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)

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)

In this paper I argue that holes are not objects, but should instead be construed as properties or relations. The argument proceeds by first establishing a claim about angles: that angles are not objects, but properties or relations. It is then argued that holes and angles belong to the same category, on the grounds that they share distinctive existence and identity conditions. This provides an argument in favour of categorizing holes as one categorizes angles. I then argue that a commitment (...) to the existence of properties to be identified with holes provides sufficient resources to account for true claims about holes. (shrink)

Long after we have abandoned belief in a Cosmic Law Giver, still we cling to the word ‘law’ in science. It is in this same way that we cannot let go of the substantializing and pluralizing ‘universal’, even though its literal sense indicates a kind of turning, a ‘one-turning’, rather than a kind of thing . Yet ‘the problem of Universals’ is supposed to have become, again, a ‘compulsory examination question’ for philosophers. Let us reveal how this tradition begins for (...) us. (shrink)

This paper presents a uniform general account of regress problems in the form of a pentalemma—i.e., a set of five mutually inconsistent claims. Specific regress problems can be analyzed as instances of such a general schema, and this Regress Pentalemma Schema can be employed to generate deductively valid arguments from the truth of a subset of four claims to the falsity of the fifth. Thus, a uniform account of the nature of regress problems allows for an improved understanding of specific (...) regress objections or arguments, and, correspondingly, of the general logical geography of the debate about infinite regresses. This uniform approach is illustrated by a treatment of the classical epistemological problem of justification, but it encompasses a whole variety of cases including explanation and ontological grounding. Furthermore, this general account is compared and contrasted with the existing literature discussing argument schemata for regress objections, particularly with the work of Jan Willem Wieland. It is shown how such other schemata can be incorporated and superseded by the general Regress Pentalemma Schema. (shrink)

Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of ontological commitment to real (...) numbers. (shrink)

Many philosophers have declared that everything which exists is a particular. There is a weak interpretation of this doctrine which I believe to be a true proposition, and a strong one which I believe to be false.

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)

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)

Neste artigo, realiza-se uma análise do Nominalismo de Semelhança tal como formulado por Price. Inicialmente, apresento a posição de Price e suas críticas ao Realismo a respeito dos universais. Segundo ele, o Realismo não fornece uma correta explanação da semelhança inexata entre diferentes particulares. A fim de estabelecer a sua posição nominalista, ele se dedica a refutar duas objeções clássicas: o argumento do aspecto e o argumento do regresso. Posteriormente, analiso as principais críticas contra o Nominalismo de Price: o caráter (...) primitivo da relação de semelhança, o problema do estabelecimento de paradigmas e o problema do regresso. A teoria de Price não é capaz de responder a essas objeções adequadamente. (shrink)

Este ensaio consiste num exame crítico da estrutura e do valor de um conjunto diverso de argumentos por regressão ao infinito que têm sido objecto de discussão recorrente na metafísica contemporânea. O seminal livro de David Armstrong Nominalism and Realism (Armstrong 1978) contém uma das mais compreensivas discussões de argumentos regressivos em metafísica, os quais variam entre argumentos que foram de facto avançados ao longo da história da disciplina (como o Argumento do Terceiro Homem, de Platão) e argumentos construídos de (...) novo por Armstrong para fins de exame crítico. Os argumentos regressivos discutidos por Armstrong têm como alvo uma grande variedade de teorias metafísicas acerca da semelhança e da predicação, entre as quais se contam o nominalismo de predicados, o nominalismo de conceitos, o nominalismo de classes, o nominalismo de semelhança e o realismo metafísico. (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 literature, regress arguments often take one of two different forms: either they conclude that a given solution fails to solve any problem of a certain kind (the strong conclusion), or they conclude that a given solution fails to solve all problems of a certain kind (the weaker conclusion). This gives rise to a logical problem: do regresses entail the strong or the weaker conclusion, or none? In this paper I demonstrate that regress arguments can in fact take both (...) forms, and clearly set out the logical difference between them. Throughout the paper, I confine myself to metaphysical examples from the early Russell. Only now that we know they are valid can we start to discuss whether they are sound. (shrink)