Note that this schedule will be updated frequently during the semester!
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| Introduction |
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| Arguments, logical form, validity |
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| Part I: Propositional calculus | ||||||
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| Conditionals, negation; derivation rules A, MPP |
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| Derivation rules MTT, DN, CP; fallacies |
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| Logical truths; derivation rules &I, &E, or-I |
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| Derivation rules or-E, RAA; proof strategies |
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| Proofs by contradiction; necessary/sufficient; biconditional |
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| Definitions, well-formed formulas, theorems |
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| Substitution instances, theorem introduction, sequent introduction |
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| Derived rules; summary on syntax |
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| Truth tables; knights and knaves |
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| Truth-functional validity; expressiveness |
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| Mathematical induction |
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| Consistency of propositional calculus; completeness |
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| Review session (Bring your own questions!) |
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| (Class cancelled due to snow!) |
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| Test No. 1 |
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| Part II: Predicate calculus | ||||||
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| Logical form 'all' and 'some' |
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| Examples with nested quantifiers |
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| Universal quantifier rules |
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| Existential quantifier rules |
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| Proofs with quantifiers |
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| Well-formed formulas; propositional functions |
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| Midsemester Break |
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| Formalization of inference rules |
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| Equivalences |
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| Quantifier switches; proof-strategies |
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| Theorems, substitution instances |
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| TI, SI; interpretation |
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| Models |
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| Spring Break |
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| Spring Break |
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| Spring Break |
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| Consistency; completeness; decidability |
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| Review (bring your own questions) |
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| Test No. 2 |
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| Part III: Applications | ||||||
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| Identity |
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| Quantities; history of logic |
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| Spring Carnival |
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| Properties of relations |
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| Functional relations |
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Axioms for natural numbers (Essay outline due) |
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| Proofs in PA |
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| Meta-theorems: categoricity, Gödel's incompleteness thm. |
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Natural deduction calculus (Essay due) |
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| Rational numbers, cardinalities |
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| Cardinality of real numbers, decidability |
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Review (bring your own questions) (All homeworks, redo's, etc. due) |
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Final Exam: 5:30-8:30pm, PH A18C |
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