Donald L.M. Baxter
For Hume, the ideas of space and of time are each a general idea of some indivisible objects arranged in a certain manner with additional qualities that make them conceivable to the mind. He argues that the structures of these ideas reflect the structures of space and time. Thus, space and time are not infinitely divisible, and there cannot be empty space nor time without succession. Hume’s idiosyncratic theory can be seen to be reasonable if one pays careful attention to the fact that Hume, in accordance with his skepticism, is concerned only to give vent to views about space and time as they appear in experience. The chapter focuses on explicating Hume’s central arguments rather than trying to give a comprehensive treatment.
This article examines a number of issues and problems that motivate at least much of the literature in the philosophy of mathematics. It first considers how the philosophy of mathematics is related to metaphysics, epistemology, and semantics. In particular, it reviews several views that account for the metaphysical nature of mathematical objects and how they compare to other sorts of objects, including realism in ontology and nominalism. It then discusses a common claim, attributed to Georg Kreisel that the important issues in the philosophy of mathematics do not concern the nature of mathematical objects, but rather the objectivity of mathematical discourse. It also explores irrealism in truth-value, the dilemma posed by Paul Benacerraf, epistemological issues in ontological realism, ontological irrealism, and the connection between naturalism and mathematics.