Schedule

HOME Philosophy 120A
Autumn 2007

Introduction to Logic

Class Schedule

Topics for each of the MWF lectures are listed below, along with the corresponding reading assignments in Language, Proof and Logic (LPL), listed by section numbers. In addition to the readings in LPL, you should read the relevant sections of the Software Manual, as needed. Look at chapters 2 and 3 immediately, along with the assignment for September 27. Look at chapter 4 by October 1, and chapter 5 by October 8. You will very likely want to use these chapters for subsequent reference. The Supplement for class on December 7 can be downloaded from the Lecture Notes web page.

 Date Topics Covered Reading September 26 Using the software: how to submit homework files. Individual constants; predicate symbols; atomic sentences. Introduction, pp. 1–10; §1.1 – §1.3 September 28 General first-order languages; valid and sound arguments; methods of proof. §1.4, §2.1, §2.2 October 1 Formal proofs; constructing proofs in Fitch; demonstrating nonconsequence. §2.3 – §2.5 October 3 Negation symbol: Ø; conjunction symbol: ‚; disjunction symbol: ƒ; remarks about the game. §3.1 – §3.4 October 5 Ambiguity and parentheses; equivalent ways of saying things; translation. §3.5 – §3.7 October 8 Tautologies and logical truth; logical and tautological equivalence; logical and tautological consequence. §4.1 – §4.3 October 10 Tautological consequence in Fitch; valid inference steps; proof by cases. §4.4,  §5.1, §5.2 October 12 Indirect proof (proof by contradiction); arguments with inconsistent premises; conjunction rules. §5.3, §5.4, §6.1 October 15 Disjunction rules; negation rules. §6.2, §6.3 October 17 The proper use of subproofs; strategy and tactics; proofs without premises. §6.4 – §6.6 October 19 Material conditional symbol: ®; biconditional symbol: «; conversational implicature. §7.1 – §7.3 October 22 Informal methods of proof; formal rules of proof for ® and «. §8.1, §8.2 October 24 Soundness and completeness; valid arguments: some review exercises. §8.3, §8.4 October 26 MIDTERM EXAM October 29 Variables and atomic wffs; the quantifier symbols: ", \$; wffs and sentences. §9.1 – §9.3 October 31 Semantics for the quantifiers; the four Aristotelian forms. §9.4, §9.5 November 2 Translating complex noun phrases; tautologies and quantification. §9.6, §10.1 November 5 First-order validity and consequence; first-order equivalence and DeMorgan’s laws. §10.2, §10.3 November 7 Other quantifier equivalences; multiple uses of a single quantifier. §10.4,  §11.1 November 9 Mixed quantifiers; the step-by-step method of translation; paraphrasing English. §11.2 – §11.4 November 12 HOLIDAY November 14 Ambiguity and context sensitivity; prenex form. §11.5, §11.7 November 16 Prenex form (continued); some extra translation problems. §11.8 November 19 Valid quantifier steps; the method of existential instantiation; the method of general conditional proof. §12.1 – §12.3 November 21 Proofs involving mixed quantifiers; universal quantifier rules. §12.4, §13.1 November 23 THANKSGIVING HOLIDAY November 26 Existential quantifier rules; strategy and tactics. §13.2 – §13.3 November 28 Soundness and completeness; review exercises: practice with proofs. §13.4 – §13.5 November 30 Numerical quantification. §14.1 December 3 Proving numerical claims. §14.2 December 5 The: Russell’s theory of definite descriptions. §14.3 December 7 Properties of relations; infinite domains. Supplement, §15.5 December 10 FINAL EXAM: 8:30 - 10:20 am