Complex systems are to be seen as typically having multiple levels of organization. For instance, in the behavioural and cognitive sciences, there has been a long lasting trend, promoted by the seminal work of David Marr, putting focus on three distinct levels of analysis: the computational level, accounting for the What and Why issues, the algorithmic and the implementational levels specifying the How problem. However, the tremendous developments in neuroscience knowledge about processes at different scales of organization together with the (...) complexity of today cognitive theories suggest that there will hardly be only three levels of explanation. Instead, there will be many different degrees of commitments corresponding to the different granularities—from high-level (behavioural) models to low-level (neural and molecular) models of the cognitive research program. For instance, Bayesian approaches, that are usually advocated for formalizing Marr’s computational level and rational behaviour, have even been adopted to model synaptic plasticity and axon guidance by molecular gradients. As a result, we can consider the behavioural scientist as dealing with models at a multiplicity of levels. The purpose of this Research Topic in Frontiers in Theoretical and Philosophical Psychology is to promote an approach to the role of the levels and explanation and models which is of interest for cognitive scientists, neuroscientists, psychologists, behavioural scientists, and philosophers of science. (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)