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Protagoras

Duo Logoi

"Logos" is greek for speech  ("logoi" is the plural).  A logos in this sense is a position or argument that one brings to the issue.  Plato and Aristotle refer to "eristic" debates in which the goal was to win a verbal victory, rather than to find the truth. Some people today regard trial lawyers and politicians as playing such high stakes verbal games.  As a sophist, Protagoras was in the business of teaching young people the techniques of winning eristic debates.  Thus his claim;

"There are two sides to every question."

is taken by Aristotle to mean that no matter what someone holds, the clever debater can produce an opposite argument (enthymeme) and give an opposing speech (logoi).  Aristotle gives several examples of such verbal manipulations, which came to be called "sophisms."

"in rhetoric a spurious enthymeme may be based on the confusion of some particular probability with absolute probability. Now no particular probability is universally probable: as Agathon says, One might perchance say that was probable -- That things improbable oft will hap to men. For what is improbable does happen, and therefore it is probable that improbable things will happen. Granted this, one might argue that "what is improbable is probable." But this is not true absolutely. As, in eristic, the imposture comes from not adding any clause specifying relationship or reference or manner; so here it arises because the probability in question is not general but specific. It is of this line of argument that Corax's Art of Rhetoricis is composed. If the accused is not open to the charge -- for instance if a weakling be tried for violent assault -- the defense is that he was not likely to do such a thing. But if he is open to the charge -- i.e. if he is a strongman -- the defence is still that he was not likely to do such a thing, since he could be sure that people would think he was likely to do it. And so with any other charge: the accused must be either open or not open to it: there is in either case an appearance of probable innocence, but whereas in the latter case the probability is genuine, in the former it can only be asserted in the special sense mentioned. This sort of argument illustrates what is meant by making the worse argument seem the better. Hence people were right in objecting to the training Protagoras undertook to give them. It was a fraud; the probability it handled was not genuine but spurious, and has a place in no art except Rhetoric and Eristic."  Aristotle, Rhetoric, Book II, Chapter 24 [1401a]

Aristotle uses two examples of sophistic logoi here. The first sophism uses an ambiguity in uses of the word "probable" to reach an absurd conclusion.  Anything at all that happens, however rare, has some degree of probability.  Thus we can say that there is a degree of probability that even the most improbable things will happen.  So far this is clear so long as we keep the point that improbable things have a low degree of probability; in other words, improbable things are improbable.  But the sophist blurs the point about degree in moving quickly to the argument that since there is a probability that improbable things will happen, it follows that "what is improbable is probable."   If you think such sophisms are impractical, just analyze carefully the logoi of politicians, especially in matters like war and money.

The second case involves a sort of trial argument.  Both cases exemplify types of sophisms in which the weaker argument is made to appear to be the stronger argument.  Aristotle regards such eristic methods as spurious and frauds.  He identifies Protagoras as an originator and teacher of such sophisms. 

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