|
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 |
|