Information on the class -- grading, sections, homework; and an introduction to what logic is, and how we will be approaching it in this class.
Here we begin describing the formal structures underlying reasoning - arguments, statements, and the recursive nature of statement operators.
Translating natural language into the formal notation of sentential logic, including necessary & sufficient conditions, and recursively structured compound statements.
Discussion of functions, truth functions, the truth functions symbolized by statement operators, and the construction of truth tables to evaluate compound expressions.
Using truth tables to assess relations of equivalence, consistency and implication among sets of statements; and assessing argument validity.
An introduction to the proof method in sentential logic, with examples using five inference rules (MP, MT, DS, HS, simp).
Additional inference rules (dil, DI, conj), and three replacement rules (CE, DN, comm). Examples of more complicated proofs.
Introduction of final seven replacement rules (DeM, BE, contra, dist, exp, assoc, dup); and introduction to the method of indirect proof.
Introduction to conditional proof; multiple and nested subproofs; using the proof method to verify that a statement is a tautology.
Clarification of issues that often cause problems, including: negation, the interpretation of statement variables and operator specificity in rule schematics, and requirements on subproofs.
Discussion of the following informal fallacies: Genetic fallacy, ad hominem (including several subtypes), and ad populam (including subtypes)
Discussion of the following informal fallacies: appeal to pity, straw man, appeal to force, appeal to authority.
Discussion of the following informal fallacies: appeal to ignorance, slippery slope, alternate description, composition/division.
Discussion of the following informal fallacies: false cause, hasty generalization, weak analogy, begging the question; and formal fallacies of affirming the consequent & denying the antecedent.
No new informal fallacies are introduced, rather this is a discussion of additional examples of the fallacies introduced in previous lectures.