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Wednesday, 5 September 2012

Contingency and the plurality of logics

I´ve been rehearsing, at least since Beirut, the idea that there is a link between contingency and some kind of dependence. The link can be presented in terms of the notion of virtual that Deleuze uses to understand Leibniz´s notion of contingency in Le Pli (see previous post here). A judgment is virtual if its truth depends on the rest of the world - and not if it depends on an infinite series. So, "Adam sins", Leibniz´s example, is true due to Adam, to sin but also to the Eden, to the serpent, to whatever else is there in the world. The stronger way to understand this - which I take to be the most interesting - is that contingent truths are truths which truth-maker is the whole world. In contrast, necessary truths display some degree of independence: their truth-makers is less the whole world. We can maybe think of logical truths as independent of all circumstances (like Kant wished ethical necessity to be). We don´t need to appeal to the whole world to find out that 2 + 2 is 4, the demonstration can be done in a number of steps somehow smaller than the cardinality of the world. I said somehow because, for Leibniz, we are dealing with infinities in both cases, as Deleuze stresses.

This account of contingency - that is occasionalist if we take occasionalism as the thesis that all relations need mediators - is certainly Couturatian enough. The difference between contingency and necessity is a difference of degree, as Couturat understood, such that God could contemplate contingent truths in the same way as we contemplate necessary ones. One could then proceed to defend a process philosophy by claiming that there is no such thing as necessary truths - as there is nothing that is independent from the rest of the world (no furniture of reality beyond processes). Necessary truths would be (more) independent from the rest of the world. If it is a matter of degree, we can think of them as primary folds that hold the weight of subsequent folds but have an independent shape.

This account of necessity makes me think of logical truths (assuming some of them are necessary) in the context of the plurality of logics. Surely, if something is logically true, it is independent of other features of this possible world. This world is made possible by the logic that makes something true independent of the other features of this world. In other words, this is a world that belongs to a constellation of possible worlds associated to a logic. Now, the problem posed by the plurality of logic - the crucial concern of universal logic as I take it - is the decision problem. In fact, this is a central problem posed for all sorts of pluralities (the plurality of fruits, as much as the plurality of geometries). I take it is a contingent matter of fact that this world belongs to such a constellation (and not another). It is contingent that logic L is valid in this world - and not logic L´. What necessary truth could determine that this world is, say, classical and not paraconsistent? So, it is contingent and this shows up in discussions about dialeteism (see Priest or Bobenrieth, for example).

But now we can think further of this contingency. If a contingent truth is one that depends on the rest of the world, we can say that the classicality (say) of this world depends on everything in it. This reminds us of the Quinean sphere: it is as if the choice of a logic is independent from the rest of the world only if we make it so by fiat. But we can go perhaps further and say that the logic associated to each world (those that are possible in our logical standard and those that are impossible in our logical standard - but possible in another) depends on all the other worlds, on the way these constellations of possible worlds are assembled together. Perhaps when we ask questions about the plurality of logics we point towards contingencies that lie beyond a single world.

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