Graham Priest

This paper concerns two paradoxes involving propositions. The first is Russell's paradox from Appendix B of The Principles of Mathematics, a version of which was later given by Myhill. The second is a paradox in the framework of possible worlds, given by Kaplan. This paper shows a number of things about these paradoxes. First, we will see that, though the Russell/myhill paradox and the Kaplan paradox might appear somewhat different, they are really just variants of the same phenomenon. Though they do this in different ways, the core of each paradox is to use the notion of a proposition to construct a function, f, from the power set of some set into the set itself. Next we will see how this paradox fits into the Inclosure Schema. Finally, I will provide a model of the paradox in question, showing its results to be non‐trivial, though inconsistent.

Problems about the accidental properties of properties motivate us--force us, I think--not to identify properties with the sets of their instances. If we identify them instead with functions from worlds to extensions, we get a theory of properties that is neutral with respect to disputes over counterpart theory, and we avoid a problem for Lewis's theory of events. Similar problems about the temporary properties of properties motivate us--though this time they probably don't force us--to give up this theory as well, and to identify properties with functions from ⟨world, time⟩ pairs to extensions. Again, the replacement theory is neutral with respect to a metaphysical dispute that the old theory (arguably) forces us to take a stand on--the dispute over whether objects have temporal parts. It also allows us to give a smoother semantics for predication, to better accommodate our intuitions about which objects temporary properties are properties of, and to make temporally self-locating beliefs genuinely self -locating.

This paper discusses the major theme of Adrian Moore’s The Evolution of Modern Metaphysics. Moore argues that the philosophical theories of many modern Western philosophers, seen as the project of making sense of the world—in the most general sense of that notion—lead to self-referential contradiction. I agree with him. Moore takes this as a sign that this project requires the need of some non-propositional notion of making sense. Contrary to this, I argue (as in Beyond the Limits of Thought) that it simply indicates the dialetheias at the limits of the project.

Our normal discourse is replete with discussion of things which do not exist — the objects of fiction, of illusion and hallucination, of religious worship, of misguided fears and other intentional states. Let us call such discourse empty. How to account for the meaning of empty discourse, and such truth values as its statements have, are perennial and thorny philosophical topics. Many positions are well known; in this book of five chapters Azzouni advocates another. Empty discourse is literally about nothing; nonetheless, one may give an account of how its sentences are both meaningful and have appropriate truth values. In the first three chapters, the ideas are applied to the objects of mathematics, hallucination, and fiction, respectively. Chapter 5 fills out the picture with a discussion of truth-conditional semantics. Chapter 4 broaches the question of how all this is relevant to a broader question: the unity of the sciences.The book is ingenious and clearly argued.1 There are many perceptive discussions — for example, of the way we talk about fictional objects, and about hallucination. And although it is not the main aim of the book, it mounts a number of telling arguments against alternative positions. And even if the book did not persuade at least this reader of its main thesis, it has estabished a genuinely novel and intriguing position …