CSHPM Bi-Weekly Online Colloquia
CSHPM Bi-Weekly Online Colloquia
The Canadian Society for the History and Philosophy of Science and Technology is hosting bi-weekly online colloquia through August. For regular updates on the programme, and joining instructions, see the News section of their website http://www.cshpm.org/ or follow them on Facebook.
The next talk is on 4 September at 19:00 BST
The talk will last 30 mins followed by a Q&A
JEAN-PIERRE MARQUIS, Professor of Philosophy at the Université de Montréal, will talk on:
TITLE: On Mathematical Style
ABSTRACT: In this short talk, I will propose a notion of mathematical style, based on a specific case, namely Bourbaki's mathematics. The main goal is to capture the "structuralist style" of mathematics, but also to provide a general and supple framework to capture other types of style. In the spirit of Paolo Mancosu's challenge presented in his article in the Stanford Encyclopedia of Philosophy on the same topic, I want to show that a style in the sense that I propose has an inherent epistemic component and is not merely an aesthetic addition to a discourse.
Past talks include:
JAMIE TAPPENDEN, Professor of Philosophy at the University of Michigan, Ann Arbour, will speak on:
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.
BRENDA DAVISON, Senior Lecturer in Mathematics at Simon Fraser University
TITLE: Divergent series and Numeric Computation
ABSTRACT: In a paper published in 1856, G.G. Stokes (1819-1903) used a divergent series to compute many values of the Airy integral. Some of these values had been previously computed via a convergent series but this method was too laborious to make all of the desired calculations. This talk will examine how Stokes numerically computed a
class of definite integrals, including the Airy integral, using divergent infinite series. Emphasis will be placed on what lead Stokes to use this method, what types of physical problems required these solutions, how Stokes justified using his method, and how the results obtained were verified. How, when and for what purpose did other mathematicians and physicists use this method during the mid-19th century, before divergent series were given a rigorous treatment, will also be discussed.