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Hypokeimenon and the concreta

Thinking about hypokeimenon in Aristotle and the need for something that hooks whatever exists to something concrete (a material aitia). Substance - as opposed to, say, actual entities - is not enough to hook anything to concreta as abstract things can be substantial (as they are for Aristotle) and mere permanence under variations in time is not enough to make anything a proper concrete object (Leibniz had substances without proper concrete objects). In fact, I believe hypokeimenon should be thought of as something that breaks the Leibniz's law. It should in fact enable indiscernibles to be different. I would venture that a conception of substrata that is compatible with Leibniz's law (specifically with the identity of indiscernibles) is not doing justice to what substrata should be. The appeal to matter as an hypokeimenon (mentioned by Aristotle himself in the Book Alpha) is an attempt to appeal directly to what is concrete. If properly understood, it enables indiscernible to be different because matter cannot be translated into properties, the material constitution of something is not a property (and this is why Kripke takes "this table" to be necessarily tied to its material constitution - its material constitution is not a description that can be different in a different possible world, in another possible world the table has to have the same material hypokeimenon).

Other accounts of the hypikeimenon seem to do the same trick. Duns Scotus' haecceitas appeals to demonstratives while a Kripkean take would appeal to proper names. In both cases, it is clear that only among concreta there are particulars that could have logical demonstratives and logical proper names (in the sense that these things would not be explained away by descriptions or bundles of properties). Leibniz, to be sure, would have Adam, for example, as no more than an abbreviation for a collection of properties - including, famously, being a sinner. Proper names and demonstratives are part of a vocabulary that doesn't make sense outside the realm of concreta - the realm of being situated, of being indexed, of being in a place with respect to whatever else exists. This is the realm where to be is to meet whatever else there is. Situation is crucially concrete, it is an affair of objects and ultimately alien to properties as such (the time of objects is irrevocably A-ist, while properties, in that sense, can have a temporality that is reduced to a B-series).

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