Peter Richard Forrest

Either from concrete examples such as tomatoes on a plate, an egg carton full of eggs and so on, or simply because of the braces notation, we come to have some intuitions about the sorts of things sets might be. (See Maddy 1990.) First we tend to think of a set of particulars as itself a particular thing.. Second, even after the distinction between settheory and mereology has been carefully explained we tend to think of the members of a set as in some sense parts. And third we tend to think that there is something represented by the braces. Now if there were experts who got their intuitions from elsewhere then we could discard these rather crude ideas about egg cartons and so on. But I suspect the intuitions of experts are, just like those of the rest of us, based on notation and simple examples.

That God is of great beauty is religiously significant as a component of the widespread hope of a blessed experience in this or the next life. This motivates the project of formulating the strongest coherent thesis of divine beauty. This chapter has two parts. In Section 9.1 I argue for the incoherence of Perfect Divine Beauty. The natural reaction to this incoherence is to replace the idea of perfection, but in a way that coheres with the theists’ religious tradition. I explore a range of such replacements, motivating the thesis of Pre-eminent Divine Beauty, that the actual divine beauty is infinitely greater than that of the physical universe. In Section 9.2 I examine various arguments against God’s great beauty. They are the Argument from Divine Simplicity (and the related the Argument from Divine Spirituality), the Argument from Divine Necessity, and the Argument from Moral Righteousness.

This chapter argues that we have inconsistent intuitions about the structure of space (or spacetime, or some stuff, the aether, that fills space or spacetime). A contradiction is obtained from eleven premises, each of which is either directly intuitive or supported by intuitions. The use of so many premises results from the desire to exhibit as clearly as possible the places where one might decide some intuition is to be undermined. Nonetheless the argument for inconsistency is straightforward: our intuitions support the existence of a _supersponge_, namely a region of less than the total volume but not disjoint from any connected part of space of positive diameter. But the complement of a supersponge is an intuitively impossible region. Yet, intuitively a region of less than maximal volume must have a complement. So some intuition must be abandoned.

Typical structural universals are not just the mereological sum of their constituents. Hence, there is the Structure Problem of explaining this non-mereological structure. The Instantiation Problem is that the predicate "U is instantiated by x, y, etc., in that order" is ill-suited to be a primitive, unanalyzed predicate. The proposed solution to these problems is based on the observation that if universal U is said to supervene upon universals V, W, etc., then it is the instantiation of U that supervenes on the instantiation of V, W, etc. Assuming there are few subvenient universals, which is admittedly a speculation, their instantiation may be explained in ways that would be uneconomic if there were too many.

Consider the things that exist—the entities—and let us suppose they are mereologically structured, that is, some are parts of others. The project of ontology within the bounds of bare mereology use this structure to say which of these entities belong to various ontological kinds, such as properties and particulars. My purpose in this paper is to defend the most radical section of the project, the mereological theory of the exemplification of universals. Along the way I help myself to several hypotheses: the existence of merely possible worlds; that particulars have thisnesses; and that mereology is far from classical. Moreover, the way I characterize instantiation might be judged too complicated to be plausible. At the end of the paper, I reply to these objections based on complexity.

In this paper I propose an indubitability analysis of knowledge. The motivation for this analysis is a conviction I have that the Cartesian analysis of knowledge as indubitability is not completely mistaken, although it requires considerable weakening if it is to be satisfactory. My analysis may be contrasted to those which treat knowledge as a species of the genus justified true belief. For although on my analysis, ‘S knows that p’ entails ‘S has a justified true belief that p’, I am not proposing indubitability as a differentia distinguishing knowledge from other members of the genus justified true belief. The situation here is analogous to that of the conceptual relation between vermillion and red: ‘X is vermillion’ entails ‘X is red’, but there is no straightforward differentia which would entitle us to think of vermillion as a species of the genus red. Another point of contrast is that species-of-justified-true-belief analyses start with an analysis which is too weak and strengthen it. My starting point is an analysis which is too strong which I then weaken.

David Armstrong in his A Combinatorial Theory of Possibility proposes that non-actual possibilities may be treated as fictions grounded in instantiated universals. In this paper, I first provide some objections to his theory. Then I make the case for Foundational Nominalism, the Armstrong inspired thesis that the whole of ontology supervenes on particulars described much as in the Quinean Nominalism that Armstrong rejected as an ontological ostrich. Finally, I argue that Foundational Nominalism permits a fictional theory of possibilities similar to Brian Skyrms’ Tractarian Nominalism.

Conceivability is, I say, prima facie evidence for possibility. Hence, we may count the cost of theories about possibility by listing the ways in which, according to the theory in question, something conceivable is said nonetheless to be impossible. More succinctly we may state a principle, Hume's razor to put alongside Ockham's. Hume's razor says that necessities are not to be multiplied more than necessary. In this paper I count the cost of David Lewis's modal realism, showing that many of the objections are replied to by Lewis only at the cost of multiplying necessities.

Consider the things that exist—the entities—and let us suppose they are mereologically structured, that is, some are parts of others. The project of ontology within the bounds of bare mereology use this structure to say which of these entities belong to various ontological kinds, such as properties and particulars. My purpose in this paper is to defend the most radical section of the project, the mereological theory of the exemplification of universals. Along the way I help myself to several hypotheses: the existence of merely possible worlds; that particulars have thisnesses; and that mereology is far from classical. Moreover, the way I characterize instantiation might be judged too complicated to be plausible. At the end of the paper, I reply to these objections based on complexity.