Systematic Philosophy

to know what can be known

What Is Validity?

In everyday speech, the word “valid” is often used to mean “good”, “reasonable” or “correct”. Throw all that away. In philosophy, “valid” is a technical term with a very specific meaning. And it doesn’t mean “good”, “reasonable” or “correct”.

What validity is

In philosophy, “validity” is a property of arguments. Every argument represents one or more conclusions as each being entailed by various steps in the argument. Now this representation can be correct or incorrect. An argument may say that step C is entailed by steps A and B, but steps A and B may or may not actually entail step C. To say that an argument is “valid” is to say that in every case where the argument represents a conclusion as being entailed by one or more steps, that conclusion actually is entailed by those steps.

More simply, to say that an argument is “valid” is just to say that all of the entailment relations the argument represents actually hold.

How to test for validity

To test for validity, you need to be able to test for entailment. That is to say, you need to know how to tell whether some collection of propositions entails some specific proposition. Once you know how to test for entailment, testing for validity is a straightforward process.

That process is as follows. Take the argument in question. Look at its first conclusion. Look at the steps the argument says are supposed to entail that conclusion. Do those steps actually entail the conclusion? If not, the argument is invalid. If so, go on to the next conclusion. Repeat this process. If you make it to the end and find that every represented entailment actually holds, the argument is valid.

Several examples

Let’s look at a few examples. Consider the following argument:

  1. All cats are animals.
  2. All animals are things.
  3. Therefore, all cats are things. [1,2]

This argument has just one conclusion: step 3. It represents step 3 as being entailed by steps 1 and 2. Do steps 1 and 2 actually entail step 3? If so, the argument is valid. If not, the argument is invalid.  Of course, steps 1 and 2 do entail step 3. So the argument is valid.

Next, consider this argument:

  1. All cats are animals.
  2. All dogs are animals.
  3. Therefore, all cats are dogs. [1,2]

This argument is like the first in several ways. It has just one conclusion: step 3. It represents that conclusion as being entailed by steps 1 and 2. But unlike the first argument, in this case steps 1 and 2 do not actually entail step 3. It follows that this argument is invalid.

Now consider this:

  1. All cows can fly.
  2. All things that can fly are triangular.
  3. Therefore, all cows are triangular. [1,2]

As before, this argument has only one conclusion: step 3. It represents this conclusion as being entailed by steps 1 and 2. Do steps 1 and 2 entail step 3? The answer is yes, so the argument is valid. This does not mean that the argument is good. On the contrary, the argument is terrible. How can a terrible argument be valid? Remember, as we are using the term “valid”, validity and goodness are not the same. What matters for validity is only whether the represented entailments actually hold. In this case, the only represented entailment does hold, so the argument is valid.

 

Let’s consider a slightly more complex example:

  1. All cats are robots.
  2. No dogs are robots.
  3. Therefore, no dogs are cats. [1,2]
  4. If no dogs are cats, then all cats are fish.
  5. Therefore, all dogs are fish. [3,4]

This argument has two conclusions: step 3 and step 5. To assess it for validity, we start with the first conclusion, step 3. The argument represents step 3 as being entailed by steps 1 and 2. Do steps 1 and 2 actually entail step 3? The answer is yes. So far, so good. Now we move on to the next conclusion, step 5. The argument represents step 5 as being entailed by steps 3 and 4. Do these steps actually entail step 5? The answer is no. So the argument is invalid.

Finally, consider this example:

  1. Therefore, Santa Claus exists. [1]

Shockingly, according to our definition of “argument”, this is an argument. Is it a good argument? Clearly not. Is it valid? The argument represents only one entailment: step 1 entailing itself. Does that entailment hold? All propositions entail themselves, so the answer is yes. Thus the argument, despite being bad, is valid.

Validity and arguments

As we saw above, validity alone is not enough to make an argument good. Arguments can be both valid and bad. Still, there is some relation between validity and the quality of an argument. As we will see, every good argument is valid. This is because every good argument is transparently valid, and any argument that is “transparently valid” is also valid.

Next up: What is soundness?

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Written by Geoff Anders

May 20, 2011 at 11:36 pm

Posted in Uncategorized

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