Logic Concepts

I. Argument Form vs. Content

A. An argument =df a set of claims (statements that can be true or false) one of which (the conclusion) is intended to be supported by the others (premises).

B. Some Examples

1. P1: If Lassie is a dog, then Lassie is a mammal

P2: Lassie is a dog.

C: Lassie is a mammal.

[Good Overall Argument]

2. P1: If Lassie is a dolphin, then Lassie is a mammal.

P2: Lassie is a dolphin.

C: Lassie is a mammal.

[Bad Argument—Good Form but Bad Content]

3. P1: All dogs are mammals.

P2: All cats are mammals.

C: All dogs are cats.

[Bad Argument—Good Content but Bad Form]

4. P1: All collies are mammals.

P2: All dogs are mammals.

C: All collies are dogs.

[Bad Argument—Good Content (and even a true conclusion) but Bad Form]

C. Content:

1. Good Content = All the premises are true.

2. Bad Content = Some premise is false.

D. Form

1. Form = what arguments 1 and 2 above have in common and what arguments 3 and 4 have in common.

2. Good Form = A truth-preserving machine—good input (true premises) yields good output (true conclusion).

3. Bad Form = Not a good truth-preserving machine—good input (true premises) can easily yield bad output (false conclusion).

II. Deductive Concepts

A. Good Deductive Form = Valid

1. An argument is valid =df If the premises are true, then the conclusion must be true.

2. An argument is valid =df It is impossible for the premises to all be true but the conclusion false.

B. Good Overall Deductive Argument = Sound

An argument is sound =df It is both valid and has all true premises.

III. Inductive Concepts

A. Good Inductive Form = Strong

1. An argument is strong =df If the premises are true, then the conclusion is probably true.

2. An argument is strong =df It is improbable for the premises to all be true but the conclusion false.

B. Good Overall Deductive Argument = Cogent

An argument is cogent =df It is both strong and has all true premises.