NEIL W. TENNANT

tennant.9@osu.edu

If you email me, please use the header PHIL 652: YOURNAME.

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Professor
Department of Philosophy

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?? Term 200? PHIL 652: Non-Classical Logics Lecture/seminar Aims of this course. We aim to impart an appreciation of the great variety of non-classical logics, their philosophical motivations, and their proof-theoretic and semantic properties. We shall examine both extensions of classical logic, such as modal logic, and deviant subsystems of classical logic, such as intuitionistic, relevant, and paraconsistent logics. Topics. We shall be covering topics drawn from the following list: The logical systems C (classical), I (intuitionistic), M (minimal), IR (intuitionistic relevant), Anderson-Belnap R (relevant), E (entailment), T, B, K, S4, S5 (modal). Proof-theoretic systems for these logics. Semantical treatments. Relations among systems. Philosophical motivations. Applications. Textbook: Alan Ross Anderson and Nuel D. Belnap, eds., Entailment: The Logic of Relevance and Necessity, Vol. I, Princeton University Press, 1975. Chapter 1.

Reading
(on Reserve in Department):

• 1930. Heyting, Arend. `Die formalen Regeln der intuitionistischen Logik', Sitzungsberichte der Preussischen Akademie der Wissenschaften (Physikalisch-mathematische Klasse), pp. 42--56.
• 1930. Nelson, E. J. `Intensional relations', Mind, n.s., vol. 39, pp. 440--53.
• 1931. Heyting, Arend. `Die intuitionistische Grundlegung der Mathematik', Erkenntnis, vol. 2, pp. 106--115.
• 1932. Kolmogorov, A. `Zur Deutung der intuitionistischen Logik', Mathematische Zeitschrift, vol. 35, pp. 58--65.
• 1933. Parry, William T. `Ein Axiomensystem für eine neue Art von Implikation (Analytische Implikation)', Ergebnisse eines mathematischen Kolloquiums, vol. 4, pp. 5--6.
• 1936. Johansson, Ingebrigt. `Der Minimalkalkül, ein reduzierter intuitionistischer Formalismus', Compositio Mathematica, vol. 4, pp. 119--136.
• 1947. Goodman, Nelson. `The problem of counterfactual conditionals', The Journal of Philosophy, vol. 44, pp. 113--128.
• 1949. McKinsey, J. C. C. and Tarski, Alfred. `Some theorems about the sentential calculi of Lewis and Heyting', The Journal of Symbolic Logic, vol. 13, pp. 1--15.
• 1950. Moh, Shaw Kei. `The Deduction Theorems and Two New Logical Systems', Methodos, vol. 2, pp. 56--75.
• 1951. Church, Alonzo. `The Weak Theory of Implication,' in Kontrolliertes Denken, Untersuchungen zum Logikkalkül und zur Logik der Einzelwissenschaften, eds. A. Menne, A. Wilhelmy, and H. Angsil, Munich (Kommissions-Verlag Karl Alber), pp. 22-37.
• 1956. Ackermann, Wilhelm. `Begründung einer strengen Implikation', The Journal of Symbolic Logic, vol. 21, pp. 113--128.
• 1958. Ackermann, Wilhelm. `Über die Beziehung zwischen strikter und strenger Implikation', Dialectica, vol. 12, pp. 213-222.
• 1959. Smiley, T. J. `Entailment and deducibility', Proceedings of the Aristotelian Society, n.s., vol. 59, pp. 233--54.
• 1959. Von Wright, Georg Henrik. `A note on entailment', The Philosophical Quarterly, vol. 9, pp. 363-5.
• 1960. Anderson, Alan Ross, Belnap, Nuel D. Jr., and Wallace, John R. `Independent axiom schemata for the pure theory of entailment', Zeitshchrift für mathematische Logik und Grundlagen der Mathematik, vol. 6, pp. 93--5.
• 1960. Belnap, Nuel D. Jr. `Entailment and relevance', The Journal of Symbolic Logic, vol. 25, pp. 144--6.
• 1961. Anderson, Alan Ross and Belnap, Nuel D. Jr. `Enthymemes', Journal of Philosophy, vol. 58, pp. 713--723.
• 1962. Anderson, Alan Ross and Belnap, Nuel D. Jr. `Tautological entailments', Philosophical Studies, vol. 13, pp. 9--24.
• 1962a. Anderson, Alan Ross and Belnap, Nuel D. Jr. `The pure calculus of entailment', The Journal of Symbolic Logic, vol. 27, pp. 19--52.
• 1963. Hacking, Ian. `What is strict implication?', The Journal of Symbolic Logic, vol. 28, pp. 51--71.
• 1965. Kripke, Saul. `Semantical analysis of intuitionistic logic I', in J. N. Crossley and M. A. E. Dummett, eds., Formal Systems and Recursive Functions, North-Holland, Amsterdam, pp. 92--130.
• 1968. Meyer, Robert K. `Entailment and relevant implication', Logique et Analyse, n.s., vol. 11, pp. 472--79.
• 1969. Bennett, Jonathan F. `Entailment', The Philosophical Review, vol. 78, pp. 197--236.
• 1970. Stalnaker, Robert C. and Thomason, Richmond H. `A semantic analysis of conditional logic', Theoria, vol. 36, pp. 23--42.
• 1971. Lewis, David. `Completeness and decidability of three logics of counterfactual conditionals', Theoria, vol. 37, pp. 74--85.
• 1971. Meyer, Robert K. `Entailment', The Journal of Philosophy, vol. 68, pp. 808--818.
• 1972. Dunn, J. Michael.` A Modification of Parry's Analytic Implication', Notre Dame Journal of Formal Logic, vol. 13, no. 2, pp. 195-205.
• 1972. Urquhart, Alasdair. `Semantics for relevant logics', The Journal of Symbolic Logic, vol. 37, pp. 159--69.
• 1972a. Routley, Richard and Meyer, Robert K. `The semantics of entailment (II)', Journal of Philosophical Logic, vol. 1, pp. 53--73.
• 1972b. Routley, Richard and Meyer, Robert K. `The semantics of entailment (III)', Journal of Philosophical Logic, vol. 1, pp. 192--208.
• 1973. Routley, Richard and Meyer, Robert K. `The semantics of entailment (I)', in H. Leblanc, ed., Truth, syntax, modality, North-Holland, Amsterdam, pp. 199--243.
• 1974. Fine, Kit. `Models for entailment', Journal of Philosophical Logic, vol. 3, pp. 347--72.
• 1974. Meyer, Robert K. `Entailment is not strict implication', Australasian Journal of Philosophy, vol. 52, pp. 212--231.
• 1978. Tennant, Neil. Natural Logic, Edinburgh University Press, sec. 5.8, Kripke semantics for intuitionistic logic.
• 1979. Priest, Graham. `The Logic of Paradox', Journal of Philosophical Logic, vol. 8, pp. 219--41.
• 1979. Tennant, Neil. `Entailment and Proofs', Proceedings of the Aristotelian Society, vol. LXXIX, pp. 167-189.
• 1979. Tennant, Neil. `Language games and intuitionism', Synthese, vol. 42, pp. 297-314
• 1980. Tennant, Neil. `A Proof-theoretic approach to entailment', Journal of Philosophical Logic, vol. 9, pp. 185-209.
• 1984. Tennant, Neil. `Perfect validity, entailment and paraconsistency', Studia Logica, vol. XLIII, pp. 179-198.
• 1985. Tennant, Neil. `Minimal logic is adequate for Popperian science', British Journal for Philosophy of Science, vol. 36, pp. 325-329.
• 1986. Tennant, Neil. `The Withering Away of Formal Semantics?', Mind and Language, vol. 1, pp. 302-318.
• 1987. Tennant, Neil. `Natural Deduction and Sequent Calculus for Intuitionistic Relevant Logic', Journal of Symbolic Logic, vol. 52, pp. 665-690.
• 1989. Tennant, Neil. `Truth Table Logic, with a Survey of Embeddability Results', Notre Dame Journal of Formal Logic, vol. 30, pp. 459-484.
• 1994. Tennant, Neil. `Intuitionistic Mathematics Does Not Need Ex Falso Quodlibet', Topoi, pp. 127-133.
• 1994. Tennant, Neil. `Transmission of Truth and Transitivity of Proof', in D. Gabbay, ed., What is a Logical System?, Oxford University Press, pp. 161-177.
• 1996. Tennant, Neil. `Delicate Proof Theory', in J. Copeland, ed., Logic and Reality: Essays on the Legacy of Arthur Prior, Oxford University Press, pp. 351-385.
• 1997. Tennant, Neil. The Taming of The True, Clarendon Press, Oxford. Chapter 9, `Finding the Right Logic'.
• 1999. Tennant, Neil. `Negation, Absurdity and Contrariness', in D. Gabbay and H. Wansing, eds., What is Negation, Kluwer, Dordrecht, pp. 199--222.
• 2000. Priest, Graham and Tanaka, Koji. `Paraconsistent logic'
• 1988. Priest, Graham, `When Inconsistency is Inescapable: A Survey of Paraconsistent Logics,' South African Journal of Philosophy, vol. 7, pp. 83--9.
• 200X. Priest, Graham. `Paraconsistent Logic', in D. Gabbay and F. Guenther, Handbook of Philosophical Logic, 2nd edition, Volume 7. Kluwer Academic Publishers. Forthcoming.

Assessment:

Item	Date due	Weight
Midterm exam	tba	50%
Term paper	tba	50%

Policy on attendance at classes

Plagiarism

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