During this conference speakers will present various philosophical perspectives on explanation and understanding within mathematics.Philosophy has a long and lively tradition of analysing the nature of explanation. Given that explanation is considered to be one of the cardinal aims of the sciences, this notion is central to philosophy of science. This discipline has made important developments to account for the role explanations play in scientific activities by presenting unificationist, causal, pragmatic, interventionist and mechanistic approaches to explanation.Initially, explanation in the field of mathematics received less attention and remained a puzzling notion. There is a growing consensus that mathematicians are and can be interested in an explanation, beyond the mere justification, of a mathematical result. Starting with Steiner (1978), a small yet growing body of literature deals with the distinction between explanatory and non-explanatory proofs in mathematics. The underlying idea is that all proofs show that a theorem is true, but some proofs also reveal why the theorem is true.Other discussions, such as Kitcher (1981), do not locate explanatoriness on the level of a proof, but instead on the more general level of a complete set of beliefs. Only recently philosophers drew attention to other cases of mathematical explanations, such as explanatory theorems (Lange 2016) and explanatory definitions (Lehet 2019).A current trend is that philosophers of science emphasize the relation between explanation and understanding, and stress the need for theories of scientific understanding (De Regt & Dieks 2005). In the literature on mathematical explanation an explicit discussion on the relation between explanation and understanding is rare. More generally, philosophers of mathematics have touched upon the notion of mathematical understanding (Avigad 2008) but are yet to develop a detailed account of what mathematical understanding consists of.
|Effective start/end date||5/12/19 → 31/12/20|
Flemish discipline codes
- General philosophy of science
- science congress