A new argument against mathematical Platonism

Ex nihilo nihil fit or from nothing nothing comes (Aristotle-Aquinas). Each truth having an ontological footprint must thus have a sufficient explanation. There are no brute facts in reality. Now, beyond a certain complexity threshold, mathematical truths aren’t provable (Gödel-Chaitin). But then it follows that mathematical truths have no ontological import. It's therefore not true that there exist mathematical abstract objects, so that we arrive at a new argument against mathematical Platonism.

Meillassoux on mathematics and the absolute

In his After Finitude Quentin Meillassoux aims to project unreason into the things themselves. He aims to establish that the ultimate truth about reality is that there are no reasons, no causes, no grounds and no explanations for anything. Everything exists or happens for no reason whatsoever. The absolute is pure hyperchaos. Moreover, he holds that mathematics is the proper language to describe reality as hyperchaos. But why would he think so? Isn't mathematics the science par excellence about the realm of a priori necessary truths? So, if reality is radically contingent, how then could mathematics be the proper science to describe it? As Meillassoux conceeds in After Finitude, he has indeed not yet convincingly deduced his Badiouian claim about mathematics as the true metaphysics of reality.

Now, in a paper of Peter Hallward entitled Anything is Possible: A Reading of Quentin Meillassoux's After Finitude we find a quite interesting passage about Meillassoux's quest for establishing mathematics as the language of the absolute: "Meillassoux admits that he has not worked out a full version of this deduction. [..] In a recent lecture, Meillassoux gave a [...] clue to the future development of [it] by insisting on the absolutely arbitrary, meaningless and contingent nature of mathematical signs qua signs (e.g. signs produced through pure replication or reiteration, indifferent to any sort of pattern or 'rhythm'). Perhaps an absolutely arbitrary discourse will be adequate to the absolutely contingent nature of things."

Is this focus on the signs of mathematics as being radically contingent a promising pathway to a convincing argument for Meillassoux's claim? This week I suddenly realized that there might be a more compelling argument available for Meillassoux. It can be found in a short piece that I wrote more than ten years ago (in Dutch). In it I argue that almost all mathematical truths are true for no reason whatsoever. But then, mathematics does indeed seem to be the proper science to describe reality as being a radical contingent hyperchaos. Here we appear to have the argument Meillassoux is looking for, i.e. an argument for the thesis that mathematics, and mathematics alone, is the proper language of the absolute.

An argument for a world-for-us epistemology

That the world appears exhaustively mathematizable, can be cashed out as argument for the claim that we only have access to the-world-for-us. Let me explain. Mathematics can be applied succesfully to the world. But why is this in fact the case? Why is the world so perfectly mathematizable? This asks for some kind of explanation. But how to explain this? On metaphysical realism, there does not seem to be a straightforward explanation (although some philosophers, such as Craig, have opted for a theistic solution). However, on a world-for-us epistemology the almost perfect applicability of mathematics to reality is no surprise. For if mathematics is just extended rigorous thought (which seems plausible to me), then it is no wonder at all that the world as it is thought by us (i.e., the-world-for-us) is inherently mathematical. In fact, on an epistemology according to which we can only access the-world-for-us the successful applicability of mathematics is simply something one would expect. Therefore it seems to me that the fact that the world appears exhaustively mathematizable increases the likelihood of a world-for-us epistemology. Clearly, it is what Meillassoux has dubbed 'correlationism' in his much discussed book After Finitude.