While it is widely acknowledged that knowledge can be acquired via testimony, it has been argued that understanding cannot. While there is no consensus about what the epistemic relationship of understanding consists in, I argue here that regardless of how understanding is conceived there are kinds of understanding that can be acquired through testimony: easy understanding and easy-s understanding. I address a number of aspects of understanding that might stand in the way of being able to acquire understanding through testimony, (...) focusing on understanding ’s paradigmatic form and what it means to say that in order to understand something you need to “grasp” some information or the relationship between bits of information. I argue that in cases of both easy and easy-s understanding, no aspect of understanding stands in the way of it being able to acquire it through testimony. As a result, while not all understanding be acquired through testimony in all instances and for all subjects, this failure of acquisition is only a product of the complexity of the relevant information or one’s unfamiliarity with it, and not a product of the epistemic relationship of understanding. (shrink)

Claims pertaining to understanding are made in a variety of contexts and ways. As a result, few in the philosophical literature have made an attempt to precisely characterize the state that is y understanding x. This paper builds an account that does just that. The account is motivated by two main observations. First, understanding x is somehow related to being able to manipulate x. Second, understanding is a mental phenomenon, and so what manipulations are required to be an understander must (...) only be mental manipulations. Combining these two insights, the paper builds an account (URM) of understanding as a certain representational capacity—specifically, understanding x involves possessing a representation of x that could be manipulated in useful ways. By tying understanding to representation, the account correctly identifies that understanding is a fundamentally cognitive achievement. However, by also demanding that which representations count as understanding-conferring be determined by their practical effects, URM captures the insight that understanding is vitally connected to practice. URM is fully general, and can apply equally well to understanding states of affairs, understanding events, and even understanding people and works of art. The ultimate test of URM is its applicability in actual scientific and philosophical discourse. To that end the paper discusses the importance of understanding in the philosophy of science, psychology, and computer science. (shrink)

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. (shrink)

This paper examines the problem of extending the programme of mathematical constructivism to applied mathematics. I am not concerned with the question of whether conventional mathematical physics makes essential use of the principle of excluded middle, but rather with the more fundamental question of whether the concept of physical infinity is constructively intelligible. I consider two kinds of physical infinity: a countably infinite constellation of stars and the infinitely divisible space-time continuum. I argue (contrary to Hellman) that these do not. (...) pose any insuperable problem for constructivism, and that constructivism may have a useful new perspective to offer on physics. (shrink)