Hud Hudson presents an innovative view of the metaphysics of human persons according to which human persons are material objects but not human organisms. In developing his account, he formulates and defends a unique collection of positions on parthood, persistence, vagueness, composition, identity, and various puzzles of material constitution. The author also applies his materialist metaphysics to issues in ethics and in the philosophy of religion. He examines the implications for ethics of his metaphysical views for standard arguments addressing the (...) moral permissibility of our treatment of human persons and their parts, fetuses and infants, the irreversibly comatose, and corpses. He argues that his metaphysics provides the best foundation in the philosophy of religion for the Christian doctrine of the resurrection of the body. Hudson addresses a broad range of metaphysical issues, but among his most strikingly original contributions are his defense of the "Partist" view and his argument for the compatibility of Christianity with a materialistic theory of human persons. (shrink)

Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

Most philosophers of mathematics try to show either that the sort of knowledge mathematicians have is similar to the sort of knowledge specialists in the empirical sciences have or that the kind of knowledge mathematicians have, although apparently about objects such as numbers, sets, and so on, isn't really about those sorts of things as well. Jody Azzouni argues that mathematical knowledge really is a special kind of knowledge with its own special means of gathering evidence. He analyses the linguistic (...) pitfalls and misperceptions philosophers in this field are often prone to, and explores the misapplications of epistemic principles from the empirical sciences to the exact sciences. What emerges is a picture of mathematics both sensitive to mathematical practice, and to the ontological and epistemological issues that concern philosophers. (shrink)

If we must take mathematical statements to be true, must we also believe in the existence of abstract eternal invisible mathematical objects accessible only by the power of pure thought? Jody Azzouni says no, and he claims that the way to escape such commitments is to accept true statements which are about objects that don't exist in any sense at all. Azzouni illustrates what the metaphysical landscape looks like once we avoid a militant Realism which forces our commitment to anything (...) that our theories quantify. Escaping metaphysical straitjackets, while retaining the insight that some truths are about objects that do exist, Azzouni says that we can sort scientifically-given objects into two categories: ones which exist, and to which we forge instrumental access in order to learn their properties, and ones which do not, that is, which are made up in exactly the same sense that fictional objects are. He offers as a case study a small portion of Newtonian physics, and one result of his classification of its ontological commitments, is that it does not commit us to absolute space and time. (shrink)

In order to perfectly describe the world, it is not enough to speak truly. One must also use the right concepts - including the right logical concepts. One must use concepts that "carve at the joints", that give the world's "structure". There is an objectively correct way to "write the book of the world". Much of metaphysics, as traditionally conceived, is about the fundamental nature of reality; in the present terms, this is about the world's structure. Metametaphysics - inquiry into (...) the status of metaphysical questions - turns on structure. The question of whether ontological, causal, or modal questions are "substantive" is in large part a question of whether the world has ontological, causal, and modal structure - whether quantifiers, causal relations, and modal operators carve at the joints. (shrink)

Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

Several of these essays have been printed whole in journals; others are in varying degrees new. Two main themes run through them. One is the problem of meaning, particularly as involved in the notion of an analytic statement. The other is the notion of ontological, commitment, particularly as involved in the problem of universals.

Quine has called the question, ‘What is there?’ the “ontological question.” But if we call this question by that name, what name shall we use for the question, ‘What are we asking when we ask “What is there?”’? I shall call it ‘the meta-ontological question’. I shall call the attempt to answer the meta-ontological question ‘meta-ontology’ and any proposed answer to it ‘a meta-ontology’. In this essay, I shall briefly sketch a meta-ontology. The meta-ontology I shall present is broadly Quinean. (...) I am, in fact, willing to call it an exposition of Quine’s meta-ontology. (shrink)

This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; ...

Call a quantifier unrestricted if it ranges over absolutely all things: not just over all physical things or all things relevant to some particular utterance or discourse but over absolutely everything there is. Prima facie, unrestricted quantification seems to be perfectly coherent. For such quantification appears to be involved in a variety of claims that all normal human beings are capable of understanding. For instance, some basic logical and mathematical truths appear to involve unrestricted quantification, such as the truth that (...) absolutely everything is self-identical and the truth that the empty set has absolutely no members. Various metaphysical views too appear to involve unrestricted quantification, such as the physicalist view that absolutely everything is physical. (shrink)

Ordinary English contains different forms of quantification over objects. In addition to the usual singular quantification, as in 'There is an apple on the table', there is plural quantification, as in 'There are some apples on the table'. Ever since Frege, formal logic has favored the two singular quantifiers ∀x and ∃x over their plural counterparts ∀xx and ∃xx (to be read as for any things xx and there are some things xx). But in recent decades it has been argued (...) that we have good reason to admit among our primitive logical notions also the plural quantifiers ∀xx and ∃xx. More controversially, it has been argued that the resulting formal system with plural as well as singular quantification qualifies as ‘pure logic’; in particular, that it is universally applicable, ontologically innocent, and perfectly well understood. In addition to being interesting in its own right, this thesis will, if correct, make plural quantification available as an innocent but extremely powerful tool in metaphysics, philosophy of mathematics, and philosophical logic. For instance, George Boolos has used plural quantification to interpret monadic second-order logic and has argued on this basis that monadic second-order logic qualifies as “pure logic.” Plural quantification has also been used in attempts to defend logicist ideas, to account for set theory, and to eliminate ontological commitments to mathematical objects and complex objects. (shrink)

On reading the last sentence, did you interpret me as saying falsely that everything — everything in the entire universe — was packed into my carry-on baggage? Probably not. In ordinary language, ‘everything’ and other quantifiers (‘something’, ‘nothing’, ‘every dog’, ...) often carry a tacit restriction to a domain of contextually relevant objects, such as the things that I need to take with me on my journey. Thus a sentence of the form ‘Everything Fs’ is true as uttered in a (...) context C if and only if everything that is relevant in C satisfies the predicate ‘F’; ‘everything’ ranges just over the contextually relevant things. Such generality is restricted in a context-relative way. (shrink)

The paper is an extended discussion of what I call the ‘dismissive attitude’ towards metaphysical questions. It has three parts. In the first part, I distinguish three quite different versions of dismissivism. I also argue that there is little reason to think that any of these positions is correct about the discipline of metaphysics as a whole; it is entirely possible that some metaphysical disputes should be dismissed and others should not be. Doing metametaphysics properly requires doing metaphysics first. I (...) then put two particular disputes on the table to be examined in the rest of the paper: the dispute over whether composite objects exist, and the dispute about whether distinct objects can be colocated. In the second part of the paper, I argue against the claim that these disputes are purely verbal disputes. In the third part of the paper, I present a new version of dismissivism, and argue that it is probably the correct view about the two disputes in question. They are not verbal disputes, and the discussion about them to date has not remotely been a waste of time. At this stage, however, our evidence has run out. I argue that neither side of either dispute is simpler than the other, and that the same objections in fact arise against both sides. (For example, the compositional nihilist does not in fact escape the problem of the many, and the one-thinger does not in fact escape the grounding problem.). (shrink)

Ordinary language and scientific language enable us to speak about, in a singular way, what we recognize not to exist: fictions, the contents of our hallucinations, abstract objects, and various idealized but nonexistent objects that our scientific theories are often couched in terms of. Indeed, references to such nonexistent items-especially in the case of the application of mathematics to the sciences-are indispensable. We cannot avoid talking about such things. Scientific and ordinary languages thus enable us to say things about Pegasus (...) or about hallucinated objects that are true, such as "Pegasus was believed by the ancient Greeks to be a flying horse," or "That elf I'm now hallucinating over there is wearing blue shoes." Standard contemporary metaphysical views and semantic analyses of singular idioms on offer in contemporary philosophy of language have not successfully accommodated these routine practices of saying true and false things about the nonexistent while simultaneously honoring the insight that such things do not exist in any way at all. That is, philosophers often feel driven to claim that such objects do exist, or they claim that all our talk isn't genuine truth-apt talk, but only pretence. This book reconfigures metaphysics in radical ways that allow the accommodation of our ordinary ways of speaking of what does not exist while retaining the absolutely crucial presupposition that such objects exist in no way at all, have no properties, and so are not the truth-makers for the truths and falsities that are about them. (shrink)

While well-known for his book-length work, philosopher Peter Unger's articles have been less widely accessible. These two volumes of Unger's Philosophical Papers include articles spanning more than 35 years of Unger's long and fruitful career. Dividing the articles thematically, this first volume collects work in epistemology and ethics, among other topics, while the second volume focuses on metaphysics. Unger's work has advanced the full spectrum of topics at the heart of philosophy, including epistemology, metaphysics, philosophy of language and philosophy of (...) mind, and ethics. Unger advances radical positions, going against the so-called "commonsense philosophy" that has dominated the analytic tradition since its beginnings early in the twentieth century. In epistemology, his articles advance the view that nobody ever knows anything and, beyond that, argue that nobody has any reason to believe anything--and even beyond that, they argue that nobody has any reason to do anything, or even want anything. In metaphysics, his work argues that people do not really exist--and neither do puddles, plants, poodles, and planets. But, as Unger has often changed his favored positions, from one decade to the next, his work also advances the opposite, "commonsense" positions: that there are in fact plenty of people, puddles, plants and planets and, quite beyond that, we know it all to be true. On most major philosophical questions, both of these sides of Unger's significant work are well represented in this major two volume collection. Unger's vivid writing style, intellectual vitality, and fearlessness in the face of our largest philosophical questions, make these volumes of great interest not only to the philosophical community but to others who might otherwise find contemporary philosophy dry and technical. (shrink)

The purpose of this article is to delimit what can and cannot be claimed on behalf of second-order logic. The starting point is some of the discussions surrounding my Foundations without Foundationalism: A Case for Secondorder Logic.

Quine has called the question, ‘What is there?’ the “ontological question.” But if we call this question by that name, what name shall we use for the question, ‘What are we asking when we ask “What is there?”’? I shall call it ‘the meta-ontological question’. I shall call the attempt to answer the meta-ontological question ‘meta-ontology’ and any proposed answer to it ‘a meta-ontology’. In this essay, I shall briefly sketch a meta-ontology. The meta-ontology I shall present is broadly Quinean. (...) I am, in fact, willing to call it an exposition of Quine’s meta-ontology. (shrink)

The ramifications are explored of taking physical theories to commit their advocates only to ‘physically real’ entities, where ‘physically real’ means ‘causally efficacious’ (e.g., actual particles moving through space, such as dust motes), the ‘physically significant’ (e.g., centers of mass), and the merely mathematical—despite the fact that, in ordinary physical theory, all three sorts of posits are quantified over. It's argued that when such theories are regimented, existential quantification, even when interpreted ‘objectually’ (that is, in terms of satisfaction via variables, (...) rather than by substitution-instances) need not imply any ontological commitments. (shrink)

NOWADAYS, even schoolchildren babble about "null sets" and "singletons" and "one-one correspondences," as if they knew what they were talking about. But if they understand even less than their teachers, which seems likely, they must be using the technical jargon with only an illusion of understanding. Beginners are taught that a set having three members is a single thing, wholly constituted by its members but distinct from them. After this, the theological doctrine of the Trinity as "three in one" should (...) be child's play. (shrink)

The problem of absolute generality has attracted much attention in recent philosophy. Agustin Rayo and Gabriel Uzquiano have assembled a distinguished team of contributors to write new essays on the topic. They investigate the question of whether it is possible to attain absolute generality in thought and language and the ramifications of this question in the philosophy of logic and mathematics.

Our only channel of information about the world is the impact of external forces on our sensory surfaces. So says science itself. There is no clairvoyance. How, then, can we have parlayed this meager sensory input into a full-blown scientific theory of the world? This is itself a scientific question. The pursuit of it, with free use of scientific theory, is what I call naturalized epistemology. The Roots of Reference falls within that domain. Its more specific concern, within that domain, (...) is reference to concrete and abstract objects: what such reference consists in, and how we achieve it. (shrink)

The purpose of this article is show that second-order logic, as understood through standard semantics, is intimately bound up with set theory, or some other general theory of interpretations, structures, or whatever. Contra Quine, this does not disqualify second-order logic from its role in foundational studies. To wax Quinean, why should there be a sharp border separating mathematics from logic, especially the logic of mathematics?

The purpose of this article is to delimit what can and cannot be claimed on behalf of second-order logic. The starting point is some of the discussions surrounding my Foundations without Foundationalism: A Case for Secondorder Logic.