This book is an exploration of philosophical questions about infinity. Graham Oppy examines how the infinite lurks everywhere, both in science and in our ordinary thoughts about the world. He also analyses the many puzzles and paradoxes that follow in the train of the infinite. Even simple notions, such as counting, adding and maximising present serious difficulties. Other topics examined include the nature of space and time, infinities in physical science, infinities in theories of probability and decision, the nature of (...) part/whole relations, mathematical theories of the infinite, and infinite regression and principles of sufficient reason. (shrink)

Bertrand Russell was one of the greatest logicians since Aristotle, and one of the most important philosophers of the past two hundred years. As we approach the 125th anniversary of the Nobel laureate's birth, his works continue to spark debate, resounding with unmatched timeliness and power. The Problems of Philosophy, one of the most popular works in Russell's prolific collection of writings, has become core reading in philosophy. Clear and accessible, this little book is an intelligible and stimulating guide to (...) those problems of philosophy which often mistakenly lead to its status as too lofty and abstruse for the lay mind. Focusing on problems he believes will provoke positive and constructive discussion, Russell concentrates on knowledge rather than metaphysics, steering the reader through his famous 1910 distinction between "knowledge by acquaintance and knowledge by description," and introducing important theories of Descartes, Kant, Hegel, Hume, Locke, Plato, and others to lay the foundation for philosophical inquiry by general readers and scholars alike.With a new introduction by John Perry, this valuable work is a perfect introduction to the field and will continue to stimulate philosophical discussion as it has done for nearly forty years. (shrink)

This book on infinite regress arguments provides (i) an up-to-date overview of the literature on the topic, (ii) ready-to-use insights for all domains of philosophy, and (iii) two case studies to illustrate these insights in some detail. Infinite regress arguments play an important role in all domains of philosophy. There are infinite regresses of reasons, obligations, rules, and disputes, and all are supposed to have their own moral. Yet most of them are involved in controversy. Hence the question is: what (...) exactly is an infinite regress argument, and when is such an argument a good one? (shrink)

Infinite regress arguments play an important role in many distinct philosophical debates. Yet, exactly how they are to be used to demonstrate anything is a matter of serious controversy. In this paper I take up this metaphilosophical debate, and demonstrate how infinite regress arguments can be used for two different purposes: either they can refute a universally quantified proposition (as the Paradox Theory says), or they can demonstrate that a solution never solves a given problem (as the Failure Theory says). (...) In the meantime, I show that Black’s view on infinite regress arguments (1996, this journal) is incomplete, and how his criticism of Passmore can be countered. (shrink)

Based mainly on unpublished papers this is the first detailed study of the early, neo-Hegelian period of Bertrand Russell's career. It covers his philosophical education at Cambridge, his conversion to neo-Hegelianism, his ambitious plans for a neo-Hegelian dialectic of the sciences and the problems which ultimately led him to reject it.

Gonzalo Rodriguez-Pereyra offers a fresh philosophical account of properties. How is it that two different things (such as two red roses) can share the same property (redness)? According to resemblance nominalism, things have their properties in virtue of resembling other things. This unfashionable view is championed with clarity and rigor.

ld English manors have their ghosts. And though I would not want to call analytic philosophy a ‘manor’, nor exactly ‘old’, it certainly is of some decent English origin, and it left adolescence a while ago. No wonder then, that it is not exempt from haunting terrors. One particular spectre has been haunting it for decades; it already gave some analytic pioneers the creeps, and we still now and then find people terrified by it: the ghost of old Bradley has (...) not yet found its rest and keeps on threatening people with his notorious regress. The present essay is a lecture in exorcism; much of the fear old Bradley spread, so I will argue, peters out once we dare to look it in the eye. However, this essay is not primarily exegetical, and especially not an attempt in interpreting Bradley. I find Bradley’s writings, to say the least, not particularly accessible. Discussions of isolated passages from his longer treatises will probably be less fruitful than a careful study of the positions within the whole argumentative structure, supplied by the examination of Bradley’s intellectual upcoming. His treatments on relations and properties, in which he develops the famous regress argument, are motivated by a radical goal: a vindication of some form of monism. To reach this goal, he tries to deconstruct the most basic categories of our ordinary conceptual framework. Thus, he holds that.. (shrink)

It is almost universally believed that some infinite regresses are vicious, and also almost universally believed that some are benign. In this paper I argue that regresses can be vicious for several different sorts of reasons. Furthermore, I claim that some intuitively vicious regresses do not suffer from any of the particular aetiologies that guarantee viciousness to regresses, but are nevertheless so on the basis of considerations of parsimony. The difference between some apparently benign and some apparently vicious regresses, then, (...) turns out to be a matter of a more general assessment of costs and benefits, making viciousness of regresses in some cases less of a local matter than is usually thought. (shrink)

This article articulates and defends F. H. Bradley's regress argument against external relations using contemporary analytic techniques and conceptuality. Bradley's argument is usually quickly dismissed as if it were beneath serious consideration. But I shall maintain that Bradley's argument, suitably reconstructed, is a powerful argument, plausibly premised, and free of such obvious fallacies as petitio principii. Thus it does not rest on the question‐begging assumption that all relations are internal, as Russell, and more recently van Inwagen, maintain. Bradley does not (...) attack external relations in order to affirm a doctrine of internal relations, and his monism is not derived from the internality of all relations, but from the self‐contradictory nature of all relations. For Bradley, it is the “relational situation”as such that is ontologically defective. (shrink)

To what extent do true predications correspond to truthmakers in virtue of which those predications are true? One sort of predicate which is often thought to not be susceptible to an ontological treatment is a predicate for instantiation, or some corresponding predication (trope-similarity or set-membership, for example). This paper discusses this question, and argues that an "ontological" approach is possible here too: where this ontological approach goes beyond merely finding a truthmaker for claims about instantiation. Along the way a version (...) of the problem of the regress of instantiation is posed and solved. (shrink)

Bertrand Russell argued that any attempt to get rid of universals in favor of resemblances fails. He argued that no resemblance theory could avoid postulating a universal of resemblance without falling prey to a vicious infinite regress. He added that admitting such a universal of resemblance made it pointless to avoid other universals. In this paper I defend resemblance nominalism from both of Russell's points by arguing that (a) resemblance nominalism can avoid the postulation of a universal of resemblance without (...) falling into a vicious infinite regress, and (b) even if resemblance nominalism had to admit a universal of resemblance, this would not make it pointless to avoid postulating other universals. (shrink)

Do non‐symmetric relations apply to the objects they relate in an order? According to the standard view of relations, the difference between aRb and bRa obtaining, where R is non‐symmetric, corresponds to a difference in the order in which the non‐symmetric relation R applies to a and b. Recently Kit Fine has challenged the standard view in his important paper ‘Neutral Relations’ arguing that non‐symmetric relations are neutral, lacking direction or order. In this paper I argue that Fine cannot account (...) for the application of non‐symmetric relations to their relata; so far from being neutral, these relations are inherently directional. (shrink)

Richard Gaskin analyses what is distinctive about sentences and the propositions they express--what marks them off from mere aggregates of words and meanings respectively. Since he identifies the world with all the true and false propositions, his account has significant implications for our understanding of the nature of reality.

What is the Problem of Universals? In this paper we take up the classic question and proceed as follows. In Sect. 1 we consider three problem solving settings and define the notion of problem solving accordingly. Basically I say that to solve problems is to eliminate undesirable, unspecified, or apparently incoherent scenarios. In Sect. 2 we apply the general observations from Sect. 1 to the Problem of Universals. More specifically, we single out two accounts of the problem which are based (...) on the idea of eliminating apparently incoherent scenarios, and then propose modifications of those two accounts which, by contrast, are based on the idea of eliminating unspecified scenarios. In Sect. 3 we spell out two interesting ramifications. (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)

I address an intuition commonly endorsed by metaphysicians, that there must be a fundamental layer of reality, i.e., that chains of ontological dependence must terminate: there cannot be turtles all the way down. I discuss applications of this intuition with reference to Bradley’s regress, composition, realism about the mental and the cosmological argument. I discuss some arguments for the intui- tion, but argue that they are unconvincing. I conclude by making some suggestions for how the intuition should be argued for, (...) and discussing the ramifications of giving the justification I think best. (shrink)

Applying the rules and systems of mathematics and logic to instance ontology, this work argues for the validity and problem-solving capacities of instance ontology, and associates it with a version of the realist position which is named by the author as moderate realism.

Ever since F. H. Bradley first formulated his famous regress argument philosophers have been hard at work trying to refute it. The argument fails, it has been suggested, either because its conclusion just does not follow from its premises, or it fails because one or more of its premises should be given up. In this paper, the Bradleyan argument, as well as some of the many and varied reactions it has received, is scrutinized.

Gaskin's book The Unity of the Proposition is very rich in material. I will focus only on its central thesis: Gaskin holds that Bradley's regress (more precisely, one particular version of it) is not only innocent, but in fact philosophically significant because it plays a crucial role in solving what Gaskin calls the problem of the unity of the proposition . In what follows, I first explain what that problem is meant to be ( section 1 ), then I present (...) and criticise Gaskin's proposal about how Bradley's regress bears on the problem ( section 2 ), and finally I sketch an alternative approach to the problem ( section 3 ). (shrink)

The purpose of the following, paper is to consider whether there is a fundamenital division of the objects with which metaphysics is concerned into two classes, universals and particulars, or whetlher there is any method of overcoming this dualism. My own opinion is that the dualism is ultimate; on the other hand, many men with whom, in the main, I am in close agreement, hold that it is not ultimate. I do not feel the grounds in favour of its ultimate (...) nature to be very conclusive, and in what follows I should lay stress rather on the distinctions and considerations introduced during the argument than on the conclusion at which the argument arrives. (shrink)

Infinite regress arguments are part of a philosopher's tool kit of argumentation. But how sharp or strong is this tool? How effectively is it used? The typical presentation of infinite regress arguments throughout history is so succinct and has so many gaps that it is often unclear how an infinite regress is derived, and why an infinite regress is logically problematic, and as a result, it is often difficult to evaluate infinite regress arguments. These consequences of our customary way of (...) using this tool indicate that there is a need for a theory to re-orient our practice. My general approach to contribute to such a theory, consists of collecting and evaluating as many infinite regress arguments as possible, comparing and contrasting many of the formal and non-formal properties, looking for recurring patterns, and identifying the properties that appeared essential to those patterns. Two very general questions guided this work: How are infinite regresses generated in infinite regress arguments? How do infinite regresses logically function as premises in an argument? In answering these questions I clarify the notion of an infinite regress; identify different logical forms of infinite regresses; describe different kinds of infinite regress arguments; distinguish the rhetoric from the logic in infinite regress arguments; and suggest ways of improving our discussion and our practice of constructing and evaluating these arguments. (shrink)

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A version of Bradley's regress can be endorsed in an effort to address the problem of the unity of states of affairs or facts, thereby arriving at a doctrine that I have called fact infinitism . A consequence of it is the denial of the thesis, WF, that all chains of ontological dependence are well-founded or grounded. Cameron has recently rejected fact infinitism by arguing that WF, albeit not necessarily true, is however contingently true. Here fact infinitism is supported by (...) showing that Cameron's argument for the contingent truth of WF is unsuccessful. (shrink)

Trope theory is the view that the world is a world of abstract particular qualities. But if all there is are tropes, how do we account for the truth of propositions ostensibly made true by some concrete particular? A common answer is that concrete particulars are nothing but tropes in compresence. This answer seems vulnerable to an argument (first presented by F. H. Bradley) according to which any attempt to account for the nature of relations will end up either in (...) contradiction, nonsense, or will lead to a vicious infinite regress. I investigate Bradley’s argument and claim that it fails to prove what it sets out to. It fails, I argue, because it does not take all the different ways in which relation and relata may depend on one another into account. If relations are entities that are distinct from yet essentially dependent upon their relata, the Bradleyan problem is solved. We are then free to say that tropes in compresence are what make true propositions ostensibly made true by concrete particulars. (shrink)

This dissertation is on infinite regress arguments in philosophy. Its main goals are to explain what such arguments from many distinct philosophical debates have in common, and to provide guidelines for using and evaluating them. Two theories are reviewed: the Paradox Theory and the Failure Theory. According to the Paradox Theory, infinite regress arguments can be used to refute an existentially or universally quantified statement (e.g. to refute the statement that at least one discussion is settled, or the statement that (...) discussions are settled only if there is an agreed-upon criterion to settle them). According to the Failure Theory, infinite regress arguments can be used to demonstrate that a certain solution fails to solve an existentially or universally quantified problem (e.g. to demonstrate that a certain solution fails to settle all discussions, or that it fails to settle even one discussion). In the literature, the Paradox Theory is fairly well-developed, and this dissertation provides the Failure Theory with the same tools. (shrink)

In the early twentieth century an apparently obscure philosophical debate took place between F. H. Bradley and Bertrand Russell. The historical outcome was momentous: the demise of the movement known as British Idealism, and its eventual replacement by the various forms of analytic philosophy. Since then, a conception of this debate and its rights and wrongs has become entrenched in English-language philosophy. Stewart Candlish examines afresh the events of this formative period in twentieth-century thought and comes to some surprising conclusions.

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)

D. W. Mertz provides a "new" competitor in the universals debate by reviving, developing, and defending the medieval doctrine of Moderate Realism. This book is a substantial contribution to ontology and logic, combining interesting new arguments for polyadic relations and unit attributes, careful and thorough historical studies, and a logic that could solve many old problems.

Richard Gaskin presents a work in the philosophy of language.

An argument that the major metaphysical theories of facts give us no good reason to accept facts in our catalog of the world. -/- In this book Arianna Betti argues that we have no good reason to accept facts in our catalog of the world, at least as they are described by the two major metaphysical theories of facts. She claims that neither of these theories is tenable—neither the theory according to which facts are special structured building blocks of reality (...) nor the theory according to which facts are whatever is named by certain expressions of the form “the fact that such and such.” There is reality, and there are entities in reality that we are able to name, but, Betti contends, among these entities there are no facts. -/- Drawing on metaphysics, the philosophy of language, and linguistics, Betti examines the main arguments in favor of and against facts of the two major sorts, which she distinguishes as compositional and propositional, giving special attention to methodological presuppositions. She criticizes compositional facts (facts as special structured building blocks of reality) and the central argument for them, Armstrong's truthmaker argument. She then criticizes propositional facts (facts as whatever is named in “the fact that” statements) and what she calls the argument from nominal reference, which draws on Quine's criterion of ontological commitment. Betti argues that metaphysicians should stop worrying about facts, and philosophers in general should stop arguing for or against entities on the basis of how we use language. (shrink)

Reviewed Work: Explaining Explanation by David-Hillel Ruben .