The Frege-Russell view is that existence is a second-order property rather than a property of individuals. One of the most compelling arguments for this view is based on the premise that there is an especially close connection between existence and number. The most promising version of this argument is by C.J.F Williams (1981, 1992). In what follows, I argue that this argument fails. I then defend an account according to which both predications of number and existence attribute properties to individuals.

This inquiry is motivated by the question: if atheism is true, is it nevertheless the case that holiness or sacredness is exemplified? I believe the answer to this question is affirmative, and that the path to its affirmation lies in the rejection of the traditional assumption that holiness is a single and simple property of a divinity that eludes analysis. The opposite view, that there are several complex properties comprising holiness, makes it manifest that there are holy beings, even a (...) holy ‘supreme being’, even if there is no God and no gods. (shrink)

‘Quantified pure existentials’ are sentences (e.g., ‘Some things do not exist’) which meet these conditions: (i) the verb EXIST is contained in, and is, apart from quantificational BE, the only full (as against auxiliary) verb in the sentence; (ii) no (other) logical predicate features in the sentence; (iii) no name or other sub-sentential referring expression features in the sentence; (iv) the sentence contains a quantifier that is not an occurrence of EXIST. Colin McGinn and Rod Girle have alleged that standard (...) first-order logic cannot adequately deal with some such existentials. The article defends the view that it can. (shrink)

It is often said that the ontological argument fails because it wrongly treats existence as a first-level property or predicate. This has proved a controversial claim, and efforts to evaluate it are complicated by the fact that the words ‘existence is not a property/predicate’ have been used by philosophers to make at least three different negative claims: (a) one about a first-level phenomenon possessed by objects like horses, stones, you and me; (b) another about the logical form of assertions of (...) existence; and (c) still another about a second-level phenomenon possessed by concepts when they are instantiated. I argue that only the last of these claims, originally voiced by Kant, is both plausible and relevant to the ontological argument. And I try to show that the relevance of the Kantian version comes from its providing the underlying justification for a different, and far less controversial, criticism of the ontological argument. (shrink)

While I do not accept any current analysis of theoretical terms I also reject certain criticisms of them. Specifically, I reject the criticism that the paradoxes of material implication and the counterfactual problem eliminate the explicit definition view; and I also reject the criticism that explicitly defined theoretical terms do not refer to anything which "really exists" or do not have "excess meaning." I do argue, however, that the explicit definition view confuses and conflates the concepts of criterion and meaning (...) analysis. I also defend reduction sentences against the counterfactual difficulty, but show, too, how this view is already logically committed to the network or postulational view of meaning. Finally, I show how the concept of reduction sentences confuses in several ways the concepts of criterion and meaning analysis--although not in quite the same way as explicit definitions do. (shrink)

Names name, but there are no individuals who are named by names. This is the key to an elegant and ideologically parsimonious strategy for analyzing the Buddhist catuṣkoṭi. The strategy is ideologically parsimonious, because it appeals to no analytic resources beyond those of standard predicate logic. The strategy is elegant, because it is, in effect, an application of Bertrand Russell's theory of definite descriptions to Buddhist contexts. The strategy imposes some minor adjustments upon Russell's theory. Attention to familiar catuṣkoṭi from (...) Vacchagotta and Nagarjuna as well as more obscure catuṣkoṭi from Khema, Zhi Yi, and Fa Zang motivates the adjustments. The result is a principled structural distinction between affirmative and negative catuṣkoṭi, as well as analyses for each that compare favorably to more recent efforts from Tillemans, Westerhoff, and Priest. (shrink)

Computational complexity theory is a branch of computer science dedicated to classifying computational problems in terms of their difficulty. While computability theory tells us what we can compute in principle, complexity theory informs us regarding our practical limits. In this chapter I argue that the science of \emph{quantum computing} illuminates complexity theory by emphasising that its fundamental concepts are not model-independent, but that this does not, as some suggest, force us to radically revise the foundations of the theory. For model-independence (...) never has been essential to those foundations. The fundamental aim of complexity theory is to describe what is achievable in practice under various models of computation for our various practical purposes. Reflecting on quantum computing illuminates complexity theory by reminding us of this, too often under-emphasised, fact. (shrink)

I argue that Kant's and Frege's refutations of the ontological argument are more similar than has generally been acknowledged. As I clarify, for both Kant and Frege, to say that something exists is to assert of a concept that it is instantiated. With such an assertion one expresses that there is a particular relation between the instantiating object and a rational subject - a particular mode of presentation for the object in question. By its very nature such a relation cannot (...) be the property of an object and thus cannot be included in the concept of that object. Thus the ontological argument, which takes existence to be a part of the concept of the supreme being, cannot, according to Kant and Frege, succeed. A secondary goal of the paper is to illuminate what I take to be an important affinity between Kant's and Frege's views more generally: that Frege's fundamental distinction between the sense and the referent of a proposition echoes, in an important way, Kant's distinction between concepts and the formal principles for their application to experience. (shrink)

Thanks to the Inlaks Foundation in India, I was able to do my doctoral research on Our Talk About Nonexistents at Oxford in the early eighties. The two greatest philosophers of that heaven of analytical philosophy - Peter Strawson and Michael Dummett - supervised my work, reading and criticising all the fledgling philosophy that I wrote during those three years. At Sir Peter's request, Gareth Evans, shortly before his death, lent me an unpublished transcript of Kripke's John Locke Lectures. Work (...) on the Appendix about Indian Philosophy was supervised by the late Professor Bimal Krishna Matilal with whom informal but intense philosophical conversations used to spill over into dinner at his place almost every other day. It was Professor Matilal who sent me, over a summer, to study a tough Navya-Nyaya text under his own Nyaya teacher Pandit Visvabandhu Tarkatirtha at Calcutta. All four of these teachers were as kind to me as my life-long mentor in philosophy Professor Pranab Kumar Sen, whose clarity and depth remain the unreachable regu lative ideal of my intellect. When I came back to India, my life became blissfully free of the agonising anxiety to publish, until, after a conference at Jadavpur University where I gave an impromptu paper, ironically enough, on Non-doings, I met Derek Parfit. He had a six-hour conversation with me, explicitly planning my life. Five years had already elapsed since I had finished my D. Phil, but Derek read my thesis and liked it. (shrink)

Attempts to analyze negative existential statements face the following familiar problem. If a negative existential statement—say, “Hamlet does not exist” or “the golden mountain does not exist”—is true, its subject term must lack an object of reference. But, absent such an object, it seems that nothing true or false can be said about “it.” In particular, if there is no Hamlet to talk about, we surely cannot truthfully say that “he” does not exist. Hence, the truth of true negative existentials—and (...) there are many—seems to preclude their truth and falsity. Call this “the negative existential problem.”. (shrink)