Sven Delarivière

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 (at least for now) towards a pluralist vision on mathematical explanation.

I will, in this dissertation, set up my conceptual characterisation of “understanding” and “the understanding subject.” Recent discussions in epistemology have started to take seriously the question whether some epistemic properties may be suitably attributed (to a lesser or equal extent) to entities other than human individuals, such as groups (collective epistemology), artefacts (android epistemology) or individuals in conjunction with “external” components (extended epistemology). The rising debate in epistemology shares similarities with developments from cognitive science (e.g. distributed, extended, and artificial cognition) and philosophy of mind (e.g. theories of agency, collective intentionality, active externalism and emergence), where there is already a widespread literature and several developed frameworks and analytic toolboxes. But so far these developments have only to a very limited extent influenced the epistemology literature. Furthermore, the literature is fragmented based on the properties and entities they discuss. Focusing on epistemic subjecthood, generally, would force us to consider what unites the demarcation principles at work in the particulars as well as what the explanatory role of epistemic subjecthood amounts to and how it fares in explaining entities beyond human individuals.

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.

Both a traditional notion of free will, present in human beings, and artificial intelligence are often argued to be inherently incompatible with determinism. Contrary to these criticisms, this paper defends that an account of free will compatible with determinism, the responsibility strategy (coined here) specifically, is a variety of free will worth wanting as well as a variety that is possible to (in principle) artificially construct. First, freedom will be defined and related to ethics. With that in mind, the two theses of free will are addressed (namely could have done otherwise and source origination) for both human beings and artificial agents.