Heusser Philosophy 100 SG 5c

Moral Reasoning: Validity and Soundness

“Valid” is used in philosophy to apply to arguments as a whole, not individual statements. An argument is said to be valid when it follows a pattern such that it is impossible for any argument following that pattern to have its conclusion be false if its premises are true. Argument #1 below is valid. If (1) and (2) are true, (3) must be true; it is impossible for (3) to be false given that (1) and (2) are true. Note that validity is not a claim that (1) and (2) are in fact true. It is only the claim that if (1) and (2) are true, (3) must be true.

A “sound” argument is one that is valid and has true premises. To claim that the above argument is sound then is to claim that (3) must be true given (1) and (2), and that (1) and (2) are true. Note that in evaluating soundness in arguments two distinct flaws need to be watched for: the validity of the argument, and the truth of its premises.

Some Valid (#1-4) and Invalid (#5-9) Argument Forms:

Note that “True” and “False” indicate the truth-values of the premises or conclusion.

1) All A are B 2) All tigers are mammals True

All B are C Valid All mammals are animals

\All A are C \All tigers are mammals True

3) All pigs are fish False 4) All dogs are fish False

All fish are birds All fish are mammals

\All pigs are birds False \All dogs are mammals True

5) All A are B 6) All tigers are animals True

All C are B Invalid All mammals are animals

\All A are C \All tigers are mammals True

7) All cats are animals True

All dogs are animals

\All cats are dogs False

8) All pigs are fish False 9) All dogs are fish False

All birds are fish All mammals are fish

\ All pigs are birds False \ All dogs are mammals True