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)

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)

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 (...) class='Hi'>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)

In a recent paper, Jeanne Peijnenburg and David Atkinson [ Studia Logica, 89:333-341 ] have challenged the foundationalist rejection of infinitism by giving an example of an infinite, yet explicitly solvable regress of probabilistic justification. So far, however, there has been no criterion for the consistency of infinite probabilistic regresses, and in particular, foundationalists might still question the consistency of the solvable regress proposed by Peijnenburg and Atkinson.

We have earlier shown by construction that a proposition can have a welldefined nonzero probability, even if it is justified by an infinite probabilistic regress. We thought this to be an adequate rebuttal of foundationalist claims that probabilistic regresses must lead either to an indeterminate, or to a determinate but zero probability. In a comment, Frederik Herzberg has argued that our counterexamples are of a special kind, being what he calls ‘solvable’. In the present reaction we (...) investigate what Herzberg means by solvability. We discuss the advantages and disadvantages of making solvability a sine qua non , and we ventilate our misgivings about Herzberg’s suggestion that the notion of solvability might help the foundationalist. (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.

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)

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)

According to infinitism, beliefs can be justified by an infinite chain of reasons. So far, infinitism has rarely been taken seriously and often even dismissed as inconsistent. However, Peijnenburg and Atkinson have recently argued that beliefs can indeed be justified by an infinite chain of reasons, if justification is understood probabilistically. In the following, I will discuss the formal result that has led to this conclusion. I will then introduce three probabilistic explications of justification and examine to (...) which extent they support Peijnenburg’s and Atkinson’s claim. (shrink)

In this paper I show that the existence of an infinite temporal regress does not undermine the soundness of Craigs version of the Kalam Cosmological Argument. To this end I shall focus on a particular complication that Craig raises against one of his arguments in support of a finite temporal regress. I will show that this complication can be made innocuous by extending the notion of A-theoretic time, which is presupposed by Craigs argument, to include a notion of (...) temporal becoming that is compatible with the existence of an infinite regress of temporal events. All this shows that God could have created an infinite temporal regress a finite time in the past without this entailing a contradiction. (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 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.

Recent work by Peijnenburg, Atkinson, and Herzberg suggests that infinitists who accept a probabilistic construal of justification can overcome significant challenges to their position by attending to mathematical treatments of infinite probabilistic regresses. In this essay, it is argued that care must be taken when assessing the significance of these formal results. Though valuable lessons can be drawn from these mathematical exercises (many of which are not disputed here), the essay argues that it is entirely unclear (...) that the form of infinitism that results meets a basic requirement: namely, providing an account of infinite chains of propositions qua reasons made available to agents. (shrink)

We discuss two objections that foundationalists have raised against infinite chains of probabilistic justification. We demonstrate that neither of the objections can be maintained.

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)

Scoring rules measure the accuracy or epistemic utility of a credence assignment. A significant literature uses plausible conditions on scoring rules on finite sample spaces to argue for both probabilism—the doctrine that credences ought to satisfy the axioms of probabilism—and for the optimality of Bayesian update as a response to evidence. I prove a number of formal results regarding scoring rules on infinite sample spaces that impact the extension of these arguments to infinite sample spaces. A common condition (...) in the arguments for probabilism and Bayesian update is strict propriety: that according to each probabilistic credence, the expected accuracy of any other credence is worse. Much of the discussion needs to divide depending on whether we require finite or countable additivity of our probabilities. I show that in a number of natural infinite finitely additive cases, there simply do not exist strictly proper scoring rules, and the prospects for arguments for probabilism and Bayesian update are limited. In many natural infinite countably additive cases, on the other hand, there do exist strictly proper scoring rules that are continuous on the probabilities, and which support arguments for Bayesian update, but which do not support arguments for probabilism. There may be more hope for accuracy-based arguments if we drop the assumption that scores are extended-real-valued. I sketch a framework for scoring rules whose values are nets of extended reals, and show the existence of a strictly proper net-valued scoring rules in all infinite cases, both for f.a. and c.a. probabilities. These can be used in an argument for Bayesian update, but it is not at present known what is to be said about probabilism in this case. (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)

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.

In this article we analyze the claim that a probabilistic interpretation of the infinite epistemic regress problem leads to a unique solution, the so called “completion” of the regress. This claim is implicitly based on the assumption that the standard Kolmogorov axioms of probability theory are suitable for describing epistemic probability. This assumption, however, has been challenged in the literature, by various authors. One of the alternatives that have been suggested to replace the Kolmogorov axioms in case of (...) an epistemic interpretation of probability, are belief functions, introduced by Shafer in 1976. We show that when one uses belief functions to describe the infinite epistemic regress problem, it is no longer the case that the solution is unique. We also argue that this complies with common sense. (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)

Support functions $s(h,e)=p(h\backslash e)-p(h)$ are widely used in discussion of explanation, causality and, recently, in connection with the possibility or otherwise of probabilistic induction. With this latter application in view, a rather complete analysis of the variety of support functions, their interrelationships and their "non-deductive" and "inductive" components is presented. With the restriction to two propositions, three variable probabilities are enough to discuss such problems. The analysis is illustrated by graphs, a Venn diagram and by using the (...) Laplace Rule of Succession as an illustrative example. It is concluded that within this framework one cannot prove or disprove the possibility of probabilistic induction. (shrink)

Most analytic epistemologists, foundationalists and coherentists alike, have rejected the possibility of an infinitely long, non-recurring regress of justified beliefs. it is instructive to inquire why this notion has received nearly universal condemnation. in a review of recent work six sorts of arguments against infinite justificatory chains are examined. it is concluded firstly that, while regresses in which each belief is justified solely via relations to further beliefs cannot exist, the impossiblity of other sorts of infinite justificatory (...) chains has not been shown, and secondly that there may nevertheless be sound methodological reasons for provisionally rejecting the infinite regress possibility while more satisfactory alternatives are explored. (shrink)

In Metaepistemology and Skepticism (Rowman & Littlefield:\n1995), Richard Fumerton defends foundationalism. As part of\nthe defense he rejects infinitism--the view that holds that\nthe solution to the problem of the regress of justificatory\nreasons is that the reasons are infinitely many and\nnonrepeating. I examine some of those arguments and attempt\nto show that they are not really telling against (at least\nsome versions of) infinitism. Along the way I present some\nobjections to his account of inferential justification.

There are important similarities between the epistemic regress problem and the problem of the criterion. Each turns on plausible principles stating that epistemic reasons must be supported by epistemic reasons but that having reasons is impossible if that requires having endless regresses of reasons. These principles are incompatible with the possibility of reasons, so each problem is a paradox. Whether there can be an antiskeptical solution to these paradoxes depends upon the kinds of reasons that we need in order (...) to attain our epistemic goals. This article explains the problems and considers the ways in which two different conceptions of human flourishing support the value of different kinds of reasons. One conception requires reasons that allow an easy solution to these paradoxes. The other—rational autonomy—requires reasons that depend upon endless regresses. So we cannot have the kinds of fully transparent reasons required for rational autonomy. (shrink)

This paper examines how coherence of the contents of evidence affects the transmission of probabilistic support from the evidence to the hypothesis. It is argued that coherence of the contents in the sense of the ratio of the positive intersection reduces the transmission of probabilistic support, though this negative impact of coherence may be offset by other aspects of the relations among the contents. It is argued further that there is no broader conception of coherence whose (...) impact on the transmission of probabilistic support is never offset by other aspects of the relations among the contents. The paper also examines reasons for the contrary impression that coherence of the contents increases the transmission of probabilistic support, especially in the special case where the hypothesis to evaluate is the conjunction of the contents of evidence. (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)

In this paper I explore alternative ways of addressing the infinite regress problem of inference, as it was depicted in Lewis Carroll’s ‘What the Tortoise said to Achilles’. Roughly put, the problem is that if a claim to the effect that one’s premises give support to one’s conclusion must itself be part of one’s premises, then an infinite regress of reasons ensues. I discuss some recent attempts to solve that problem, but I find all of them to (...) be wanting. Those attempts either require the reasoner to believe that her premises give support to her conclusion, or to take her premises to give support to her conclusion, where taking is not a doxastic attitude. I conclude that, on the face of the failure of those attempts to solve the problem, there is a strong prima facie case for allowing inference to be blind. (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)

As is well known, implication is transitive but probabilistic support is not. Eells and Sober, followed by Shogenji, showed that screening off is a sufficient constraint for the transitivity of probabilistic support. Moreover, this screening off condition can be weakened without sacrificing transitivity, as was demonstrated by Suppes and later by Roche. In this paper we introduce an even weaker sufficient condition for the transitivity of probabilistic support, in fact one that can be made (...) as weak as one wishes. We explain that this condition has an interesting property: it shows that transitivity is retained even though the Simpson paradox reigns. We further show that by adding a certain restriction the condition can be turned into one that is both sufficient and necessary for transitivity. (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)

'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.

As is well known, implication is transitive but probabilistic support is not. Eells and Sober, followed by Shogenji, showed that screening off is a sufficient constraint for the transitivity of probabilistic support. Moreover, this screening off condition can be weakened without sacrificing transitivity, as was demonstrated by Suppes and later by Roche. In this paper we introduce an even weaker sufficient condition for the transitivity of probabilistic support, in fact one that can be made (...) as weak as one wishes. We explain that this condition has an interesting property: it shows that transitivity is retained even though the Simpson paradox reigns. We further show that by adding a certain restriction the condition can be turned into one that is both sufficient and necessary for transitivity. (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)

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.

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)

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 show that in our theoretical representations of argument, vicious infinite regresses of self-reference may arise with respect to each of the three usual, informal criteria of argument cogency: the premises are to be relevant, sufficient, and acceptable. They arise needlessly, by confusing a cogency criterion with argument content. The three types of regress all are structurally similar to Lewis Carroll’s famous regress, which involves quantitative extravagance with no explanatory power. Most attention is devoted to the sufficiency criterion, (...) including its relation to the view au courant that inferring necessarily involves the thinker taking her premises to support her conclusion. I contend that this view is mistaken and likewise that arguments make no such assumption or inference claim as that the premises support the conclusion. The core of the positive alternative model I propose is that there is commitment to, but not claiming, the proposition that the premises support the conclusion. (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.