NEIL W. TENNANT

tennant.9@osu.edu

If you email me, please use the header PHIL 250: YOURNAME.

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Professor
Department of Philosophy

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Autumn Term 2011 PHIL 250: Introduction to Symbolic Logic Lecture/Recitation Caldwell Laboratory Room 277 MW, 9:30-11:18 a.m. Grader: Erik Wedin Aims of this course We aim to give the student a thorough grounding in the techniques of formal logic: translating sentences of English into formal logical notation, analyzing arguments for validity, providing formal proofs for valid arguments, and constructing counterexamples to invalid ones. We shall concentrate on the connectives of propositional logic, but shall also explain the workings of the quantifiers of first-order logic. This is not just a technical exercise, but involves philosophical consideration of issues such as reference, predication, quantification, identity, descriptions, truth and meaning. We shall explain the basic concepts of metalogic, which is the study of logical systems themselves. The most important properties to be studied are the soundness and completeness of systems of proof with respect to a chosen semantics. Our systems of proof will be those of natural deduction, with their characteristic introduction and elimination rules for the connectives and the quantifiers. This affords a unified approach to the study of classical logic and its most important subsystems. Topics We shall be covering topics drawn from the following list: Formal v. natural languages. Eliminating syntactic ambiguity. Categorizing expressions: names, function signs, predicates, connectives, quantifiers, variable-binding term-forming operators. Formal grammars, and the notion of a well-formed formula. Interpretation of the connectives by means of truth-tables. Translations between English and sentences in a formal notation. Validity of argument. Logical consequence and logical truth. Compactness of logical consequence. Counterexamples to invalid arguments. Introduction and elimination rules. The absurdity rule. Classical negation rules. Discharging assumptions in the course of an argument. The notion of a formal proof of a conclusion from a set of undischarged assumptions. Deducibility and theoremhood. Interdefinability of logical operators in the classical case. Interderivability of rules of inference. Truth sets. Disjunctive normal forms. Soundness and completeness of classical propositional logic. Textbook Natural Logic, Edinburgh University Press, 2nd edn., 1990. Second-hand copies might be available at SBX. You can also purchase a printout of a digitized photocopy, either online at http://uniprint.osu.edu/, or at the OSU Bookstore, or at Barnes and Noble on High Street. Handouts Analyzing formal sentences Partial answers to previous exercise sheet Axioms for ordering Definition of formula in the language of the theory of orderings Notes on arguments, proofs and counterexamples Skills Exercise templates in propositional logic Propositional Proofs Translation exercises Model answers to the translation exercises Deductive Exercises Model Answers to the Deductive Exercises Exercises on counterexamples Solutions to exercises on counterexamples Exercises on describing finite models Some Simple Exercises in Natural Deduction Aristotle's syllogisms Model Answers to exercises in Natural Logic Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5 Exercise 6 Exercise 7 Exercise 8 Exercise 9

Basic Concepts and Techniques
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Assessment:

Item	Date	Weight
Midterm exam	Wednesday, October 26, 2011, in class	50%
Final exam (see revision sheet )	Tuesday, December 6, 2011, 9:30-11:18 AM	50%

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