[PhilPhys] LTT: Tuesday - Simon DeDeo - Hard Proofs and Good Reasons

[Center for Phil Sci]

The Center for Philosophy of Science invites you to join us for our Lunch
Time Talk .  Attend in person, room 1117 on the 11th floor of the Cathedral
of Learning at the University of Pittsburgh or visit our live stream on
YouTube at *https://www.youtube.com/channel/UCrRp47ZMXD7NXO3a9Gyh2sg
<https://www.youtube.com/channel/UCrRp47ZMXD7NXO3a9Gyh2sg>*.

*Lunch Time Talk - Simon DeDeo*

*Tuesday, January 21 @ 12:00 pm - 1:30 pm EDT*

To follow along via Zoom, use this link: https://pitt.zoom.us/j/99250265423

*Title: Hard Proofs and Good Reasons*
*Abstract:  *Practicing mathematicians often assume that mathematical
claims, when they are true, have good reasons to be true. Such a state of
affairs is “unreasonable”, in Wigner’s sense, because basic results in
computational complexity suggest that there are a large number of theorems
that have only exponentially-long proofs, and such proofs cannot serve as
good reasons for the truths of what they establish. Either mathematicians
are adept at encountering only the reasonable truths, or what
mathematicians take to be good reasons do not always lead to equivalently
good proofs. Both resolutions raise new problems: either how it is that we
come to care about the reasonable truths before we have any inkling of how
they might be proved, or why there should be good reasons, beyond those of
deductive proof, for the truth of mathematical statements. Taking this
dilemma seriously provides a new way to make sense of the unstable
ontologies found in contemporary mathematics, and new ways to understand
how proofs serve not only as certificates of truth, but as explanations and
reasons-for.
See associated preprint at https://arxiv.org/abs/2410.18994
<https://arxiv.org/abs/2410.18994>
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