I believe in metaphysical nihilism, the thesis that there could have been no concrete objects, because I believe in a version of the subtraction argument, the subtraction argument*, that proves it. But both Jonathan Lowe (2002) and Alexander Paseau (2002) express doubts about the subtraction argument*. Paseau thinks the argument is invalid, and Lowe argues that invoking concrete* objects is unnecessary. Furthermore Lowe attempts to rebut my objections (Rodriguez-Pereyra 2000) to his anti-nihilist argument (Lowe 1998). In this paper I defend (...) the subtraction argument* from Paseau's and Lowe's criticisms as well as show that the premises of Lowe's anti-nihilist argument are still lacking support. (shrink)

In this paper I argue that Modal Realism, the thesis that there exist non-actual possible individuals and worlds, can be made compatible with Metaphysical Nihilism, the thesis that it is possible that nothing concrete exists. Modal Realism as developed by Lewis rules out the possibility of a world where nothing concrete exists and so conflicts with Metaphysical Nihilism. In the paper I argue that Modal Realism can be modified so as to be compatible with Metaphysical Nihilism. Such a modification makes (...) Modal Realism neither incur further theoretical costs nor lose its theoretical benefits. Thus such a modification constitutes an improvement of Modal Realism. (shrink)

The study of metaphysical possibility involves two central questions: What are possible worlds? Is there an empty possible world? In looking at the first question we consider the different accounts of possible worlds—Lewisian realism, ersatzism, etc. In looking at the second question we consider the discussions of metaphysical nihilism, the modal ontological arguments, etc. In this paper I am drawing these two questions together in order to show how the position we hold on one of these issues affects the position (...) we should hold on the other. (shrink)

Jonathan Lowe argues that metaphysics should be restored to a central position in philosophy, as the most fundamental form of inquiry, whose findings underpin those of all other disciplines. He portrays metaphysics as charting the possibilities of existence, by identifying the categories of being and the relations between them. He sets out his own original metaphysical system, within which he seeks to answer many of the deepest questions in philosophy. 'a very rich book... deserves to be read carefully by anyone (...) interested in any of the many subjects he discusses.' Katherine Hawley, British Journal of the Philosophy of Science. (shrink)

David Armstrong's book is a contribution to the philosophical discussion about possible worlds. Taking Wittgenstein's Tractatus as his point of departure, Professor Armstrong argues that nonactual possibilities and possible worlds are recombinations of actually existing elements, and as such are useful fictions. There is an extended criticism of the alternative-possible-worlds approach championed by the American philosopher David Lewis. This major work will be read with interest by a wide range of philosophers.

By nihilism I shall understand the thesis that it is metaphysically possible that there are no concrete objects. I think there is a version of an argu- ment, the subtraction argument, which proves nihilism nicely (see Baldwin 1996 and Rodriguez-Pereyra 1997). But E. J. Lowe, who is no nihilist, has a very interesting argument purporting to show that concrete objects exist necessarily (Lowe 1996, 1998). In this paper I shall defend nihilism from Lowe’s argument.

Gonzalo Rodriguez-Pereyra (1997) has refined an argument due to Thomas Baldwin (1996), which claims to prove nihilism, the thesis that there could have been no concrete objects, and which apparently does so without reliance on any heavy-duty metaphysics of modality. This note will show that on either reading of its key premiss, the subtraction argument Rodriguez-Pereyra proposes is invalid. [A sequel to this paper, 'The Subtraction Argument(s)', was published in Dialectica in 2006.].

The following quotation, from Frank Jackson, is the beginning of a typical exposition of the debate between those metaphysicians who believe in temporal parts, and those who do not: The dispute between three-dimensionalism and four-dimensionalism, or more precisely, that part of the dispute we will be concerned with, concerns what persistence, and correllatively, what change, comes to. Three-dimensionalism holds that an object exists at a time by being wholly present at that time, and, accordingly, that it persists if it is (...) wholly present at more than one time. For short, it persists by enduring. Four-dimensionalism holds that an object exists at a time by having a temporal part at that time, and it persists if it has distinct temporal parts at more than one time. For short, it persists by perduring. In the light of these comments, some readers will perhaps find the question that forms the title of this paper a little puzzling. They may have learned to use the terms ‘fourdimensionalism’ ‘perdurantism’ and ‘belief in temporal parts’ interchangeably; or perhaps even to define one in terms of the other. Such a usage, however, is inapposite. We might imagine a Flatland-like world of two spatial dimensions and one temporal, whose philosophers are divided between a theory of persistence on which they persist by having temporal parts, and a theory on which they persist by being wholly located in each of several times. This is just the same issue we face, but at least the label ‘four-dimensionalism’ seems inapposite: the four-dimensionalist Flatlanders believe in only three dimensions! (shrink)

I investigate two asymmetrical approaches to knowledge of absolute possibility and of necessity--one which treats knowledge of possibility as more fundamental, the other according epistemological priority to necessity. Two necessary conditions for the success of an asymmetrical approach are proposed. I argue that a possibility-based approach seems unable to meet my second condition, but that on certain assumptions--including, pivotally, the assumption that logical and conceptual necessities, while absolute, do not exhaust the class of absolute necessities--a necessity-based approach may be able (...) to do so. (shrink)

In this paper I present the Discrete Space-Time Thesis, in a way which enables me to defend it against various well-known objections, and which extends to the discrete versions of Special and General Relativity with only minor difficulties. The point of this presentation is not to convince readers that space-time really is discrete but rather to convince them that we do not yet know whether or not it is. Having argued that it is an open question whether or not space-time (...) is discrete, I then turn to some possible empirical evidence, which we do not yet have. This evidence is based on some slight differences between commonly occurring differential equations and their discrete analogs. (shrink)