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Robinson's Podcast Podcast
Ask Me Anything | July 2024

Ask Me Anything | July 2024

Robinson's Podcast vor 2 Jahren

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1:29:36

Patreon: https://bit.ly/3v8OhY7

This is the inaugural AMA for Robinson’s Podcast. It is supported
by the members of the podcast’s Patreon. In this installment,
Robinson answers questions about the reality of mathematics,
podcasting, moral facts, ice cream, the nature of time, literary
books for neophytes, and more.

Denying Infinity: https://doi.org/10.1080/01445340.2024.2344346

Abstract: Abraham Robinson is well-known as the inventor of
nonstandard analysis, which uses nonstandard models to give the
notions of infinitesimal and infinitely large magnitudes a
precise interpretation. Less discussed, although subtle and
original—if ultimately flawed—is Robinson’s work in the
philosophy of mathematics. The foundational position he inherited
from David Hilbert undermines not only the use of nonstandard
analysis, but also Robinson’s considerable corpus of pre-logic
contributions to the field in such diverse areas as differential
equations and aeronautics. This tension emerges from Robinson’s
disbelief in the existence of infinite totalities (any mention of
them is ‘literally meaningless’) and the fact that much of his
work involves them. I argue that he treats infinitary avenues of
mathematics as useful tools to avoid this difficulty, but that
this is not successful to the extent that these tools must be
justified by a conservative extension from finitary mathematics.
While Robinson provides a compelling and unorthodox pragmatic
justification for the role of formal systems in mathematical
practice despite their apparent infinitary presuppositions, he
deflates mainstream mathematics to a collection of games that
occasionally produces meaningful results. This amounts to giving
up on a commitment to reconciling his finitism with his
mathematical practice.

Robinson’s Website: http://robinsonerhardt.com

Robinson Erhardt researches symbolic logic and the foundations of
mathematics at Stanford University. Join him in conversations
with philosophers, scientists, and everyone in-between.