Philosophy Faculty Reading List and Course Outline PART IA PAPER 03: LOGIC

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1 SYLLABUS Course Outline Philosophy Faculty Reading List and Course Outline PART IA PAPER 03: LOGIC The Part IA logic course is in two parts, one on formal logic and one on philosophical logic. Section A: Formal Logic Basic concepts: formalized languages; object-language and metalanguage; use and mention; validity, implication and consistency. Truth-functional logic: truth-functions, tautologies, proof. Introduction to first-order logic: the language of quantifiers and variables; validity and counterexamples; elements of the logic of identity. Classes and relations. Elements of probability calculus. Section B: Philosophical Logic Problems of translation between natural and formal languages. Names, variables and descriptions; referential and substitutional readings of the quantifiers. Necessity, analyticity and the a priori. Meaning, intention and conventions. This compulsory course aims to introduce students to some basic issues in the philosophy of logic and language and to the idea of a formal logic. There is a complex interplay between these informal and formal elements of the course. The key notion is the idea of a valid argument (e.g. All men are mortal; Socrates is a man; so, Socrates is mortal). Arguments can be constructed in English and in the various formal languages which the logician invents, and formalised arguments are supposed to tell us something about the corresponding English arguments. Hence we need to know what validity is and why it is significant: are all good arguments valid? Are all valid arguments good? Validity of English arguments is an imprecise and intuitive notion, but validity of arguments framed in a formal language can be made precise. Students will be introduced to two simple formal languages, those of truth-functional and first-order logic, and shown how validity is defined for each. They will practise moving between English and these languages, and they will reflect on the problems this generates. This task will assist the understanding of philosophical writings, many of which 1 employ the symbols of truth-functional and first-order logic. Students will be introduced to the idea of formal derivations using natural deduction. They will also study the elements of probability theory, a part of mathematics that creates almost as many philosophical problems as it solves. The notion of meaning is central to the philosophy of logic and to the philosophy of language in general. The course covers the relationships between meaning and intention. Is there a stable distinction to be drawn between analytic truths, which are true solely in virtue of their meaning (e.g. All bachelors are unmarried) and synthetic truths, which require the world to be a certain way (e.g. Most people die before the age of 80)? How is this related to two others, that between necessary and contingent truths and that between a priori and a posteriori truths? Objectives Students will be expected to: 1. Acquire a broad understanding of the scope and purpose of logic. 2. Learn how to symbolize natural language arguments using formal languages, and how to test the resulting formalizations for correctness. 3. Begin studying philosophical issues in logic. 4. Develop their powers of philosophical analysis and argument through study of what constitutes a valid argument. Prerequisites None Preliminary Reading For the idea of formal logic: GUTTENPLAN, Samuel, The Languages of Logic. 2nd ed. (Oxford: Blackwell, 1997). For some philosophical reflection on logic-related matters, dip into the opening chapters of : SAINSBURY, R. Mark, Logical Forms (Oxford: Blackwell, 1991). For a brisk overview of some issues both formal and philosophical see: PRIEST, Graham, Logic: A Very Short Introduction (Oxford: Oxford University Press, 2000). Also available online at: 2

2 The way this reading list is structured Readings typically divide into (A) and (B) lists below: some attempt is made to put material in the basic (A)-lists into a sensible reading order. (B)-lists are for dipping into: no-one expects you to read everything on the (B) list on a topic, but do read something. The divisions are of course somewhat arbitrary, and different supervisors will want to take different views about what is basic needed to make a shot at a supervision essay and what pushes on the debate rather further. SECTION A: FORMAL LOGIC BASIC CONCEPTS The textbook for this part of the course is: MAGNUS, P.D., and Tim BUTTON, Forallx: Cambridge [Online]. Available at: (Accessed: 01 October 2017). forallx was originally written by P.D. Magnus. Magnus has very generously made the work available under a Creative Commons license. This licenses derivative work, and the text has been altered for the Cambridge course. (Students should feel free to express their gratitude to Magnus, who can be reached at Important Warning. Every logic textbook is idiosyncratic in various ways. Quite apart from differences in emphasis, different books may use: different nomenclature (e.g. predicate logic rather than first-order logic ); different deductive systems (e.g. taking different rules as primitive); different notational conventions (e.g. ~ or instead of for negation; Appendix A of forallx: Cambridge version summarises the various alternatives). At the risk of repetition, the official textbook for this part of the course is forallx: Cambridge. This is what you will be taught from, and it is what you will be examined on. If in doubt, ask the lecturer, your supervisor, or your logic class tutor. (B) Further Reading With the Important Warning in mind, students may sometimes wish to read beyond the textbook. This article discusses the idea of logical consequence, going into a bit more detail than sections 1-4 of forallx: BEALL, J.C., and Greg RESTALL, 'Logical Consequence', in E.N. Zalta, ed., Stanford Encyclopedia of Philosophy (Winter 2016 Edition) [Online]. Available at: (Accessed: 31 July 2017). The following offer some alternative approaches to paraphrasing between formal and natural languages: FORBES, Graeme, Modern Logic: A Text in Elementary Symbolic Logic (Oxford: Oxford University Press, 1994), chs. 2, 5 & 7. GOLDFARB, Warren, Deductive Logic (Cambridge, MA: Hackett, 2003), sects. 1-8, & SMITH, Peter, An Introduction to Formal Logic (Cambridge: Cambridge University Press, 2009), chs & TELLER, Paul, A Modern Formal Logic Primer (Englewood Cliffs, NJ: Prentice Hall, 1989), vol. 1; ch. 2 & vol. 2; ch. 4. Also available online at: CLASSES AND RELATIONS STEINHART, Eric, More Precisely: The Math You Need to Do Philosophy (Peterborough, ON: Broadview Press, 2009), chs. 1 & 2. The book's website is at: Some further support materials and exercises can be found there. PAPINEAU, David, Philosophical Devices: Proofs, Probabilities, Possibilities, and Sets (Oxford: Oxford University Press, 2012), ch. 1 'Naive sets and Russell's paradox'. Also available online at: (B) Further Reading Everyone could profit from looking at: HODGES, Wilfrid, Logic (London: Penguin, 1977), sects [Another introductory treatment of relations] POLLOCK, John L., Technical Methods in Philosophy (Boulder, CO: Westview Press, 1990), ch. 1, sects [An alternative to Steinhart] SMITH, Peter, An Introduction to Formal Logic (Cambridge: Cambridge University Press, 2009), ch. 32. [Helpful introduction to relations] 3 4

3 Mathematically-inclined might prefer some brisker introduction to core concepts and notation of set theory. Try: DEVLIN, Keith, The Joy of Sets. 2nd ed. (New York, NY: Springer, 1993), ch. 1 'Naive set theory'. HALMOS, P., Naïve Set Story (New York, NY: Springer, 1974). ELEMENTS OF PROBABILITY CALCULUS STEINHART, Eric, More Precisely: The Math You Need to Do Philosophy (Peterborough, ON: Broadview Press, 2009), ch. 5 'Probability'. (B) Further reading For alternative introductions to the calculus, two accessible treatments are: HACKING, Ian, An Introduction to Probability and Inductive Logic (Cambridge: Cambridge University Press, 2001). [Especially the part 'How to Calculate Probabilities'] KYBURG, Henry E., Probability and Inductive Logic (London: Macmillan, 1970), ch. 2 'The probability calculus'. Available on Moodle. GRICE, H. P., Studies in the Way of Words (Cambridge, MA: Harvard University Press, 1989), ch. 2 'Logic and conversation'. Also available online at: Reprinted in F. Jackson, ed., Conditionals (Oxford: Oxford University Press, 1991). And here are some useful surveys: HAACK, Susan, Philosophy of Logics (Cambridge: Cambridge University Press, 1978), pp Also available online at: SAINSBURY, R. Mark, Logical Forms (Oxford: Blackwell, 1991; 2nd rev. ed. 2000), ch. 2, especially sects SMITH, Peter, An Introduction to Formal Logic (Cambridge: Cambridge University Press, 2003; 2009), chs. 7, 14 & 15. (B) Further reading Three good discussions are: LEPORE, Ernest, Meaning and Argument (Oxford: Blackwell, 2000), chs. 3, 4, 6 & 7. JACKSON, Frank, 'Indicative Conditionals', in E. Craig, ed., Routledge Encyclopedia of Philosophy [Online]. Available at: (Accessed: 28 July 2017). WOODS, Michael J., Conditionals (Oxford: Clarendon Press, 1997), chs. 1, 2 & 4. Jackson's views are further developed in: PHILOSOPHICAL LOGIC PROBLEMS OF TRANSLATION BETWEEN NATURAL AND FORMAL LANGUAGES Our main focus in part IA is the question about the relationship between the ordinary language propositional connectives and their formal logic counterparts. We are particularly interested in the relationship between the English if then, and the material conditional. (NB some texts use rather than ) For some introductory remarks, see: MAGNUS, P.D., and Tim BUTTON, Forallx: Cambridge, sects. 9 & [Online]. Available at: (Accessed: 28 July 2017). PRIEST, Graham, An Introduction to Non-Classical Logic: From If to Is. 2nd rev. ed. (Cambridge: Cambridge University Press, 2008), sects Also available online at: The absolute must read article is by Grice, in which he introduces the idea of a controversial implicature: 5 JACKSON, Frank, 'On Assertion and Indicative Conditionals', Philosophical Review, 88 (1979): Reprinted in F. Jackson, ed., Conditionals (Oxford: Oxford University Press, 1991). [NB: this is an article the edited volume in the Oxford Readings in Philosophy series, not Jackson's monograph!] After that you could look at the following, which is wonderfully rich, and worth looking at if only to convince yourself that the issues here are difficult and not-trivial: EDGINGTON, Dorothy, 'Indicative Conditionals', in E.N. Zalta, ed., Stanford Encyclopedia of Philosophy (Winter 2014 Edition) [Online]. Available at: (Accessed: 31 July 2017). Finally, look at this excellent (advanced) discussion of some attacks on Grice's notion of implicature, which helps clarify exactly what his notion should be (it also ties together themes from this topic, and the topic of Meaning, Intention and Convention): SAUL, Jennifer M., 'Wayne A. Davis, Implicature: Intention, Convention, and Principle in the Failure of Gricean Theory', Noûs, 35 (2001):

4 NAMES, VARIABLES, AND DESCRIPTIONS (A) Basic Reading One of the deepest ideas that we meet in elementary logic is treatment of quantified expressions (e.g. "everyone loves someone") with quantifiers and variables. For a brisk reminder of the modern treatment, re-read the chapters on First-Order Logic from forallx. We have Frege (and Peirce) to thank for realising that logic could be approached in this way. For a hint at Frege's achievements, read: ENGEL, Pascal, The Norm of Truth: An Introduction to the Philosophy of Logic (London: Harvester Wheatsheaf, 1991), 58-61, POTTER, Michael, Reason's Nearest Kin (Oxford: Oxford University Press, 2000), pp [starting half-way down p. 62]. Also available online at: The landmark explanation of Frege's achievement is hard to read, but worth it: DUMMETT, Michael, Frege: Philosophy of Language (London: Duckworth, 1973; 2nd ed. 1981), ch. 2, especially pp Reprinted in R.I.G. Hughes, ed., A Philosophical Companion to First-Order Logic (Indianapolis, IN: Hackett, 1993). One of the most startling deployments of the use of quantifiers and variables is in Russell's Theory of Descriptions. This is sometimes regarded as the paradigm of analytic philosophy. Russell first presented his Theory of Descriptions in On Denoting, Mind, 14 (1905): But this is a much more accessible explanation: RUSSELL, Bertrand, Introduction to Mathematical Philosophy (London: Allen and Unwin, 1919), ch. 16. Reprinted in P. Ludlow, ed., Readings in the Philosophy of Language (Cambridge, MA: MIT Press, 1997); also in G. Ostertag, ed., Definite Descriptions: A Reader (Cambridge, MA: MIT Press, 1998), ch. 3; and in A. P. Martinich, ed., The Philosophy of Language (Oxford: Oxford University Press, 1990). The following is an excellent analysis of Russell's arguments: SAINSBURY, R. Mark, 'Philosophical Logic', in A. Grayling, ed., Philosophy 1: A Guide through the Subject (Oxford: Oxford University Press, 1995), sects You should also read the classic debate between Russell and Strawson: STRAWSON, Peter, 'On Referring', Mind, 59 (1950): Reprinted in his Logico-Linguistic Papers (London: Methuen, 1971); and in G. Ostertag ed., Definite Descriptions: A Reader (Cambridge, MA: MIT Press, 1998); also in A. P. Martinich and D. Sosa, eds., Analytic Philosophy: An Anthology (Oxford: Blackwell, 2001). RUSSELL, Bertrand, 'Mr Strawson on Referring', Mind, 66 (1957): (B) Further Reading on Definite Descriptions The debate surrounding Russell's Theory continues, with the following landmarks: DONNELLAN, Keith, 'Reference and Definite Descriptions', Philosophical Review, 75 (1966): Reprinted in P. Ludlow, ed., Readings in the Philosophy of Language (Cambridge, MA: MIT Press, 1997); also in G. Ostertag, ed., Definite Descriptions: A Reader (Cambridge, MA: MIT Press, 1998); and in A. P. Martinich, ed., The Philosophy of Language (Oxford: Oxford University Press, 1990). KRIPKE, Saul, 'Speaker's Reference and Semantic Reference', Midwest Studies in Philosophy, 2 (1977): Reprinted in P. Ludlow, ed., Readings in the Philosophy of Language (Cambridge, MA: MIT Press, 1997); and in G. Ostertag, ed., Definite Descriptions: A Reader (Cambridge, MA: MIT Press, 1998). For commentary on these, and for further assessment, look at: LUDLOW, Peter, 'Descriptions', in E.N. Zalta, ed., Stanford Encyclopedia of Philosophy (Fall 2013 Edition) [Online]. Available at: (Accessed: 14 July 2016). SAINSBURY, R. Mark, 'Philosophical Logic', in A. Grayling, ed., Philosophy 1: A Guide through the Subject (Oxford: Oxford University Press, 1995), sects The next stage in the discussion of variables and quantifiers considers how we should understand quantification. This is a difficult topic, and before going in, you need to make sure you really understand the semantics for quantifiers presented in forallx. One of the foremost defenders of substitutional quantification was Ruth Barcan Marcus, and this is a clear introduction to her reasons for favouring it. MARCUS, Ruth Barcan, 'Interpreting Quantification', Inquiry, 5 (1962): After reading this, take a look at two fairly light surveys of the options: ENGEL, Pascal, The Norm of Truth: An Introduction to the Philosophy of Logic (London: Harvester Wheatsheaf, 1991), pp HAACK, Susan, Philosophy of Logics (Cambridge: Cambridge University Press, 1978), ch. 4, sects. 1 & 3. Also available online at: 7 8

5 NECESSITY, ANALYCITY, AND THE A PRIORI (A) Basic Reading We need to distinguish three distinctions: necessary / contingent; analytic / synthetic; and a priori / a posteriori. For an introduction to these three distinctions, try: PAPINEAU, David, Philosophical Devices: Proofs, Probabilities, Possibilities, and Sets (Oxford: Oxford University Press, 2012), chs. 4 & 5. Also available online at: The classic empiricist view is that necessity, analyticity and a priori come as a single package. For a defense of this view, see: AYER, A.J., Language, Truth and Logic. 2nd ed. (London: Gollancz, 1946), ch. 4 'The a priori'. Reprinted in P.K. Moser, ed., A Priori Knowledge (Oxford: Oxford University Press, 1987). HUME, David, Enquiry Concerning Human Understanding, edited by P.H. Nidditch (Oxford: Oxford University Press, 1999), sect. 12, part 3. Also available online at: But there have been two prominent sorts of attack on this view. The first was from Kant, who claimed that there are synthetic a priori truths. See: KANT, Immanuel, Critique of Pure Reason, Introduction. Various translations are available, of which the best known and most widely used are those by N. Kemp Smith (London: Macmillan, 1929) - available online at: and by P. Guyer and A.W. Wood (Cambridge: Cambridge University Press, 1998). Also available online at: There is also a rather looser "tidied up" version by J. Bennett freely available online at: BENNETT, Jonathan, Kant's Analytic (Cambridge: Cambridge University Press, 1966), chs. 1 & 2. Also available online at: The second attack on the empiricist view was Kripke s claim that there are contingent a priori truths and necessary a posteriori truths. See: KRIPKE, Saul, 'A Priori Knowledge, Necessity, and Contingency', in P.K. Moser, ed., A Priori Knowledge (Oxford: Oxford University Press, 1987), ch. 7. [Excerpt of his Naming and Necessity] For discussion, try: AHMED, Arif, Saul Kripke (London: Continuum, 2007), ch. 3 'Necessity'. Also available online at: 9 CASULLO, Albert, 'Kripke on the a Priori and the Necessary', Analysis, 37 (1977): PAPINEAU, David, Philosophical Devices: Proofs, Probabilities, Possibilities, and Sets (Oxford: Oxford University Press, 2012), ch. 6 'Naming and necessity'. Also available online at: You might also want to look at this wide-ranging textbook treatment: GRAYLING, A.C., An Introduction to Philosophical Logic. 3rd ed. (Oxford: Blackwell, 1997), ch. 3 'Necessity, analyticity, and the a priori'. (B) Further Reading WALKER, Ralph, ed., Kant on Pure Reason (Oxford: Oxford University Press, 1982). [Essays by Parsons and Hopkins] VAN CLEVE, James, Problems from Kant (Oxford: Oxford University Press, 1999), ch. 2 'Necessity, analyticity, and the a priori'. Also available online at: MEANING, INTENTION, AND CONVENTIONS (A) Basic Reading You must start with the classic: GRICE, H.P., 'Meaning', Philosophical Review, 66 (1957): Reprinted in P. Strawson, ed., Philosophical Logic (Oxford: Oxford University Press, 1967); and in A.P. Martinich, ed., The Philosophy of Language (Oxford: Oxford University Press, 1985); also in A.P. Martinich and D. Sosa, eds., Analytic Philosophy: An Anthology (Oxford: Blackwell, 2001). For a development of Grice's view, which shifts from intention to conventions, see: BLACKBURN, Simon, Spreading the Word (Oxford: Oxford University Press, 1984), ch. 4 'Conventions, intentions, thoughts'. Also available on Moodle. And for critical discussions, see: MILLER, Alexander, Philosophy of Language (London: UCL Press, 1998), ch. 7 'Sense, intention, and speech acts'. Also available online at: PLATTS, M., Ways of Meaning. 2nd ed. (Cambridge, MA: MIT Press, 1997), ch. 3 'Shades of meaning'. 10

6 (B) Further Reading This is a nice article on post-gricean attempts to offer intention- (and possibly convention) based approaches to semantics: BORG, Emma, 'Intention-Based Semantics', in E. Lepore and B.C. Smith, eds., The Oxford Handbook of Philosophy of Language (Oxford: Oxford University Press, 2005), pp Also available online at: The pioneer of convention-based approaches, though, was Lewis; it might help to read his presentation alongside Rescorla s survey: LEWIS, David Convention (Oxford: Blackwell, 1969), chs. 1 & 4. RESCORLA, Michael, 'Convention', sect. 7, in E.N. Zalta, ed., Stanford Encyclopedia of Philosophy (Spring 2011 Edition) [Online]. Available at: (Accessed: 14 July 2016). Finally, take a look at a fun but subtle attack on the importance of conventions: DAVIDSON, Donald, 'A Nice Derangement of Epitaphs', in E. Lepore, ed., Truth and Interpretation: Perspectives on the Philosophy of Donald Davidson (Oxford: Blackwell, 1988). Reprinted in E. Lepore and K. Ludwig, eds., The Essential Davidson (Oxford: Oxford University Press, 2006), pp