Notes no. 3: Validity, Truth and Knowledge

Validity, Truth, Knowledge, and the Good Life
Keith Burgess-Jackson
Validity is a property (feature, characteristic, attribute) of argument forms. Some argument forms have it; some do not. Valid argument forms are those that are truth-preserving. This means that if you put truths into them (as premises), you will get a truth out of them (as the conclusion). If we did not value truth, we would not value valid-ity. Like currency, validity has only extrinsic (instrumental) value. It is valued as a means to something else we value (namely, truth) but not as an end in itself. This is not to say that validity has no value; it is to specify the type of value it has. (Some things, such as friend-ship and knowledge, are valued both intrinsically and extrinsically.)
By definition, no valid argument has both true premises and a false conclusion. (If it did, it would not be truth-preserving.) Think of it this way. It is logically impossible (i.e., ruled out by definition) for an argument to have all three of the following properties:
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| is valid |
| has true premises |
| has a false conclusion |
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Suppose a given argument is known to have two of these properties. Then it can be inferred immediately that it lacks the third. There are three cases:
1. If a valid argument has true premises, then it does not have a false conclusion (i.e., it has a true conclusion).
2. If a valid argument has a false conclusion, then it does not have true premises (i.e., it has at least one false prem-ise).
3. If an argument has true premises and a false conclusion, then it is not valid (i.e., it is invalid).
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We can go further. Suppose a given argument is known to have one of these properties. Then it can be inferred immediately that it lacks at least one of the others. There are three cases:
4. If an argument is valid, then either (a) it has a false premise or (b) it has a true conclusion (or both).
5. If an argument has true premises, then either (a) it is in-valid or (b) it has a true conclusion (or both).
6. If an argument has a false conclusion, then either (a) it is invalid or (b) it has a false premise (or both).
What this shows is that if you remember the definition of “validity,” you will be in a position to draw inferences about arguments from what you know about them—even if you know very little. Inference, whether inductive or deductive, mediate or immediate, is a means of extending knowledge. Because we value knowledge, we value truth (which is essential to it). Because we value truth, we value validity (which is a means to it). Validity turns out to be the key to knowl-edge! But wait; it gets better. If knowledge is essential to the good life, as the Greek philosopher Socrates implied when he said that the unexamined life is not worth living, then validity is the key to the good life. And you wondered why we were studying validity! 2