Wholly Hypothetical Syllogisms
نویسندگان
چکیده
In antiquity we encounter a distinction of two types of hypothetical syllogisms. One type are the 'mixed hypothetical syllogisms'. The other type is the one to which the present paper is devoted. These arguments went by the name of 'wholly hypothetical syllogisms'. They were thought to make up a self-contained system of valid arguments. Their paradigm case consists of two conditionals as premisses, and a third as conclusion. Their presentation, either schematically or by example, varies in different authors. For instance, we find 'If (it is) A, (it is) B; if (it is) B, (it is) C; therefore, if (it is) A, (it is) C'. The main contentious point about these arguments is what the ancients thought their logical form was. Are A, B, C schematic letters for terms or propositions? Is 'is', where it occurs, predicative, existential, or veridical? That is, should 'A ?att' be translated as 'it is an A', 'A exists', 'As exist' or 'It is true/the case that A'? If A, B, C are term letters, and 'is' is predicative, are the conditionals quantified propositions or do they contain designators? If one cannot answer these questions, one can hardly claim to know what sort of arguments the wholly hypothetical syllogisms were. In fact, all the above-mentioned possibilities have been taken to describe them correctly. In this paper I argue that it would be mistaken to assume that in antiquity there was one prevalent understanding of the logical form of these arguments even if the ancients thought they were all taLking about the same kind of argument. Rather, there was a complex development in their understanding, starting from a term-logical conception and leading to a propositional-logical one. I trace this development from Aristotle to Philoponus and set out the deductive system on which the logic of the wholly hypothetical syllogisms was grounded. At the close of antiquity we encounter a distinction of two types of hypothetical syllogisms. One type, sometimes called 'mixed hypothetical syllogisms', contain a mixture of complex and simple premisses; they encompass e.g. arguments of the kind modus ponens.' The other type is the one to which the present paper is devoted. These arguments variously went by the names of 'syllogisms by analogy', 'hypothetical syllogisms', 'wholly hypothetical syllogisms', 'wholly hypothetical arguments', ' "through three" arguments', "'through three" syllogisms'. They were thought to make up a self-contained system of syllogisms or valid arguments. C Koninklijke Brill NV, Leiden, 2000 Phronesis XLV12 Accepted September 1999 'I discuss this type of arguments and their system in Stoic philosophy in my 'Stoic syllogistic', Oxford Studies in Ancient Philosophy 1996, 133-92.
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