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Extra resources for Extensions As Representative Objects In Frege's Logic
That is to say, Theophrastus had perhaps taken an important step towards developing a sentential logic. 5 7 He claimed that the Neo-Peripatetic commentators had not restricted the combinations of subject terms that can appear in hypothetical syllogisms, so that the most general form of the major premiss in a substitutional syllogism might be 'If A is B, then C is D', in which the subject terms are different singulars. Furthermore, he noted that, in scholia to Ammonius's commentary on the Prior Analytics, there is an example of a totally hypothetical syllogism with differing singular subject terms: 'If the sun is over the earth, it is day; if mood of the third figure rather than the second; in any case, the resemblance to the categorical syllogisms is clear.
47 48 THE ARISTOTELIAN BACKGROUND 27 the work of his followers and associates to discover exactly how this development proceeded-and especially to the work of his immediate successor Theophrastus, whose name the later, NeoPeripatetic commentators often associated with the subject. But, as I mentioned in the introduction to this chapter, this work is lost in its original form. In order to chart the development of hypothetical syllogistic in the early Peripatos beyond Aristotle, then, it is necessary to turn instead to the reports of the commentators themselves.
I mean, for example, that B is large of necessity given that A is white and B is large of necessity given that A is not white. For, when this particular thing-the B---is large of necessity given that that particular thing-the A-is white, but C is not white given that B is large, then it is necessary that, if A is white, C is not white. And, when it is necessary that the latter of two things is the case given that the former is the case, then it is necessary that the former is not the case given that the latter is not the case.