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Published online by Cambridge University Press: 13 April 2010
In the Prior Analytics Aristotle examines syllogisms that contain apodeictic and problematic premisses, as well as combinations of these with assertoric premisses. Of these various syllogisms, it is the mixed apodeictic-assertoric type that has received the most attention. Aristotle discusses this type of syllogism in Prior Analytics I.ix–xii. In this paper I will deal primarily with these syllogisms, which I will henceforth refer to simply as ‘apodeictic’.
1 McCall, Storrs, Aristotle's Modal Syllogisms (Amsterdam: North Holland, 1963).Google Scholar
2 The distinction between the external and internal interpretations is of course extensionally equivalent to the well-known distinction between de dicto and de re necessity.
3 Of course there is much more that can be said about this distinction. But all that matters as far as my interpretation of Aristotle's modal logic is concerned is that he does distinguish these two types of property.
4 The ancients did not use the notion of inclusion in a sense in which things could be said to include themselves. However, there are equivalent formulations of these principles that refer instead to terms ‘belonging’ to one another: indeed, this is the terminology Aristotle himself uses in the Prior Analytics. And of course Aristotle allows terms to belong to themselves.
5 This was pointed out by R. J. Hankinson.