Tuesday, April 21, 2015

Difference between valid argument and sound argument

One of the biggest eye-openers of my education was learning what philosophers mean by the phrase "valid argument." As used by philosophers, a valid argument is not necessarily the same as a "sound" argument. A valid argument is one whose logic is solid, even if the premises are false. For example, take this argument:

If pigs had wings, they could fly.
Pigs have wings.
Therefore, they can fly.

The premises are false, but the logical structure of the argument is solid. If you accepted that pigs had wings, and that their having wings meant they could fly; then the conclusion that they can fly would necessarily follow. Philosophers would thus say the argument is valid; because the truth of both premises would establish the conclusion. But the argument is not "sound" in the philosophical sense; because it suffers from false premises - pigs don't have wings; and even if they did, that wouldn't mean they could fly. Even one false premise makes it unsound - a sound argument must have both valid logic and all true premises. Then, and only then, can we say with certainty that the conclusion necessarily follows.

Here is an example of an argument that is not valid:

Jeff Sparks is a history buff.
Jeff Sparks likes Mexican food.
Therefore, Jeff Sparks loves baseball.

The premises are true - I am a history buff, and I love Mexican food. But the conclusion that I like baseball has no logical connection with these things. Therefore, the argument is invalid - even if the premises were both true, that wouldn't mean the conclusion is true. I do like baseball, but my love of history and Mexican food doesn't establish it. I could just as easily have concluded "Therefore, Jeff Sparks hates baseball," which is false. An invalid argument could have either a true or a false conclusion. It could go either way, which makes it different from a valid argument, where a conclusion necessarily follows from the premises being true.

Here is an example of a "sound" argument, as that word is used by philosophers:

All spaniels are dogs.
All dogs are animals.
Therefore, all spaniels are animals.

The argument is valid, and the premises are true. Therefore, the conclusion must be true. That's what philosophers mean by "sound," as contrasted with what they mean by "valid."

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