Logic and Reasoning Chapter 1

argument

a series of statements where at least some are premises and where one statement is the conclusion

standard/argument form

way of structuring arguments that makes it clear what the argument is about / statement, statement, statement, conclusion

Explanation

Reasons why or how something occurred. Explains why something is true to help someone understand. Fit phenomenon int pattern

deductive argument

an argument in which it is claimed that the conclusion follows necessarily from the premises or an argument in which it is claimed that if the premises are true, then it is impossible for the conclusion to be false.

inductive argument

argument in which it is claimed that the premises make the conclusion probable; or an argument in which it is claimed that if the premises are true, then it is improbable for the conclusion to be false.

valid

argument in which the conclusion follows necessarily from the premises; or an argument in which if the premises are true, then it is impossible for the conclusion to be false

invalid

in which the conclusion does not necessarily fall from the premises; or an argument in which if the premises are true, then it is possible for the conclusion to be false

sound

a deductive argument that is valid and has all true premises

unsound

a deductive argument that is invalid or that has at least 1 false premise

strong

type of inductive argument in which if the premises are true, then the conclusion is probable; or an argument in which if the premises are true then it is improbable that the conclusion is false

weak

an inductive argument type in which if the premises are true the conclusion is improbable

counterexample

evidence that shows the statement is false. shows the possibility that premises assumed to be true do not make the conclusion necessarily true.

is truth value a property of arguments or statements?

only statements can be true or false

is validity property of statements or arguments

arguments

is cogency arguments or statements

property of inductive arguments

conditional statement

if P, then Q

when is a conditional statement true?

when both antecedent and consequents are true

modus ponens

1) if P, then Q. 2) P C) So, Q

Modus Tollens

1) If P, then Q 2) Not Q C) So, not P

hypothetical syllogism

1) If P, then Q. 2) if Q, then R. C) So if P, then R

Disjunction syllogism

1) P or Q 2) Not Q C) So, P

counterexample to a premise

used to show a premise is false

counterexample to an argument

shows that an argument is invalid. premises are true but conclusion is false

affirming the consequent (fallacy)

1) If P, then Q 2). Q C) so, P

denying the antecedent

1) if P, then Q 2) Not P 3) so, not Q