The construction of a formal argument Logic The construction of a formal argument

Logic: the study of the correct rules of reasoning Reason vs. Rhetoric Propositions: declarative statements that assert a claim They are either true or false Analytic vs. Synthetic propositions (Kant) analytic: predicate adds nothing to the subject E.g. 2 + 2=4 Deductive reasoning Pure rationalism; no new information from the world Synthetic: predicate adds knowledge to subject. Conclusions come from our observation of the world E.g. “The rose is red.”

Induction Drawing conclusions from observation of particular cases Scientific method Knowledge is always a matter of probability We frame expectations of future events Arguments not “valid” in formal sense; rather, “strong” or “weak” Analogical reasoning (“if it cures cancer in mice, it should cure cancer in people”) Occam’s Razor

abduction Reasoning “to the best explanation” Seeks to add explanatory reason “Occam’s razor” Seek simplist explanation Is there a God? (utilizing abductive reasib)

Deductive reasoning {deduce: to derive a conclusion from something known) Syllogisms: formal arguments with premises and conclusions Truth preserving (as in a mathematical equation) Validity vs. soundness A valid and sound argument should always be true Categorical syllogism A) Socrates is a man B) All men are mortal C) therefore: Socrates is mortal (valid & sound argument) A) Socrates is a dolphin B) All dolphins are mortal C) Therefore: Socrates is mortal (valid but unsound)

Hypothetical Syllogism forms Modus Ponens: (affirming the antecedent) If P, then Q A) If it rains the ball game will be cancelled B) It’s raining C) the game is cancelled Modus Tallens (denying the consequent) If P, then Q; Not P; not Q B) It is not raining C) the game is not cancelled

Invalid Hypothetical forms Denying the antecedent A) if P, then Q B) not P C) therefore, not Q Example A) If Mary is a mother, she is a woman B) Mary is not a mother C) Therefore, Mary is not a woman

Invalid Hypothetical Forms Affirming the consequent A) If P, then Q B) Q C) therefore, P Example: If Mary if a mother, she is a woman Mary is a woman Therefore, she is a mother

Necessary vs. Sufficient Necessary—”A” is required for “B” result (To earn good grades one must study diligently) Sufficient—”A” is one cause of “B” result (beheading is sufficient for death) Necessary and sufficient (For the world to be made right, Jesus must return)

Logical fallacies: a lifelong pursuit