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Friday, 28 April 2017

Universal metaphysics - the Priest-Garcia-Cogburn approach

Alexandre Costa-Leite and I have been postulating a universal metaphysics that go hand in hand in the path open by universal logic. Such metaphysics doesn't stop anywhere short of the logically impossible for it is not tied to a logical system in particular. Rather, it considers all the different logics in order to take modal (and post-modal) notions such as necessity, causation and ground as indexed to a particular galaxy (a set of possible world corresponding to a logic). To be clear, universal metaphysics can take several forms; let's consider four:
a) It can take the form of a refusal of the great picture, and so there are no metaphysical conclusions that could encompass all galaxies at once. One could have metaphysical claims about each galaxy, but only in a contrastive manner and so the each-all inference would not hold - having metaphysical claims about each galaxy entails nothing concerning all the galaxies.
b) It can take the form of assuming one specific logic - say, the classical one - and consider that there are relevant arguments, maybe based on entrenchment, that would make this logic better than any other and the one to be preferred for a non-neutral but yet absolute and coherent set of metaphysical claims.
c) It can assume that metaphysical claims can be made about all galaxies and pay the price of contradiction - universal metaphysics would be incoherent, paradoxical; in this view, something consistent could be said about each specific galaxy, but nothing consistent could be said about all galaxies but still something paraconsistent could be said about all galaxies and we assume that contradictions don't undermine determinations.
d) It can simply deny the possibility of any metaphysics and derive an anti-metaphysical argument from the plurality of galaxies along the following lines: once logic is crucial for any metaphysical claim (because, for instance, one needs the space of possible worlds defined) and once there are many logics, then there is no ground for any metaphysical claim whatsoever. Universal metaphysics then become no metaphysics.

I used to understand these alternatives in terms akin to those presented by Kit Fine in his "Tense and Reality". There he primarily considers the relation between perspectives and reality as it appears in the problem of time in McTaggart. Fine considers four possibilities: the denial of the existence of time (which would be akin to alternative d), the denial that reality is absolute to claim that it is scattered, dependent on perspectives and encompassing no totality, what he calls perspectivism (akin to a), the denial that reality is neutral by assuming a presentist approach to tense according to which only what is now the case exists (akin to b) and the denial that reality is coherent and the assumption of what he calls fragmentalism where there are fragments of consistent reality that add up to a non-consitent über-reality (this is akin to c). The adoption of a universal metaphysics of the type c would involve the paradoxical conclusion that there are inconsitencies - or contradictions - in the world. Here, of course, one can just bite the bullet and say that we find contradictions because there they are.

Jon Cogburn, based on the work of Priest and Livingston, have developed the idea of a paradoxo-metaphysics. He presents it in his well-crafted Garcian Meditations with respect to the metaphysics espoused by Tristan Garcia. The general idea can be introduced considering a metaphysics that would entail that metaphysics is impossible - the task of metaphysics then could be constructed as that of giving a maximally general account of what reality is like such that metaphysics is impossible. The consequence could be to drop the ladder after climbing through it. But one could refuse such a move and this is indeed the gesture Priest does with respect to paradoxes such as Russell's: he embraces the paradoxical situation that a Russell set is both a member and not a member of the universe of sets. He then posits contradictions in the world (dialetheas). This is a first case of paradoxico-metaphysics. Cogburn goes on to show how this works in Garcia's metaphysics: Garcia embraces an allism, in Lewis terms, according to which everything is – it is sufficient to be determined, or to have a property, to be something. Now, the world most surely has properties and is determined, but it is not distinctively something. As Garcia holds that a contradictory determination is still a bona fide determination (a white and non-white surface is still determined because it cannot be a only-white surface, say), Cogburn feels inclined to ascribe him with a version of paradoxico-metaphysics. And he contrasts this position with that of Marcus Gabriel who denies the existence of the world - acting as if an alternative akin to a would be a best bet. Garcia, he argues, would rather go for a full-blooded paradoxical position akin to fragmentalism and to c.

Now, paradoxico-metaphysics opens a horizon for universal metaphysics. Cogburn puts it in terms of Priest's analysis of Russell's paradox according to which the main steps are Existence (or Being), Transcendence and Closure. The acceptance of the three premisses would entail a contradiction and, if the contradiction (i.e. the paradox) is welcomed, would entail a position akin to fragmentalism or c. Those are the full-blown paradoxico-metaphysical doctrines. Further, if Existence is denied to avoid the paradox, one is back to a position like a; one can also deny Transcendence to avoid contradiction and then argue for a position like b or deny Closure to also avoid contradiction and end up close to d. So it seems like Fine's categories more or less map into Priest's. And further his option for fragmentalism also goes in the direction of paradoxico-metaphysics.

But a number of questions concerning universal metaphysics remain. The most pressing ones relate to the way one is to go about, say, paradoxico-metaphysics. How should one count, relate or otherwise individuate contradictions? The common way to proceed is the same as in universal logic: to use a classical meta-logic. Could paradoxico-metaphysics provide an alternative to classical metametaphysics?

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