Metaphysics, Mathematics, and Meaning brings together Nathan Salmon's influential papers on topics in the metaphysics of existence, non-existence, and fiction; modality and its logic; strict identity, including personal identity; numbers and numerical quantifiers; the philosophical significance of Godel's Incompleteness theorems; and semantic content and designation. Including a previously unpublished essay and a helpful new introduction to orient the reader, the volume offers rich and varied sustenance for philosophers and logicians.

A dissertation in the tradition of logical positivism includes a discussion of the functions and methods of philosophy and a critique of ethics and theology.

In arithmetic, if only because many of its methods and concepts originated in India, it has been the tradition to reason less strictly than in geometry, ...

٣ ك٠ايم . ثم ع . ع ب عرس . ع يلتسين/تيسل كقهن تهنف.تتهك ؟رإئو. ا فىجين، ثهىميينتاتمتهييم ٠يإوثمق يبز. تينة «تم» يينم٠ همت٠كبه،فؤإ .ووهم.كوب. ...

Philosophers have met with many problems in discussing the interconnected concepts being, identity, and truth, and have advanced many theories to deal with them. Williams argues that most of these problems and theories result from an inadequate appreciation of the ways in which the words "be," "same," and "true" work. By means of linguistic analysis he shows that being and truth are not properties, and identity is not a relation. He is thus able to demystify a number of metaphysical issues (...) concerning the meaning of the word "I," the relation between the mental and the physical, objects of thought, times and places, and the nature of reality. Williams presents his views clearly, with a minimum of technicality, and with rich and apt examples, so that they will be accessible to readers not versed in symbolic logic. (shrink)

There will be a few themes. One to get us going: expansion versus contraction. About an object, o, and the region, R, of space(time) in which o is exactly located,1 we may ask: i) must there exist expansions of o: objects in filled superregions2 of R? ii) must there exist contractions of o: objects in filled subregions of..

This work is the long awaited sequel to the author’s classic Frege: Philosophy of Language. But it is not exactly what the author originally planned. He tells us that when he resumed work on the book in the summer of 1989, after a long interruption, he decided to start afresh. The resulting work followed a different plan from the original drafts. The reader does not know what was lost by their abandonment, but clearly much was gained: The present work may (...) be the most compactly organized of Dummett’s philosophical books, and its value as commentary on Frege is enhanced by its being organized as a study of Die Grundlagen der Arithmetik and selected parts of Grundgesetze. Moreover, since Dummett has been thinking and writing about Frege for forty years, we have a single, mature chronological stage of his thought. (shrink)

In "Frege: Philosophy of Mathematics" Dummett recommends the following thesis, (PNP): the correct analysis of any sentence containing a plural noun phrase will show that the phrase is functioning predictively. According to Dummett, (PNP), applied to numerical predications such as the leaves are 1,000' is the key premise in Frege's argument against Mill's theory of numbers. But Frege never subscribed to (PNP) and he rejected such numerical predications, and point out how Frege's own semantic theory for plural noun phrases obscures (...) his idea of a relation. (shrink)

I argue that composition as identity is incompatible with the possibility of emergent properties (as characterized in the paper) and so should be rejected.

Consensus has it that generic sentences such as “Dogs bark” and “Birds fly” contain, at the level of logical form, an unpronounced generic operator: Gen. On this view, generics have a tripartite structure similar to overtly quantified sentences such as “Most dogs bark” and “Typically, birds fly”. I argue that Gen doesn’t exist and that generics have a simple bipartite structure on par with ordinary atomic sentences such as “Homer is drinking”. On my view, the subject terms of generics are (...) kind-referring. The interesting truth conditions characteristic of generics arise from the interesting ways in which kinds inherit properties from their members. (shrink)

§ i. After deserting for a time the old Euclidean standards of rigour, mathematics is now returning to them, and even making efforts to go beyond them. ...

In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume ...

Philosophers have met with many problems in discussing the interconnected concepts being, identity, and truth, and have advanced many theories to deal with them. Professor Williams argues that most of these problems and theories result from an inadequate appreciation of the ways in which the words `be', `same', and `true' work. By means of linguistic analysis he shows that being and truth are not properties, and identity is not a relation. He is thus able to demystify a number of metaphysical (...) issues concerning the meaning of the word `I', the relation between the mental and the physical, objects of thought, times and places, and the nature of reality. Williams presents his views clearly, with a minimum of technicality, and with rich and apt examples, so that they will be accessible to readers not versed in symbolic logic. (shrink)

This paper is devoted to the study of bare nominal arguments (i.e., determinerless NPs occurring in canonical argumental positions) from a crosslinguistic point of view. It is proposed that languages may vary in what they let their NPs denote. In some languages (like Chinese), NPs are argumental (names of kinds) and can thus occur freely without determiner in argument position; in others they are predicates (Romance), and this prevents NPs from occurring as arguments, unless the category D(eterminer) is projected. Finally, (...) there are languages (like Germanic or Slavic) which allow both predicative and argumental NPs; these languages, being the ‘union’ of the previous two types, are expected to behave like Romance for certain aspects of their nominal system (the singular count portion) and like Chinese for others (the mass and plural portions). This hypothesis (the ‘Nominal Mapping Parameter’) is investigated not just through typological considerations, but also through a detailed contrastive analysis of bare arguments in Germanic (English) vs. Romance (Italian). Some general consequences of this view, which posits a limited variation in the mapping from syntax into semantics, for current theories of Universal Grammar and acquisition are considered. (shrink)

It is argued that the English bare plural (an NP with plural head that lacks a determiner), in spite of its apparently diverse possibilities of interpretation, is optimally represented in the grammar as a unified phenomenon. The chief distinction to be dealt with is that between the generic use of the bare plural (as in Dogs bark) and its existential or indefinite plural use (as in He threw oranges at Alice). The difference between these uses is not to be accounted (...) for by an ambiguity in the NP itself, but rather by explicating how the context of the sentence acts on the bare plural to give rise to this distinction. A brief analysis is sketched in which bare plurals are treated in all instances as proper names of kinds of things. A subsidiary argument is that the null determiner is not to be regarded as the plural of the indefinite article a. (shrink)

In this paper, I argue against Millian Descriptivism: that is, the view that, although sentences that contain names express singular propositions, when they use those sentences speakers communicate descriptive propositions. More precisely, I argue that Millian Descriptivism fares no better (or worse) than Fregean Descriptivism: that is, the view that sentences express descriptive propositions. This is bad news for Millian Descriptivists who think that Fregean Descriptivism is dead.

This paper presents a theory of empty names that is consistent with direct-reference theory and Millianism.

John Stuart Mill (1843) thought that proper names denote individuals and do not connote attributes. Contemporary Millians agree, in spirit. We hold that the semantic content of a proper name is simply its referent. We also think that the semantic content of a declarative sentence is a Russellian structured proposition whose constituents are the semantic contents of the sentence’s constituents. This proposition is what the sentence semantically expresses. Therefore, we think that sentences containing proper names semantically express singular propositions, which (...) are propositions having individuals as constituents. For instance, the sentence ‘George W. Bush is human’ semantically expresses a proposition that has Bush himself as a constituent. Call this theory Millianism. Many philosophers initially find Millianism quite appealing, but find it much less so after considering its many apparent problems. Among these problems are those raised by non-referring names, which are sometimes (tendentiously) called empty names. Plausible examples of empty names include certain names from fiction, such as ‘Sherlock Holmes’, which I shall call fictional names, and certain names from myth and false scientific theory, such as ‘Pegasus’ and ‘Vulcan’, which I shall call mythical names. I have defended Millianism from objections concerning empty names in previous work (Braun 1993). In this paper, I shall re-present those objections, along with some new ones. I shall then describe my previous Millian theory of empty names, and my previous replies to the objections, and consider whether the theory or replies need revision. I shall next consider whether fictional and mythical names are really empty. I shall argue that at least some utterances of mythical names are. (shrink)

This essay interprets Butler’s distinction between identity in the loose and popular sense and in the strict and philosophical sense. Suppose there are different standards for counting the same things. Then what are two distinct things counting strictly may be one and the same thing counting loosely. Within a given standard identity is one-one. But across standards it is many-one. An alternative interpretation using the parts-whole relation fails, because that relation should be understood as many-one identity. Another alternative making identity (...) relative to sort fails, because whole and parts can be of the same sort. (shrink)

English has plural terms as well as singular terms. But our standard formal languages, e.g., the predicate calculus, feature only singular terms. How can the plural idiom be formalized?‘Changing the subject’ is by far the most common plurals strategy among both philosophers and linguists: a plural term is replaced by a singular term standing for some complex object that ‘contains’ the individuals to which the plural term alludes. For example, one might simply replace ‘A, B imply C’ with ‘{A, B} (...) implies [singular] C’. We uncover a surprising variety of ways to change the subject, of ever‐increasing complexity and ingenuity. Our question is whether any can made to work. (shrink)

The heart of philosophy is metaphysics, and at the heart of the heart lie two questions about existence. What is it for any contingent thing to exist? Why does any contingent thing exist? Call these the nature question and the ground question, respectively. The first concerns the nature of the existence of the contingent existent; the second concerns the ground of the contingent existent. Both questions are ancient, and yet perennial in their appeal; both have presided over the burial of (...) so many of their would-be undertakers that it is a good induction that they will continue to do so. For some time now, the preferred style in addressing such questions has been deflationary when it has not been eliminativist. Ask Willard Quine what existence is, and you will hear that "Existence is what existential quantification expresses. "! Ask Bertrand Russell what it is for an individual to exist, and he will tell you that an individual can no more exist than it can be numerous: there 2 just is no such thing as the existence of individuals. And of course Russell's eliminativist answer implies that one cannot even ask, on pain of succumbing to the fallacy of complex question, why any contingent individual exists: if no individual exists, there can be no question why any individual exists. Not to mention Russell's modal corollary: 'contingent' and 'necessary' can only be said de dicto (of propositions) and not de re (of things). (shrink)

Written by Anthony Kenny, a leading figure in contemporary philosophy, this volume guides the reader through a concise and accessible explanation and assessment of Frege's radical and lasting contributions to our understanding of language, meaning, and the foundations of arithmetic.

This volume contains all of Frege's extant unpublished writings on philosophy and logic other than his correspondence, written at various stages of his career.

Plural predication is a pervasive part of ordinary language. We can say that some people are fifty in number, are surrounding a building, come from many countries, and are classmates. These predicates can be true of some people without being true of any one of them; they are non-distributive predications. However, the apparatus of modern logic does not allow a place for them. Thomas McKay here explores the enrichment of logic with non-distributive plural predication and quantification. His book will be (...) of great interest to philosophers of language, linguists, metaphysicians, and logicians. (shrink)

A thorough and closely argued examination of a central issue in philosophical logic, an issue which is shown to have profound implications for the philosophy of language and much of metaphysics.