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.

Immensely intelligible, thought-provoking guide by Nobel prize-winner considers such topics as the distinction between appearance and reality, the existence and nature of matter, idealism, inductive logic, intuitive knowledge, many other subjects. For students and general readers, there is no finer introduction to philosophy than this informative, affordable and highly readable edition that is "concise, free from technical terms, and perfectly clear to the general reader with no prior knowledge of the subject."—The Booklist of the American Library Association.

Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obscured previous (...) discussions of these projects, and presents clear, concise accounts of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed. (shrink)

The problem of universals, important in the history of philosophy, remains a crucial issue today not only for metaphysics, but also for the philosophy of science. This anthology offers a comprehensive presentation of twenty-eight analyses of the problem of universals. It opens with analyses presented by Plato and Aristotle and then provides selections from the views of the medieval scholars Abelard, Aquinas, Duns Scotus, and Ockham. It then traces the development of Western thought on this fundamental topic from the modern (...) through the contemporary period and includes the work of Kant, Hegel, Husserl, Heidegger, Russell, Quine, Strawson, Carnap, and Allaire. To aid the student in understanding these investigations into the nature of universals, each reading is preceded by a concise introduction by the editor. (shrink)

In this volume, John Bacon argues that it is difficult to deny the existence of particularized properties and relations, which in modern philosophy are sometimes called `tropes'. In so doing, he advances a powerful and sophisticated metaphysical theory according to which both ordinary particulars and properties and relations are bundles of tropes.

Four- Dimensionalism defends the thesis that the material world is composed of temporal as well as spatial parts. This defense includes a novel account of persistence over time, new arguments in favour of the four-dimensional ontology, and responses to the challenges four- dimensionalism faces." "Theodore Sider pays particular attention to the philosophy of time, including a strong series of arguments against presentism, the thesis that only the present is real. Arguments offered in favour of four- dimensionalism include novel arguments based (...) on time travel, the debate between spacetime substantivalists and relationalists, and vagueness. Also included is a comprehensive discussion of the paradoxes of coinciding material objects, and a novel resolution of those paradoxes based on temporal counterpart theory. In conclusion Sider replies to prominent objections to four- dimensionalism, including discussion of the problem of the rotating homogenous disk. (shrink)

Chris Daly; Tropes, Proceedings of the Aristotelian Society, Volume 94, Issue 1, 1 June 1994, Pages 253–262, https://doi.org/10.1093/aristotelian/94.1.253.

A theory purporting to solve the problem of universals must be able to explain predication, recurrence, and classification. How Platonism does this is well known. Here I take a hard look at an attempt by M.J. Cresswell to give an Aristotelian answer and show it to be a complete and utter failure. The answer does not eliminate commitment to universals and it is only half an answer anyway because it does not cover relational predicates, an omission that Russell noted dooms (...) answers by other philosophers as well. (shrink)

Contemporary logicians sometimes discuss questions like ‘What criterion is there for deciding whether a portion of language or a theory is committed to the existence of anything?’, ‘Does mathematics require us to countenance or tolerate abstract entities?’. In the course of these discussions ancient problems about universals reappear in a new dress. Quine, for one, would agree that it is not by our use of general terms that we commit ourselves to the existence of anything, for general terms like ‘red’ (...) and ‘five’ are not names. Nor does the use of names commit one to corresponding entities, for we sometimes use a name non–designatively. “Names,” as Quine says, “are in fact altogether immaterial to the onto–logical issue.” Quine argues that there is only one way in which we can find out what entities a theory commits us to. Given that the theory is expressed in the symbolism of quantification theory, we discover what entities the theory is committed to by examining what entities have to be values of our bound variables if the statements made in the theory are to be true. “To be is purely and simply to be the value of a variable”. I want to argue in this paper that Quine’s criterion of ontological commitment cannot distinguish genuine from bogus ontological commitment and is therefore inadequate. (shrink)

Indispensability arguments for realism about mathematical entities have come under serious attack in recent years. To my mind the most profound attack has come from Penelope Maddy, who argues that scientific/mathematical practice doesn't support the key premise of the indispensability argument, that is, that we ought to have ontological commitment to those entities that are indispensable to our best scientific theories. In this paper I defend the Quine/Putnam indispensability argument against Maddy's objections.

The primary purpose of this paper is to argue that particulars in the actual world are nothing but complexes of universals. I begin by briefly presenting bertrand russell's version of this view and exposing its primary difficulty. I then examine the key assumption which leads russell to difficulty and show that it is mistaken. The rejection of this assumption forms the basis of an alternative version of the view which is articulated and defended.

This paper examines the view that ordinary particulars are complexes of universals. Russell's attempt to develop such a theory is articulated and defended against some common misinterpretations and unfounded criticisms in Section I. The next two sections address an argument which is standardly cited as the primary problem confronting the theory: (1) it is committed to the necessary truth of the principle of the identity of indiscernibles; (2) the principle is not necessarily true. It is argued in Section II that (...) a proponent of the theory need not accept (1) and an argument against (2) is presented in Section III. The final section attempts to show that Russell's theory ultimately fails because of inadequacies in its treatment of space and time. The paper closes with a suggestion for remedying this difficulty. (shrink)

An argument for realism (i.E., The ontological thesis that there exist universals) has emerged in the writings of david armstrong, Fred dretske, And michael tooley. These authors have persuasively argued against traditional reductive accounts of laws and nature. The failure of traditional reductive accounts leads all three authors to opt for a non-Traditional reductive account of laws which requires the existence of universals. In other words, These authors have opted for accounts of laws which (together with the fact that there (...) are laws) entail that realism is true. This argument for realism which emerges from the work of armstrong, Dretske, And tooley is discussed and criticized. Conclusions from the discussion question the tenability of all reductive accounts of laws. (shrink)

The essay constructs an ontological theory designed to capture the categories instantiated in those portions or levels of reality which are captured in our common sense conceptual scheme. It takes as its starting point an Aristotelian ontology of “substances” and “accidents”, which are treated via the instruments of mereology and topology. The theory recognizes not only individual parts of substances and accidents, including the internal and external boundaries of these, but also universal parts, such as the “humanity” which is an (...) essential part of both Tom and Dick, and also “individual relations”, such as Tom’s promise to Dick, or their current handshake. (shrink)

Although philosophy has undergone a number of revolutions since the turn of the century, the existence of universals is still debated largely in the terms employed by Moore and Russell around 1910. A recent article by Alan Donagan illustrates this nicely, for Donagan expounds and defends what he takes to be the principal argument for universals given by Russell in The Problems of Philosophy. I shall comment critically on the case Donagan makes for Russell's metaphysical realism, but my main concern (...) is to establish a point of more general interest—namely, that the most plausible strategy for defending a commitment to universals actually raises more problems than it promises to solve. (shrink)

In this short text, a distinguished philosopher turns his attention to one of the oldest and most fundamental philosophical problems of all: How it is that we are able to sort and classify different things as being of the same natural class? Professor Armstrong carefully sets out six major theories—ancient, modern, and contemporary—and assesses the strengths and weaknesses of each. Recognizing that there are no final victories or defeats in metaphysics, Armstrong nonetheless defends a traditional account of universals as the (...) most satisfactory theory we have.This study is written for advanced students, but as Armstrong goes considerably beyond his earlier work on this topic, it will interest professional scholars as well. Carefully plotted and clearly written, Universals is both a paradigm of exposition and a case study on the value of careful analysis of fundamental issues in philosophy. (shrink)

v. 1. Nominalism and realism.--v. 2. A theory of universals.

First, The doctrine of naturalism, That reality is spatio-Temporal, Is defended. Second, The doctrine of materialism or physicalism, That this spatio-Temporal reality involves nothing but the entities of physics working according to the principles of physics, Is defended. Third, It is argued that these doctrines do not constitute a "first philosophy." a satisfactory first philosophy should recognize universals, In the form of instantiated properties and relations. Laws of nature are constituted by relations between universals. What universals there are, And what (...) relations hold between them, Must be discovered "a posteriori" by scientific investigation. (shrink)

What is it for a particular to have a property? many proposed analyses of this situation may be called relational accounts. The particular has some relation, R, To some entity p. R may be the relation of falling under, Being a member of, Resembling or "participating." p may be a predicate, A concept, A class, A paradigm instance or a form. A number of arguments seek to prove that all these accounts are involved in various vicious infinite regresses. These arguments (...) are classified, Their resemblances and differences noted, And their soundness assessed. (edited). (shrink)

Arda Denkel, in "Real Resemblances," argues for a moderate Nominalism where substances objectively have properties and relations, the latter being particulars, but dependent particulars, grouped into classes by objective relations of resemblance. This view is contrasted unfavorably with the view that properties and relations are universals instantiated by particulars. It is conceded that Denkel's scheme has much to commend it. But it is argued that the universals view has much more to be said for it than Denkel allows, and that (...) it is indeed, on balance, the superior view. (shrink)

The pair democreteanism-Platonism (nothing/something is outside space-Time) differs from the pair nominalism-Realism (universals are/are not nameable entities). Nominalism need not be democretean, And democreateanism is nominalist only if conceptualism is rejected. Putnam's critique of nominalism is thus invalid. Quine's theory is democretean-When-Possible: quine is also a minimalist platonist. Conceptualists and realists agree that universals exist but not as physical objects. Nominalists accept universals only as "facons de parler".

First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

With this third edition of Nelson Goodman's The Structure of Appear ance, we are pleased to make available once more one of the most in fluential and important works in the philosophy of our times. Professor Geoffrey Hellman's introduction gives a sustained analysis and appreciation of the major themes and the thrust of the book, as well as an account of the ways in which many of Goodman's problems and projects have been picked up and developed by others. Hellman also (...) suggests how The Structure of Appearance introduces issues which Goodman later continues in his essays and in the Languages of Art. There remains the task of understanding Good man's project as a whole; to see the deep continuities of his thought, as it ranges from logic to epistemology, to science and art; to see it therefore as a complex yet coherent theory of human cognition and practice. What we can only hope to suggest, in this note, is the b. road Significance of Goodman's apparently technical work for philosophers, scientists and humanists. One may say of Nelson Goodman that his bite is worse than his bark. Behind what appears as a cool and methodical analysis of the conditions of the construction of systems, there lurks a radical and disturbing thesis: that the world is, in itself, no more one way than another, nor are we. It depends on the ways in which we take it, and on what we do. (shrink)

Fictionalist approaches to ontology have been an accepted part of philosophical methodology for some time now. On a fictionalist view, engaging in discourse that involves apparent reference to a realm of problematic entities is best viewed as engaging in a pretense. Although in reality, the problematic entities do not exist, according to the pretense we engage in when using the discourse, they do exist. In the vocabulary of Burgess and Rosen (1997, p. 6), a nominalist construal of a given discourse (...) is revolutionary just in case it involves a “reconstruction or revision” of the original discourse. Revolutionary approaches are therefore prescriptive. In contrast, a nominalist construal of a given discourse is hermeneutic just in case it is a nominalist construal of a discourse that is put forth as a hypothesis about how the discourse is in fact used; that is, hermeneutic approaches are descriptive. I will adopt Burgess and Rosen’s terminology to describe the two different spirits in which a fictionalist hypothesis in ontology might be advanced. Revolutionary fictionalism would involve admitting that while the problematic discourse does in fact involve literal reference to nonexistent entities, we ought to use the discourse in such a way that the reference is simply within the pretense. The hermeneutic fictionalist, in contrast, reads fictionalism into our actual use of the problematic discourse. According to her, normal use of the problematic discourse involves a pretense. According to the pretense, and only according to the pretense, there exist the objects to which the discourse would commit its users, were no pretense involved. My purpose in this paper is to argue that hermeneutic fictionalism is not a viable strategy in ontology. My argument proceeds in two steps. First, I discuss in detail several problematic consequences of any interesting application of hermeneutic fictionalism. Of course, if there is good evidence that hermeneutic fictionalism is correct in some cases, then some of these drastic consequences would have to be accepted.. (shrink)