The Consistency of Probabilistic Regresses. A Reply to Jeanne Peijnenburg and David Atkinson

In a recent paper, Jeanne Peijnenburg and David Atkinson [Studia Logica, 89(3):333-341 (2008)] 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.     

Infinitism and probabilistic justification

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.     

Finite Reasons Without Foundations

This article develops a theory of reasons that has strong similarities to Peter Klein's infinitism. The view it develops, Framework Reasons, upholds Klein's principles of avoiding arbitrariness (PAA) and avoiding circularity (PAC) without requiring an infinite regress of reasons. A view of reasons that holds that the “reason for” relation is constrained by PAA and that PAC can avoid an infinite regress if the “reason for” relation is contextual. Moreover, such a view of reasons can maintain that skepticism is false by the maintaining that there is more to epistemic justification than can be expressed in any reasoning session. One crucial argument for Framework Reasons is that justification depends on a background of plausibility considerations. The final section of the article applies this view of reasons to Michael Bergmann's argument that any nonskeptical epistemology must embrace epistemic circularity.     

A Quintet,a Quartet,a Trio,a Duo? The Epistemic Regress Problem,Evidential Support,and Skepticism

In his topical article, Andrew Cling claims that the best extant formulation of the so-called epistemic regress problem rests on five assumptions that are too strong. Cling offers an improved version that rests on a different set of three core epistemic assumptions, each of which he argues for. Despite of owing a great deal to Cling’s ideas, I argue that the epistemic regress problem surfaces from more fundamental assumptions than those offered by Cling. There are ultimately two core assumptions—in fact two contradictory strands within the concept of epistemic support—which jointly create a powerful challenge for our pursuit of paramount epistemic values.

Probabilistic Regresses and the Availability Problem for Infinitism

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.     

Discussions

Summary  In their paper, ‘When are thought experiments poor ones?’ (Peijnenburg and David Atkinson, 2003, Journal of General Philosophy of Science 34, 305-322.), Jeanne Peijnenburg and David Atkinson argue that most, if not all, philosophical thought experiments are “poor” ones with “disastrous consequences” and that they share the property of being poor with some (but not all) scientific thought experiments. Noting that unlike philosophy, the sciences have the resources to avoid the disastrous consequences, Peijnenburg and Atkinson come to the conclusion that the use of thought experiments in science is in general more successful than in philosophy and that instead of concocting more “recherché” thought experiments, philosophy should try to be more empirical. In this comment I will argue that Peijnenburg’s and Atkinson’s view on thought experiments is based on a misleading characterization of both, the dialectical situation in philosophy as well as the history of physics. By giving an adequate account of what the discussion in contemporary philosophy is about, we will arrive at a considerably different evaluation of philosophical thought experiments.

For I am convinced that we now find ourselves at an altogether decisive turning point in philosophy, and that we are objectively justified in considering that an end has come to the fruitless conflict of systems. We are already at the present time, in my opinion, in possession of methods which make any such conflict in principle unnecessary. What is now required is their resolute application. (Schlick, ‘The Turning Point in Philosophy’, 1930/1959, p. 54).

     

(Non)Issues of Infinite Regress in Modeling Motor Behavior

In the past, infinite regress criticisms that have been raised about models of motor behavior have been reserved for executive-type models (e.g., Beek & Meijer, 1988). On the basis of Gödel's (1930/1986) proof that an algorithm cannot prove its own validity, the authors reason that executive- as well as self-organized-type explanatory models of motor behavior have infinite regress difficulties. The conclusion offered in the present article is that judgments on a model's theoretical importance should be based not on issues of infinite regress but on other relevant characteristics, such as its propensity for falsification (Popper, 1959).     

The Virtuous Tortoise

There is no philosophically interesting distinction to be made between inference‐rules and premises. That there is such a distinction is often held to follow from the possibility of infinite regress illustrated by Carroll's story of Achilles and the tortoise. I will argue that this is wrong on three separate grounds. Consequently, Carroll's fable provides no motivation to abandon the traditional logical separation of arguments into their premises and conclusions. There is no proposition that must be taken to be a rule and must not be taken as a premise.     

Does Klein’s infinitism offer a response to Agrippa’s trilemma?

The regress of reasons threatens an epistemic agent’s right to claim that any beliefs are justified. In response, Peter Klein’s infinitism argues that an infinite series of supporting reasons of the right type not only is not vicious but can make for epistemic justification. In order to resist the sceptic, infinitism needs to provide reason to think that there is at least one justified belief in the world. Under an infinitist conception this involves showing that at least one belief is supported by an infinite series of supporting reasons. This paper argues that showing this makes problems for the infinitist. The finite minds problem that prevents completion of an infinite series is well documented. This paper examines alternative attempts to provide evidence of infinity that the infinitist might take, whether by using a notion of justification without infinite reasons or by altering the notion of evidence. It concludes that both of these fail and consequently infinitism is unable to offer a solution to Agrippa’s trilemma.     

The Trouble with Infinitism

One way to solve the epistemic regress problem would be to show that we can acquire justification by means of an infinite regress. This is infinitism. This view has not been popular, but Peter Klein has developed a sophisticated version of infinitism according to which all justified beliefs depend upon an infinite regress of reasons. Klein's argument for infinitism is unpersuasive, but he successfully responds to the most compelling extant objections to the view. A key component of his position is his claim that an infinite regress is necessary, but not sufficient, for justified belief. This enables infinitism to avoid a number of otherwise compelling objections. However, it commits infinitism to the existence of an additional feature of reasons that is necessary and, together with the regress condition, sufficient for justified belief. The trouble with infinitism is that any such condition could account for the connection between justification and truth only by undermining the rationale for the regress condition itself.     

Internalist Foundationalism and the Problem of the Epistemic Regress*

I provide a construal of the epistemic regress problem and I take issue with the contention that a foundationalist solution is incompatible with an internalist account of warrant. I sketch a foundationalist solution to the regress problem that respects a plausible version of internalism. I end with the suggestion that the strategy that I have presented is not available only to the traditional versions of foundationalism that ascribe foundational status to experiential beliefs. It can also be used to generate a version of internalist foundationalism based on reliabilist principles.     

The Regress of Pure Powers Revisited

The paper aims to elucidate in better detail than before the dispute about whether or not dispositional monism—the view that all basic properties are pure powers—entails a vicious infinite regress. Particular focus is on Alexander Bird's and George Molnar's attempts to show that the arguments professing to demonstrate a vicious regress are inconclusive because they presuppose what they aim to prove, notably that powers are for their nature dependent on something else. I argue that Bird and Molnar are mistaken. It is true that dispositional monism is popularly assumed to characterize powers as dependent entities, but this is not what the arguments aim to prove. They merely aim to demonstrate that it would be absurd to assume that all properties are dependent in this way. Finally, it is argued that there is an unresolved tension in Bird's and Molnar's accounts of powers. They characterize them as being for their nature dependent on the manifestations that they are for, and yet ontologically independent of those same manifestations. Until that tension is resolved, their accounts are not equipped to remove the threat of vicious regress.     

The reductio argument against epistemic infinitism

Synthese - Epistemic infinitism, advanced in different forms by Peter Klein, Scott Aikin, and David Atkinson and Jeanne Peijnenburg, is the theory that justification of a proposition for a person...     

Regress and the Doctrine of Epistemic Original Sin

Existing solutions to the epistemic regress problem, and the theories of justification built upon them, are inadequate, for they fail to diagnose the root source of the problem. The problem is rooted in our attachment to a pernicious dogma of modern epistemology: the idea that a judgement must be supported by some kind of reason or evidence to be justified. The epistemic analogue of the doctrine of original sin, this idea renders every judgement in need of redemption – guilty until shown to be innocent – distorting our understanding of reason at a very deep level, and preventing us from conceptualizing a satisfactory solution to the problem. If we opt for a more context–sensitive mechanism for assigning default epistemic status, however, we get a more plausible picture of justification, an epistemology more in tune with epistemic practice, and an elegant solution to the regress problem.     

Cognitive processes in well-defined and ill-defined problem solving

We investigated the relationship between two kinds of problem solving using Kitchener's model of hierarchical cognitive processing. We predicted that performance on well-defined problems (i. e. those with a single, guaranteed solution) would be independent of ill-defined problems (i. e. those with multiple, non-guaranteed solutions). We also predicted that self-reported epistemic beliefs (i. e. assumptions about the nature and acquisition of knowledge) would be related to ill-defined, but not well-defined, solutions. Results confirmed these predictions. We concluded that well-defined and ill-defined problems require separate cognitive processes and that epistemic beliefs play an important role in ill-defined problem solving. These findings supported Kitchener's three-level model of problem solving.     

The dialectics of infinitism and coherentism: inferential justification versus holism and coherence

This paper formally explores the common ground between mild versions of epistemological coherentism and infinitism; it proposes—and argues for—a hybrid, coherentist–infinitist account of epistemic justification. First, the epistemological regress argument and its relation to the classical taxonomy regarding epistemic justification—of foundationalism, infinitism and coherentism—is reviewed. We then recall recent results proving that an influential argument against infinite regresses of justification, which alleges their incoherence on account of probabilistic inconsistency, cannot be maintained. Furthermore, we prove that the Principle of Inferential Justification has rather unwelcome consequences—formally resembling the Sorites paradox—as soon as it is iterated and combined with a natural Bayesian perspective on probabilistic inferences. We conclude that strong versions of foundationalism and infinitism should be abandoned. Positively, we provide a rough sketch for a graded formal coherence notion, according to which infinite regresses of epistemic justification will often have more than a minimal degree of coherence.     

Burge on Perceptual Entitlement

This article is concerned with the question of the nature of the epistemic liaison between experience and belief. The problem, often known as the problem of nondoxastic justification, is to see how a causal transition between experience and belief could assume a normative dimension, that is, how perceptual experience serves to justify beliefs about the world. Currently a number of theories have been proposed to resolve this problem. The article considers a particular solution offered by Tyler Burge which, among other things, introduces a new type of positive epistemic status or warrant, namely, entitlement. It contends that Burge's notion of entitlement cannot be of any help in resolving the problem of nondoxastic justification. Burge's account is compared and contrasted with other, similar, approaches to the problem of nondoxastic justification.     

Human knowledge and the infinite progress of reasoning

The purpose of this paper is to explain how infinitism—the view that reasons are endless and non-repeating—solves the epistemic regress problem and to defend that solution against some objections. The first step is to explain what the epistemic regress problem is and, equally important, what it is not. Second, I will discuss the foundationalist and coherentist responses to the regress problem and offer some reasons for thinking that neither response can solve the problem, no matter how they are tweaked. Then, I want to present the infinitist solution to the problem and defend it against some of the well known objections to it.     

Permissible Epistemic Trade-Offs

Recent rejections of epistemic consequentialism, like those from Firth, Jenkins, Berker, and Greaves, have argued that consequentialism is committed to objectionable trade-offs and suggest that consequentialism's propensity for trade-offs hints at a larger problem. Here I argue that sanctioning trade-offs isn't a fault of a theory of epistemic normativity, because there are permissible epistemic trade-offs. I give examples of permissible epistemic trade-offs in pedagogy, in changes of worldview, and in indirect epistemic decisions. I also show that views that sanction trade-offs have an easier time than their rivals in explaining both why we ought to be open-minded and how arguments with suppositions get their argumentative force. These considerations don't eliminate the consequentialist's burden to respond to the objectionable cases, but they do undermine the idea that no correct theory of epistemic normativity properly sanctions trade-offs.     

Paradigms and Russell's Resemblance Regress

Resemblance Nominalism is the view that denies universals and tropes and claims that what makes F-things F is their resemblances. A famous argument against Resemblance Nominalism is Russell's regress of resemblances, according to which the resemblance nominalist falls into a vicious infinite regress. Aristocratic Resemblance Nominalism, as opposed to Egalitarian Resemblance Nominalism, is the version of Resemblance Nominalism that claims that what makes F-things F is that they resemble the F-paradigms. In this paper I attempt to show that a recently advocated strategy to stop Russell's regress by using paradigms does not succeed.