Description
Introduces students to the structure and evaluation of deductive arguments. The core of this course is sentence logic with proofs and predicate logic with quantifiers and proofs. Will learn to translate natural language into symbolic notation and test for validity using natural deduction.
Grading Basis
Graded
Prerequisites
MATH 99 with a grade of C (2.0) or better or a grade of 3 or higher on the Smarter Balanced exam or appropriate placement score
Course Learning Outcomes
Core Topics
- Introduction to argument structures: Deductive vs. inductive. Validity, invalidity, soundness, cogency.
- History of logic: Aristotle and categorical logic, Stoics and propositional, Leibniz, Frege, Russell , and birth of predicate logic.
- Traditional argument forms/syllogisms.
- Fallacies: Affirming the consequent, denying the antecedent, etc. (optional: informal).
- Sentence translation from natural language into truth-functional (TF) logic using variables (P,Q,R) and connectives (&,v,>,~).
- Sentence analysis in TF logic: consistency, contradiction, and tautology.
- Truth tables for truth-functional logic (minimum of three variables).
- Rules of inference: modus ponens, modus tollens, disjunctive syllogism hypothetical syllogism, addition, simplification, conjunction, constructive dilemma.
- Rules of replacement: commutation, association, double negation, De Morgan’s, distribution, transposition, implication, exportation, tautology, material equivalence.
- TF Proofs: Direct, indirect, conditional.
- Predicate translation: universal and existential quantifiers.
- Proofs: universal instantiation (UI) and generalization (UG) and existential instantiation (EI) and generalization (EG).
- Using rules of inference and replacement in predicate logic: direct proofs (optional: indirect and conditional).
- (optional): Proofs with overlapping quantifiers i.e. (3x)(3y).
- (optional): Basics of S5.