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)

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 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.

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)

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)

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.

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.

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)

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)

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.

Abstract / 摘要 Relational Quantum Mechanics (RQM) posits that all physical properties are relative to the observer. However, Riedel (2024) identifies a critical logical challenge: the Unrestricted Iteration Principle (UIP), which leads to an infinite regress of relativization. This paper proposes a resolution by introducing the Universal Field of Intelligence (UFI) as the absolute substrate of information. We argue that while interaction outcomes are perspectival, the UFI functions as the Ultimate Observer or the "One True Realm" (一真法界), providing the (...) foundational phase-alignment mechanism that ensures global coherence. By terminating the iteration at the level of the foundational field, this model reconciles the flexibility of relational facts with the ontological necessity of a unified reality. -/- 關係量子力學 (RQM) 主張所有物理屬性皆相對於觀測者。然而，Riedel (2024) 指出了一個關鍵的邏輯挑戰：不限制疊代原則 (UIP)，這會導致相對化的無限回歸。本論文透過引入「宇宙智能場」 (UFI) 作為資訊的絕對基底，提出了一套解決方案。我們主張，雖然交互作用的結果是觀點性的 (perspectival)，但 UFI 作為「最終觀測者」或「一真法界」，提供了確保全域相干的基礎相位對齊機制。透過在基礎場層面終結這種疊代，本模型調和了關係性事實的靈活性與統一實相在學術本體論上的必要性。 . (shrink)

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.

'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.

The established view about regress problems has it that they, roughly speaking, come in only one variety. This view is mistaken. Two types of problems are typically subsumed under the label of regress problems – stopping problems and starting problems. Both problem types share the same surface structure in terms of necessary and sufficient conditions, but their deeper founding structure reveals some key differences. Stopping problems rely on a regress clause, raise the question whether infinite chains are possible, and (...) present terminatism, infinitism, and nihilism as potential solutions. In contrast, standard starting problems, which many regress problems are, rely on a founding clause and not on a regress clause, do not raise questions about the possibility of infinite chains, and offer only two potential solutions, terminatism and nihilism. Non-standard starting problems also allow for infinitism as a viable solution, but nevertheless they differ structurally in various aspects from stopping problems. (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)

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.

I will explore the paradoxical nature of epistemic access. By critiquing the traditional conception of mental states that are labelled as ’knowledge’, I demonstrate the susceptibility of these states to an infinite regress, thus, challenging their existence and validity. I scrutinise the assumption that an epistemic agent can have complete epistemic access to all facts about a given object while simultaneously being ignorant of certain truths that impact the very knowledge claims about the object. I further analyse the implications (...) of this paradox when attempting to fine-grain the parameters of epistemic access, which happens to reveal the vacuity of such definitions and the inevitability of the regress. (shrink)

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)

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)

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)

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)

In his commentary on Aristotle’s _De interpretatione_, Ammonius puts forward an argument for the priority of categorical over hypothetical syllogisms. The argument relies on two of the Five Modes of Agrippa, the modes from infinite regress and from hypothesis. Much of the argument, however, remains unclear and open to doubt. The present chapter sheds new light on the argument by considering it against the backdrop of two related arguments given by Pseudo-Ammonius and Alexander of Aphrodisias in their commentaries on (...) the _Prior Analytics_. The chapter argues that all three arguments originate in Theophrastus’ discussion of Aristotle’s treatment of syllogisms from a hypothesis. They rely on the view that stating a hypothetical proposition _If P, then Q_ does not amount to the unqualified assertion of a conditional proposition, but rather to a conditional assertion of _Q_ on the supposition that _P_. (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)

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)

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)

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)

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.

In PV 3.440ab and 473cd–474ab, Dharmakīrti raises the argument of infinite regress twice. The argument originates from the same argument stated by Dignāga in his Pramāṇasamuccaya 1.12ab1, in which the fault of infinite regress is called aniṣṭhā. In Pramāṇasamuccayavṛtti 1.12b2, Dignāga presents another type of argument of infinite regress driven by memory, which is elucidated by Dharmakīrtian commentators. The arguments were criticized by Kumārila Bhaṭṭa and Bhaṭṭa Jayanta and even more intensively so by two modern scholars, Jonardon (...) Ganeri and Birgit Kellner. In this paper, I first examine the source of the arguments—Pramāṇasamuccayavṛtti 1.12 and its translation, based on which I provide my interpretation of the two models of arguments of infinite regress. I then offer my response, according to Dharmakīrti and his commentators, to Ganeri’s and Kellner’s critiques. By doing so, I attempt to identify the essence of these arguments is and find out to what extent one can defend the infinite regress argument in Dignāga’s and Dharmakīrti’s theory. (shrink)

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)

InMetaphysics Γ, Ch. 4, Aristotle speaks of both infinite regress and question-begging, but does not explicitly relate them. We get the impression that he thinks that to use one of these arguments to avoid the other is to jump from the frying-pan into the fire. This relationship is illustrated in terms of the ignorant belief that everything can be proved, and of attempts to prove the Law of Noncontradiction.

It has been argued that an infinite regress of entailments cannot justify a proposition, _q_. For if it could, then it can be shown that any proposition can be justified in that manner, incuding ¬_q_. This chapter shows that this _reductio ad absurdum_ weakens in the face of a so-called probabilistic regress, in which justification is only probabilistic. The reason is that, whereas a regress of entailments offers no entry point for the world, in the probabilistic regress the empirical (...) thrust is carried by an infinite number of conditional probabilities. This chapter explains to what extent these conditional probabilities differ from the basic beliefs that lie at the heart of epistemic foundationalism. (shrink)

The representations of deep convolutional neural networks (CNNs) are formed from generalizing similarities and abstracting from differences in the manner of the empiricist theory of abstraction (Buckner, Synthese 195:5339–5372, 2018). The empiricist theory of abstraction is well understood to entail infinite regress and circularity in content constitution (Husserl, Logical Investigations. Routledge, 2001). This paper argues these entailments hold a fortiori for deep CNNs. Two theses result: deep CNNs require supplementation by Quine’s “apparatus of identity and quantification” in order to (...) (1) achieve concepts, and (2) represent objects, as opposed to “half-entities” corresponding to similarity amalgams (Quine, Quintessence, Cambridge, 2004, p. 107). Similarity amalgams are also called “approximate meaning[s]” (Marcus & Davis, Rebooting AI, Pantheon, 2019, p. 132). Although Husserl inferred the “complete abandonment of the empiricist theory of abstraction” (a fortiori deep CNNs) due to the infinite regress and circularity arguments examined in this paper, I argue that the statistical learning of deep CNNs may be incorporated into a Fodorian hybrid account that supports Quine’s “sortal predicates, negation, plurals, identity, pronouns, and quantifiers” which are representationally necessary to overcome the regress/circularity in content constitution and achieve objective (as opposed to similarity-subjective) representation (Burge, Origins of Objectivity. Oxford, 2010, p. 238). I base myself initially on Yoshimi’s (New Frontiers in Psychology, 2011) attempt to explain Husserlian phenomenology with neural networks but depart from him due to the arguments and consequently propose a two-system view which converges with Weiskopf’s proposal (“Observational Concepts.” The Conceptual Mind. MIT, 2015. 223–248). (shrink)

The infinite regress of Carroll’s ‘What the Tortoise said to Achilles’ is interpreted as a problem in the epistemology of mathematical proof. An approach to the problem that is both diagrammatic and non-logical is presented with respect to a specific inference of elementary geometry.

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. --.

[Winner of the 2017 AILACT Essay Prize Prize.] I argue against the skeptical epistemological view exemplified by the Groarkes that “all theories of informal argument must face the regress problem.” It is true that in our theoretical representations of reasoning, infinite regresses of self-justification regularly and inadvertently arise with respect to each of the RSA criteria for argument cogency (the premises are to be relevant, sufficient, and acceptable). But they arise needlessly, by confusing an RSA criterion with argument (...) content, usually premise material. (shrink)

Philosophical regress arguments typically arise when an explanation is taken to demand another explanation of the same form, generating the appearance of an unbounded sequence. Standard responses—foundational, coherentist, infinitist, or deflationary—attempt to manage such sequences, but they all presuppose that the regress is in principle formulable. This paper challenges that assumption. I argue that many classical regresses arise only when a relation defined for items within a domain is illicitly applied to the domain as a whole. The mistake is (...) structural rather than epistemic: the whole is not an element of the domain governed by the relevant explanatory relation. Once this level-shift and domain-closure constraint is made explicit, certain well-known regresses turn out not to require a stopping point; they fail to start. A sequence of the form X \rightarrow R(X) \rightarrow R^2(X) cannot extend to the whole, because R is not defined at that level. Attempts to initiate such regresses rest on a category error. The resulting framework dissolves a wide range of regress formulations in metaphysics, epistemology, philosophy of science, and philosophy of mind. Rather than providing another principle for terminating a chain, the paper identifies a structural condition under which the chain is not merely vicious but impossible to formulate. (shrink)

In this paper we clarify a regress argument for metaphysical foundationalism, distinguishing strong and modest versions of this argument. We suggest that while the strong version is open to objection, the modest version is much more plausible and it supports a methodological stance: one ought to refrain from assuming that anti-foundationalism is metaphysically possible. This modest stance follows from our argument that currently we lack reasons to believe anti-foundationalism is possible. This stance opens a new topic in the debate between (...) foundationalism and anti-foundationalism, placing a burden on the anti-foundationalist to provide reasons to think that anti-foundationalism is possible. (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 background to this paper is the question of how rational belief is possible in the light of the commonly presented infinite regress in reasons. The paper investigates the neglected question of whether this regress is vicious. I argue that given the genuine requirements of rational belief, The regress would require the rational believer to hold an infinity of beliefs, Which is impossible. The regress would not entail the rational believer holding an infinitely complex belief, Which, Admittedly, Would be (...) logically impossible. (shrink)