Theophrastus on prosleptic syllogisms

Theophrastus, a student and successor of Aristotle, in addition to describing his master's logical system, also tried to reform and expand it. Furthermore, he introduced forms of argument that were either not mentioned at all in Aristotle's works or that Aristotle merely referred to in passing. One of these forms proposed by Theophrastus is prosleptic syllogisms. Although brief references to this type of argument can be found in Aristotle's Organon, the elaboration of these arguments and their specific naming is related to Theophrastus.This particular form of argument does not fit into Aristotle's  system. Of course, for some of these types of arguments, equivalents can be found among the moods of Aristotelian syllogism. But not all of them can be reduced to categorical syllogism. It seems that the discussion of prosleptic syllogisms is beginning a second-order logic and a discussion of the relationship between concepts and universals.Key words: Theophrastus, prosleptic proposition, prosleptic syllogism, second order logic