Early sections of the paper develop a view of the natural numbers and a view of counting which are suggested by the remarks of several modern philosophers. Further investigation of these views leads to one of the main theses of the paper: a special kind of quantifier, the "numerical quantifier" is essential to counting. The remainder of the paper suggests the rudiments of a new view of the natural numbers, a view which maintains that numerical quantifiers are one kind of (...) natural number. (shrink)
This brief paperback is designed for symbolic/formal logic courses. It features the tree method proof system developed by Jeffrey. The new edition contains many more examples and exercises and is reorganized for greater accessibility.
Richard Jeffrey is beyond dispute one of the most distinguished and influential philosophers working in the field of decision theory and the theory of knowledge. His work is distinctive in showing the interplay of epistemological concerns with probability and utility theory. Not only has he made use of standard probabilistic and decision theoretic tools to clarify concepts of evidential support and informed choice, he has also proposed significant modifications of the standard Bayesian position in order that it provide a (...) better fit with actual human experience. Probability logic is viewed not as a source of judgment but as a framework for explaining the implications of probabilistic judgments and their mutual compatability This collection of essays spans a period of some 35 years and includes what have become some of the classic works in the literature. There is also one completely new piece, while in many instances Jeffrey includes afterthoughts on the older essays. (shrink)
Edited by three leading figures in the field, this exciting volume presents cutting-edge work in decision theory by a distinguished international roster of contributors. These mostly unpublished papers address a host of crucial areas in the contemporary philosophical study of rationality and knowledge. Topics include causal versus evidential decision theory, game theory, backwards induction, bounded rationality, counterfactual reasoning in games and in general, analyses of the famous common knowledge assumptions in game theory, and evaluations of the normal versus extensive form (...) formulations of complex decision problems. (shrink)
"Frederic Schick, Journal of Philosophy This book uses elementary logical and mathematical means to philosophical end: elucidation of the notions of subjective ...
"To some people, life is very simple . . . no shadings and grays, all blacks and whites. . . . Now, others of us find that good, bad, right, wrong, are many-sided, complex things. We try to see every side; but the more we see, the less sure we are.".
From a point of view like de Finetti's, what is the judgmental reality underlying the objectivistic claim that a physical magnitude X determines the objective probability that a hypothesis H is true? When you have definite conditional judgmental probabilities for H given the various unknown values of X, a plausible answer is sufficiency, i.e., invariance of those conditional probabilities as your probability distribution over the values of X varies. A different answer, in terms of conditional exchangeability, is offered for use (...) when such definite conditional probabilities are absent. (shrink)
The approach to decision theory floated in my 1965 book is reviewed (I), challenged in various related ways (II–V) and defended, firstad hoc (II–IV) and then by a general argument of Ellery Ells's (VI). Finally, causal decision theory (in a version sketched in VII) is exhibited as a special case of my 1965 theory, according to the Eellsian argument.
Isaac Levi and I have different views of probability and decision making. Here, without addressing the merits, I will try to answer some questions recently asked by Levi (1985) about what my view is, and how it relates to his.
Logicism Lite counts number‐theoretical laws as logical for the same sort of reason for which physical laws are counted as as empirical: because of the character of the data they are responsible to. In the case of number theory these are the data verifying or falsifying the simplest equations, which Logicism Lite counts as true or false depending on the logical validity or invalidity of first‐order argument forms in which no numbertheoretical notation appears.
This book offers a concise survey of basic probability theory from a thoroughly subjective point of view whereby probability theory is a mode of judgement. Written by one of the greatest figures in the field of probability theory, the book is both a summation and a synthesis of a lifetime of wrestling with such problems and issues.
This paper discusses simultaneous belief updates. I argue here that modeling such belief updates using the Principle of Minimum Information can be regarded as applying Jeffrey conditionalization successively, and so that, contrary to what many probabilists have thought, the simultaneous belief updates can be successfully modeled by means of Jeffrey conditionalization.
Jonathan Weisberg has argued that Jeffrey Conditioning is inherently “anti-holistic” By this he means, inter alia, that JC does not allow us to take proper account of after-the-fact defeaters for our beliefs. His central example concerns the discovery that the lighting in a room is red-tinted and the relationship of that discovery to the belief that a jelly bean in the room is red. Weisberg’s argument that the rigidity required for JC blocks the defeating role of the red-tinted light (...) rests on the strong assumption that all posteriors within the distribution in this example are rigid on a partition over the proposition that the jelly bean is actually red. But individual JC updates of propositions do not require such a broad rigidity assumption. Jeffrey conditionalizers should consider the advantages of a modest project of targeted updating focused on particular propositions rather than seeking to update the entire distribution using one obvious partition. Although Weisberg’s example fails to show JC to be irrelevant or useless, other problems he raises for JC (the commutativity and inputs problems) remain and actually become more pressing when we recognize the important role of background information. (shrink)
Bayesian decision theory can be viewed as the core of psychological theory for idealized agents. To get a complete psychological theory for such agents, you have to supplement it with input and output laws. On a Bayesian theory that employs strict conditionalization, the input laws are easy to give. On a Bayesian theory that employs Jeffrey conditionalization, there appears to be a considerable problem with giving the input laws. However, Jeffrey conditionalization can be reformulated so that the problem (...) disappears, and in fact the reformulated version is more natural and easier to work with on independent grounds. (shrink)
Richard Jeffrey's generalization of Bayes' rule of conditioning follows, within the theory of belief functions, from Dempster's rule of combination and the rule of minimal extension. Both Jeffrey's rule and the theory of belief functions can and should be construed constructively, rather than normatively or descriptively. The theory of belief functions gives a more thorough analysis of how beliefs might be constructed than Jeffrey's rule does. The inadequacy of Bayesian conditioning is much more general than Jeffrey's (...) examples of uncertain perception might suggest. The ``parameter α '' that Hartry Field has introduced into Jeffrey's rule corresponds to the "weight of evidence" of the theory of belief functions. (shrink)
Since the beginning of the ?eighties of the present century, a circle of relatively young American sociologists who are followers of Jeffrey Alexander are making energetic and spectacular efforts to supply sociology with a uniform and comprehensive theoretical framework by continuing Talcott Parsons' lifework. The present article is an appreciation of Alexander's achievements in the justification of a general sociological theory (especially a theory of action and social order) while pointing to objections that can be raised against the character (...) of his theory. A scrutiny of Alexander's metatheoretical deliberations and of his interpretations of sociological classics such as Marx, Durkheim, Weber, and Parsons reveals that Alexander's metatheoretical frame is not flexible enough to actually reconstruct the problem situation of the classics. Pointers are given toward a theory of action that is not subject to the antinomy of utilitarianism and normativism, so that it is more adequate and appropriate to the heritage of the sociological classics, both from a theoretical and an interpretative angle. (shrink)
In Tsuji 1997 the concept of Jeffrey-Keynes algebras was introduced in order to construct a paraconsistent theory of decision under uncertainty. In the present paper we show that these algebras can be used to develop a theory of decision under uncertainty that measures the degree of belief on the quasi (or partial) truth of the propositions. As applications of this new theory of decision, we use it to analyze Popper's paradox of ideal evidence and to indicate a possible way (...) of formalizing Keynes' theory of economic action. (shrink)
This paper is partly a tribute to Richard Jeffrey, partly a reflection on some of his writings, The Logic of Decision in particular. I begin with a brief biography and some fond reminiscences of Dick. I turn to some of the key tenets of his version of Bayesianism. All of these tenets are deployed in my discussion of his response to the St. Petersburg paradox, a notorious problem for decision theory that involves a game of infinite expectation. Prompted by (...) that paradox, I conclude with some suggestions of avenues for future research. (shrink)
Abstract. Suppose that several individuals who have separately assessed prior probability distributions over a set of possible states of the world wish to pool their individual distributions into a single group distribution, while taking into account jointly perceived new evidence. They have the option of (i) first updating their individual priors and then pooling the resulting posteriors or (ii) first pooling their priors and then updating the resulting group prior. If the pooling method that they employ is such that they (...) arrive at the same final distribution in both cases, the method is said to be externally Bayesian, a property first studied by Madansky (1964). We show that a pooling method for discrete distributions is externally Bayesian if and only if it commutes with Jeffrey conditioning, parameterized in terms of certain ratios of new to old odds, as in Wagner (2002), rather than in terms of the posterior probabilities of members of the disjoint family of events on which such conditioning originates. (shrink)
Jeffrey Stout addresses two of the main criticisms of liberal democracy by its contemporary neotraditionalist Christian critics: that liberal democracy is destructive of social tradition, and thereby of virtue in the citizenry, and that liberal democracy is inherently secular, committed to expunging religious voices from the public arena. I judge that Stout effectively answers these charges: liberal democracy has its own tradition, it cultivates the virtues relevant to that, and it is not inherently hostile to piety. What Stout does (...) not do, I suggest, is take the next step of showing, positively, that Christianity can and should affirm the substance of liberal democratic society. This is due, in good measure, to the fact that Stout never tells us, except in off-hand comments, what he takes the substance of liberal democracy to be. And this, in turn, is due to his way of employing pragmatism: he uses pragmatism to give an account of human society generally, not of liberal democratic society. I raise some questions about the general account that pragmatism gives of human society, and thus about the account that it would give of liberal democracy. (shrink)
A glance at the sky raises my probability of rain to .7. As it happens, the conditional probabilities of each state given rain remain the same, and similarly for their conditional probabilities given no rain. As Jeffrey (1983, Ch. 11) points out, my new distribution P2 is therefore fixed by the law of total probability. For example, P2(RC) = P2(RC | R)P2(R)+P2(RC | ¯.
Jeffrey Tillman is perceptive in noticing that certain Protestant theologians have used evolutionary theory to become more sympathetic to Roman Catholic views of Christian love. But he is incorrect in saying that these formulations deemphasize a place for self-sacrifice in Christian love. Christian love defined as a strenuous equal-regard for both other and self also requires sacrificial efforts to restore love as equal-regard when finitude and sin undermine genuine mutuality and community.
To the Editor: It was with great interest that our Canadian Palliative Sedation Therapy Guideline working group read Jeffrey Berger's recent article ("Rethinking Guidelines for the Use of Palliative Sedation," May-June 2010). Given our own group's efforts to develop national guidelines, we have rethought the issue of palliative sedation therapy several times over the past year.The use of clear and concise definitions is fundamental to the development of any consensus guidelines on this topic. In the article, the term "palliative (...) sedation to unconsciousness," or PSU, implies the concerning assumption that sedation will knowingly be to unconsciousness in the palliative case under consideration. This conflicts with .. (shrink)
Jeffrey (1983) proposed a generalization of conditioning as a means of updating probability distributions when new evidence drives no event to certainty. His rule requires the stability of certain conditional probabilities through time. We tested this assumption (“invariance”) from the psychological point of view. In Experiment 1 participants offered probability estimates for events in Jeffrey’s candlelight example. Two further scenarios were investigated in Experiment 2, one in which invariance seems justified, the other in which it does not. Results (...) were in rough conformity to Jeffrey (1983)’s principle. (shrink)
A simple rule of probability revision ensures that the final result of a sequence of probability revisions is undisturbed by an alteration in the temporal order of the learning prompting those revisions. This Uniformity Rule dictates that identical learning be reflected in identical ratios of certain new-to-old odds, and is grounded in the old Bayesian idea that such ratios represent what is learned from new experience alone, with prior probabilities factored out. The main theorem of this paper includes as special (...) cases (i) Field's theorem on commuting probability-kinematical revisions and (ii) the equivalence of two strategies for generalizing Jeffrey's solution to the old evidence problem to the case of uncertain old evidence and probabilistic new explanation. (shrink)
I show that David Lewis’s principal principle is not preserved under Jeffrey conditionalization. Using this observation, I argue that Lewis’s reason for rejecting the desire as belief thesis and Adams’s thesis applies also to his own principal principle. 1 Introduction2 Adams’s Thesis, the Desire as Belief Thesis, and the Principal Principle3 Jeffrey Conditionalization4 The Principal Principles Not Preserved under Jeffrey Conditionalization5 Inadmissible Experiences.
Richard Jeffrey and Michael Goldstein have both introduced systematic approaches to the structure of opinion changes. For both approaches there are theorems which indicate great generality and width of scope. The main questions addressed here will be to what extent the basic forms of representation are intertranslatable, and how we can conceive of such programs in general.
Many strands are woven into the ideas and work of Jeffrey Gray. From a background of classical languages and a spell in military intelligence spent honing skills in languages and typing, he took two BA degrees (in modern languages and psychology) at Oxford University. He then trained as a clinical psychologist at the Institute of Psychiatry (IOP), London, capping this with a PhD on the sources of emotional behaviour.
Suppose n Bayesian agents need to make a decision as a group. The groupas a whole is also supposed to be a Bayesian agent whose probabilities andutilities are derived or aggregated in reasonable ways from the probabilitiesand utilities of the group members. The aggregation could beex ante, i.e., interms of expected utilities, or it could be ex post, i.e., in terms of utilitiesonly, or in terms of utilities and probabilities separately. This study exploresthe ex post approach. Using the Bolker/Jeffrey (...) framework, we show thatex post aggregation is subject to an instability phenomenon. That is, it mayhappen that the group preference between actions ``flips back and forth'''' dependingon the level of detail in which the decision problem is described. Structurally verysimilar phenomena also occur elsewhere in social choice theory, in statistics (Simpson''sParadox), and in voting theory (Ostrogorski''s Paradox). (shrink)
In this commentary, after first summarizing the three major theses of Jeffrey's paper Probability and Falsification: Critique of the Popper Program, and sketching out what I take to be his central argument, I criticize Jeffrey on two grounds. The first is that he has failed to explain why his version of Bayesianism provides us with better theories upon which to make decisions; the second is that he has offered a theory about decision-making that by-passes the important question: How (...) can we make more rational decisions? (shrink)
(2013). Review of Jeffrey P. Spike, Thomas R. Cole, Richard Buday, Freeman Williams, and Mary Ann Pendino, The Brewsters. The American Journal of Bioethics: Vol. 13, No. 3, pp. 52-54. doi: 10.1080/15265161.2013.760988.
In this paper, I argue for a view largely favorable to the Thirder view: when Sleeping Beauty wakes up on Monday, her credence in the coin’s landing heads is less than 1/2. Let’s call this “the Lesser view.” For my argument, I (i) criticize Strict Conditionalization as the rule for changing de se credences; (ii) develop a new rule; and (iii) defend it by Gaifman’s Expert Principle. Finally, I defend the Lesser view by making use of this new rule.
Since Francis Crick popularized the term `Neural Correlate of Consciousness' (NCC), it has been the focus of what is perhaps the most exciting research area in the cognitive sciences. Different researchers and laboratories have offered different brain structures as candidates for the NCC prize. Different chunks of gray matter have been identified as the potential seat of consciousness. Some researchers attempt to identify the NCC via a characterization of the cognitive aspects of consciousness, such as its functional significance or intentional (...) directedness, while others attempt a direct identification of the NCC, without any cognitive intermediary. Needless to say, no consensus is in sight on any of this. (shrink)
Jonathan Weisberg claims that certain probability assessments constructed by Jeffrey conditioning resist subsequent revision by a certain type of after-the-fact defeater of the reasons supporting those assessments, and that such conditioning is thus “inherently anti-holistic.” His analysis founders, however, in applying Jeffrey conditioning to a partition for which an essential rigidity condition clearly fails. Applied to an appropriate partition, Jeffrey conditioning is amenable to revision by the sort of after-the-fact defeaters considered by Weisberg in precisely the way (...) that he demands. (shrink)
In this article, I suggest an argument that seems to show a conflict between the reflection principle and conditionalization. In particular, I show that when the reflection principle is formulated in a standard way, the principle conflicts with Jeffrey conditionalization. And it is argued that the source of the conflict resides in an ambiguity of the standard formulation. Furthermore, I attempt to rescue the principle using Bayes factors. That is, I suggest a new formulation of the principle so as (...) to avoid the conflict. (shrink)
