Summary
Plato's sophisms from the dialogue "Euthydemos" discussed in the present paper can be divided into two subject groups: one relating to the problem of omniscience, the other one dealing with the question of family relations. Both are, however, united by the same class feature, that is, the argumentation technique, which in this case consists in changing the predicate volume of the initial assertion by eliminating or adding certain attributes. If a part of the predicate is eliminated, we may say that the predicate is generalized; if, on the contrary, some information is added to the predicate, then it is specialized.
To illustrate this point, we may turn to one of the sophisms relating to omniscience (293b-d):
If you know something, then you have knowledge.
If you do not know something, then you do not have knowledge.
However, if someone has knowledge, then it is impossible for him not to have knowledge.
Therefore you know everything.
In this case in the first two assertions the predicate is generalized. If we omit the object "something" from the assertion "You know something", it results in the assertion "You know" (or "You have knowledge"); if we omit the object "something" from the assertion "You do not know something", then we shall produce the assertion " You do not know" (or "You do not have knowledge"). This describes the main principle on which all the sophisms we have singled out as a special class is based.
As is illustrated below, the possibility of solving these sophisms is based on a simple rule, derived from the assertion term distribution table; that is, any (un)extended term may be generalized and any unextended term may be specialized. In the sophisms which are being discussed here only the predicate is being manipulated with; consequently, the rule in question may be reformulated as follows: In assertive statements the predicate may be generalized and in negative statements the predicate may be specialized. Then, if we return to the sophism relating to omniscience, we shall find that the first argument is correct and the second one is incorrect, as in this latter case, a negative predicate has been specialized.
The consistency, with which the sophists Euthydemos and Dionysodoros use the method of changing the predicate volume, leads us to the assumption that they are quite deliberate in doing so; moreover, it seems plausible that the sophists themselves may have had a certain idea of the rules restricting the use of these methods in assertive and negative statements. It is probable that certain pre-Aristotelian "protosyllogistics" which did not yet know the distinction between the general and the particular but which already distinguished between assertive and negative statements and subject and predicate, may have been the theoretical foundation of conclusions of this type.