CRIT 111-018 Foundations Logical Reasoning - Exam #1

Argument

A set of propositions consisting of a conlusion and premises

Deductive argument

Tries to establish its conclusion with necissity or certainty

EX.

• All humans are mammals

• Caleb is a human

• Therefore, Caleb is a mammal

Inductive argument

Concerned with probability

EX.

• Most humans love ice cream

• Caleb is a human

• Therefore, Caleb (probably) loves ice cream

Premise indicators

• Since

• Because

• Given that

• The reason is

Conclusion indicators

• This means

• So

• Therefore

• It follows

Enthymeme

Any argument that has a missing premise or conclusion

EX. missing conclusion

• Jones has more experience in congress than Smith, never takes bribes, knows the working class well. Do I really need to say more?

EX. missing premise

• Don’t vote for Smith. Last time he was in charge gas prices skyrocketed

Valid

If the premises are true, the conclusion must be true

Invalid

The premises can be true while the conclusion is still false

Sound

Valid, premises are true

Unsound

Invalid, has at least one false premise

Valid argument example

• All As are Bs

• C is A

• Therefore, C is B

Invalid argument example

Direct

• Sally lives in North America

• Sally does not live in Mexico

• So, Sally lives in the United States

Counterexample: Sally lives in Canada

Indirect

• All cats are animals

• All cats makes purr sounds

• All animals make purr sounds

Logical form of an argument

EX.

• All As are Bs, No Bs are Cs, so No As are Cs

Direct counterexample

Involves describing a concrete case in which the premises of the argument are true but the conclusion is false

Indirect counterexample

Involves producing a new argument, with the same logical form, which has true premises and a false conclusion

Strong

The conclusion is made probable given the premises

Weak

The conclusion is not made probable given the premises

Cogent

Strong, has true premises

Not cogent

Weak, has at least one false premise

How additional information affects an argument

EX.

• My car won’t start

• Therefore, the car battery is dead

New information

• This has never happened before (no effect)

• The car horn works (weakens)

• The car horn doesn’t work (strengthens)

*Car horns are powered by the car battery