Although all mathematical truths are necessary, mathematicians take certain combinations of mathematical truths to be ‘coincidental’, ‘accidental’, or ‘fortuitous’. The notion of a ‘ mathematical coincidence’ has so far failed to receive sufficient attention from philosophers. I argue that a mathematical coincidence is not merely an unforeseen or surprising mathematical result, and that being a misleading combination of mathematical facts is neither necessary nor sufficient for qualifying as a mathematical coincidence. I argue that although the components of a mathematical coincidence (...) may possess a common explainer, they have no common explanation ; that two mathematical facts have a unified explanation makes their truth non-coincidental. I suggest that any motivation we may have for thinking that there are mathematical coincidences should also motivate us to think that there are mathematical explanations, since the notion of a mathematical coincidence can be understood only in terms of the notion of a mathematical explanation. I also argue that the notion of a mathematical coincidence plays an important role in scientific explanation. When two phenomenological laws of nature are similar, despite concerning physically distinct processes, it may be that any correct scientific explanation of their similarity proceeds by revealing their similarity to be no mathematical coincidence. (shrink)

My aim in this thesis is to explain how a non-reductionist metaphysics can accommodate the causal relevance of the psychological and of the special sciences generally. According to physicalism, all behavior is caused by brain-states; given "folk-psychology", behavior is caused by some psychological state. If psychological states are distinct from brain states, then our behavior is overdetermined and this, it is claimed, is unacceptable. I argue that this consequence is not unacceptable. I claim that our explanatory practice should guide our (...) ontological commitment. If we can offer true explanations that appeal to more than one event, then we are committed to overdetermination for the event explained. I argue that accepting overdetermination is not absurd and that we can give an adequate account of causal relevance for psychological and other supervenient properties. The result is a partial defense of both property and event pluralism. Recent work by Davidson, Fodor, Jackson, Kim, Pettit and Yablo receives explicit and critical discussion. (shrink)