Abstract
Cassirer’s critique of Russell’s philosophy of mathematics and the Neo-Kantian philosophy of science and mathematics as a whole is of special relevance in the context of modern mathematics and mathematical physics. The fact that the modern standard axiomatic architecture of mathematical theories does not take into account the object-based character of mathematical knowledge, which was stressed after Kant by Cassirer, complicates the application of new mathematical theories in natural sciences and technology. In particular, this can explain why modern physical string theory is empirically unverifiable; it can be adjusted to accommodate a wide range of possible outcomes of observations and experiments. At the same time, there are reasons to believe that certain recent approaches in foundations of mathematics such as category theory, topos theory, and Univalent Foundations may help to improve the situation in the near future. The problem of applicability of new mathematical knowledge in science and technology shows that the Kantian approach in philosophy of mathematics is at least partly relevant to today’s mathematics.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
