Systematic Philosophy

to know what can be known

What Is Transparent Validity?

When assessing arguments, philosophers often talk about validity. Validity is important. But more important than validity is a particular species of validity: transparent validity. Let’s talk about that.

What transparent validity is

Transparent validity is very similar to validity. To say that an argument is “valid” is to say that in every case where that argument represents a conclusion as being entailed by one or more steps, those steps actually do entail that conclusion. To say that an argument is “transparently valid” is to say that in every case where that argument represents a conclusion as being entailed by one or more steps, those steps immediately entail that conclusion.

From the definitions of “validity” and “transparent validity”, it follows that every argument that is transparently valid is also valid. The reverse is not true, however. Some arguments that are valid are not transparently valid. Let’s call any argument that is valid but not transparently valid “opaquely valid”.

How to test for transparent validity

To test for transparent validity, you need to be able to test for immediate entailment. This means that you need to know how to tell whether some collection of propositions immediately entails some specific proposition. If you know how to test for immediate entailment, testing for transparent validity is a straightforward process.

The process is as follows. Take the argument in question. Look at its first conclusion. Examine the steps the argument says are supposed to entail that conclusion. Merely by considering those steps and the concept of immediate entailment, can you see that those steps immediately entail the conclusion in question? If not, the argument is not transparently valid. On the other hand, if you can see that the steps immediately entail the conclusion, then go on to the next conclusion. Repeat the process. If you make it through the argument and find immediate entailments in every case, the argument is transparently valid.

Some examples

Consider the following argument:

  1. Every thing loves my baby.
  2. My baby does not love any thing but me.
  3. Therefore, I am my baby. [1,2]

Surprisingly, this argument is valid! Steps 1 and 2 really do entail step 3. But while it is valid, it is not transparently valid. Consider only steps 1 and 2 and the concept of immediate entailment. Do not derive any further propositions. On this basis alone, can we see that steps 1 and 2 together immediately entail step 3? The answer is no. To get from steps 1 and 2 to the final conclusion, we have to derive at least one further proposition.

Now consider this:

  1. Every thing loves my baby.
  2. Therefore, my baby loves my baby. [1]
  3. My baby does not love any thing but me.
  4. Therefore, I am my baby. [2,3]

What about this argument? Consider only steps 1 and 2 and the concept of immediate entailment. Do not derive any further propositions. Merely on that basis, can we see that step 1 immediately entails step 2? The answer is yes. So step 1 immediately entails step 2. Now consider only steps 2, 3 and 4 and the concept of immediate entailment. Do not derive any further propositions. Merely on that basis can we see that steps 2 and 3 together immediately entail step 4? Again the answer is yes. So steps 2 and 3 immediately entail step 4. These are all of the entailments the argument represents. It follows that in every case where the argument represents steps as entailing a conclusion, those steps immediately entail the relevant conclusion. It follows that the argument is transparently valid.

Your mind is blown.

The second argument above is transparently valid. The first is not. For other, more striking examples, consider almost any argument whose premises are the axioms of arithmetic, which does not draw any intermediate conclusions and whose final conclusion is some interesting fact about numbers that follows from the axioms. Such an argument will be valid but not transparently valid. Now fill in all of the missing intermediate conclusions. The argument will become transparently valid.

Haggling about the details

Some people will look at the first argument above and declare that they can see that the final conclusion follows without deriving any intermediate conclusions. What do we say about that? First, it matters whether such people are right. If they are wrong, then the example is just fine as it stands. If they are right, then it matters whether the same is true for everyone. If some people can see that the final conclusion follows without deriving any intermediate conclusions but others can’t, then we should say that the first argument above is transparently valid to some people and not transparently valid to others. If it turns out that everyone can see, merely by considering the first two steps and the concept of immediate entailment, that the first two steps entail the third, then the example is simply a bad example.

Whichever way any particular example comes out, though, this entire discussion should make it clear what it is for an argument to be transparently valid. That was our original purpose here.

Generating transparent validity

There is a simply expressible recipe for making transparently valid arguments opaque or making opaquely valid arguments transparent. To make a transparently valid argument into an opaquely valid one, just delete one or more of the argument’s intermediate conclusions. This will usually work. To render an opaquely valid argument transparent, simply add the right intermediate conclusions back in.

Transparent validity and argument quality

Transparent validity is one of the two qualities that must be checked when assessing an argument. Furthermore, it is always possible to check an argument for transparent validity. Thus transparent validity is extremely important. Gaining the ability to check for transparent validity is absolutely essential.

In terms of necessary and sufficient conditions, transparent validity is necessary for an argument to be good, but is not sufficient on its own to make an argument good. In this regard, transparent validity is just like validity.

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Written by Geoff Anders

May 23, 2011 at 4:38 pm

Posted in Uncategorized

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