CSHPM Online Colloquium: Jamie Tappenden

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Nicolas Fillion

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Aug 15, 2020, 7:15:44 PM8/15/20
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***CSHPM Online Colloquium: Jamie Tappenden ***

In those isolated times, the Canadian Society for History and Philosophy of Mathematics
(http://www.cshpm.org/) is organizing a bi-weekly 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.

JAMIE TAPPENDEN, Professor of Philosophy at the University of Michigan, Ann Arbour, will
deliver the third talk of the CSHPM Online Colloquium series.

DATE: August 21th
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: Frege on Computation and Deduction: Herbart, Fischer and "Aggregative, Mechanical Thinking"
ABSTRACT: This paper reconstructs some details of Frege's early intellectual environment
and reads "Grundlagen" in light of them. The contextual information is of considerable
interest in its own right, but here I'll concentrate on using the information to interpret
some passages and features of "Grundlagen". The reading identifies unnoticed dialectical
structure and thematic cohesion linking the introduction and conclusion of "Grundlagen"
pertaining to, among other things, the deductive character of mathematics versus the
"aggregative mechanical thinking" proposed by Kuno Fischer. Specific points include:
a) The opening pages of "Grundlagen" present interrelated goals in a way that has not
so far been noticed; The successful achievement of these goals is implicitly announced
in sections 87-8, the beginning of "Grundlagen"'s conclusion.
b) The goals include establishing the value of mathematical reasoning and the "fine"
structure of mathematical concepts as well as establishing the nature of arithmetic
(and mathematics more generally) as deductive rather than computational. The solution
(among other things) binds together the deductiveness of mathematical reasoning, the
fine structure of mathematical concepts, explanation and the possibility (due to the
fruitfulness of mathematical concepts) of extending knowledge via deduction alone.
c) The goals are framed by a contrast between Kuno Fischer and Johann Herbart on the
nature and value of arithmetic, a contrast whose significance and ramifications would
have been obvious to those in Frege's environment but which slips past us today.
d) Frege's rejection of Fischer's picture --- on the surface just a rejection of the
phrase "aggregative mechanical thinking" in connection with arithmetic --- is motivated
by a broader opposition to Fischer's dismissive stance on the value of thinking in
arithmetic. Fischer's evaluation had significant consequences for education and academic
politics as well as philosophy, points to which Frege clearly alludes.
e) Further complexity that would have been clear to Frege's intended readers is implicit
in the reference to Herbart. This is true in particular of Frege's use of a Herbartian
technical expression "working out" (Bearbeitung). Frege's effort to define number in
"Grundlagen" would have been recognized by his readers as a clear example of "working
out" in Herbart's sense.

Please distribute this information to all who might be interested. The information to join
the session via Zoom is as follows:

Topic: CSHPM Online Colloquium: Jamie Tappenden's Talk
Time: Aug 21, 2020 11:00 AM Pacific Time (US and Canada)

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