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 firstorder 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 
Firstorder validity and consequence; firstorder 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 stepbystep 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 
