[FOM] Mirna Dzamonja on an alleged "crisis" in foundations
Timothy Y. Chow
tchow at math.princeton.edu
Mon Mar 4 11:06:27 EST 2019
The following preprint appeared on the arXiv almost a year ago but I only
just learned about it, and I don't recall it being discussed here on FOM:
---
A new foundational crisis in mathematics, is it really happening?
Mirna Dzamonja
https://arxiv.org/pdf/1802.06221.pdf
Abstract: The article reconsiders the position of the foundations of
mathematics after the discovery of HoTT. Discussion that this discovery
has generated in the community of mathematicians, philosophers and
computer scientists might indicate a new crisis in the foundation of
mathematics. By examining the mathematical facts behind HoTT and their
relation with the existing foundations, we conclude that the present
crisis is not one. We reiterate a pluralist vision of the foundations of
mathematics. The article contains a short survey of the mathematical and
historical background needed to understand the main tenets of the
foundational issues.
---
There are a few statements scattered through the article that I would
quibble with, but overall I agree with the main points that the author
makes.
Tim
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