In this paper I shall defend the traditional claim that Aristotle's nonsubstantial particulars discussed in the second chapter of the Categories are unsharable particulars against G. E. L. Owen's claim that they are sharable universals. I shall proceed by presenting first a sketch of the traditional position that makes explicit why it holds that non-substantial particulars are unsharable particulars. Secondly, I shall sketch Owen's position and recount how it differs in certain important respects from the traditional position. Thirdly, I shall (...) present some of my own considerations that I believe support the traditional position at the expense of Owen's position. Finally, I shall offer what I take to be the primary reason Aristotle was committed to the existence of such odd items as non-substantial particulars. (shrink)

I argue there are two ways predication relations can hold according to the Categories: they can hold directly or they can hold mediately. The distinction between direct and mediated predication is a distinction between whether or not a given prediction fact holds in virtue of another predication fact’s holding. We can tell Aristotle endorses this distinction from multiple places in the text where he licenses an inference from one predication fact’s holding to another predication fact’s holding. The best explanation for (...) each such inference is that he takes some predication facts to be mediated by others. Once the distinction between direct and mediated predication has been explained and argued for, I show how it can help solve a persistent problem for the traditional view of non-substantial particulars in the Categories—that is, the view that non-substantial particulars are particular in the sense of being non-recurrent. Along with vindicating the traditional view, the direct/mediated predication distinction gives us a distinctive way of understanding what it is for something to be recurrent (or non-recurrent) as well as a better understanding of Aristotle’s broader commitments in the Categories as a whole. (shrink)

"However that may be, Aristotelian syllogistic concerned itself exclusively with monadic predicates. Hence it could not begin to investigate multiple quantification. And that is why it never got very far. None the less, the underlying grammar of Aristotle's logic did not in itself..