Richard Lawrence PhD

October 1st until March 31st, 2022

Affiliation: Eberhard Karls Universität Tübingen

Research for a study about:

Frege among the formalists

Mathematical Formalism and Frege's Theory of Content

My project investigates Frege's views about the content of
mathematical language via his engagement with mathematical formalism.
Formalism is an approach to the foundations of mathematics which arose
in the 19th century. Frege saw formalism as a rival to his own
logicist foundational program, and argued against it throughout his
career. The project examines these arguments alongside the views of
the early formalists Frege engaged with, especially Hankel, Heine,
Thomae, Weierstrass, and Hilbert. In these arguments, Frege expresses
a basically representational theory of content: he thinks signs stand
for, or designate, their references. Formalists, by contrast, have a
non-representational view of content: a sign's meaning lies in its
role in calculations. The central issue between Frege and formalists
is thus: do signs in mathematics stand for other things, distinct from
those signs themselves? Placing these views in their historical and
mathematical context illuminates both the formalists' and Frege's positions.

Lecture

Mathematical formalism through the eyes of Weierstrass and Thomae

Date: December 06th, 2021

Time: 5–6.30pm (CET)

Online Plattform: Please find futher information at Logic Café

Abstract:

Mathematical formalism is the view that mathematics can be seen as a
'game of symbols'. One important formulation of this view was given by
Johannes Thomae, who compared signs for numbers with chess pieces:
according to Thomae's formalism, such signs are given meaning by our
rules for calculating with them, just as wooden pieces are given
meaning by the rules of chess. This view was attacked at length by
Frege, and also played an important role in Wittgenstein's thought. I
argue that in order to understand mathematical formalism and Thomae's
chess analogy, we need to see them in the context of a nineteenth
century rivalry between Weierstrass and Riemann the foundations of
analysis. Thomae's formalism belongs to the Weierstrass camp and is
part of a strategy for building analysis on algebraic foundations.