Ideas and Ideals

The article is about Meillassoux’s ideas regarding mathematics. According to Kant, our cognitive abilities are fundamentally limited. We cannot know what is beyond our cognitive abilities. There is no guarantee that the knowledge of a thing in itself does not require the abilities, that a man simply does not have. In addition, according to Kant, mathematics requires intuition. Meillassoux argues that mathematics offers the opportunity to explore the properties of things in themselves. He argues that the laws of logic and physics are contingent, while the laws of mathematics are reliable. The article states that the laws of mathematics cannot be reliable while of the laws of logic are contingent. In addition, the laws of physics are essentially connected with those of mathematics, and we should carefully clear up the question of the extent to which they can be contingent with the same laws of mathematics. Hilbert does not accidentally introduce the idea of ​​a predetermined harmony between mathematics and physics, and Wigner points to this also. We cannot assume that mathematics provides an outlet to things in themselves, and physics is a strictly empirical science that studies only contingency. It is necessary to distinguish in physics the invariant and variable parts for a given mathematics. In addition, it is pointed out that modern mathematics does not always set itself the goal of describing the world, and even more so the thing in itself: a significant part of it is engaged in the construction of models that can describe the phenomenon under study only approximately. The issue of the ontology of Meillassoux’s mathematics is investigated and its proximity to modern Pythagoreanism is indicated. The conclusion states that modern formal mathematics overcomes Kant's limitations, but does not overcome transcendental limitations at all.