Logic and Reasoning Unit 1 Study guide

unsound argument

a deductive argument that is invalid, has one or more false premises, or both

necessary condition

a condition or factor that must be present for something to occur. It's required or essential

sufficient condition

a condition or factor that if it's satisfied, it guarantees the outcome

Modus tollens

If P then Q. not-Q. therefore, not-P

Other words for modus tollens

denying the consequent

Affirming the consequent

If P then Q. Q. Therefore, P

principle of charity

when reconstructing an argument, you should attempt to give the speaker the best argument you can reasonably give

fallacy of equivocation

Using the same term in an argument in different places but the word has different meanings.

Dual systems theory

argues that we have two cognitive systems, one for controlled cognition and one for automatic cognition

System 1

the intuitive, automatic, unconscious, and fast way of thinking

System 2

the deliberate, controlled, conscious, and slower way of thinking

Argument

A statement to prove or convince someone or something. It contains premise(s) and a conclusion and it can be invalid or valid

explanation

A statement that provides an understanding of reasons, causes, etc. behind them; makes something clear

deductive argument

when the premise of the argument guarantees the truth of the conclusion

inductive argument

when the premise doesn't guarantee the truth of the conclusion 100% but there's a chance that it does

valid argument

when it's impossible for the premises to be true and the conclusion to be false

invalid argument

when the conclusion doesn't logically follow the premises

Sound argument

a valid argument where the premises are true; so, the conclusion must be true as well

belief bias

people tend to think invalid arguments are valid if the conclusion is something they already believe in

enthymeme

an incomplete argument

counterexample

a possible situation that proves that the premises are true but the conclusion is false

negation of a statement

saying the opposite of the claim

indicative conditional

"if p, then q"

MEMORIZE

a conditional statement is false when the antecedent is true but the consequent is false

Modus ponens

if P then Q. P. Therefore, Q

Other words for modus ponens

Affirming the antecedent / the law of detachment

Denying the antecedent

If P then Q. Not-P. Therefore, not-Q

Hypothetical syllogism (HS)

If P then Q. If Q then R. Therefore, if P then R

categorial syllogism / aristotelian syllogism

No As are Bs. All As are Cs. Some Cs are not B

two forms of contraposition

If P then Q. If not-Q then not-P.
If not-Q then not-P. So, if p then q.

double negation

p = ~~p
(p = not-not-p)

Exclusive-OR (XOR)

A or B but not both

Inclusive-OR

either or both are true

Disjunctive Syllogism

P or Q. Not-P. Therefore, Q.

Constructive Dilemma

P or Q. if P then R. If Q then S. Therefore, R or S.

Universal modus ponens

All As are Bs. Some Ps are As. So. some Ps are Bs

Universal modus tollens

All Fs are Gs. Some things are not Gs. So, some things are not Fs

All Fs are Gs. b is not a G. So, b is not an F