Stockholm-Uppsala seminariet i teoretisk filosofi, Uppsala 14 oktober 2016, 10–12:45. Engelska Parken, Rum 2-0024.

10:00–11:15 Speaker Richard Dawid. Commentator Lars-Göran Johansson.

    Mathematical Understanding and Explanation without Proof

The debate on novel confirmation addresses one of the classical questions in the philosophy of science. Does confirmation by novel empirical data (novel confirmation) provide stronger confirmation of a theory than the consistency of a theory with empirical data that has entered the theory’s construction process (accommodation)? While it was initially thought that Bayesian confirmation theory rules out an extra value of novel confirmation, more recently some suggestions about how to achieve such confirmation extra value after all have been put forward. The present talk will discuss the issue at a general level and propose a novel mechanism that generates confirmation extra value for novel confirmation via an assessment of the number of possible alternatives to the theory in question.

11:15–11:30 Coffee break

11:30–12:45: Speaker Stefan Buijsman. Commentator: Daniel Fogal.

   Mathematical Understanding and Explanation without Proof

An upcoming trend in the philosophy of mathematics is the attention to mathematical explanations of mathematical facts. So far research has focussed on the question when a proof counts as explanatory, as opposed to when a proof is non-explanatory. I will argue that we can draw a similar distinction between justifications for mathematical facts that are not formal proofs. In order to do so I set up a general argument scheme that reasons from the presence of understanding to the high likelyhood of the presence of an explanation. The most plausible reason for understanding why something is the case, I will argue, is that this understanding was reached via an explanation. With this general argument scheme I will look at a case where we find understanding of a mathematical fact in the absence of any formal proofs, thus allowing me to argue that other types of justifications for mathematical facts can also be explanatory.