This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.

I argue that on very weak assumptions about truth (in particular, that there are coherent norms governing the use of "true"), there is a proposition absolutely inexpressible with conventional language, or something very close. I argue for this claim "constructively": I use a variant of the Berry Paradox to reveal a particular thought for my readership to entertain that very strongly resists conventional expression. I gauge the severity of this expressive limitation within a taxonomy of expressive failures, and argue that (...) despite its strength there is nothing incoherent about admitting its existence. The argument forms part of a project of clarifying precisely what trade-offs are required to secure the kinds of expressive power truth theorists typically want, in the process showing that the admission of very strong expressive limitations may ultimately prove to be the lesser of two evils. (shrink)

It seems obvious that I could have failed to exist. My parents could easily never have met, in which case I should never have been conceived and born. The like applies to everyone. More generally, it seems plausible that whatever exists in space and time could have failed to exist. Events could have taken an utterly different course. Our existence, like most other aspects of our lives, appears frighteningly contingent. It is therefore surprising that there is a proof of my (...) necessary existence, a proof that generalizes to everything whatsoever. I will explain the proof and discuss what to make of it. A first reaction is that a ‘proof’ of such an outrageous conclusion must contain some dreadful fallacy. Yet the proof does not collapse under scrutiny. Further reflection suggests that, suitably interpreted, it may be sound. So interpreted, the conclusion is not outrageous, although it may not be the view you first thought of. (shrink)

The book also sheds new light on the nature of metaphysical theorizing by exploring the interaction of semantic and metaphysical issues, the connections between different metaphysical issues, and the nature of ontological commitment.

This book, one of the first full-length studies of the modalities to emerge from the debate to which Saul Kripke, David Lewis, Ruth Marcus, and others are contributing, is an exploration and defense of the notion of modality de re, the idea that objects have both essential and accidental properties. Plantinga develops his argument by means of the notion of possible worlds and ranges over such key problems as the nature of essence, transworld identity, negative existential propositions, and the existence (...) of unactual objects in other possible worlds. He also applies his logical theories to the elucidation of two problems in the philosophy of religion: the problem of evil and the ontological argument. (shrink)

According to many actualists, propositions, singular propositions in particular, are structurally complex, that is, roughly, (i) they have, in some sense, an internal structure that corresponds rather directly to the syntactic structure of the sentences that express them, and (ii) the metaphysical components, or constituents, of that structure are the semantic values — the meanings — of the corresponding syntactic components of those sentences. Given that reference is "direct", i.e., that the meaning of a name is its denotation, an apparent (...) consequence of this view is that any proposition expressed by a sentence containing a name that denotes a contingent being S is itself contingent — notably, the proposition [S does not exist]. Assuming that an entity must exist to have a property, necessarily, [S does not exist] must exist in order to be true. It seems to follow that, necessarily, [S does not exist] is not true and, hence, that S is not contingent after all. Past approaches to the problem — notably, those of Prior and Adams — lead to highly undesirable consequences for quantified modal logic. In this paper, several solutions to this puzzle are developed that preserve actualism, the structured view of propositions, the direct theory of reference, and the intuition that [S does not exist] is indeed possible without the adverse consequences for QML of previous solutions. (shrink)

‘A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science.’ This paper is an attempt to follow Russell’s advice by using a puzzle about the contingent a priori to test and explore certain theories of reference and modality. No one could claim that (...) the puzzle is of any great philosophical importance by itself, but to understand it, one has to get clear about certain aspects of the theory of reference; and to solve it, one has to think a little more deeply than one is perhaps accustomed about what it means to say that a statement is contingent or necessary. (shrink)

‘A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science.’ This paper is an attempt to follow Russell’s advice by using a puzzle about the contingent a priori to test and explore certain theories of reference and modality. No one could claim that (...) the puzzle is of any great philosophical importance by itself, but to understand it, one has to get clear about certain aspects of the theory of reference; and to solve it, one has to think a little more deeply than one is perhaps accustomed about what it means to say that a statement is contingent or necessary. (shrink)

Trenton Merricks presents an original argument for the existence of propositions, and defends an account of their nature. He draws a variety of controversial conclusions, for instance about supervaluationism, the nature of possible worlds, truths about non-existent entities, and whether and how logical consequence depends on modal facts.

Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.

I argue on linguistic grounds that when Mary comes to know what it's like to see a red thing, she comes to know a certain inexpressible truth about the character of her own experience. This affords a "no concept" reply to the knowledge argument. The reason the Knowledge Argument has proven so intractable may be that we believe that an inexpressible concept and an expressible concept cannot have the same referent.

The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as ∃x t=x; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted that in order (...) to specify the truth conditions of certain sentences involving constants or variables that don’t denote, one has to apparently quantify over things that are not identical to anything. In this paper I defend a contingentist, non-Meinongian metaphysics within a positive free logic. I argue that although certain names and free variables do not actually refer to anything, in each case there might have been something they actually refer to, allowing one to interpret the contingentist claims without quantifying over mere possibilia. (shrink)