In this paper I argue that the infinite regress of resemblance is vicious in the guise it is given by Russell but that it is virtuous if generated in a (contemporary) trope theoretical framework. To explain why this is so I investigate the infinite regress argument. I find that there is but one interesting and substantial way in which the distinction between vicious and virtuous regresses can be understood: The Dependence Understanding. I argue, furthermore, that to be (...) able to decide whether an infinite regress exhibits a dependence pattern of a vicious or a virtuous kind, facts about the theoretical context in which it is generated become essential. It is precisely because of differences in context that he Russellian resemblance regress is vicious whereas its trope theoretical counterpart is not. (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)

One of the standard objections against the impossibility of infinite regress is associated with David Hume and Paul Edwards, but originates with William Ockham. They claim that in an infinite regress every member of the series is explained, and nothing is unexplained. Every member is explained by the one before it, and the series as a whole is nothing over and above its members, and so needs no cause of its own. Utilizing the well-known Thomistic distinction between essentially (...) ordered and accidentally ordered causal series, I show that the Hume-Edwards-Ockham objection fails to touch Aquinas’s argument against the impossibility of infinite regress in an essentially ordered series. However, Aquinas also argues that accidentally ordered causal series can only regress infinitely if supported by an everlasting essential cause. The Hume-Edwards-Ockham objection does raise a question about this thesis, but I show how St. Thomas can reply to it convincingly. (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)

This paper uses a schema for infinite regress arguments to provide a solution to the problem of the infinite regress of justification. The solution turns on the falsity of two claims: that a belief is justified only if some belief is a reason for it, and that the reason relation is transitive.

According to Johansson (2009: 22) an infinite regress is vicious just in case “what comes first [in the regress-order] is for its definition dependent on what comes afterwards.” Given a few qualifications (to be spelled out below (section 3)), I agree. Again according to Johansson (ibid.), one of the consequences of accepting this way of distinguishing vicious from benign regresses is that the so-called Russellian Resemblance Regress (RRR), if generated in a one-category trope-theoretical framework, is vicious and that, (...) therefore, the existence of tropes only makes sense if trope-theory is understood (minimally) as a two-category theory which accepts, besides the existence of tropes, also the existence of at least one universal: resemblance.1 I disagree. But how can that be? How can Johansson and I agree about what distinguishes a vicious from a benign regress, yet disagree about which regresses are vicious and which are benign? In this paper I attempt to answer that question by first setting out and defending the sense of viciousness which both Johansson and I accept, only to then argue that to be able to determine if a particular regress is vicious in this sense, more than features intrinsic to the regress itself must be taken into account. This is why, although the RRR as originally set out by Russell is vicious, the seemingly identical resemblance regress which ensues in a one-category (standard) trope-theoretical context is not (provided, that is, that we accept certain views about how the nature of tropes relates to the resemblance between tropes, and given that we set our theory in a truthmaker theoretical framework – all of which are standard assumptions for proponents of (the standard-version of) the trope-theory).2. (shrink)

A prominent Thomistic cosmological argument maintains that an infinite regress of causes, which exhibits a certain pattern of ontological dependence among its members, would be vicious and so must terminate in a first member. Interestingly, Jonathan Schaffer offers a similar argument in the contemporary grounding literature for the view called metaphysical foundationalism. I consider the striking similarities between both arguments and conclude that both are unsuccessful for the same reason. I argue this negative result gives us indirect reason to (...) consider metaphysical infinitism as a genuine possibility, the view that chains of ontological dependence or ground can descend indefinitely. (shrink)

Wolff’s relation to Leibniz and Kant’s relation to both are notoriously vexed questions. First, this paper argues that Wolff’s most serious departure from Leibniz consists in his (so far overlooked) rejection of the latter’s infinitism. Second, it contends that the controversies that surrounded Wolff’s early acceptance of infinite causal regress and prompted his conversion to finitism played a prominent role in shaping the theses of Kant’s Antinomies. Whereas Leibniz and the early Wolff considered infinite regress to provide support (...) for the contingency of the world and the existence of God, Wolff’s enemies condemned it as Spinozistic. After Wolff, the claim that an infinite chain of causes is impossible became the standard view among both Wolffian and anti-Wolffian metaphysicians. (shrink)

Some philosophers follow mctaggart in holding that there is a vicious infinite regress of tensed predications. Other philosophers claim there is no regress. The author argues that there is a regress, But it is benign.

This article offers a reconstruction of an argument against infinite regress formulated by Aristotle in Posterior Analytics I 22. I argue against the traditional interpretation of the chapter, according to which singular terms and summa genera, in virtue of having restrict logical roles, provide limits for predicative chains, preventing them from proceeding ad infinitum. As I intend to show, this traditional reading is at odds with some important aspects of Aristotle’s theory of demonstration. More importantly, it fails to explain (...) how his proof is connected to a defence of the existence of ultimate explanations, a connection that must be the case if I 19-22 is advancing a foundationalist way-out to a sceptical challenge raised in I 3. (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)

In this dissertation we discuss infinite regress arguments from both a historical and a logical perspective. Throughout we deal with arguments drawn from various areas of philosophy. ;We first consider the regress generating portion of the argument. We find two main ways in which infinite regresses can be developed. The first generates a regress by defining a relation that holds between objects of some kind. An example of such a regress is the causal regress used in some (...) versions of the Cosmological Argument. The second sort of regress is generated by defining a certain procedure that can be repeated indefinitely many times. This will often be a procedure of analysis or of explanation. ;We then argue that for purposes of discussing regressive viciousness it is helpful to divide regresses into two main types. One type raises primarily epistemological issues. In this class we find the regress of justification often used in foundational arguments in epistemology. We also discuss certain arguments that treat theories of predication as attempts to explain predication. Our other class contains those regresses that raise primarily metaphysical problems. This class includes the causal regress as well as those arguments concerned with predication as an ontological problem. ;We agree with some philosophers that one problem that arises in the case of vicious regression is circularity. We show how this problem can be generalized to include other apparently non-circular regresses. The other main problem in epistemological regresses arises as a result of certain conditions that are placed on the relation involved. We look in detail at the epistemological justification regress to illustrate this last point. ;With respect to metaphysical regresses we again find several types of viciousness arguments. One problem is whether the infinite collection required for the regress is even possible. Another problem is whether an infinite number of events can occur in a finite time. These we deal with only briefly. The main difficulty with these regresses, considered as regresses and not just as infinite sets, again turns out to be certain conditions built into the relation involved. We focus on some arguments about causal regression to illustrate this point. ;Finally, we find no absolutely general conditions for regressive viciousness. There is, however, a certain limited range of ways in which a regress may be vicious. We make these ways explicit. (shrink)

I will argue for two main points. First, the regress imbedded in infinitism need not be subject to the Structural Objection; and second, the Structural Objection does not pose a real problem for any regress. I will not be arguing for the correctness of my proposal directly. That is, as will become apparent soon, my proposal rests on two principles of reasoning which together entail infinitism and I will not present my arguments for those principles here. The purpose of this (...) paper is to show that the objections raised by Gillett do not pose a grave problem for infinitism. (shrink)

A comment on Paul Schoemaker's target article in Behavioral and Brain Sciences, 14 (1991), p. 205-215, "The Quest for Optimality: A Positive Heuristic of Science?" (https://doi.org/10.1017/S0140525X00066140). This comment argues that the optimizing model of decision leads to an infinite regress, once internal costs of decision (i.e., information and computation costs) are duly taken into account.

I will argue for two main points. First, the regress imbedded in infinitism need not be subject to the Structural Objection; and second, the Structural Objection does not pose a real problem for any regress. I will not be arguing for the correctness of my proposal directly. That is, as will become apparent soon, my proposal rests on two principles of reasoning which together entail infinitism and I will not present my arguments for those principles here. The purpose of this (...) paper is to show that the objections raised by Gillett do not pose a grave problem for infinitism. (shrink)

Infinite regress arguments are used by philosophers as methods of refutation. A hypothesis is defective if it generates an infinite series when either such a series does not exist or its supposed existence would not serve the explanatory purpose for which it was postulated.

'Chains of Being' argues that there can be infinite chains of dependence or grounding. Cameron also defends the view that there can be circular relations of ontological dependence or grounding, and uses these claims to explore issues in logic and ontology.

I examine a number of infinite regress arguments whose infinite regresses are presented or described in terms of recurring questions and answers in order to determine whether such recurring questions have any role in generating these infinite regresses, or in disqualifying the recurring answers. I argue that despite the existence of such infinite regress arguments and the suggestions of some philosophers, these recurring questions have no such roles. Some ways of handling these infinite (...) regress arguments are then proposed. (shrink)

Now that the winds have died down, flood waters have receded, and rebuilding has begun, the brand of public-oriented journalism found in the midst of the storms must not be forgotten. --.

I describe the general structure of most infinite regress arguments; introduce some basic vocabulary; present a working hypothesis of the nature and derivation of an infinite regress; apply this working hypothesis to various infinite regress arguments to explain why they fail to entail an infinite regress; describe a common mistake in attempting to derive certain infinite regresses; and examine how infinite regresses function as a premise.

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)

In "The God Delusion", Richard Dawkins gives, but runs together, two criticisms of the argument from design. One is evolutionary and scientific; the other is a philosophical infinite regress argument. Disentangling them makes Dawkins' views clearer. The regress relies on the premiss that a designer must be more complex than the thing designed. I offer two comments about theists who might accept the regress, citing God's infinity. These comments defend Dawkins: but only by making him, when using his regress (...) argument, an atheist who knows (if his "complexity" premiss holds) that God cannot exist. (shrink)

This paper compares and contrasts two infinite regress arguments against higher-order theories of consciousness that were put forward by the Buddhist epistemologists Dignāga (ca. 480–540 CE) and Dharmakīrti (ca. 600–660). The two arguments differ considerably from each other, and they also differ from the infinite regress argument that scholars usually attribute to Dignāga or his followers. The analysis shows that the two philosophers, in these arguments, work with different assumptions for why an object-cognition must be cognised: for Dignāga (...) it must be cognised in order to enable subsequent memory of it, for Dharmakīrti it must be cognised if it is to cognise an object. (shrink)

Infinite regress arguments are a powerful tool in Aristotle, but this style of argument has received relatively little attention. Improving our understanding of infinite regress arguments has become pressing since recent scholars have pointed out that it is not clear whether Aristotle’s infinite regress arguments are, in general, effective or indeed what the logical structure of these arguments is. One obvious approach would be to hold that Aristotle takes infinite regress arguments to be per impossibile arguments, (...) which derive an infinite sequence. Due to his finitism, Aristotle then rejects such a sequence as impossible. This paper argues that this obvious approach does not work, even for its most amenable cases. The paper argues instead that infinite regress arguments involve domain-specific infinities, and so there is not a general finitism which underpins infinite regress arguments in Aristotle, but rather domain-specific reasons that there cannot be an infinite number of entities in each domain in which Aristotle invokes an infinite regress argument. (shrink)

In his article “Directed Duties and Inalienable Rights,” Hillel Steiner advances an argument to show that there cannot be inalienable rights. This “impossibility theorem,” as well as providing an interesting result by itself, could break the theoretical deadlock in the debate between proponents of interest theory, on the one hand, and proponents of will theory, on the other. In this article, I comment on Steiner’s argument, and I try to show why it does not work. I then expound a paradoxical (...) outcome of the Hohfeldian analytical framework and examine how it might be amended to avoid this outcome. (shrink)

The aim of this paper is to examine the medieval posterity of the Aristotelian and Pyrrhonian treatments of the infinite regress argument. We show that there are some possible Pyrrhonian elements in Autrecourt's epistemology when he argues that the truth of our principles is merely hypothetical. By contrast, Buridan's criticisms of Autrecourt rely heavily on Aristotelian material. Both exemplify a use of scepticism.

We model infinite regress structures -not arguments- by means of ungrounded recursively defined functions in order to show that no such structure can perform the task of providing determination to the items composing it, that is, that no determination process containing an infinite regress structure is successful.

In this paper, I examine how the Mode of Infinite Regress functions in Pyrrhonian scepticism. I argue that it is used both to generate an infinite regress of reasons and to show that such infinite regresses are epistemically defective. I clarify precisely how this occurs while examining the Mode’s efficaciousness and whether ancient philosophers might have accepted infinite regresses of reasons. I ultimately argue that they would not for reasons which have hitherto not been (...) adequately appreciated and which shed further light on how the Mode of Infinite Regress functions, its efficacy, and the relevant notions of justification at stake. (shrink)

There is a long-standing debate in epistemology on the structure of justification. Some recent work in formal epistemology promises to shed some new light on that debate. I have in mind here some recent work by David Atkinson and Jeanne Peijnenburg, hereafter “A&P”, on infinite regresses of probabilistic support. A&P show that there are probability distributions defined over an infinite set of propositions {\ such that \ is probabilistically supported by \ for all i and \ has (...) a high probability. Let this result be “APR”. A&P oftentimes write as though they believe that APR runs counter to foundationalism. This makes sense, since there is some prima facie plausibility in the idea that APR runs counter to foundationalism, and since some prominent foundationalists argue for theses inconsistent with APR. I argue, though, that in fact APR does not run counter to foundationalism. I further argue that there is a place in foundationalism for infinite regresses of probabilistic support. (shrink)

“Wuqiong,” namely the concept of infinite regress has been identified with the hallmark of the Huayan scholasticism, which is dubbed as “chongchong wujin” (repetitive containment ad infinitum). Such an inconceivable perspective is drawn from the Huayan thinkers’ presupposition that a part contains the whole, which is again composed of such parts. But many philosophical traditions, in general, try to avoid the infinite regress as one of the logical fallacies. This paper examines the Buddhist literature that alludes to “wuqiong” (...) as infinite regress, and highlights that the Huayan thinkers also had a critical attitude toward this issue when they discussed the ontological status of the dissociated factors. But they also used the term in a positive sense of inexhaustiveness. This twofold usage of the term seems to show that the Huayan thinkers critically incorporated the elements of previous scholarship even when they created their own unique metaphysical theories. ‘무궁’, 곧 무한소급은 ‘중중무진’으로 표현되는 화엄교학과 동일시되어 왔다. 그것은 부분이 전체를 포함한다는 화엄사상가들의 이론적 전제로부터 각각의 부분들에 전체가 끊임없이 내포된다는 불가사의한 세계관이 도출되기 때문이다. 그러나 불교철학은 물론, 서양철학에서도 무한소급은 논리적 오류로서 회피해야 하는 것으로 간주되어 왔다. 이와 관련하여 본 논문에서는 화엄사상 성립 이전의 몇몇 불교 문헌들에서 특히 유위 4상(相), 득(得)과 같은 불상응행법을 설정할 경우 ‘무궁과’라는 논리적 오류가 발생함을 지적한 사례들을 살펴보았는데, 그러한 비판이 화엄의 문헌들에도 거의 그대로 수용되고 있음을 확인할 수 있다. 그러나 화엄의 문헌에는 ‘무궁’이라는 용어가 ‘무궁진’, ‘무진’, ‘무변’과 동의어로서 긍정적인 맥락에서 사용하고 있는 경우도 자주 발견된다. 이처럼 화엄의 문헌에 이중적인 의미로 사용된 ‘무궁’이라는 개념은 화엄사상가들이 자신들의 독특한 형이상학을 제시하면서도 그들 이전의 여러 교학체계들을 비판적으로 수용했음을 보여주는 증거라고 할 수 있을 것이다. (shrink)

I propose a counterfactual theory of infinite regress arguments. Most theories of infinite regress arguments present infinite regresses in terms of indicative conditionals. These theories direct us to seek conditions under which an infinite regress generates an infinite inadmissible set. Since in ordinary language infinite regresses are usually expressed by means of infinite sequences of counterfactuals, it is natural to expect that an analysis of infinite regress arguments should be based (...) on a theory of counterfactuals. The Stalnaker–Lewis theory of counterfactuals, augmented with some fundamental notions from metric-spaces, provides a basis for such an analysis of infinite regress arguments. Since the technique involved in the analysis is easily adaptable to various analyses, it facilitates a rigorous comparison among conflicting philosophical analyses of any given infinite regress. (shrink)