Sophia Arbeiter

This paper presents a novel position in the philosophy of logic: I argue that _validity_ is a thick concept. Hence, I propose to consider _validity_ in analogy to other thick concepts, such as _honesty_, _selfishness_ or _justice_. This proposal is motivated by the debate on the normativity of logic: while logic textbooks seem simply descriptive in their presentation of logical truths, many have argued that logic has consequences for how we ought to reason, for what we ought to believe, or for what we ought to infer. How can logic be normative, if it appears to be descriptive? According to the proposal of this paper, the normativity of logic can be explained because a thick concept is in play: _validity_. Thus, I argue that the debate on how to best characterize validity and the debate on logic’s normativity are more connected than we think, because _validity_ is a thick concept.

This volume features more than 20 essays that explore the work of one of the most important contemporary philosophers of mathematics. It will help readers to better appreciate this significant and prolific philosopher. Within philosophy of mathematics, Penelope Maddy initially advocated realism. She then went on to advance naturalism. Both of her positions became very influential in the field, along with her other work in the philosophy of logic. The contributors comment on and otherwise engage with Maddy’s work. They also weigh in on the state of set theory and its philosophy, the philosophy and history of logic, naturalism, skepticism, and the myriad other areas to which Maddy left her mark. Overall, coverage traces her influence on these various ideas over the years. It will also help readers to better understand how philosophers working at the forefront of these areas see these concepts today. These essays will be essential reading for the wide group of philosophers working in these different areas as well as graduate students studying philosophy of mathematics and logic and the other related issues to which Maddy has contributed. The volume will also appeal to logicians and set theorists in general, as well as to philosophers working in analytic philosophy more widely, as well as to those working in the history of philosophy.