NEIL W. TENNANT

tennant.9@osu.edu

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

Professor
Department of Philosophy


Autumn Term 2007

PHIL 250: Introduction to Symbolic Logic

Lecture/Recitation

Scott Laboratory

Room 0040
(Views of classroom)
TR, 1:30-3:18 p.m.

Grader:

Michael Ferreira

Although required to undertake the duties only of a grader, Michael has kindly offered to hold office hours in the Philosophy TA Room on the second floor of University Hall, in the periods immediately after class on Tuesdays and Thursdays.

Administrative announcements

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 UniPrint Tuttle location (near Oxley's coffee shop).

Handouts

Analyzing formal sentences (.pdf file)
Partial answers to previous exercise sheet (.pdf file)
Axioms for ordering (Word file)
Definition of formula in the language of the theory of orderings (Word file)
Notes 1 (Word file)
Skills (Word file)
Exercise templates in propositional logic (Word file)
Propositional Proofs (.pdf file)
Translation exercises (.pdf file)
Model answers to the translation exercises (.pdf file)
Deductive Exercises (.pdf file)
Model Answers to the Deductive Exercises (.pdf file)
Exercises on counterexamples (.pdf file)
Solutions to exercises on counterexamples (.pdf file)
Exercises on describing finite models (Word file)

Model Answers to exercises in Natural Logic

Exercise 1 (.pdf file)
Exercise 2 (.pdf file)
Exercise 3 (.pdf file)
Exercise 4 (.pdf file)
Exercise 5 (.pdf file)
Exercise 6 (.pdf file)
Exercise 7 (.pdf file)
Exercise 8 (.pdf file)
Exercise 9 (.pdf file)

Class Calendar

Basic Concepts and Techniques
(These web pages are under construction and are continually being revised and expanded.)

Assessment:
Item Date Weight
Midterm exam Thursday, October 25, 2007, in class 50%
Final exam (see revision sheet ) Wednesday, December 5, 2007, 1:30-3:18 PM 50%

Policy on attendance at classes

Accommodations for Disabilities

Plagiarism