Stoic Logic and Multiple Generality
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Augustine on Knowledge
Augustine on Knowledge Divine Illumination as an Argument Against Scepticism ANITA VAN DER BOS RMA: RELIGION & CULTURE Rijksuniversiteit Groningen Research Master Thesis s2217473, April 2017 FIRST SUPERVISOR: dr. M. Van Dijk SECOND SUPERVISOR: dr. dr. F.L. Roig Lanzillotta 1 2 Content Augustine on Knowledge ........................................................................................................................ 1 Acknowledgements ................................................................................................................................ 4 Preface .................................................................................................................................................... 5 Abstract ................................................................................................................................................... 6 Introduction ............................................................................................................................................ 7 The life of Saint Augustine ................................................................................................................... 9 The influence of the Contra Academicos .......................................................................................... 13 Note on the quotations ........................................................................................................................ 14 1. Scepticism ........................................................................................................................................ -
Gottlob Frege Patricia A
Gottlob Frege Patricia A. Blanchette This is the penultimate version of the essay whose final version appears in the Oxford Handbook of Nineteenth-Century German Philosophy, M. Forster and K. Gjesdal (eds), Oxford University Press 2015, pp 207-227 Abstract Gottlob Frege (1848-1925) made significant contributions to both pure mathematics and philosophy. His most important technical contribution, of both mathematical and philosophical significance, is the introduction of a formal system of quantified logic. His work of a more purely- philosophical kind includes the articulation and persuasive defense of anti-psychologism in mathematics and logic, the rigorous pursuit of the thesis that arithmetic is reducible to logic, and the introduction of the distinction between sense and reference in the philosophy of language. Frege’s work has gone on to influence contemporary work across a broad spectrum, including the philosophy of mathematics and logic, the philosophy of language, and the philosophy of mind. This essay describes the historical development of Frege’s central views, and the connections between those views. Introduction Friedrich Ludwig Gottlob Frege was born on November 8, 1848 in the Hanseatic town of Wismar. He was educated in mathematics at the University of Jena and at the University of Göttingen, from which latter he received his doctorate in 1873. He defended his Habilitation the next year in Jena, and took up a position immediately at the University of Jena. Here he spent his entire academic career, lecturing in mathematics and logic, retiring in 1918. His death came on July 26, 1925 in the nearby town of Bad Kleinen.1 Frege is best known for three significant contributions to philosophy. -
Analyticity, Balance and Non-Admissibility of in Stoic Logic
Susanne Bobzien Analyticity, Balance and Roy Dyckhoff Non-admissibility of Cut in Stoic Logic Abstract. This paper shows that, for the Hertz–Gentzen Systems of 1933 (without Thin- ning), extended by a classical rule T 1 (from the Stoics) and using certain axioms (also from the Stoics), all derivations are analytic: every cut formula occurs as a subformula in the cut’s conclusion. Since the Stoic cut rules are instances of Gentzen’s Cut rule of 1933, from this we infer the decidability of the propositional logic of the Stoics. We infer the correctness for this logic of a “relevance criterion” and of two “balance criteria”, and hence (in contrast to one of Gentzen’s 1933 results) that a particular derivable sequent has no derivation that is “normal” in the sense that the first premiss of each cut is cut-free. We also infer that Cut is not admissible in the Stoic system, based on the standard Stoic axioms, the T 1 rule and the instances of Cut with just two antecedent formulae in the first premiss. Keywords: Sequent, Analyticity, Stoic logic, Proof theory, Decidability, Relevance, Balance, Cut-admissibility. Introduction and Overview There is dispute and uncertainty about the exact details of much of the logic of the Stoics. The primary sources are fragmentary and the secondary sources fail to provide a coherent account. We ignore the Stoics’ modal logic and consider only their propositional logic, which may be regarded as a frag- ment of what we now call classical propositional logic. It is a substructural logic and a relevant logic, with that term broadly conceived: the rule of Thinning is neither present nor admissible and an atom-sharing property, as in [11], i.e. -
3 Arcesilaus and Carneades
C:/ITOOLS/WMS/CUP/552750/WORKINGFOLDER/BCP/9780521874762C03.3D 58 [58–80] 24.9.2009 7:15AM harald thorsrud 3 Arcesilaus and Carneades Arcesilaus initiated a sceptical phase in the Academy after taking over in c. 268 BCE. He was motivated in part by an innovative reading of Plato’s dialogues. Where his predecessors found positive doctrines to be systematically developed, he found a dialectical method of arguing and the sceptical view that nothing can be known (akatalêpsia, De Or. 3.67,seeDL4.28, 4.32). He also advanced this conclusion in opposition to the ambitious system of the Stoics, claiming further that the appropriate response to the pervasive uncertainty generated by his method is the suspension of judgement (epochê). Arcesilaus’ dialectical method was practiced without significant modification in the Academy until Carneades, who became head sometime before 155 BCE.1 Carneades both continued and strength- ened Arcesilaus’ method (ND 1.11, Acad. 2.16, see also Acad. 1.46, and Eusebius, Praep. evang. 14.7.15). Sextus marks the change by referring to Plato’s Academy as Old, Arcesilaus’ as Middle, and Carneades’ as New (PH 1.220). Since the main interpretative issues regarding both Arcesilaus and Carneades depend on the concepts of akatalêpsia and epochê,we must try to determine what they mean, how they are related, and what attitude the Academics take towards them – i.e. in what sense, if any, are these their sceptical doctrines? iarcesilaus The view that Arcesilaus derived from Plato’s dialogues might have taken one of two very different forms. He might have discovered some arguments that show knowledge is not possible. -
The Modal Logic of Potential Infinity, with an Application to Free Choice
The Modal Logic of Potential Infinity, With an Application to Free Choice Sequences Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Ethan Brauer, B.A. ∼6 6 Graduate Program in Philosophy The Ohio State University 2020 Dissertation Committee: Professor Stewart Shapiro, Co-adviser Professor Neil Tennant, Co-adviser Professor Chris Miller Professor Chris Pincock c Ethan Brauer, 2020 Abstract This dissertation is a study of potential infinity in mathematics and its contrast with actual infinity. Roughly, an actual infinity is a completed infinite totality. By contrast, a collection is potentially infinite when it is possible to expand it beyond any finite limit, despite not being a completed, actual infinite totality. The concept of potential infinity thus involves a notion of possibility. On this basis, recent progress has been made in giving an account of potential infinity using the resources of modal logic. Part I of this dissertation studies what the right modal logic is for reasoning about potential infinity. I begin Part I by rehearsing an argument|which is due to Linnebo and which I partially endorse|that the right modal logic is S4.2. Under this assumption, Linnebo has shown that a natural translation of non-modal first-order logic into modal first- order logic is sound and faithful. I argue that for the philosophical purposes at stake, the modal logic in question should be free and extend Linnebo's result to this setting. I then identify a limitation to the argument for S4.2 being the right modal logic for potential infinity. -
Language Logic and Reality: a Stoic Perspective (Spring 2013)
Language Logic and Reality: A Stoic Perspective Aaron Tuor History of Lingustics WWU Spring 2013 1 Language, Logic, and Reality: A Stoic perspective Contents 1 Introduction: The Tripartite Division of Stoic Philosophy.............................3 2 Stoic Physics...................................................................................................4 3 Stoic Dialectic.................................................................................................4 3.1 A Stoic Theory of Mind: Logos and presentations..........................4 3.2 Stoic Philosophy of Language: Lekta versus linguistic forms.........6 3.3 Stoic Logic.......................................................................................7 3.3.1 Simple and Complex Axiomata........................................7 3.3.2 Truth Conditions and Sentence Connectives....................8 3.3.3 Inference Schemata and Truths of Logic..........................9 3.4 Stoic Theory of Knowledge.............................................................10 3.4.1 Truth..................................................................................10 3.4.2 Knowledge........................................................................11 4 Conclusion: Analysis of an eristic argument..................................................12 4.1 Hermogenes as the Measure of "Man is the measure."...................13 Appendix I: Truth Tables and Inference Schemata...........................................17 Appendix II: Diagram of Communication.........................................................18 -
Against Logical Form
Against logical form Zolta´n Gendler Szabo´ Conceptions of logical form are stranded between extremes. On one side are those who think the logical form of a sentence has little to do with logic; on the other, those who think it has little to do with the sentence. Most of us would prefer a conception that strikes a balance: logical form that is an objective feature of a sentence and captures its logical character. I will argue that we cannot get what we want. What are these extreme conceptions? In linguistics, logical form is typically con- ceived of as a level of representation where ambiguities have been resolved. According to one highly developed view—Chomsky’s minimalism—logical form is one of the outputs of the derivation of a sentence. The derivation begins with a set of lexical items and after initial mergers it splits into two: on one branch phonological operations are applied without semantic effect; on the other are semantic operations without phono- logical realization. At the end of the first branch is phonological form, the input to the articulatory–perceptual system; and at the end of the second is logical form, the input to the conceptual–intentional system.1 Thus conceived, logical form encompasses all and only information required for interpretation. But semantic and logical information do not fully overlap. The connectives “and” and “but” are surely not synonyms, but the difference in meaning probably does not concern logic. On the other hand, it is of utmost logical importance whether “finitely many” or “equinumerous” are logical constants even though it is hard to see how this information could be essential for their interpretation. -
Gottlob Frege: on Sense and Reference Professor Jeeloo Liu [Introduction]
Phil/Ling 375: Meaning and Mind [Handout #13] Gottlob Frege: On Sense and Reference Professor JeeLoo Liu [Introduction] I. Language and the World ___ How does language depict reality? Does reality have the same structure as the structure of language? For instance, the basic linguistic structure is a subject and a predicate, and the basic structure of the world is a particular and a universal (e.g. “Socrates is wise”). The subject usually is something of the world and we describe some property it has or does not have. A is F is true is A is really F, is false when A is not F. II. Different Elements of Language Singular terms: Terms that designate particular things Proper names Indexicals: now, today, here, I… Demonstratives: that, this… Pronouns (singular): he, she,… Definite descriptions (the so-and-so): Indefinite (singular) descriptions (a so-and-so) General terms: Terms that designate a kind of things or a certain property Mass nouns ___ natural kind terms (‘water,’ ‘tiger,’ ‘lemon’) ___ non-natural kind terms (‘bachelor’, ‘contract,’ ‘chair’) Adjectives (predicates): colors, shapes, etc. III. Traditional Theories of Meaning Prior to Frege [A] The Ideational Theory ___ The meaning of a linguistic expression is the speaker’s idea that is associated with the expression. [B] Mill’s Theory [the Object Theory] ___ The meaning of a singular term is the thing designated by that term; ___ the meaning of a name is just what the name stands for; the name does not have any other meaning e.g. ‘Socrates’ means Socrates e.g. ‘Dartmouth’ e.g. -
DRAFT: Final Version in Journal of Philosophical Logic Paul Hovda
Tensed mereology DRAFT: final version in Journal of Philosophical Logic Paul Hovda There are at least three main approaches to thinking about the way parthood logically interacts with time. Roughly: the eternalist perdurantist approach, on which the primary parthood relation is eternal and two-placed, and objects that persist persist by having temporal parts; the parameterist approach, on which the primary parthood relation is eternal and logically three-placed (x is part of y at t) and objects may or may not have temporal parts; and the tensed approach, on which the primary parthood relation is two-placed but (in many cases) temporary, in the sense that it may be that x is part of y, though x was not part of y. (These characterizations are brief; too brief, in fact, as our discussion will eventually show.) Orthogonally, there are different approaches to questions like Peter van Inwa- gen's \Special Composition Question" (SCQ): under what conditions do some objects compose something?1 (Let us, for the moment, work with an undefined notion of \compose;" we will get more precise later.) One central divide is be- tween those who answer the SCQ with \Under any conditions!" and those who disagree. In general, we can distinguish \plenitudinous" conceptions of compo- sition, that accept this answer, from \sparse" conceptions, that do not. (van Inwagen uses the term \universalist" where we use \plenitudinous.") A question closely related to the SCQ is: under what conditions do some objects compose more than one thing? We may distinguish “flat” conceptions of composition, on which the answer is \Under no conditions!" from others. -
All Souls College
All Souls College Annual Report and Financial Statements for the year ended 31 July 2014 Registered as a Charity in England and Wales, no: 1138057. Registered address: High Street, Oxford OX1 4AL ALL SOULS COLLEGE Year ended 31 July 2014 Table of Contents Pages Report of the Governing Body 2 - 23 Reference and Administrative Information 24 - 27 Auditor’s Report 28 - 29 Principal Accounting Policies 30 - 33 Consolidated Statement of Financial Activities 34 Consolidated and College Balance Sheets 35 Consolidated Cashflow Statement 36 Notes to the Financial Statements 37 - 57 1 ALL SOULS COLLEGE Report of the Governing Body Year ended 31 July 2014 REPORT OF THE GOVERNING BODY The Warden and Fellows of All Souls College present their Annual Report for the year ended 31 July 2014 under the Charities Act 2011 and the Charities SORP 2005 together with the audited financial statements for the year. INTRODUCTION The College of All Souls of the Faithful Departed, of Oxford – known as All Souls College – was founded by Henry VI and Henry Chichele (Archbishop of Canterbury) in 1438. Today the College is primarily an academic research institution with particular strengths in the Humanities, Mathematics, Social and Natural Sciences and an outstanding library. It also has strong ties to public life. Although the Warden and Fellows of the College are involved in teaching and supervision of research in the University, there are no undergraduate members. On 31 July 2014 there were seventy-seven Fellows of All Souls, twenty-nine Emeritus (i.e. retired academic) and seven Honorary Fellows, many of whose continuing research the College was actively supporting. -
Oxford Studies in Ancient Philosophy. Volume 31, Winter 2006
LIVING IN DOUBT: CARNEADES’ PITHANON RECONSIDERED SUZANNE OBDRZALEK I though the interpretation of ancient texts is inevitably di¶cult, Carneades presents what one might call a worst-case scenario. In the first place, he wrote nothing. To complicate matters, Carneades’ views were so obscure that his faithful disciple Clitomachus con- fessed that he could never figure out what Carneades actually be- lieved (Cic. Acad. 2. 139). Showing remarkable fortitude in the face of such an obstacle, Clitomachus, attempting to play Plato to Carneades’ Socrates, reportedly recorded Carneades’ teachings in 400 books (D.L. 4. 67). Not one remains. None the less, Clito- machus’ attempt to make a philosophy of Carneades’ anti-theoreti- cal stance was not a complete failure; Carneades had a tremendous influence on the later Academy as well as the Stoa, and his views (or lack thereof) have been handed down to us by both Sextus Em- piricus and Cicero. These sources are, however, problematic. As a Pyrrhonist, Sextus was critical of the Academy and may have ex- aggerated what he took to be Carneades’ dogmatism. Cicero, on the other hand, a student of Philo, was undoubtedly influenced in his interpretation of Carneades by his teacher’s dogmatic scepti- cism. Carneades is perhaps best known for proposing the pithan»e phantasia (probable impression) as a criterion for life. However, the status of his theory of the pithanon (probable) is completely unclear.1 Was it merely a dialectical move against the Stoic charge of apraxia (inaction)? Was it a theory that Carneades himself en- ã Suzanne Obdrzalek 2006 I would like to thank Alan Code, Tony Long, Julius Moravcsik, and David Sedley for their comments on this paper. -
B Philosophy (General) B
B PHILOSOPHY (GENERAL) B Philosophy (General) For general philosophical treatises and introductions to philosophy see BD10+ Periodicals. Serials 1.A1-.A3 Polyglot 1.A4-Z English and American 2 French and Belgian 3 German 4 Italian 5 Spanish and Portuguese 6 Russian and other Slavic 8.A-Z Other. By language, A-Z Societies 11 English and American 12 French and Belgian 13 German 14 Italian 15 Spanish and Portuguese 18.A-Z Other. By language, A-Z 20 Congresses Collected works (nonserial) 20.6 Several languages 20.8 Latin 21 English and American 22 French and Belgian 23 German 24 Italian 25 Spanish and Portuguese 26 Russian and other Slavic 28.A-Z Other. By language, A-Z 29 Addresses, essays, lectures Class here works by several authors or individual authors (31) Yearbooks see B1+ 35 Directories Dictionaries 40 International (Polyglot) 41 English and American 42 French and Belgian 43 German 44 Italian 45 Spanish and Portuguese 48.A-Z Other. By language, A-Z Terminology. Nomenclature 49 General works 50 Special topics, A-Z 51 Encyclopedias 1 B PHILOSOPHY (GENERAL) B Historiography 51.4 General works Biography of historians 51.6.A2 Collective 51.6.A3-Z Individual, A-Z 51.8 Pictorial works Study and teaching. Research Cf. BF77+ Psychology Cf. BJ66+ Ethics Cf. BJ66 Ethics 52 General works 52.3.A-Z By region or country, A-Z 52.5 Problems, exercises, examinations 52.65.A-Z By school, A-Z Communication of information 52.66 General works 52.67 Information services 52.68 Computer network resources Including the Internet 52.7 Authorship Philosophy.