Invited speakers include:
Eric Brian (Paris)
The General Rules of
The talk will deal with the issue: Is there a specific form of sociology to be developed for mathematics or is it appropriate to consider mathematics from the standpoint of general sociology?
Examples will be taken from history and sociology of analysis and the calculus of probability.
Juliet Floyd (Boston)
Proof and Purposiveness
I shall explore some of the difficulties surrounding talk of aesthetics (or taste) in mathematics. 1) Shall we take terms of criticism, as they occur within working mathematics, to be truly “aesthetic”? 2) Can such factors, if taken into consideration, be considered epistemologically relevant? 3) How systematic do we take mathematicians’ uses of such terms to be? 4) How important is it to focus on the patter surrounding proof – supposing that at least some of the patter is ornamental? 5) What does it mean when we look at mathematical structures and objects as aesthetic objects? I approach these questions through discussion of Kant’s and Wittgenstein’s contributions.
Richard Heinrich (Vienna)
Teacher's Pet? Philosophical Remarks on the Specialty of Mathematics
Volker Peckhaus (Paderborn)
The Indispensability of Mathematical Reasoning
Horst Struve (Cologne)
Is Mathematics Special? -
That Depends on the Context.
The answer to the question whether mathematics is special depends on what we take mathematics to be. Conceptions of mathematics are marked by the cultural and social contexts (mathematical practice) in which these conceptions are passed on and formed. This presentation will discuss two such contexts: The teaching of mathematics in schools and the context which brought about the modern, formalistic conception of mathematics.
In the first part, empirical investigations (in the sense of Löwe & Müller’s “Empirical Philosophy of Mathematics”) will be used to show that pupils acquire a largely empirical understanding of mathematics in school. Mathematical theories serve to describe and explain certain phenomena of reality. This conception of mathematics was also held by mathematicians of past centuries, explicitly for instance by M. Pasch. In the second part of the presentation the historical context of the issue is outlined, which – starting from this conception – has led to the modern Hilbertian conception of mathematics.
The answer to the question “Is mathematics special?” depends on the area the question refers to. Compared to the natural sciences, the mathematics taught in schools is not special; conversely, the modern formalistic conception is. One aim of this presentation is to shed light on the context in which this historical development has taken place. Modern mathematics is not independent of context, much rather it is its context that is ‘special’.
For the complete list of all speakers please see the PROGRAM.