Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters. The book addresses the need for a theory of infinity, and reviews both old and new theories of infinity. It (...) discussing the purposes of studying infinity and the troubles with traditional approaches to the problem, and concludes by offering a solution to some existing paradoxes. (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)

What is the relation between a reason and an action when the reason explains the action by giving the agent's reason for doing what he did? We may call such explanations rationalizations, and say that the reason rationalizes the action. In this paper I want to defend the ancient - and common-sense - position that rationalization is a species of ordinary causal explanation. The defense no doubt requires some redeployment, but not more or less complete abandonment of the position, as (...) urged by many recent writers. (shrink)

A wide-ranging study of the central concepts in epistemology - belief, truth and knowledge. Professor Armstrong offers a dispositional account of general beliefs and of knowledge of general propositions. Belief about particular matters of fact are described as structures in the mind of the believer which represent or 'map' reality, while general beliefs are dispositions to extend the 'map' or introduce casual relations between portions of the map according to general rules. 'Knowledge' denotes the reliability of such beliefs as representations (...) of reality. Within this framework Professor Armstrong offers a distinctive account of many of the main questions in general epistemology - the relations between beliefs and language, the notions of proposition, concept and idea, the analysis of truth, the varieties of knowledge, and the way in which beleifs and knowledge are supported by reasons. The book as a whole if offered as a contribution to a naturalistic account of man. (shrink)

Epistemology or the theory of knowledge is one of the cornerstones of analytic philosophy, and this book provides a clear and accessible introduction to the subject. It discusses some of the main theories of justification, including foundationalism, coherentism, reliabilism, and virtue epistemology. Other topics include the Gettier problem, internalism and externalism, skepticism, the problem of epistemic circularity, the problem of the criterion, a priori knowledge, and naturalized epistemology. Intended primarily for students taking a first class in epistemology, this lucid and (...) well-written text would also provide an excellent introduction for anyone interested in knowing more about this important area of philosophy. (shrink)

The phenomenon of mutual support presents a specific challenge to the foundationalist epistemologist: Is it possible to model mutual support accurately without using circles of evidential support? We argue that the appearance of loops of support arises from a failure to distinguish different synchronic lines of evidential force. The ban on loops should be clarified to exclude loops within any such line, and basing should be understood as taking place within lines of evidence. Uncertain propositions involved in mutual support relations (...) are conduits to each other of independent evidence originating ultimately in the foundations. We examine several putative examples of benign loops of support and show that, given the distinctions noted, they can be accurately modeled in a foundationalist fashion. We define an evidential "tangle," a relation among three propositions that appears to require a loop for modeling, and prove that all such tangles are trivial in a sense that precludes modeling them with an evidential circle. (shrink)

What is Knowledge? Where does it come from? Can we know anything at all? This lucid and engaging introduction grapples with these central questions in the theory of knowledge, offering a clear, non-partisan view of the main themes of epistemology including recent developments such as virtue epistemology and contextualism. Duncan Pritchard discusses traditional issues and contemporary ideas in thirteen easily digestible sections, including: the value of knowledge the structure of knowledge virtues and faculties perception testimony and memory induction scepticism. _What (...) is this thing called Knowledge?_ contains many helpful student-friendly features including study questions, annotated further reading, a glossary and a guide to web resources. Clear and interesting examples are used throughout. This is an ideal first textbook in the theory of knowledge for undergraduates taking a first course in philosophy. (shrink)

In the last decade, the familiar problem of the regress of reasons has returned to prominent consideration in epistemology. And with the return of the problem, evaluation of the options available for its solution is begun anew. Reason’s regress problem, roughly put, is that if one has good reasons to believe something, one must have good reason to hold those reasons are good. And for those reasons, one must have further reasons to hold they are good, and so a regress (...) of reasons looms. In this new study, Aikin presents a full case for infinitism as a response to the problem of the regress of reasons. Infinitism is the view that one must have a non-terminating chain of reasons in order to be justified. The most defensible form of infinitism, he argues, is that of a mixed theory – that is, epistemic infinitism must be consistent with and integrate other solutions to the regress problem. (shrink)

Some philosophers have claimed that it is meaningless or paradoxical to consider the probability of a probability. Others have however argued that second-order probabilities do not pose any particular problem. We side with the latter group. On condition that the relevant distinctions are taken into account, second-order probabilities can be shown to be perfectly consistent. May the same be said of an infinite hierarchy of higher-order probabilities? Is it consistent to speak of a probability of a probability, and of a (...) probability of a probability of a probability, and so on, {\em ad infinitum}? We argue that it is, for it can be shown that there exists an infinite system of probabilities that has a model. In particular, we define a regress of higher-order probabilities that leads to a convergent series which determines an infinite-order probability value. We demonstrate the consistency of the regress by constructing a model based on coin-making machines. (shrink)

This paper evaluates Peter Klein’s objection to foundationalism. According to Klein, foundationalism fails because it allows arbitrariness “at the base.” I first explain that this objection can be interpreted in two ways: either as targeting dialectical foundationalism or as targeting epistemic foundationalism. I then clarify Klein’s concept of arbitrariness. An assertion or belief is assumed to be arbitrary if and only if it lacks a reason that is “objectively and subjectively available.” Drawing on this notion, I evaluate Klein’s objection. I (...) first argue that his objection construed as targeting dialectical foundationalism fails, since nothing prevents dialectical foundationalism from ruling out arbitrary assertions. I then argue that the objection seen as targeting epistemic foundationalism cannot be disqualified in the way some foundationalists believe. However, I show that also the objection so construed does not succeed, since epistemic foundationalism need not countenance arbitrary beliefs. (shrink)

Once upon a time, coherentism was the dominant response to the regress problem in epistemology, but in recent decades the view has fallen into disrepute: now almost everyone is a foundationalist (with a few infinitists sprinkled here and there). In this paper, I sketch a new way of thinking about coherentism, and show how it avoids many of the problems often thought fatal for the view, including the isolation objection, worries over circularity, and concerns that the concept of coherence is (...) too vague or metaphorical for serious theoretical use. The key to my approach is to take a familiar tool from discussions of the regress problem -- namely, directed graphs depicting the support relations between beliefs -- and to use that tool in a more sophisticated manner than it is standardly employed. (shrink)

Justification, or at least ‘justification’, bulks large in recent epistemology. The view that knowledge consists of true-justified-belief has been prominent in this century, and the justification of belief has attracted considerable attention in its own right. But it is usually not at all clear just what an epistemologist means by ‘justified’, just what concept the term is used to express. An enormous amount of energy has gone into the attempt to specify conditions under which beliefs of one or another sort (...) are justified; but relatively little has been done to explain what it is for a belief to be justified, what that is for which conditions are being sought. The most common procedure has been to proceed on the basis of a number of obvious cases of justified belief, without pausing to determine what property it is of which these cases are instances. Now even if there were some single determinate concept that all these theoriests have implicitly in mind, this procedure would be less than wholly satisfactory. For in the absence of an explicit account of the concept being applied, we lack the most fundamental basis for deciding between supposed intuitions and for evaluating proposed conditions of justification. And in any event, as philosophers we do not seek merely to speak the truth, but also to gain an explicit, reflective understanding of the matters with which we deal. We want to know not only when our beliefs are justified, but also what it is to enjoy that status. True, not every fundamental concept can be explicated, but we shall find that much can be done with this one. (shrink)

In this important new work, Haack develops an original theory of empirical evidence or justification, and argues its appropriateness to the goals of inquiry. In so doing, Haack provides detailed critical case studies of Lewis's foundationalism; Davidson's and Bonjour's coherentism; Popper's 'epistemology without a knowing subject'; Quine's naturalism; Goldman's reliabilism; and Rorty's, Stich's, and the Churchlands' recent obituaries of epistemology.

Her belief is true, but it isn't knowledge. This is a classic illustration of a central problem in epistemology: determining what knowledge requires in addition to true belief.

We show that as a chain of confirmation becomes longer, confirmation dwindles under screening-off. For example, if E confirms H1, H1 confirms H2, and H1 screens off E from H2, then the degree to which E confirms H2 is less than the degree to which E confirms H1. Although there are many measures of confirmation, our result holds on any measure that satisfies the Weak Law of Likelihood. We apply our result to testimony cases, relate it to the Data-Processing Inequality (...) in information theory, and extend it in two respects so that it covers a broader range of cases. (shrink)

In “Theories of Justification,” Richard Fumerton begins an overview of several prominent positions on the nature of justification by isolating epistemic justification from nonepistemic justification. He also distinguishes between “having justification for a belief” and “having a justified belief,” arguing that the former is conceptually more fundamental. Fumerton then addresses the possibility that justification is a normative matter, suggesting that this possibility has little to offer as a concept of epistemic justification. He also critically examines more specific attempts to capture (...) the structure and content of epistemic justification. These include traditional foundationalism and variants thereof, externalist versions of foundationalism, contextualism, coherentism, and “mixed” theories which combine aspects of coherentism and foundationalism. (shrink)

First issued in translation as a two-volume work in 1975, this classic book provides the first complete development of the theory of probability from a subjectivist viewpoint. It proceeds from a detailed discussion of the philosophical mathematical aspects to a detailed mathematical treatment of probability and statistics. De Finetti’s theory of probability is one of the foundations of Bayesian theory. De Finetti stated that probability is nothing but a subjective analysis of the likelihood that something will happen and that that (...) probability does not exist outside the mind. It is the rate at which a person is willing to bet on something happening. This view is directly opposed to the classicist/ frequentist view of the likelihood of a particular outcome of an event, which assumes that the same event could be identically repeated many times over, and the 'probability' of a particular outcome has to do with the fraction of the time that outcome results from the repeated trials. (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)

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)

For most of their respective existences, reliabilism and evidentialism (that is, process reliabilism and mentalist evidentialism) have been rivals. They are generally viewed as incompatible, even antithetical, theories of justification.1 But a few people are beginning to re-think this notion. Perhaps an ideal theory would be a hybrid of the two, combining the best elements of each theory. Juan Comesana (forthcoming) takes this point of view and constructs a position called “Evidentialist Reliabilism.” He tries to show how each theory can (...) profit by borrowing elements from the other. Comesana concentrates on reliabilism’s problems and how it might be improved by infusions from evidentialism. This paper follows a similar tack. My emphasis, however, is the reverse of Comesana’s. I highlight problems for evidentialism and show how it could benefit by incorporating reliabilist themes. I am not sanguine that evidentialists will see it my way. They might even view my proposals as an insidious attempt to convert evidentialists to reliabilism. Well, I won’t debate the best way to formulate this paper’s recipe. At any rate, it began with the idea (which anteceded my reading of Comesana) of creating a synthesis of reliabilism and evidentialism. It retains significant strands of that idea, although the synthesis theme does not pervade the entire paper. What is mentalist evidentialism? Its original formulation was succinct. (shrink)

Adequate epistemic justification is best conceived as the appearance, over time, of knowledge to the subject. ‘Appearance’ is intended literally, not as a synonym for belief. It is argued through consideration of examples that this account gets the extension of ‘adequately justified belief’ at least roughly correct. A more theoretical reason is then offered to regard justification as the appearance of knowledge: If we have a knowledge norm for assertion, we do our best to comply with this norm when we (...) express as assertions only beliefs that appear to us to be knowledge. If we are doing our best, there is little point in further sanctions. So a norm of knowledge for assertion would lead to a secondary norm of justified belief as the appearance of knowledge, marking a point at which our assertions may be corrected but should not be blamed. (shrink)

This paper argues for a completely universal scepticism, according to which no beliefs at all are justified to the least degree. The argument starts with a version of the Agrippan trilemma, according to which, if we accept that a belief is justified, we must choose between foundationalism, coherentism of a particular sort, and an infinite regress of justified beliefs. Each of these theories is given a careful specification in terms of the relationship of “justifiedness in p depending on justifiedness in (...) q”. It is then argued that no beliefs – not even beliefs about phenomenal experiences – are foundational in the required way. Both coherentism and infinitism are untenable, since, since they face various objections, most significantly the objection that acceptance of either would commit one to allowing that all beliefs were justified. Because the three possible accounts of justificational structure all fail radically, it is concluded that no beliefs are justified. (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.

Andrew Cling presents a new version of the epistemic regress problem, and argues that intuitionist foundationalism, social contextualism, holistic coherentism, and infinitism fail to solve it. Cling’s discussion is quite instructive, and deserving of careful consideration. But, I argue, Cling’s discussion is not in all respects decisive. I argue that Cling’s dilemma argument against holistic coherentism fails.

Richard Foley has suggested that the search for a good theory of epistemic justification and the analysis of knowledge should be conceived of as two distinct projects. However, he has not offered much support for this claim, beyond highlighting certain salutary consequences it might have. In this paper, I offer some further support for Foley’s claim by offering an argument and a way to conceive the claim in a way that makes it as plausible as its denial, and thus levelling (...) the playing field. The burden of proof then lies with those who seek to deny Foley’s radical suggestion. (shrink)

Bayesianism provides a rich theoretical framework, which lends itself rather naturally to the explication of various “contrastive” and “non-contrastive” concepts. In this (brief) discussion, I will focus on issues involving “contrastivism”, as they arise in some of the recent philosophy of science, epistemology, and cognitive science literature surrounding Bayesian confirmation theory.

So far no known measure of confirmation of a hypothesis by evidence has satisfied a minimal requirement concerning thresholds of acceptance. In contrast, Shogenji’s new measure of justification (Shogenji, Synthese, this number 2009) does the trick. As we show, it is ordinally equivalent to the most general measure which satisfies this requirement. We further demonstrate that this general measure resolves the problem of the irrelevant conjunction. Finally, we spell out some implications of the general measure for the Conjunction Effect; in (...) particular we give an example in which the effect occurs in a larger domain, according to Shogenji justification, than Carnap’s measure of confirmation would have led one to expect. (shrink)

APA PsycNET abstract: This is the first volume of a two-volume work on Probability and Induction. Because the writer holds that probability logic is identical with inductive logic, this work is devoted to philosophical problems concerning the nature of probability and inductive reasoning. The author rejects a statistical frequency basis for probability in favor of a logical relation between two statements or propositions. Probability "is the degree of confirmation of a hypothesis (or conclusion) on the basis of some given evidence (...) (or premises)." Furthermore, all principles and theorems of inductive logic are analytic, and the entire system is to be constructed by means of symbolic logic and semantic methods. This means that the author confines himself to the formalistic procedures of word and symbol systems. The resulting sentence or language structures are presumed to separate off logic from all subjectivist or psychological elements. Despite the abstractionism, the claim is made that if an inductive probability system of logic can be constructed it will have its practical application in mathematical statistics, and in various sciences. 16-page bibliography. (PsycINFO Database Record (c) 2016 APA, all rights reserved). (shrink)

I argue against the orthodox view of the relationship between propositional and doxastic justification. The view under criticism is: if p is propositionally justified for S in virtue of S's having reason R, and S believes p on the basis of R, then S's belief that p is doxastically justified. I then propose and evaluate alternative accounts of the relationship between propositional and doxastic justification, and conclude that we should explain propositional justification in terms of doxastic justification. If correct, this (...) proposal would constitute a significant advance in our understanding of the sources of epistemic justification. (shrink)

First published in 1949 expressly to introduce logical positivism to English speakers. Reichenbach, with Rudolph Carnap, founded logical positivism, a form of epistemofogy that privileged scientific over metaphysical truths.

Introduction As the title indicates, the chief focus of this book is epistemic justification. But just what is epistemic justification and what is its place ...

From 1929 onwards, C. I. Lewis defended the foundationalist claim that judgements of the form 'x is probable' only make sense if one assumes there to be a ground y that is certain (where x and y may be beliefs, propositions, or events). Without this assumption, Lewis argues, the probability of x could not be anything other than zero. Hans Reichenbach repeatedly contested Lewis's idea, calling it "a remnant of rationalism". The last move in this debate was a challenge by (...) Lewis, defying Reichenbach to produce a regress of probability values that yields a number other than zero. Reichenbach never took up the challenge, but we will meet it on his behalf, as it were. By presenting a series converging to a limit, we demonstrate that x can have a definite and computable probability, even if its justification consists of an infinite number of steps. Next we show the invalidity of a recent riposte of foundationalists that this limit of the series can be the ground of justification. Finally we discuss the question where justification can come from if not from a ground. (shrink)

A compact, coherent introduction to the study of rational belief, this text provides points of entry to such areas of philosophy as theory of knowledge, methodology of science, and philosophy of language. The book is accessible to all undergraduates and presupposes no philosophical training.

With this treatise, an insightful exploration of the probabilistic connection between philosophy and the history of science, the famous economist breathed new life into studies of both disciplines. Originally published in 1921, this important mathematical work represented a significant contribution to the theory regarding the logical probability of propositions. Keynes effectively dismantled the classical theory of probability, launching what has since been termed the “logical-relationist” theory. In so doing, he explored the logical relationships between classifying a proposition as “highly probable” (...) and as a “justifiable induction.” Unabridged republication of the classic 1921 edition. (shrink)