***CSHPM Online Colloquium: Silvia De Toffoli ***
In these isolated times, the Canadian Society for History and Philosophy of Mathematics (http://www.cshpm.org/
) is organizing an online colloquium series via Zoom. Sessions are open to CSHPM members as well as the broader scholarly community. Participants are encouraged to become members (for as little as $10-$30/year, depending on your employment status), but it is not required. Non-members can get regular updates on our activities by liking us on Facebook (https://www.facebook.com/cshpmschpm
). The talk will last 30 minutes, followed by a Q&A.
SILVIA DE TOFFOLI, Postdoc Philosophy at Princeton University, will deliver the
seventh talk of the CSHPM Online Colloquium series.
DATE: November 27th
TIME: UTC 18:00; Vancouver 11:00; Edmonton/Regina 12:00; Winnipeg 13:00; Montreal/Toronto 14:00; Halifax 15:00; St. John's 15:30
TITLE: A Fallibilist Account of Mathematical Justification
ABSTRACT: In this talk, I will put forward an account of mathematical justification that is faithful to actual mathematical practice. I will focus on mathematical doxastic justification, that is, justification for an agent's belief in a mathematical claim for mathematical reasons. In contrast to traditional views, I will argue that even in the case of mathematics justification and knowledge can come apart. I will argue that the norms for doxastic justiﬁcation at play in actual mathematical practice apply to individual agents but present an important social component. Moreover, in my view the bar on justification changes according to the social role the agent is playing. Whereas for the laywoman pure testimony is enough and for the clairvoyant the reliability of her super-power would suﬃces, for the expert mathematician a mathematical argument is needed. Such argument is what I label a simil-proof (SP), that is, an argument that looks like a proof to the relevant agents. I will characterize SPs as sharable: having a SP implies grasping how it supports its conclusion and also being able to share it in the appropriate context. This implies that being justiﬁed is connected to the ability not only of responding to criticism adequately, but also of justifying. One striking respect in which my account of mathematical justification differs from more traditional ones is that it has a fallibilist flavor: justification comes apart from truth since an agent may be justiﬁed in believing a false proposition or in believing a true proposition by improperly grasping a fallacious argument.
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Topic: CSHPM talk: Silvia De Toffoli
Time: Nov 27, 2020 11:00 AM Pacific Time (US and Canada)
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