Pythagoreanism in modern philosophy of mathematics
Philosophy
DOI:
https://doi.org/10.17072/2078-7898/2021-4-528-540Keywords:
realism, Pythagoreanism, Aristotelianism, identity of being and thought, Q. Meillassoux, M. Tegmark, R. PenroseAbstract
There are two opposing approaches in the ontology of mathematics — realistic (mathematics does not depend on the human being) and constructivist (mathematical objects are created by mathematicians) ones. P. Benacerraf objected to the realistic approach by stating that mathematics is non-causal in nature and, accordingly, it is impossible to reach it from the physical world. The objection to constructivism is based solely on the idea of the effectiveness of mathematics in applied sciences. In the 20th century, the constructivist approach was prevailing. By the end of the century, this prevalence coincided with the general tendency: a skeptical attitude towards scientific knowledge in the philosophy of science. However, at the same time, science began to play a huge role in life. This inevitably led to the emergence of realistic ontologies. The philosophy of mathematics by Q. Meillassoux, M. Tegmark, R. Penrose represents a modern kind of realism. The paper deals with Meillassoux’s theory and arrives at a conclusion about its closeness to Pythagoreanism. Mathematical knowledge gives an opportunity to get out of the circle of correlationism, provided that mathematics is understood purely formally, not intuitively. The paper shows that logic and physics cannot be contingent if mathematics is reliable. The coincidence of mathematical structures with physical ones was previously called the «pre-established harmony between mathematics and physics». Now this is explained by the fact that the universe is organized according to mathematical laws. Thus, a new Pythagoreanism appears. It differs from Platonism in that in Platonism, mathematics is an autonomous world, while in Pythagoreanism it is built into the physical world and determines its laws. The article shows the need to apply the Aristotelian ontology of matter and form. Mathematics is a form, while physical embodiment requires matter. The flow of time in the physical world is associated with matter, as well as the presence of causality in it. The author comes to a conclusion that acceptance of the idea that the universe is arranged according to mathematical laws leads to the idea of the identity of being and thought.References
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