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Leibniz and Meillassoux after finitude

Couturat famously discloses the principle of reason as the kernel of Leibniz's metaphysics. Couturat formulates the principle simply as: all truths are analytic (or rather, in pre-Fregean terms prevalent in Leibniz's time, all truths are such that the predicate is contained in the subject). For Couturat, the principle of reason derives the refusal of external relations and prefigures the appeal to monads as connected while windowless. Monads, taken as perdurantist substances (not fully present at any moment in time), are identical if indiscernible and indiscernible if identical. A mere analysis of their properties is enough to find out what are they ever going to do. But Leibniz, clearly, wanted to make room for contingency. How something (like a true statement) be analytic and not-necessary (i.e. contingent)? If there is any contingent true, this needs to be elucidated. And Leibniz makes use of his usual manoeuvre of resorting to a distinction between the finite and the infinite. While some statements require no more than a finite analysis to disclose the internal relation between its terms, others - those concerning contingencies - are of infinite complexity and only operations involving infinity (that God could perform) can reveal their truth. In other words, every truth is a priori, but only for those who can deal with infinite complexity. Contingency is somehow explained away by infinite complexity - the difference between what is contingent and what is not (what is strictly necessary, in the sense of logical necessity or logical truth) is a difference concerning the finite and the infinite. Contingent truths can be unveiled a priori by considering the harmony
between all monads, considering what makes the actual world actual - its perfection.

Now, Meillassoux also appeals to infinity, not to dispel contingency but rather to dispel what he takes to be the appearance of necessity. The appearance of necessity he wants to dispel is that of the laws of nature - they seem to be good predictors but they are so only because we fail to bear in mind that they are one among an infinite number of alternatives and we cannot use the evidence to weigh their probability. Meillassoux thinks that we are dealing with infinite many alternative worlds and that precludes us to say that the laws are predictive either because they are necessary or because there is a cosmic coincidence. We cannot take the coincidence to be cosmic exactly because of the infinite complexity involved in the class of possible alternatives. He wants us to conclude that this infinite complexity signals the contingency of all things (or, better, the facticity of most things - except for the facticity itself which is necessary). For him, going after finitude is going towards contingency and not, as Leibniz would have, dispelling it or explaining it away. We can even attempt at formulate Meillassoux's principle of unreason in terms akin to those of Couturat: all truths are synthetic. And we can add that they are so because they involve and infinite complexity - that of facticity.

This Leibniz-Couturat thesis on contingency is very interesting: contingency is just a matter of the size of the network connecting subject and predicate. If the network involves everything (the whole series of the actual world) than it is infinite and there is contingency. Otherwise, there is a necessary connection that everyone can see (every finite mind). Yes, all connections are there, the issue is just who can pick it up. Depending on the connections that we can pick up, our life is different (the issue of salvation is brought up here). Now, if we generalise the difference between an infinite mind (who can seize an infinite network connecting the two terms) and a finite mind, we can say that different minds capture different networks as necessary (and fail to capture the others, left out as contingent). I suspect there is something interesting here concerning the nature of contingency.


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