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4. Validity

 

Wireless Philosophy, Fundamentals, 7:07. Original title: CRITICAL THINKING - Fundamentals: Validity [HD]

Summary​

Paul Henne (Duke University) presents validity, the central tool for evaluating deductive arguments.

A technical term, not the everyday one​

We have all heard "that's a valid point" or "that's valid, but…". In everyday use, "valid" means roughly "good point" or "that statement is true". The philosophical notion is a different thing altogether, and applies to whole arguments: an argument is valid or invalid, while validity is not a property of statements at all.

The definition​

An argument is valid if and only if the truth of its premises guarantees the truth of its conclusion.

In other words, it is impossible for a valid argument to have all true premises unless the conclusion is true as well. When an argument is valid in this sense, we say the premises entail the conclusion.

Notice how conditional this is. Calling an argument valid says nothing about whether the premises or the conclusion are actually true, and nothing about whether the argument is good in general.

The examples​

The first is valid, and its premises happen to be true:

Premise 1: All humans are mortal.
Premise 2: Iris Murdoch is a human.
Conclusion: Therefore, Iris Murdoch is mortal.

The next is equally valid with all false premises. If all humans were immortal and Iris Murdoch were one of them, she would necessarily be immortal:

Premise 1: All humans are immortal.
Premise 2: Iris Murdoch is a human.
Conclusion: Therefore, Iris Murdoch is immortal.

Validity does not even require knowing whether the premises are true. We have no idea whether aliens exist, let alone whether they speak English, and the argument is valid anyway:

Premise 1: All aliens speak English.
Premise 2: Splock is an alien.
Conclusion: Therefore, Splock speaks English.

Henne pushes this to the limit with undefined terms, which still yield a valid argument:

Premise 1: All sliff are splat.
Premise 2: Sniff is a sliff.
Conclusion: Therefore, Sniff is a splat.

An invalid argument is one where the truth of the premises does not entail the truth of the conclusion:

Premise 1: All dogs have fur.
Premise 2: Claire has a lot of fur.
Conclusion: Therefore, Claire is a dog.

Every premise could be true while the conclusion is false, because cats have a lot of fur too.

Why validity matters at all​

If the truth of the premises is irrelevant to validity, why care about it? The short answer is that validity tells us whether an argument obeys the valid inference rules, the laws of deductive logic. It is how we make sure that the inferential steps in an argument are good ones to make.

The video closes with an exercise: is the following argument valid or invalid?

Premise 1: All fruit is a chair.
Premise 2: Square is a chair.
Conclusion: Therefore, Square is a fruit.

Key takeaway​

Validity is about the relationship between premises and conclusion, never about their truth. That is why arguments with false, unknown, or even meaningless premises can be perfectly valid, and why an argument with true premises and a true conclusion can still be invalid.