The second part of the book presents an alternative beyond the historical positions of Part I, one that defends a virtue epistemology combined with epistemic ...

In this article, I try to defend my conception of noninferential justification from important criticisms raised by Ted Poston in a recent article published in Philosophical Studies. More specifically, I argue that from within the framework of an acquaintance theory, one can still allow for fallible noninferential justification, and one can do so without losing the advantages I claim for the theory.

In this paper I argue that there is no viable alternative to construing our knowledge and justified belief as resting on a foundation restricted to truths about our internal states. Against Williamson and others I defend the claim that the internal life of a cognizer really does constitute a special sort of cognitive home that is importantly different from the rest of what we think we know and justifiably believe.

This paper (based on joint work with M.J.Schervish and J.B.Kadane) discusses some differences between the received theory of regular conditional distributions, which is the countably additive theory of conditional probability, and a rival theory of conditional probability using the theory of finitely additive probability. The focus of the paper is maximally "improper" conditional probability distributions, where the received theory requires, in effect, that P{a: P(a|a) = 0} = 1. This work builds upon the results of Blackwell and Dubins (1975).

This paper discusses some differences between the received theory of regular conditional distributions, which is the countably additive theory of conditional probability, and a rival theory of conditional probability using the theory of finitely additive probability. The focus of the paper is maximally "improper" conditional probability distributions, where the received theory requires, in effect, that P{a: P = 0} = 1. This work builds upon the results of Blackwell and Dubins.

Many people believe that there is a Dutch Book argument establishing that the principle of countable additivity is a condition of coherence. De Finetti himself did not, but for reasons that are at first sight perplexing. I show that he rejected countable additivity, and hence the Dutch Book argument for it, because countable additivity conflicted with intuitive principles about the scope of authentic consistency constraints. These he often claimed were logical in nature, but he never attempted to relate this idea (...) to deductive logic and its own concept of consistency. This I do, showing that at one level the definitions of deductive and probabilistic consistency are identical, differing only in the nature of the constraints imposed. In the probabilistic case I believe that R.T. Cox's ‘scale-free’ axioms for subjective probability are the most suitable candidates. 1 Introduction 2 Coherence and Consistency 3 The Infinite Fair Lottery 4 The Puzzle Resolved—But Replaced by Another 5 Countable Additivity, Conglomerability and Dutch Books 6 The Probability Axioms and Cox's Theorem 7 Truth and Probability 8 Conclusion: ‘Logical Omniscience’ CiteULike Connotea Del.icio.us What's this? (shrink)

I defend the principle of Phenomenal Conservatism, on which appearances of all kinds generate at least some justification for belief. I argue that there is no reason for privileging introspection or intuition over perceptual experience as a source of justified belief; that those who deny Phenomenal Conservatism are in a self-defeating position, in that their view cannot be both true and justified; and that thedemand for a metajustification for Phenomenal Conservatism either is an easily met demand, or is an unfair (...) or question-begging one. (shrink)

For Savage (1954) as for de Finetti (1974), the existence of subjective (personal) probability is a consequence of the normative theory of preference. (De Finetti achieves the reduction of belief to desire with his generalized Dutch-Book argument for Previsions.) Both Savage and de Finetti rebel against legislating countable additivity for subjective probability. They require merely that probability be finitely additive. Simultaneously, they insist that their theories of preference are weak, accommodating all but self-defeating desires. In this paper we dispute these (...) claims by showing that the following three cannot simultaneously hold: (i) Coherent belief is reducible to rational preference, i.e. the generalized Dutch-Book argument fixes standards of coherence. (ii) Finitely additive probability is coherent. (iii) Admissible preference structures may be free of consequences, i.e. they may lack prizes whose values are robust against all contingencies. (shrink)

Immediate knowledge is here construed as true belief that does not owe its status as knowledge to support by other knowledge (or justified belief) of the same subject. The bulk of the paper is devoted to a criticism of attempts to show the impossibility of immediate knowledge. I concentrate on attempts by Wilfrid Sellars and Laurence Bonjour to show that putative immediate knowledge really depends on higher-level knowledge or justified belief about the status of the beliefs involved in the putative (...) immediate knowledge. It is concluded that their arguments are lacking in cogency. (shrink)

This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly pick (...) out a point on a continuum, for instance using a roulette wheel or by flipping a countable infinity of fair coins, it follows, given the axioms of ZFC, that there are many different cardinalities between countable infinity and the cardinality of the continuum. (shrink)

This essay has two aims. The first is to correct an increasingly popular way of misunderstanding Belot's Orgulity Argument. The Orgulity Argument charges Bayesianism with defect as a normative epistemology. For concreteness, our argument focuses on Cisewski et al.'s recent rejoinder to Belot. The conditions that underwrite their version of the argument are too strong and Belot does not endorse them on our reading. A more compelling version of the Orgulity Argument than Cisewski et al. present is available, however---a point (...) that we make by drawing an analogy with de Finetti's argument against mandating countable additivity. Having presented the best version of the Orgulity Argument, our second aim is to develop a reply to it. We extend Elga's idea of appealing to finitely additive probability to show that the challenge posed by the Orgulity Argument can be met. (shrink)

In this paper I examine contemporary accounts of noninferential justification in light of what I take to be the Cartesian project of building epistemology on foundations made secure by the impossibility of error. I argue that familiar abstract arguments for foundationalism, by themselves, don’t seem to motivate Cartesianism. But I further argue that there is one version of foundationalism that is more closely linked to the way in which Descartes sought ideal knowledge.

Feldman proposed a solution to the speckled hen problem via ‘phenomenal concepts’, a solution which Fumerton accepted with reservation. Notwithstanding the existing criticisms of Feldman as being over-intellectualist, I argue that his approach fails for other reasons.

This book is concerned with the alleged capacity of the human mind to arrive at beliefs and knowledge about the world on the basis of pure reason without any dependence on sensory experience. Most recent philosophers reject the view and argue that all substantive knowledge must be sensory in origin. Laurence BonJour provocatively reopens the debate by presenting the most comprehensive exposition and defence of the rationalist view that a priori insight is a genuine basis for knowledge. This important book (...) will be at the centre of debate about the theory of knowledge for many years to come. (shrink)

Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti and Dubins, subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-­additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than κ. This generalizes our result, where we established that each finite but not countably additive probability has (...) conditional probabilities that fail to be conglomerable in some countable partition. (shrink)

This paper discusses conditional probability $$P$$ P , or the probability of A given B. When $$P>0$$ P > 0 , the ratio formula determines $$P$$ P . When $$P=0$$ P = 0 , the ratio formula breaks down. The Borel–Kolmogorov paradox suggests that conditional probabilities in such cases are indeterminate or ill-posed. To analyze the paradox, I explore the relation between probability and intensionality. I argue that the paradox is a Frege case, similar to those that arise in many (...) probabilistic and non-probabilistic contexts. The paradox vividly illustrates how an agent’s way of representing an entity can rationally influence her credal assignments. I deploy my analysis to defend Kolmogorov’s relativistic treatment of conditional probability. (shrink)

Classical acquaintance theory is any version of classical foundationalism that appeals to acquaintance in order to account for non-inferential justification. Such theories are well suited to account for a kind of infallible non-inferential justification. Why am I justified in believing that I’m in pain? An initially attractive (partial) answer is that I’m acquainted with my pain. But since I can’t be acquainted with what isn’t there, acquaintance with my pain guarantees that I’m in pain. What’s less clear is whether, given (...) classical acquaintance theory, it’s possible to have non-inferential justification to believe something false. Classical acquaintance theorists try to make room for such a possibility, but I argue that the attempts of Richard Fumerton, Ali Hasan, and Evan Fales are inadequate. I’ll focus on introspective justification, but similar issues arise for a priori justification as well. (shrink)

In this paper I argue that de Finetti provided compelling reasons for rejecting countable additivity. It is ironical therefore that the main argument advanced by Bayesians against following his recommendation is based on the consistency criterion, coherence, he himself developed. I will show that this argument is mistaken. Nevertheless, there remain some counter-intuitive consequences of rejecting countable additivity, and one in particular has all the appearances of a full-blown paradox. I will end by arguing that in fact it is no (...) paradox, and that what it shows is that conditionalisation, often claimed to be integral to the Bayesian canon, has to be rejected as a general rule in a finitely additive environment. (shrink)

It is sometimes alleged that arguments that probability functions should be countably additive show too much, and that they motivate uncountable additivity as well. I show this is false by giving two naturally motivated arguments for countable additivity that do not motivate uncountable additivity.

In “Compassionate Phenomenal Conservatism” (2007), “Phenomenal Conservatism and the Internalist Intuition” (2006), and Skepticism and the Veil of Perception (2001), Michael Huemer endorses the principle of phenomenal conservatism, according to which appearances or seemings constitute a fundamental source of (defeasible) justification for belief. He claims that those who deny phenomenal conservatism, including classical foundationalists, are in a self-defeating position, for their views cannot be both true and justified; that classical foundationalists have difficulty accommodating false introspective beliefs; and that phenomenal conservatism (...) is most faithful to the central internalist intuition. I argue that Huemer’s self-defeat argument fails, that classical foundationalism is able to accommodate fallible introspective beliefs, and that classical foundationalism captures a relatively clear internalist intuition. I also show that the motivation for phenomenal conservatism is less than clear. (shrink)

Say that an agent is "epistemically humble" if she is less than certain that her opinions will converge to the truth, given an appropriate stream of evidence. Is such humility rationally permissible? According to the orgulity argument : the answer is "yes" but long-run convergence-to-the-truth theorems force Bayesians to answer "no." That argument has no force against Bayesians who reject countable additivity as a requirement of rationality. Such Bayesians are free to count even extreme humility as rationally permissible.

Philosophers cannot agree on whether the rule of Countable Additivity should be an axiom of probability. Edwin T. Jaynes attacks the problem in a way which is original to him and passed over in the current debate about the principle: he says the debate only arises because of an erroneous use of mathematical infinity. I argue that this solution fails, but I construct a different argument which, I argue, salvages the spirit of the more general point Jaynes makes. I argue (...) that in Jaynes’s objective Bayesianism we might have good reasons to adopt Countable Additivity, and some of the major problems this adoption is known to entail need not worry us. In particular, I propose to adopt this new angle on Countable Additivity in Jon Williamson’s version of objective Bayesianism. (shrink)

I criticize Richard Fumerton’s fallibilist acquaintance theory of noninferential justification.