Aggregative consequentialism and several other popular moral theories are threatened with paralysis: when coupled with some plausible assumptions, they seem to imply that it is always ethically indifferent what you do. Modern cosmology teaches that the world might well contain an infinite number of happy and sad people and other candidate value-bearing locations. Aggregative ethics implies that such a world contains an infinite amount of positive value and an infinite amount of negative value. You can affect only a finite amount (...) of good or bad. In standard cardinal arithmetic, an infinite quantity is unchanged by the addition or subtraction of any finite quantity. So it appears you cannot change the value of the world. Modifications of aggregationism aimed at resolving the paralysis are only partially effective and cause severe side effects, including problems of “fanaticism”, “distortion”, and erosion of the intuitions that originally motivated the theory. Is the infinitarian challenge fatal? (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)

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)

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 paper critically evaluates the regress argument for infinitism. The dialectic is essentially this. Peter Klein argues that only an infinitist can, without being dogmatic, enhance the credibility of a questioned non-evident proposition. In response, I demonstrate that a foundationalist can do this equally well. Furthermore, I explain how foundationalism can provide for infinite chains of justification. I conclude that the regress argument for infinitism should not convince us.

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)

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 requires the availability to that person of an infinite, non-repeating chain of propositions, each providing a justifying reason for its successor in the chain. The reductio argument is the argument to the effect that infinitism has the consequence that no one is justified in any proposition, because there will be an (...) infinite chain of reasons supporting any proposition (and similarly, a chain supporting its negation). Four ways of defending infinitism against the reductio argument are considered and found wanting: Peijnenburg and Atkinson’s use of probabilistic chains of reasons; Klein’s concept of emergent justification; Aikin’s insistence that there be non-propositional input in the justification of any proposition; and Klein’s use of the distinction between reasons that are and are not available to a person. I contend that, in the absence of some further defence, the reductio argument makes infinitism untenable. (shrink)

As the Pyrrhonians made clear, reasons that adequately justify beliefs can have only three possible structures: foundationalism, coherentism, and infinitism. Infinitism—the view that adequate reasons for our beliefs are infinite and non-repeating—has never been developed carefully, much less advocated. In this paper, I will argue that only infinitism can satisfy two intuitively plausible constraints on good reasoning: the avoidance of circular reasoning and the avoidance of arbitrariness. Further, I will argue that infinitism requires serious, but salutary, (...) revisions in our evaluation of the power of reasoning. Thus, reasoning can not provide a basis for assenting to a proposition—where to assent to a proposition, p, means to believe that we know that p. A non-dogmatic form of provisional justification will be sketched. Finally, the best objections to infinitism, including those posed by the Pyrrhonians, will be shown (at least provisionally!) to be inadequate. (shrink)

Questions concerning the structure of justification lie at the heart of epistemology. And it is to Peter Klein’s great credit that he has added to the traditional debates a new and interesting proposal for how to understand the structure of justification. The foundationalist is convinced that all justification terminates in a foundation of noninferential justification. The coherentist is convinced that there is no escaping the “circle of belief” and the best we can do is maximize relations of coherence among our (...) beliefs. Klein’s infinitist rejects the choices offered by these two views as a false dilemma. Against the coherentist, we should insist that to have justification for believing any proposition we must have the capacity to put forward non-circular reasons in support of the proposition, non-circular reasons in support of whatever reasons we appeal to, non-circular reasons in support of those reasons and so on, ad infinitum. The foundationalist’s fear that this puts too much strain on finite beings is, Klein, argues, misguided. This chapter argues that the infinitist cannot avoid the foundationalist’s regress arguments. While it might be conceded that the infinitist has a plausible account of what it is for a belief to be _defensible_, it is not a plausible account of what it is for a belief to be _justified_. (shrink)

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)

I will assume here the defenses of epistemic infinitism are adequate and inquire as to the variety standpoints within the view. I will argue that infinitism has three varieties depending on the strength of demandingness of the infinitist requirement and the purity of its conception of epistemic justification, each of which I will term strong pure, strong impure, and weak impure infinitisms. Further, I will argue that impure infinitisms have the dialectical advantage.

This chapter argues that the various conditions that jointly constitute the relation of one subject _knowing something better_ than another amount to a case for a non-skeptical form of epistemic infinitism.

I argue in this paper that infinitism is the best answer to the dialectical regress challenge. Infinitism, as a theory of rational dialectics, has not received enough attention from scholars because major proponents of the theory have focused mainly on using infinitism to answer an epistemic regress problem. Rather than construing infinitism as an answer to the epistemic regress question, I take the theory to be addressing a dialectical regress challenge and subsequently pitch it against its (...) dialectical rivals. It emerges that dialectical infinitism addresses the regress challenge far better than its competitors if it is couched as a social contextualist thesis. (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.

Abstract Epistemic infinitism is certainly not a majority view in contemporary epistemology. While there are some examples of infinitism in the history of philosophy, more work needs to be done mining this history in order to provide a richer understanding of how infinitism might be formulated internal to different philosophical frameworks. Accordingly, we argue that the philosophy of Emmanuel Levinas can be read as operating according to an ?impure? model of epistemic infinitism. The infinite obligation inaugurated (...) by the ?face to face encounter? with the Other yields an approach to the ethics of belief that accords with infinitism. This reading of Levinas brings his ethical thought into dialogue with contemporary epistemology as well as provides an historical example of infinitism within the current debates. (shrink)

There is a rapprochement available between infinitism and foundationalism. An infinitist will hold: (a) that _any_ belief is more fully doxastically justified when it is reason-enhanced and (b) that full doxastic justification is required for a belief to rise to the level of knowledge—the most highly prized form of true belief. The foundationalist will claim (c) that there are _some_ epistemically privileged basic beliefs which do not require reasons in order to be doxastically justified. Those three claims might seem (...) incompatible, but once it is recognized that what was taken for granted in one context requires reasons in another context, a rapprochement is possible because it can be seen that foundationalism is correct that there are some privileged basic beliefs and infinitism is correct that the privilege is only conditional. (shrink)

This volume presents new work on infinitism, the view that there are no foundational reasons for beliefs--an ancient view in epistemology, now growing again in popularity. Leading epistemologists illuminate its strengths and weaknesses, and address questions new and old about justification, reasoning, responsibility, disagreement, and trust.

Pyrrhonian skepticism, specifically that which appeals to the regress argument, claims that we cannot know that something is the case or that something is not the case, because we will always lack reasons that guarantee knowledge. This imposes on contemporary epistemology the task of developing a theoretical proposal that disables the skeptical thesis and offers an adequate answer to the puzzle of Pyrrhonian skepticism. In contemporary epistemology, we can mention at least three possible paths: foundationalism (and its various strands), coherentism (...) (and its various strands) and the infinitism proposed by Peter Klein. Infinitism, as Peter Klein presents it, has some weaknesses and, for this very reason, continues to be the target of strong criticism. We believe that the pragmatic philosophy of Charles Sanders Peirce can serve as theoretical inspiration for a possible reinterpretation of Infinitism. The answers to save epistemology from skeptical attacks, whether by challenging the fragile criteria of justification or those provided by the limited solutions of naturalism and fallibilism, as well as infinitism, can, in our view, be glimpsed on the horizon of a pragmatic analysis of research, since the basis of research (empirical or not) is pragmatically determined, according to Peirce, in each investigation, in each research program or research tradition. With this, we propose that an infinitist theory inspired by Peirce's pragmatism can offer us an adequate alternative to the skepticism of epistemic regress. (shrink)

This essay is an introductory overview of the considerations in favor of epistemic infinitism, the view that the demands of justification are that one must have non-terminating series of reasons for one's beliefs if they are to be knowledge.

This is a review of Turri and Klein's "Ad Infinitum: New Essays on Epistemological Infinitism".

O problema do critério é um dos mais importantes da epistemologia. A resposta que se dá a ele definirá um aspecto fundamental das teorias do conhecimento. Neste ensaio, o problema do critério é apresentado e algumas das conseqüências geradas pela aceitação de exigências metaepistemicas são analisadas. Em especial, essas conseqüências são avaliadas em relação ao infinitismo – a teoria epistemológica segundo a qual as razões que sustentam nossas crenças devem ser infinitas em número e não-repetidas. Ao final, sustenta-se que cláusulas (...) que exigem que a metajustificação seja necessária para o conhecimento não apenas tornam as teorias epistemológicas mais plausíveis, mas também que a ausência de tais exigências acaba criando problemas muito difíceis, como o assim chamado “problema do conhecimento fácil”. PALAVRAS-CHAVE – Infinitismo. Problema do critério. Metajustificação. Conhecimento. Metaconhecimento. Ceticismo. ABSTRACT This essay discusses the Problem of the Criterion, one of the most important problems in Epistemology. The answer given to this problem will shape a fundamental aspect of theories of knowledge. It also analyzes some of the consequences epistemological theories may face in accepting metaepistemological requirements. These consequences are given special consideration with regard to Infinitism, the epistemological theory according to which the reasons that support our beliefs must be infinite and non-repeating. Finally, this essay claims not only that those propositions that require metajustification make any theory, even Infinitism, more plausible, but also that the absence of such requirements creates difficult problems, such as the so-called “Problem of Easy Knowledge.” KEY WORDS – Infinitism. Problem of the Criterion. Metajustification. Knowledge. Metaknowledge. Skepticism. (shrink)

Beneficence—the part of morality concerned with promoting people's well-being—is widely thought to be both agent-neutral and impartial: it prescribes a common aim to all, and does not favor some individuals over others. This paper explores a problem for agent-neutral, impartial beneficence from the perspective of "individualistic ethics" in the tradition of Harsanyi. The problem reveals that if we want only what is best for each of infinitely many individuals, and we are rational, then we must care about some individuals more (...) than others. I conclude that, on the individualistic approach, value must be fundamentally agent-relative. (shrink)

People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call *Countable (...) Independence*. In violating these principles, they display foibles like those of people who deviate from standard expected utility theory in more mundane cases: they choose dominated strategies, pay to avoid information, and reject expert advice. We precisely characterize the preference relations that satisfy Countable Independence in several equivalent ways: a structural constraint on preferences, a representation theorem, and the principle we began with, that every prospect has a value that some outcome could have. (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)

Anyone who has pondered the limitlessness of space and time, or the endlessness of numbers, or the perfection of God will recognize the special fascination of this question. Adrian Moore's historical study of the infinite covers all its aspects, from the mathematical to the mystical.

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 formal ontology, infinite regresses are generally considered a bad sign. One debate where such regresses come into play is the debate about fundamentality. Arguments in favour of some type of fundamentalism are many, but they generally share the idea that infinite chains of ontological dependence must be ruled out. Some motivations for this view are assessed in this article, with the conclusion that such infinite chains may not always be vicious. Indeed, there may even be room for a type (...) of fundamentalism combined with infinite descent as long as this descent is “boring,” that is, the same structure repeats ad infinitum. A start is made in the article towards a systematic account of this type of infinite descent. The philosophical prospects and scientific tenability of the account are briefly evaluated using an example from physics. (shrink)

Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.

Suppose you found that the universe around you was infinite—that it extended infinitely far in space or in time and, as a result, contained infinitely many persons. How should this change your moral decision-making? Radically, it seems, according to some philosophers. According to various recent arguments, any moral theory that is ’minimally aggregative’ will deliver absurd judgements in practice if the universe is (even remotely likely to be) infinite. This seems like sound justification for abandoning any such theory. -/- My (...) goal in this thesis is simple: to demonstrate that we need not abandon minimally aggregative theories, even if we happen to live in an infinite universe. I develop and motivate an extension of such theories, which delivers plausible judgements in a range of realistic cases. I show that this extended theory can overcome key objections—both old and new—and that it succeeds where other proposals do not. With this proposal in hand, we can indeed retain minimally aggregative theories and continue to make moral decisions based on what will promote the good. (shrink)

For aggregative theories of moral value, it is a challenge to rank worlds that each contain infinitely many valuable events. And, although there are several existing proposals for doing so, few provide a cardinal measure of each world's value. This raises the even greater challenge of ranking lotteries over such worlds—without a cardinal value for each world, we cannot apply expected value theory. How then can we compare such lotteries? To date, we have just one method for doing so (proposed (...) separately by Arntzenius, Bostrom, and Meacham), which is to compare the prospects for value at each individual location, and to then represent and compare lotteries by their expected values at each of those locations. But, as I show here, this approach violates several key principles of decision theory and generates some implausible verdicts. I propose an alternative—one which delivers plausible rankings of lotteries, which is implied by a plausible collection of axioms, and which can be applied alongside almost any ranking of infinite worlds. (shrink)