This paper examines two objections to the infinitist theory of epistemic justification, namely “the finite mind objection” and “the distinction objection.” It criticizes Peter Klein’s response to the distinction objection and offers a more plausible response. It is then argued that this response is incompatible with Klein’s response to the finite mind objection. Infinitists, it would seem, cannot handle both objections when taken together.

Klein’s account of epistemic justification, infinitism, supplies a novel solution to the regress problem. We argue that concentrating on the normative aspect of justification exposes a number of unpalatable consequences for infinitism, all of which warrant rejecting the position. As an intermediary step, we develop a stronger version of the ‘finite minds’ objection.

This article offers a limited defense of metaphysical “infinitism,” the view that there are, or might be, infinite chains of ontological dependence. According to a widespread presupposition, there must be an ultimate ground of being—most likely, a plurality of fundamental atoms. Contrary to this view, this article shows that metaphysical infinitism is internally coherent. In particular, a parallel with the debate concerning infinitism about epistemic justification is suggested, and an “emergence model” of being is put forward. According (...) to the emergence model, the being of any given entity gradually arises out of an infinite series of progressively less dependent entities—it is not wholly transmitted, as it were, from a basic, ungrounded level to all the dependent ones in a step-by-step fashion. Some objections are considered and rebutted. (shrink)

In a recent paper, “Infinitism and Epistemic Normativity,” we have problematized the relationship between infinitism and epistemic normativity. Responding to our criticisms, John Turri has offered a defense of infinitism. In this paper, we argue that Turri’s defense fails, leaving infinitism vulnerable to the originally raised objections.

This paper expands upon a way in which we might rationally doubt that there are multiple sizes of infinity. The argument draws its inspiration from recent work in the philosophy of truth and philosophy of set theory. More specifically, elements of contextualist theories of truth and multiverse accounts of set theory are brought together in an effort to make sense of Cantor’s troubling theorem. The resultant theory provides an alternative philosophical perspective on the transfinite, but has limited impact on everyday (...) mathematical practice. (shrink)

Modest Infinitism -/- Jeremy Fantl -/- Abstract -/- Infinitism, a theory of justification most recently developed and defended by Peter Klein, is the view that justification is a matter of having an infinite series of non-repeating reasons for a proposition. I argue that infinitism is preferable to other theories (like foundationalism) in that only infinitism can plausibly account for two important features of justification: 1) that it admits of degrees and 2) that a concept of complete (...) justification makes sense. (shrink)

The article discusses infinitism, the view that a belief is justified for a subject only if she possesses an infinite chain of available reasons for that belief. In its most recent and sophisticated version, the view allegedly escapes the problems that trouble its main competitors, foundationalism and coherentism, while avoiding the traditional objections which relegated it to a marginal place. The article argues that despite these improvements, sophisticated versions of infinitism face a pressing problem, viz. they are unable (...) to appropriately articulate propositional and doxastic justification. (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)

Consider the following process of epistemic justification: proposition $E_{0}$ is made probable by $E_{1}$ which in turn is made probable by $E_{2}$ , which is made probable by $E_{3}$ , and so on. Can this process go on indefinitely? Foundationalists, coherentists, and sceptics claim that it cannot. I argue that it can: there are many infinite regresses of probabilistic reasoning that can be completed. This leads to a new form of epistemic infinitism.

I evaluate two new objections to an infinitist account of epistemic justification, and conclude that they fail to raise any new problems for infinitism. The new objections are a refined version of the finite-mind objection, which says infinitism demands more than finite minds can muster, and the normativity objection, which says infinitism entails that we are epistemically blameless in holding all our beliefs. I show how resources deployed in response to the most popular objection to infinitism, (...) the original finite-mind objection, can be redeployed to address the two new objections. (shrink)

Any satisfactory epistemology must account for the distinction between propositional and doxastic justification. Can infinitism account for it? Proposals to date have been unsatisfactory. This paper advances a new infinitist account of the distinction. The discussion proceeds as follows. Section 1 sets the stage. Section 2 presents Peter Klein's account. Section 3 raises a problem for Klein's account and suggests an improvement. Section 4 raises a further challenge. Sections 5 to 7 consider several unsuccessful attempts to meet the challenge. (...) Section 8 presents my new proposal, which can meet the challenge. Section 9 concludes the discussion. (shrink)

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

Foundationalist, Coherentist, Skeptic etc., have all been united in one respect--all accept epistemic justification cannot result from an unending, and non-repeating, chain of reasons. Peter Klein has recently challenged this minimal consensus with a defense of what he calls "Infinitism"--the position that justification can result from such a regress. Klein provides surprisingly convincing responses to most of the common objections to Infinitism, but I will argue that he fails to address a venerable metaphysical concern about a certain type (...) of regress. My conclusion will be that until Klein answers these metaphysical worries he will not have restored Infinitism as a viable option in epistemology. (shrink)

In ‘Infinitism Regained’, Jeanne Peijnenburg argues for a version of infinitism wherein ‘beliefs may be justified by an infinite chain of reasons that can be actually completed’. I argue that Peijnenburg has not successfully argued for this claim, but rather has shown that certain infinite series can be computed.

Foundationalist, Coherentist. Skeptic etc., have all been united in one respect—all accept epistemic justification cannot result from an unending, and non‐repeating. chain of reasons. Peter Klein has recently challenged this minimal consensus with a defense of what he calls “Intinitism”—the position that justification can result from such a regress. Klein provides surprisingly convincing responses to most of the common objections to Infinitism, but I will argue that he fails to address a venerable metaphysical concern about a certain type of (...) regress. My conclusion will be that until Klein answers these metaphysical worries he will not have restored Infinitism as a viable option in epistemology. (shrink)

This paper is a response to Peter Klein's "Human Knowledge and the Infinite Progress of Reasoning". After briefly discussing what Klein says about the requirement, for doxastic justification, that a belief be formed in the right way, I'll make the following three points: Klein's solution to the regress problem isn't an infinitist solution, Klein's position on doxastic justification faces a troubling dilemma, and Klein's objection to foundationalism fails.

Epistemic infinitism is one of the logically possible responses to the epistemic regress problem, claiming that the justification of a given proposition requires an infinite and non-circular structure of reasons. In this paper, I will examine the dialectic between the epistemic infinitist and the regress skeptic, the sort of skeptic that bases his attack to the possibility of justification on the regress of reasons. I aim to show that what makes epistemic infinitism appear as well-equipped to silence the (...) regress skeptic is the very same thing that renders it susceptible to a powerful skeptical assault by the regress skeptic. (shrink)

Infinitism in Epistemology. This article provides an overview of infinitism in epistemology. Infinitism is a family of views in epistemology about the structure of knowledge and epistemic justification. It contrasts naturally with coherentism and foundationalism. All three views agree that knowledge or justification requires an appropriately structured chain of reasons. What form may such a […].

Infinitism is often presented as a rival to foundationalism and coherentism as available answers to the epistemic regress problem. The most prominent contemporary defense of infinitism, due to Peter Klein, rests on the notion that an agent can perpetually amplify the justification for her belief insofar as they are able to iteratively answer an interlocutor’s questions why the proffered grounds for their belief should count as providing justification for that belief. We show that this argument does not offer (...) any basis for preferring infinitism over foundationalism and coherentism, because those views are able to accommodate the insight that justification for a belief can be continually amplified. Klein’s argument for infinitism thus falls short of its aspirations of proving that infinitism qua rival of foundationalism and coherentism is the most credible solution to the epistemic regress problem. (shrink)

Any satisfactory epistemology must account for the distinction between propositional and doxastic justification. Can infinitism account for it? Proposals to date have been unsatisfactory. This paper advances a new infinitist account of the distinction. The discussion proceeds as follows. Section 1 sets the stage. Section 2 presents Peter Klein's account. Section 3 raises a problem for Klein's account and suggests an improvement. Section 4 raises a further challenge. Sections 5 to 7 consider several unsuccessful attempts to meet the challenge. (...) Section 8 presents my new proposal, which can meet the challenge. Section 9 concludes the discussion. (shrink)

The purpose of this essay is to show that the version of epistemological infinitism defended by Peter Klein is externalistic in character. I present the most important questions infinitism is supposed to resolve and also present the fundamental difference regarding internalism and externalism in epistemology. I conclude with an indication of what would be the best way to understand infinitism and how to evade the problems that emerge from Klein’s externalist infinitism.

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. (shrink)

Infinitism, in contrast to foundationalism and coherentism, claims that justification in any proposition requires the availability of an infinite chain of propositional reasons, each providing a justificatory reason for its successor in the chain. Both infinitists and some critics of the theory have at times noted the possibility that the theory may have sceptical consequences for doxastic justification. It is argued here that, for reasons that appear not to have been previously appreciated, sceptical results very definitely do follow from (...) infinitism. On one construal of infinitism, this constitutes a reductio of the theory. On an alternative construal, infinitists may embrace the sceptical conclusion, but in doing so, will take on all the problems that scepticism faces. (shrink)

This paper brings together two recent developments in the theory of epistemic justification: practical conditions on justification, and infinitism (the view thatjustification is a matter of having an infinite series of non-repeating reasons). Pragmatic principles can be used to argue that, if we’re looking for an ‘objective’ theory of the structure of justification – a theory that applies to all subjects independently of their practical context – infinitism stands the only chance at being the correct theory.

Infinitists argue that their view outshines foundationalism because infinitism can, whereas foundationalism cannot, explain two of epistemic justification’s crucial features: it comes in degrees and it can be complete. I present four different ways that foundationalists could make sense of those two features of justification, thereby undermining the case for infinitism.

O propósito deste artigo é mostrar como podem ser desenvolvidas explicações robustas de justificação e de certeza no interior do infinitismo. Primeiro, eu explico como a concepção infinitista de justificação epistêmica difere das concepções fundacionista e coerentista. Em segundo lugar, explico como o infinitista pode oferecer uma solução ao problema do regresso epistêmico. Em terceiro lugar, explico como o infinitismo, per se, é compatível com as teorias daqueles que sustentam 1) que o conhecimento requer certeza e que uma tal forma (...) superior de conhecimento é possível, bem como com as daqueles que rejeitam algum ou ambos os conjuntos em 1). Em outras palavras, o infinitismo nem endossa, nem rejeita o ceticismo, tomando-se essa tese como sendo aquela segundo a qual nós não possuímos conhecimento naquelas situações que nos parecem cognoscíveis. PALAVRAS-CHAVE – Certeza. Coerentismo. Fundacionismo. Infinitismo. Pirronismo. Regresso epistêmico. ABSTRACT The purpose of the paper is to show how robust accounts of justification and certainty can be developed within infinitism. First, I explain how the infinitist conception of epistemic justification differs from both the foundationalist and coherentist conceptions. Second, I explain how the infinitist can provide a solution to the epistemic regress problem. Third, I explain how infinitism, per se, is compatible with both the views of those who hold 1) that knowledge requires certainty and that such high-grade knowledge is possible as well as those who deny either or both conjuncts in 1). In other words, infinitism neither endorses nor rejects skepticism, taking that view to mean that we do not have knowledge in those areas commonly thought to be within our ken. KEY WORDS – Certainty. Coherentism. Foundationalism. Infinitism. Pyrrhonism. Epistemic regress. (shrink)

Infinitism, along with foundationalism and coherentism, is a logically possible solution to the epistemic regress problem. But unlike the other two views, infinitism has only been developed and defended as a plausible solution since the late 1990’s. Infinitists grant that although there is an ending point of any actual chain of cited reasons for a belief, no belief (including the last one cited) is fully justified until a reason for it is provided. In addition to differing with foundationalism (...) about the existence of so-called basic beliefs, infinitism depicts reasoning as a process through which full doxastic justification is generated, rather than as a device for merely transferring doxastic justification from one belief to another. Thus, like coherentism, infinitism attempts to account for the origin of epistemic doxastic justification without invoking self-justified beliefs whose justification is transmitted through reasoning. But infinitism parts company with coherentism by maintaining (1) that circular reasoning is unable to provide a doxastic justification for any belief and (2) that there is a linear epistemic structure of our beliefs that reflects the fact that some beliefs are epistemically prior to others. (shrink)

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. (shrink)

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. (shrink)

Epistemic infinitism is the view that infinite series of inferential relations are productive of epistemic justification. Peirce is explicitly infinitist in his early work, namely his 1868 series of articles. Further, Peirce's semiotic categories of firsts, seconds, and thirds favors a mixed theory of justification. The conclusion is that Peirce was an infinitist, and particularly, what I will term an impure infinitist. However, the prospects for Peirce's infinitism depend entirely on the prospects for Peirce's early semantics, which are (...) not good. Peirce himself revised the semantic theory later, and in so doing, it seems also his epistemic infinitism. (shrink)

This article poses two regresses for justification of moral knowledge and discusses three models for moral epistemic infinitism that arise. There are moral infinitisms dependent on empirical infinitism, what are called “piggyback” moral infinitisms. There are substantive empiricist moral infinitisms, requiring infinite chains of descriptive facts to justify normative rules. These empiricist infinitisms are developed either as infinitist egoisms or as infinitist sentimentalisms. And, finally, there are substantive rationalist moral infinitisms, requiring infinite chains of normative reasons to justify (...) moral rules. Rationalist moral infinitism is posed as a mixed view integrating moral intuitions with the demand for justifying reasons. (shrink)

This article is about the ontological dispute between finitists, who claim that only finitely many numbers exist, and infinitists, who claim that infinitely many numbers exist. Van Bendegem set out to solve the 'general problem' for finitism: how can one recast finite fragments of classical mathematics in finitist terms? To solve this problem Van Bendegem comes up with a new brand of finitism, namely so-called 'apophatic finitism'. In this article it will be argued that apophatic finitism is unable to represent (...) the negative ontological commitments of infinitism or, in other words, that which does not exist according to infinitism. However, there is a brand of infinitism, so-called 'apophatic infinitism', that is able to represent both the positive and the negative ontological commitments of apophatic finitism. Unfortunately, apophatic finitism cannot adopt that way without losing the ability to represent the positive ontological commitments of infinitism. (shrink)

ABSTRACT This essay presents the chief reasons for making a distinction between propositional and doxastic justification and, also, points out two things: no theory of propositional justification implies a theory of doxastic justification; infinitism is, essentially, a theory of propositional justification. Additionally, this paper tries to shed some light on the three conjointly sufficient conditions for a proper infinitist view of propositional justification.