski: 1900–1935 Paolo Mancosu (University of California, Berkeley) Richard Zach (University of Calgary) Calixto Badesa (Universitat de Barcelona) Final Draft—May 2004 To appear in: Leila Haaparanta, ed., The Development of Modern Logic. New York and Oxford: Oxford University Press, 2004 Contents Contents i Introduction 1 1 Itinerary I: Metatheoretical Properties of Axiomatic Systems 3 1.1 Introduction . 3 1.2 Peano’s school on the logical structure of theories . 4 1.3 Hilbert on axiomatization . 8 1.4 Completeness and categoricity in the work of Veblen and Huntington . 10 1.5 Truth in a structure . 12 2 Itinerary II: Bertrand Russell’s Mathematical Logic 15 2.1 From the Paris congress to the Principles of Mathematics 1900–1903 . 15 2.2 Russell and Poincar´e on predicativity . 19 2.3 On Denoting . 21 2.4 Russell’s ramified type theory . 22 2.5 The logic of Principia ......................... 25 2.6 Further developments . 26 3 Itinerary III: Zermelo’s Axiomatization of Set Theory and Re- lated Foundational Issues 29 3.1 The debate on the axiom of choice . 29 3.2 Zermelo’s axiomatization of set theory . 32 3.3 The discussion on the notion of “definit” . 35 3.4 Metatheoretical studies of Zermelo’s axiomatization . 38 4 Itinerary IV: The Theory of Relatives and Lowenheim’s¨ Theorem 41 4.1 Theory of relatives and model theory . 41 4.2 The logic of relatives .
    [Show full text]
  • Lecture 1: Tarski on Truth Philosophy of Logic and Language — HT 2016-17
    Lecture 1: Tarski on Truth Philosophy of Logic and Language — HT 2016-17 Jonny McIntosh [email protected] Alfred Tarski (1901-1983) was a Polish (and later, American) mathematician, logician, and philosopher.1 In the 1930s, he published two classic papers: ‘The Concept of Truth in Formalized Languages’ (1933) and ‘On the Concept of Logical Consequence’ (1936). He gives a definition of truth for formal languages of logic and mathematics in the first paper, and the essentials of the model-theoretic definition of logical consequence in the second. Over the course of the next few lectures, we’ll look at each of these in turn. 1 Background The notion of truth seems to lie at the centre of a range of other notions that are central to theorising about the formal languages of logic and mathematics: e.g. validity, con- sistency, and completeness. But the notion of truth seems to give rise to contradiction: Let sentence (1) = ‘sentence (1) is not true’. Then: 1. ‘sentence (1) is not true’ is true IFF sentence (1) is not true 2. sentence (1) = ‘sentence (1) is not true’ 3. So, sentence (1) is true IFF sentence (1) is not true 4. So, sentence (1) is true and sentence (1) is not true Tarski is worried that, unless the paradox can be resolved, metatheoretical results in- voking the notion of truth or other notions that depend on it will be remain suspect. But how can it be resolved? The second premise is undeniable, and the first premise is an instance of a schema that seems central to the concept of truth, namely the following: ‘S’ is true IFF S, 1The eventful story of Tarski’s life is told by Anita and Solomon Feferman in their wonderful biography, Alfred Tarski: Life and Logic (CUP, 2004).
    [Show full text]
  • Carnap's Contribution to Tarski's Truth
    JOURNAL FOR THE HISTORY OF ANALYTICAL PHILOSOPHY CARNAP’S CONTRIBUTION TO TARSKI’S TRUTH VOLUME 3, NUMBER 10 MONIKA GrUBER EDITOR IN CHIEF KEVIN C. KLEMENt, UnIVERSITY OF MASSACHUSETTS In his seminal work “The Concept of Truth in Formalized Lan- guages” (1933), Alfred Tarski showed how to construct a for- EDITORIAL BOARD mally correct and materially adequate definition of true sentence GaRY EBBS, INDIANA UnIVERSITY BLOOMINGTON for certain formalized languages. These results have, eventu- GrEG FROSt-ARNOLD, HOBART AND WILLIAM SMITH COLLEGES ally, been accepted and applauded by philosophers and logi- HENRY JACKMAN, YORK UnIVERSITY cians nearly in unison. Its Postscript, written two years later, SANDRA LaPOINte, MCMASTER UnIVERSITY however, has given rise to a considerable amount of contro- LyDIA PATTON, VIRGINIA TECH versy. There is an ongoing debate on what Tarski really said MARCUS ROSSBERG, UnIVERSITY OF CONNECTICUT in the postscript. These discussions often regard Tarski as pu- MARK TEXTOR, KING’S COLLEGE LonDON tatively changing his logical framework from type theory to set AUDREY YAP, UnIVERSITY OF VICTORIA theory. RICHARD ZACH, UnIVERSITY OF CALGARY In what follows, we will compare the original results with those REVIEW EDITORS presented two years later. After a brief outline of Carnap’s pro- JULIET FLOYD, BOSTON UnIVERSITY gram in The Logical Syntax of Language we will determine its sig- CHRIS PINCOCK, OHIO STATE UnIVERSITY nificance for Tarski’s final results. ASSISTANT REVIEW EDITOR SEAN MORRIS, METROPOLITAN STATE UnIVERSITY OF DenVER DESIGN DaNIEL HARRIS, HUNTER COLLEGE C 2015 MONIKA GrUBER CARNAP’S CONTRIBUTION TO TARSKI’S TRUTH couple of years ago. In particular, in addition to the previously studied languages, he decides to investigate the languages the MONIKA GrUBER structure of which cannot be brought into harmony with the principles of the theory of semantical categories.
    [Show full text]
  • The History of Logic
    c Peter King & Stewart Shapiro, The Oxford Companion to Philosophy (OUP 1995), 496–500. THE HISTORY OF LOGIC Aristotle was the first thinker to devise a logical system. He drew upon the emphasis on universal definition found in Socrates, the use of reductio ad absurdum in Zeno of Elea, claims about propositional structure and nega- tion in Parmenides and Plato, and the body of argumentative techniques found in legal reasoning and geometrical proof. Yet the theory presented in Aristotle’s five treatises known as the Organon—the Categories, the De interpretatione, the Prior Analytics, the Posterior Analytics, and the Sophistical Refutations—goes far beyond any of these. Aristotle holds that a proposition is a complex involving two terms, a subject and a predicate, each of which is represented grammatically with a noun. The logical form of a proposition is determined by its quantity (uni- versal or particular) and by its quality (affirmative or negative). Aristotle investigates the relation between two propositions containing the same terms in his theories of opposition and conversion. The former describes relations of contradictoriness and contrariety, the latter equipollences and entailments. The analysis of logical form, opposition, and conversion are combined in syllogistic, Aristotle’s greatest invention in logic. A syllogism consists of three propositions. The first two, the premisses, share exactly one term, and they logically entail the third proposition, the conclusion, which contains the two non-shared terms of the premisses. The term common to the two premisses may occur as subject in one and predicate in the other (called the ‘first figure’), predicate in both (‘second figure’), or subject in both (‘third figure’).
    [Show full text]