Remarks

Protagroas: Whatever appears to be the case to anyone is the case.

Aristotle: No one who is in Lybia, having dreamed that he was in Athens, would go to the Odeon. 

Remarks

Aristotle’s statement (from Metaphysics 1010β10-11) serves as a response to some consequences that follow from Protagoras’ above doctrine which itself issues from his more famous dictum that “man is the measure of all things”. One such consequence is as follows: Suppose that whatever appears to be the case to anyone is the case. Then anything that appears (in general) to be the case must be true. Therefore, all appearances must be true.

The problem with this conclusion is that it leads to various practical absurdities. Suppose that all appearances are true. Now imagine that you are in Lybia and that you dream that you are in Athens. Following the doctrine of Protagoras, since all appearances are true, and since an appearance of Athens has been presented in your dream, it follows that you must be in Athens. So upon waking, do you then go to the Odeon (theater of Athens)? Of course not. The simple reason is that you have strong practical reasons for believing that the dream was not real and that you are in fact not in Athens but rather in Lybia. But if you are not in Athens, then the dream appearance must be false. Therefore, the belief that all appearances are true must be false.

Such a refutation may be termed “disproof by practical refutation”. One assumes that a purported statement is true, and then demonstrates the practical absurdities that follow from it, thereby providing reasonable grounds for its rejection. It is similar to another method often used in mathematics called “disproof by contradiction”. With this method, one assumes that a statement is true and then demonstrates the logical contradiction(s) that follow from it, indicating the falsity of that statement. 

The difference between these two methods may be illustrated as follows. Suppose someone states that “truth does not exist”. A disproof by contradiction would proceed as follows: Suppose that truth does not exist. Then if the statement is true, the statement refutes (or contradicts) itself, since some truth does exist, viz., the truth of the statement that “truth does not exist”. Hence, the statement must be false.

In contrast, a disproof by practical refutation would proceed as follows: Suppose that truth does not exist. Then it is not true that “fire burns”. So you can step into a fire without fear of being burned. So try it… 

Obviously no sane person would follow through will such a belief. As we all know, fire burns. Hence, although the opponent may not concede (in words) to the truth of the statement that “fire burns”, they nonetheless do so by way of practical (in)action. Their refusal to step into a burning fire is sufficient to show that they believe that at least one statement is in fact true, which thus serves to refute the supposition.

Of course, a disproof by refutation has less demonstrative force than disproof by contradiction. The latter shows a statement to be false on logical grounds, the former on practical grounds. The problem, however, is that certain beliefs (as above) may serve to distort reality or be self-contradictory. The laws of logic may be abandoned so that any attempt to refute such views on logical grounds will ultimately fail. In such cases, one must have recourse to practical refutation.

Practical refutation serves as an example of the ancient dictum that word and deed ought to be in accord. To profess a belief and to then refuse to act in accordance with it was seen if not as a necessary, then at least as a sufficient condition for its rejection.