Section 12.1 – Truth and Validity of Logical Arguments

Valid Arguments

Argument – a sequence of statements

Conclusion (consequent) – the final statement of an argument

Premise (antecedent) – the statements that come before the conclusion.

Ex] If an animal is an amphibian, then it is a vertebrae. (Premise)

Frogs are amphibians (Premise)

Therefore, frogs are vertebrates. (Conclusion)

Valid argument – when a conclusion follows logically from the premises.

Valid conclusion – the conclusion of a valid argument

If the premises are all true, then the conclusion is true.

Invalid Arguments – an argument when the premises are true and the conclusion is false.

Modus Ponens (MP)

If p then q

p

Therefore q

Ex] if flivvers twiddle, then bokes malk

Flivvers twiddle

Therefore, bokes malk.

** An argument in modus ponens form is VALID

Modus Tollens (MT)

If p then q

~ q

Therefore ~ p

Ex] If a shirt is a De Morgan, then it has a blackbird logo.

The shirt does not have a blackbird logo.

Therefore, the shirt is not a De Morgan.

** an argument in modus tollens form is VALID.

Invalid Forms

If p then q

q

Therefore p

&

If p then q

~ p

Therefore ~ q