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Sunday, 29 September 2013

Leibniz, Aristotle and the unsubstantial sensible

This week, in my metaphysics course, I have been steadily contrasting an Aristotelian and a Leibnizian world. In fact, they could be seen as two answers to the charge Aristotle (Metaphysics, M, 4) makes of Plato (no matter whether it is a fair one) of giving up the impermanent within the realm of the sensible. Plato, as the charge goes, has accepted a Heraclitean view of the sensible that makes it accidental, transient, flowing and harboring no more than contingencies. Aristotle's attempt was to find necessities (and substantialities) within the sensible. (In Kit Fine's taxonomy of necessities, such necessary connections would be metaphysical or natural - and Aristotle is not clear they should all be uncoverable a priori, even though we normally take them to be.) Leibniz's take, on the other hand, was to take substantiality to be a mathesis universalis - substances are no more than their discernible properties and those are no more than what boils down to the substances. In Aristotle there are genuinely concrete, sensible substances while in Leibniz the model is mathematical: each substance has something impermanent to it. As a consequence, the indiscernibles are identical and the identicals are indiscernible. There is no identity (or substantiality) apart from the entity's property (apart from what occurs to the entity). In other words, Leibniz answer to Plato would be: infinite mathematics brings the sensible to the realm of the intelligible through the notion of virtual - what is unknown to finite minds that cannot take everything into consideration and yet part of what makes the world as a whole what it is. In both cases, the Heraclitean character of the sensible is exorcized.

But I wonder whether the two approaches map into Williamson's distinctions between necessitism and contingentism in ontology. (Would Aristotle be the former while Leibniz the latter?)

In any case, we can think of the way process philosophy (being, I believe, Leibnizian in spirit) thinks of the sensible in terms of an approach to infinity. The infinite is thought as the realm of the open, where there is no room for clausure - just enough room for series of captures. And then, a different infinite means a different virtual, a different conception of what the world is, of what dependence is.

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