Joachim Frans

Although there is a consensus among philosophers of mathematics and mathematicians that mathematical explanations exist, only a few authors have proposed accounts of explanation in mathematics. These accounts fit into the unificationist or top-down approach to explanation. We argue that these models can be complemented by a bottom-up approach to explanation in mathematics. We introduce the mechanistic model of explanation in science and discuss the possibility of using this model in mathematics, arguing that using it does not presuppose a Platonist view of mathematics and allows one to gain insight into why a theorem is true by answering what-if-things-had-been-different questions

In this paper we discuss three interrelated questions. First: is explanation in mathematics a topic that philosophers of mathematics can legitimately investigate? Second: are the specific aims that philosophers of mathematical explanation set themselves legitimate? Finally: are the models of explanation developed by philosophers of science useful tools for philosophers of mathematical explanation? We argue that the answer to all these questions is positive. Our views are completely opposite to the views that Mark Zelcer has put forward recently. Throughout this paper, we show why Zelcer’s arguments fail.

Mathematics seems to have a special status when compared to other areas of human knowledge. This special status is linked with the role of proof. Mathematicians often believe that this type of argumentation leaves no room for errors and unclarity. Philosophers of mathematics have differentiated between absolutist and fallibilist views on mathematical knowledge, and argued that these views are related to whether one looks at mathematics-in-the-making or finished mathematics. In this paper we take a closer look at mathematical practice, more precisely at the publication process in mathematics. We argue that the apparent view that mathematical literature, given the special status of mathematics, is highly reliable is too naive. We will discuss several problems in the publication process that threaten this view, and give several suggestions on how this could be countered.Las matemáticas parecen tener un estatuto especial cuando se las compara con otras áreas del conocimiento humano. Este estatuto especial está conectado con el papel de la demostración. Los matemáticos creen con frecuencia que este tipo de argumentos no deja margen para el error o la falta de claridad. Los filósofos de la matemática han distinguido entre una concepción absolutista y una falibilista del conocimiento matemático, argumentando que estas concepciones están relacionadas con una consideración de las matemáticas-en-proceso o en tanto que matemáticas ya hechas. En este artículo examinamos más de cerca la práctica matemática, más en concreto el proceso de publicación en matemáticas. Argumentaremos que la idea preconcebida de que la literatura matemática, dado el estatuto especial de las matemáticas, es altamente fiable, es demasiado ingenua. Discutiremos algunos problemas del proceso de edición que amenazan esta visión y haremos algunas sugerencias sobre cómo enfrentarlos.