Could groups ever be an understanding subject (an epistemic agent ascribed with understanding) or should we keep our focus exclusively on the individuals that make up the group? The way this paper will shape an answer to this question is by starting from a case we are most willing to accept as group understanding, then mark out the crucial differences with an unconvincing case, and, ultimately, explain why these differences matter. In order to concoct the cases, however, we need to (...) elucidate what it means to be attributed with understanding and what makes up an epistemic agent. I shall argue that it is abilities, above all, that guide our attributions of understanding. While it is true that understanding must go beyond single acts, this is not going beyond as in going behind them (to private occurrences which are impossible to discern and don’t themselves contribute anything of value), but beyond as in considering what people could and would do: their discernable and valuable abilities. To conceptualize whom the abilities belong to, I will specify what it means to be an epistemic agent. I shall argue that it is being a successful target of the epistemic stance. The epistemic stance (heavily inspired by Dennett’s intentional stance) forms an instrumental abstraction by attributing epistemic properties (i.e., beliefs, epistemic aims, problem-solving tactics) to an entity to explain or predict its behavior. Macro-systematicity (a higher-level pattern which a theory can exploit) is what makes the epistemic stance’s abstraction an explanatory powerful one (regardless of how that macro-systematicity is realized) and emergence (the lack of a straightforward mapping-relation between the micro and the macro) is what makes its power unique to a particular level of explanation. To end, I suggest two kinds of mapping-relations and walk through the shift from reducibility to emergence. (shrink)

PurposeIn this article, we aim to present and defend a contextual approach to mathematical explanation.MethodTo do this, we introduce an epistemic reading of mathematical explanation.ResultsThe epistemic reading not only clarifies the link between mathematical explanation and mathematical understanding, but also allows us to explicate some contextual factors governing explanation. We then show how several accounts of mathematical explanation can be read in this approach.ConclusionThe contextual approach defended here clears up the notion of explanation and pushes us towards a pluralist vision (...) on mathematical explanation. (shrink)

Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer.

Upshot: The computational theory of mind has been elaborated in many different ways throughout the last decades. In Explaining the Computational Mind, Milkowski defends his view that the mind can be explained as computational through his defense of mechanistic explanation. At no point in this book is there explicit mention of constructivist approaches to this topic. We will, nevertheless, argue that it is interesting for constructivist readers.

Understanding is a valued trait in any epistemic practice, scientific or not. Yet, when it comes to characterizing its nature, the notion has not received the philosophical attention it deserves. We have set ourselves three tasks in this paper. First, we defend the importance of this endeavor. Second, we consider and criticize a number of proposals to this effect. Third, we defend an alternative account, focusing on abilities as the proper mark of understanding.