Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters. The book addresses the need for a theory of infinity, and reviews both old and new theories of infinity. It (...) discussing the purposes of studying infinity and the troubles with traditional approaches to the problem, and concludes by offering a solution to some existing paradoxes. (shrink)

In this paper, I will present and defend an argument from the conditional character of inferential justification against the version of epistemic infinitism Klein advances. More specifically, after proposing a distinction between propositional and doxastic infinitism, which is based on a standard distinction between propositional and doxastic justification, I will describe in considerable detail the argument from conditionality, which is mainly an argument against propositional infinitism, and clarify some of its main underlying assumptions. There are various responses to be found (...) in Klein’s works to this argument, and my aim is to show that none of those responses can be plausibly held without infinitism losing its title to being a genuine non-skeptical alternative. (shrink)

I argue—contra moderate grounding pluralists such as Kit Fine and more extreme grounding pluralists such as Jessica Wilson—that there is fundamentally only one grounding/in-virtue-of relation. I also argue that this single relation is indispensable for normative theorizing—that we can’t make sense of, for example, the debate over consequentialism without it. It follows from what I argue that there is no metaethically-pure normative ethics.

An agent’s belief in a proposition, E0, is justified by an infinite regress of deferred justification just in case the belief that E0 is justified, and the justification for believing E0 proceeds from an infinite sequence of propositions, E0, E1, E2, etc., where, for all n ≥ 0, En+1 serves as the justification for En. In a number of recent articles, Atkinson and Peijnenburg claim to give examples where a belief is justified by an infinite regress of deferred justification. I (...) argue here that there is no reason to regard Atkinson and Peijnenburg’s examples as cases where a belief is so justified. My argument is supported by careful consideration of the grounds upon which relevant beliefs are held within Atkinson and Peijnenburg’s examples. (shrink)

What follows is a taxonomy of arguments that regresses of inferential justification are vicious. They fall out into four general classes: conceptual arguments from incompleteness, conceptual arguments from arbitrariness, ought-implies-can arguments from human quantitative incapacities, and ought-implies can arguments from human qualitative incapacities. They fail with a developed theory of "infinitism" consistent with valuational pluralism and modest epistemic foundationalism.

This paper is about metaphysical ‘infinitism’, the view that there are, or could be, infinite chains of ontological dependence. Its main aim is to show that, contrary to widespread opinion, metaphysical infinitism is a coherent position. On the basis of this, it is then additionally argued that metaphysical infinitism need not fare worse than the more canonical ‘foundationalist’ alternatives when it comes to formulating metaphysical explanations. In the course of the discussion, a rather unexplored parallel with the debate concerning infinitism (...) about justification is suggested. (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)

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)

If an argument can be reconstructed in at least two different ways, then which reconstruction is to be preferred? In this paper I address this problem of argument reconstruction in terms of Ryle’s infinite regress argument against the view that knowledge-how requires knowledge-that. First, I demonstrate that Ryle’s initial statement of the argument does not fix its reconstruction as it admits two, structurally different reconstructions. On the basis of this case and infinite regress arguments generally, I defend a revisionary take (...) on argument reconstruction: argument reconstruction is mainly to be ruled by charity (viz. by general criteria which arguments have to fulfil in order to be good arguments) rather than interpretation. (shrink)

This note employs the recently established consistency theorem for infinite regresses of probabilistic justification (Herzberg in Stud Log 94(3):331–345, 2010) to address some of the better-known objections to epistemological infinitism. In addition, another proof for that consistency theorem is given; the new derivation no longer employs nonstandard analysis, but utilises the Daniell–Kolmogorov theorem.

In his “Space, supervenience and substantivalism”, Le Poidevin proposes a substantivalism in which space is discrete, implying that there are unmediated spatial relations between neighboring primitive points. This proposition is motivated by his concern that relationism suffers from an explanatory lacuna and that substantivalism gives rise to a vicious regress. Le Poidevin implicitly requires that the relationist be committed to the “only x and y ” principle regarding spatial relations. It is not obvious that the relationist is committed to this (...) principle in such a context. An additional motivation for Le Poidevin's argument, that space should be considered to be discrete, is that he believes that substantivalists are committed to a vicious regress. I show that the regress is in fact not of the vicious variety. These two main arguments show that Le Poidevin's suggestion that we drop the density postulate for space is unnecessary. (shrink)