Sound, Valid, True: Difference between revisions

"Truth" refers to the factual accuracy of each individual premise and the conclusion. It's exactly what it sounds like, but ''it does not address the validity of the logic''.

 

Therefore, all turtles are animals. (True conclusion: All turtles ''are'' animals / Invalid logic: If all A are X, and all B are X, then all C are not necessarily X.) }}

 

"Validity" refers to the chain of reasoning, the logical part of the argument. An argument is valid only if it is impossible for all of the premises to be true and for the conclusion to be false. ''It does not rely on the truth of the premises or of the conclusion.''

 

All dogs are terriers. (False premise / All B are C.)<br />

Therefore, all animals are terriers. (False conclusion: All animals are not terriers / Valid logic: If all A are B, and all B are C, then all A ''are'' C.) }}

The argument as a whole is unsound. "Soundness" refers to the argument as a whole. The premises must be "true" ''and'' the logic must be "valid". (Using [[You Fail Logic Forever|a fallacy]] results in an unsound argument, as does using false premises.) If these conditions are met, the conclusion must be true as well, by the above definition of "valid".

 

Therefore, all terriers are animals. }}

 

The first thing to note is that all inductive arguments are, by their nature, invalid: induction, by its nature, relies on probability as a central element. Since the definition of validity is that, given true premises, you always end up with a true conclusion, and the definition of a probabilistic premise is that you can feed in true data and still come up with a false answer, inductive arguments are always invalid according to the strict standards of logic. This doesn't make them any less useful. For instance:

 

Therefore, Brahim is Muslim. }}

 

Theoretically, the dividing line between strong and weak inductive arguments is at 50%: at anything above 50%, the argument is strong. This can be a bit counterintuitive:

 

50.25% of humans are male.<br />

Therefore, Rory is male. }}