Thursday, October 29, 2009

Valid Inferences and Valid Arguments

I would like to distinguish between the form of a valid deduction and the validity of an argument. Formal logic deals with the forms of our inferences, and not the validity of our arguments. For example, appealing to the masses is not a valid form of argument, though it could be expressed as a valid syllogism. A valid argument must have a valid logical form; or, at least, it must be expressible in such a form. But having a valid logical form is not enough.

Admittedly, I haven't thought about this distinction before, and I would not be surprised if I suddenly reversed or qualified my position.

This might be better discussed by focusing on examples of logical fallacies.


Example 1: Begging the Question

1) If X, then ~~X
2) X
3) ~~X

This is begging the question by any account. Yet, it is a valid syllogism.


Example 2: Appeal to the Masses


This is also a logical fallacy, but it can be expressed as a valid syllogism:

1) If everybody knows that X, then X.
2) Everybody knows that X
3) X.

The form is valid. However, the argument is fallacious.


Analysis

One might try to reject the distinction I'm making by noting that the logical form, while valid, involves necessarily false premises. In other words, it might be argued that the above syllogisms are not sound. Yet, it seems to me that all of the premises in the above syllogisms are plausibly true in at least some cases. Indeed, to reject the antecedent in Example 1 would be to reject the possibility of any logical argument, since the antecedent could be anything. And to reject the antecedent in Example 2 would be to reject the possibility of common knowledge. It thus appears that the arguments cannot be said to have false premises.


It might also be argued that, in Example 2, the conditional encapsulates the logical fallacy in question, because whenever we say "everybody knows that X," we are appealing to the masses. Yet, it is not the case that, whenever we use this expression, we are making an argument. We might just be observing a commonly known fact. And, if everybody does know that X, then X is true. So, it is not clear that the conditional is false or invalid in Example 2.

Thus, the distinction I am drawing seems plausible, at least.

Any thoughts?

This post edited for clarity on January 28, 2010.