Syllogisms

syllogism

a 3 line deductive reasoning argument (2 premises, 1 conclusion)

categorical syllogism

propositions that categorize things by stating whether or not these things belong in certain categories

a sound argument

an argument where the premises are accepted as true and the argument is valid

propositional logic

a system of logic that involves the meanings of logical connectives

not p

~p

hypothetical syllogisms

a 3 line argument that has a hypothesis in the form if p then q as one of its premises

modus ponens (to affirm)

if p then q, p is true, then q is true

modus tollens (to deny)

if p then q, q is false, then p is false

affirming the consequent

if p then q, q is true, so p (invalid)

denying the antecedent

if p then q, p is false, so q (invalid)

disjunctive syllogism

uses the disjunction or to connect 2 propositions into one compound proposition. At least 1 is taken as true. p or q, not p, so q

v

or

affirming the disjunct

if p then q, p, so not q (invalid) - all premises could be true and conclusion is false

^

and

Denying the consequent

all a are b, c is not b, c is not a (valid)

Affirming the antecedent

all a are b, c is a, c is b (valid)

Affirming the consequent

all a are b, c is b, so c is a (invalid)

Rules

negative premise must yield a negative conclusion - 2 negatives cannot yield a conclusion - 2 particular premises cannot yield a conclusion