Workshop: Understanding Reflection

Idea & Motivation

The aim of this event is to gather philosophical logicians, epistemologists, and philosophers of mathematics to make progress on the analysis of what makes our knowledge of mathematical and logical principles possible, with a particular focus on the analysis of reflection as an epistemic process.

One type of question that will be discussed concerns the grounds on which our confidence in different kinds of reflection principles, statements that assert an implication between the provability of a class of sentences and their truth, can be justified. Can reflection principles be seen as formal expressions of an informal “process of reflection” involved in arithmetical reasoning? Do reflection principles express a kind of trust in a formal theory whose soundness is unconditionally accepted? Do our pre-theoretical intuitions suffice for adding such principles to formalised theories?
Such questions have only been addressed explicitly in the philosophy of mathematics in the last decade, while the vast literature in epistemology on epistemic entitlement and non-evidential warrants has not yet been systematically brought to bear on questions about the justification of reflection principles in the philosophy of mathematics and logic. This conference aims at approaching these kinds of questions from a perspectives that integrates philosophical logic, the philosophy of mathematics, epistemology, and the philosophy of language.

Further Information

Webpage of the workshop "Understanding Reflection"