Philosophy of Mathematics: Sociological Aspects and Mathematical Practice

Konferenz: Philosophy of Mathematics: Sociological Aspects and Mathematical Practice (PhiMSAMP-3). Wien, Österreich. Internet: Philosophy of Mathematics: Sociological Aspects and Mathematical Practice

Termin: 16. - 18. Mai 2008

Kurzbeschreibung

A bringing together of researchers from different fields interested in the question what makes mathematics special (if anything). Even if mathematics presents itself or is presented as a (quasi-)empirical matter, the status of an epistemic exception that mathematics forms among the sciences asks for explanations.

Themen

Papers are welcome from scholars of all disciplines, especially philosophy, mathematics, sociology, didactics, logic, epistemology, and the historical sciences.

Hauptvorträge

• Eric Brian (Paris)
  • The General Rules of Mathematical Specialty
    • 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
    • This lecture will approach the question of mathematics’ ‘specialty’ mainly by distinguishing several meanings of ‘specialty' and by describing the roles these aspects play in the contexts of epistemological questions, philosophy of science and philosophy of language. Ideas from Plato, Aristotle and Descartes will be commented upon, and the positions held by Kant and Wittgenstein will be discussed in more detail. Special attention will be paid to the role of mathematics (or `the mathematical')in generalized contexts of teaching/learning of intelligent skills as well as in linguistic meaning[s]. The attempted conclusion of this lecture is that the specialty of mathematics should, above all, be studied within the framework of a philosophical theory of symbols.

• Peckhaus,V. (Paderborn)
  • The Indispensability of Mathematical Reasoning
    • It is argued that mathematical reasoning is indispensable in everyday reasoning in both, an analytical or regressive sense, and a synthetical or progressive sense. In the analytical sense mathematical reasoning can be characterized as the transition from given propositions to the conditions necessary for their validity. In the synthetical sense it is the derivation of propositions from given principles. This reading closely connecting mathematics with logic is supported with historical examples from Euclid to Hilbert. In the aspect discussed mathematics is by no means special.

• Struve, H. (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’.