A major difficulty for currently existing theories of inductive inference involves the question of what to do when novel, unknown, or previously unsuspected phenomena occur. In this paper one particular instance of this difficulty is considered, the so-called sampling of species problem.The classical probabilistic theories of inductive inference due to Laplace, Johnson, de Finetti, and Carnap adopt a model of simple enumerative induction in which there are a prespecified number of types or species which may be observed. But, realistically, this (...) is often not the case. In 1838 the English mathematician Augustus De Morgan proposed a modification of the Laplacian model to accommodate situations where the possible types or species to be observed are not assumed to be known in advance; but he did not advance a justification for his solution. (shrink)

This paper reconstructs and evaluates the representation theorem presented by Ramsey in his essay 'Truth and Probability', showing how its proof depends on a novel application of Hölder's theory of measurement. I argue that it must be understood as a solution to the problem of measuring partial belief, a solution that in many ways remains unsurpassed. Finally I show that the method it employs may be interpreted in such a way as to avoid a well known objection to it due (...) to Richard Jeffrey. (shrink)

The question of coherence of rules for changing degrees of belief in the light of new evidence is studied, with special attention being given to cases in which evidence is uncertain. Belief change by the rule of conditionalization on an appropriate proposition and belief change by "probability kinematics" on an appropriate partition are shown to have like status.

Although the concept of uncertainty is as old as Epicurus’s writings, and an excellent quantitative theory, with entropy as the measure of uncertainty having been developed in recent times, there has been little exploration of the qualitative theory. The purpose of the present paper is to give a qualitative axiomatization of uncertainty, in the spirit of the many studies of qualitative comparative probability. The qualitative axioms are fundamentally about the uncertainty of a partition of the probability space of events. Of (...) course, it is common to speak of the uncertainty, or randomness, of a random variable, but only the partition defined by the values of the random variable enter into the definition of uncertainty, not the actual values. It is straightforward to add axioms for decision making following the general line of Savage from the 1950s. Indeed, in the spirit of Epicurus, it is really our intuitive feeling about the uncertainty of the future that motivates much of our thinking about decisions. Here, the distinction between the concepts of probability and uncertainty can be made by citing many familiar examples. Without spelling out the technical details, the axiomatization of qualitative probability with uncertainty as the most important primitive concept, it is possible to raise a different kind of question about bounded rationality. This new question is whether or not one should bound the uncertainty in thinking and investigating any detailed framework of decision making. Discussion of this point is certainly different from the question of bounding rationality by not maximizing expected utility. In practice, we naturally bound uncertainty in our analysis of decision-making problems. As in the case of formulating an alternative for maximizing expected utility, so is the case of rational alternatives to maximizing uncertainty. There are several issues to consider. In the spirit of my other work in qualitative probability, I explore alternatives rather than attempt to give a definitive argument for one single solution. (shrink)

This volume bridges contemporary philosophical conceptions of risk and responsibility and offers an extensive examination of the topic. It shows that risk and responsibility combine in ways that give rise to new philosophical questions and problems. Philosophical interest in the relationship between risk and responsibility continues to rise, due in no small part due to environmental crises, emerging technologies, legal developments, and new medical advances. Despite such interest, scholars are just now working out how to conceive of the links between (...) risk and responsibility, the implications that risks may have to conceptions of responsibility (and vice versa), as well as how such theorizing might play out in applied cases. With contributions from leading scholars, this volume brings together new work examining the interplay between risk and responsibility, exploring its varied philosophical aspects and applications to contemporary issues in law, bioethics, technology, and environmental ethics. Risk and Responsibility in Context will be of interest to philosophers working in ethics, bioethics, philosophy of law, and philosophy of technology, as well as scholars and practitioners in law, health and science management, public policy, and environmental studies. (shrink)

On our ordinary representations of space, space is composed of indivisible, dimensionless points; extended regions are understood as infinite sets of points. Region-based theories of space reverse this atomistic picture, by taking as primitive several relations on extended regions, and recovering points as higher-order abstractions from regions. Over the years, such theories have focused almost exclusively on the topological and geometric structure of space. We introduce to region-based theories of space a new primitive binary relation (‘qualitative probability’) that is tied (...) to _measure_. It expresses that one region is _smaller than or equal in size_ to another. Algebraic models of our theory are _separation_ _σ_-_algebras with qualitative probability_: \((\mathbb {B}, \ll, \preceq )\), where \(\mathbb {B}\) is a Boolean _σ_-algebra, ≪ is a separation relation on \(\mathbb {B}\), and ≼ is a qualitative probability on \(\mathbb {B}\). We show that from algebraic models of this kind we can, in an interesting class of cases, recover a compact Hausdorff topology _X_, together with a countably additive measure _μ_ on a _σ_-field of Borel subsets of that topology, and that \((\mathbb {B}, \ll, \preceq )\) is isomorphic to a ‘standard model’ arising out of the pair (_X_, _μ_). It follows from one of our main results that any closed ball in Euclidean space, \(\mathbb {R}^{n}\), together with Lebesgue measure arises in this way from a separation _σ_-algebra with qualitative probability. (shrink)

We study the phenomenon of merging of opinions for computationally limited Bayesian agents from the perspective of algorithmic randomness. When they agree on which data streams are algorithmically random, two Bayesian agents beginning the learning process with different priors may be seen as having compatible beliefs about the global uniformity of nature. This is because the algorithmically random data streams are of necessity globally regular: they are precisely the sequences that satisfy certain important statistical laws. By virtue of agreeing on (...) what data streams are algorithmically random, two Bayesian agents can thus be taken to concur on what global regularities they expect to see in the data. We show that this type of compatibility between priors suffices to ensure that two computable Bayesian agents will reach inter-subjective agreement with increasing information. In other words, it guarantees that their respective probability assignments will almost surely become arbitrarily close to each other as the number of observations increases. Thus, when shared by computable Bayesian learners with different subjective priors, the beliefs about uniformity captured by algorithmic randomness provably lead to merging of opinions. (shrink)

According to an infinite frequency principle, it is rational, under certain conditions, to set your credence in an outcome to the limiting frequency of that outcome if the experiment were repeated indefinitely. I argue that most infinite frequency principles are undesirable in at least one of the following ways: accepting the principle would lead you to accept bets with sure losses, the principle gives no guidance in the case of deterministic experiments like coin tosses and the principle relies on a (...) metaphysical property, ‘chanciness’, whose necessary and sufficient conditions are unknown. I show that a frequency principle that is based on the principal principle suffers from problems related to the definition of ‘chance’ or ‘chanciness’, which could lead to all three of the above problems. I introduce a version of the infinite frequency principle that does not rely on a notion of chance or chanciness and does not suffer from any of these problems. (shrink)

A number of philosophers have thought that fair lotteries over countably infinite sets of outcomes are conceptually incoherent by virtue of violating countable additivity. In this article, I show that a qualitative analogue of this argument generalizes to an argument against the conceptual coherence of a much wider class of fair infinite lotteries—including continuous uniform distributions. I argue that this result suggests that fair lotteries over countably infinite sets of outcomes are no more conceptually problematic than continuous uniform distributions. Along (...) the way, I provide a novel argument for a weak qualitative, epistemic version of regularity. (shrink)

The purpose of this paper is to show that if one adopts conditional probabilities as the primitive concept of probability, one must deal with the fact that even in very ordinary circumstances at least some probability values may be imprecise, and that some probability questions may fail to have numerically precise answers.

I defend an analog of probabilism that characterizes rationally coherent estimates for chances. Specifically, I demonstrate the following accuracy-dominance result for stochastic theories in the C*-algebraic framework: supposing an assignment of chance values is possible if and only if it is given by a pure state on a given algebra, your estimates for chances avoid accuracy-dominance if and only if they are given by a state on that algebra. When your estimates avoid accuracy-dominance (roughly: when you cannot guarantee that other (...) estimates would be more accurate), I say that they are sufficiently coherent. In formal epistemology and quantum foundations, the notion of rational coherence that gets more attention requires that you never allow for a sure loss (or “Dutch book”) in a given sort of betting game; I call this notion full coherence. I characterize when these two notions of rational coherence align, and I show that there is a quantum state giving estimates that are sufficiently coherent, but not fully coherent. (shrink)

O presente volume se trata de uma coletânea de artigos que reúne alguns dos trabalhos propostos para o evento “III International Colloquium of Analytic Epistemology and VII Conference of Social Epistemology”, realizado entre os dias 27 e 30 de Novembro de 2018, na Universidade Federal de Santa Maria. O “III International Colloquium of Analytic Epistemology and VII Conference of Social Epistemology” é um dos principais eventos de Epistemologia analítica da América Latina e reúne especialistas do Brasil e do exterior para (...) promover debates de alto nível sobre temas que fazem parte da agenda contemporânea no que se refere ao debate analítico contemporâneo acerca da Epistemologia. (shrink)

Frank Plumpton Ramsey (1903–30) made seminal contributions to philosophy, mathematics and economics. Whilst he was acknowledged as a genius by his contemporaries, some of his most important ideas were not appreciated until decades later; now better appreciated, they continue to bear an influence upon contemporary philosophy. His historic significance was to usher in a new phase of analytic philosophy, which initially built upon the logical atomist doctrines of Bertrand Russell and Ludwig Wittgenstein, raising their ideas to a new level of (...) sophistication, but ultimately he became their successor rather than remain a mere acolyte. (shrink)

How do scientific innovations spread within and across scientific communities? In this paper, we propose a general account of the diffusion of scientific innovations. This account acknowledges that novel ideas must be elaborated on and conceptually translated before they can be adopted and applied to field-specific problems. We motivate our account by examining an exemplary case of knowledge diffusion, namely, the early spread of theories of rational decision-making. These theories were grounded in a set of novel mathematical tools and concepts (...) that originated in John von Neumann and Oskar Morgenstern's Theory of Games and Economic Behavior and subsequently spread widely across the social and behavioral sciences. Introducing a network-based diffusion measure, we trace the spread of those tools and concepts into distinct research areas. We furthermore present an analytically tractable typology for classifying publications according to their roles in the diffusion process. The proposed framework allows for a systematic examination of the conditions under which scientific innovations spread within and across preexisting and newly emerging scientific communities. (shrink)

The present paper investigates the first step of rational belief acquisition. It, thus, focuses on justificatory relations between perceptual experiences and perceptual beliefs, and between their contents, respectively. In particular, the paper aims at outlining how it is possible to reason from the content of perceptual experiences to the content of perceptual beliefs. The paper thereby approaches this aim by combining a formal epistemology perspective with an eye towards recent advances in philosophy of cognition. Furthermore the paper restricts its focus, (...) it concentrates on the case of color perception and perceptual beliefs about color. (shrink)

Objective standards for justification or for being a reason would be desirable, but inductive skepticism tells us that they cannot be presupposed. Rather, we have to start from subjective-relative notions of justification and of being a reason. The paper lays out the strategic options we have given this dilemma. The paper explains the requirements for this subject-relative notion and how they may be satisfied. Then it discusses four quite heterogeneous ways of providing more objective standards, which combine without guaranteeing complete (...) success. (shrink)

Two compelling principles, the Reasonable Range Principle and the Preservation of Irrelevant Evidence Principle, are necessary conditions that any response to peer disagreements ought to abide by. The Reasonable Range Principle maintains that a resolution to a peer disagreement should not fall outside the range of views expressed by the peers in their dispute, whereas the Preservation of Irrelevant Evidence Principle maintains that a resolution strategy should be able to preserve unanimous judgments of evidential irrelevance among the peers. No standard (...) Bayesian resolution strategy satisfies the PIE Principle, however, and we give a loss aversion argument in support of PIE and against Bayes. The theory of imprecise probability allows one to satisfy both principles, and we introduce the notion of a set-based credal judgment to frame and address a range of subtle issues that arise in peer disagreements. (shrink)

We survey a variety of possible explications of the term “Individual Risk.” These in turn are based on a variety of interpretations of “Probability,” including classical, enumerative, frequency, formal, metaphysical, personal, propensity, chance and logical conceptions of probability, which we review and compare. We distinguish between “groupist” and “individualist” understandings of probability, and explore both “group to individual” and “individual to group” approaches to characterising individual risk. Although in the end that concept remains subtle and elusive, some pragmatic suggestions for (...) progress are made. (shrink)

This paper examines the preference-based approach to the identification of beliefs. It focuses on the main problem to which this approach is exposed, namely that of state-dependent utility. First, the problem is illustrated in full detail. Four types of state-dependent utility issues are distinguished. Second, a comprehensive strategy for identifying beliefs under state-dependent utility is presented and discussed. For the problem to be solved following this strategy, however, preferences need to extend beyond choices. We claim that this a necessary feature (...) of any complete solution to the problem of state-dependent utility. We also argue that this is the main conceptual lesson to draw from it. We show that this lesson is of interest to both economists and philosophers. (shrink)

Jim Joyce argues for two amendments to probabilism. The first is the doctrine that credences are rational, or not, in virtue of their accuracy or “closeness to the truth” (1998). The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (2010). We argue that both amendments cannot be satisfied simultaneously. To do so, we employ a (slightly-generalized) impossibility theorem of Seidenfeld, Schervish, and Kadane (2012), who show that (...) there is no strictly proper scoring rule for imprecise probabilities. -/- The question then is what should give way. Joyce, who is well aware of this no-go result, thinks that a quantifiability constraint on epistemic accuracy should be relaxed to accommodate imprecision. We argue instead that another Joycean assumption — called strict immodesty— should be rejected, and we prove a representation theorem that characterizes all “mildly” immodest measures of inaccuracy. (shrink)

There is not a unique inductive skeptical position; there are grades of inductive skepticism. There is nothing much to say about complete skepticism, but some more restricted skeptical positions may be profitably analyzed.

De Finetti gave a natural definition of “coherent probability assessment” β:E→[0,1] of a set E={X1,…,Xm} of “events” occurring in an arbitrary set of “possible worlds”. In the particular case of yes–no events, , Kolmogorov axioms can be derived from his criterion. While De Finetti’s approach to probability was logic-free, we construct a theory Θ in infinite-valued Łukasiewicz propositional logic, and show: a possible world of is a valuation satisfying Θ, β is coherent iff it is a convex combination of valuations (...) satisfying Θ, iff β agrees on E with a state of the Lindenbaum MV-algebra of Θ, iff for some Borel probability measure μ on . Thus Łukasiewicz semantics, MV-algebraic states, and Borel probability measures provide a universal representation of coherent assessments of events occurring in any conceivable set of possible worlds. (shrink)

The logical consistency of a collection of assertions about events can be viewed as a special case of coherent probability assessments in the sense of de Finetti.

The contemporary theory of epistemic democracy often draws on the Condorcet Jury Theorem to formally justify the ‘wisdom of crowds’. But this theorem is inapplicable in its current form, since one of its premises – voter independence – is notoriously violated. This premise carries responsibility for the theorem's misleading conclusion that ‘large crowds are infallible’. We prove a more useful jury theorem: under defensible premises, ‘large crowds are fallible but better than small groups’. This theorem rehabilitates the importance of deliberation (...) and education, which appear inessential in the classical jury framework. Our theorem is related to Ladha's (1993) seminal jury theorem for interchangeable (‘indistinguishable’) voters based on de Finetti's Theorem. We also prove a more general and simpler such jury theorem. (shrink)

‘Bayesian epistemology’ became an epistemological movement in the 20th century, though its two main features can be traced back to the eponymous Reverend Thomas Bayes (c. 1701-61). Those two features are: (1) the introduction of a formal apparatus for inductive logic; (2) the introduction of a pragmatic self-defeat test (as illustrated by Dutch Book Arguments) for epistemic rationality as a way of extending the justification of the laws of deductive logic to include a justification for the laws of inductive logic. (...) The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of conditionalization. (shrink)

We suggest to define objective probabilities by similarity-weighted empirical frequencies, where more similar cases get a higher weight in the computation of frequencies. This formula is justified intuitively and axiomatically, but raises the question, which similarity function should be used? We propose to estimate the similarity function from the data, and thus obtain objective probabilities. We compare this definition to others, and attempt to delineate the scope of situations in which objective probabilities can be used.

The Internet and social media have opened niches for political exploitation of human dispositions to hyper-alarmed states that amplify perceived threats relative to their objective probabilities of occurrence. Researchers should aim to observe the dynamic “ramping up” of security threat mechanisms under controlled experimental conditions. Such research necessarily begins from a clear model of standard baseline states, and should involve adding treatments to established experimental protocols developed by experimental economists. We review these protocols, which allow for joint estimation of risk (...) preferences and subjective beliefs about probabilities and their distributions. Results we have obtained on such estimates, from populations in various countries, are gathered for comparison. Most people show moderate risk aversion in non-alarmed states. We also find universal heterogeneity in risk preference structures, with substantial sub-samples weighting probabilities in such a way as to display “probability pessimism”, while others make risky choices in accordance with expected utility theory. (shrink)

Part II: Suppes and the mature theory. Representation and uniqueness.

What is the place of coherence, or structural rationality, in good first-personal deliberation? According to Kolodny (2005), considerations of coherence are irrelevant to good first-personal deliberation. When we deliberate, we should merely care about the reasons or evidence we have for our attitudes. So, considerations of coherence should not show up in deliberation. In response to this argument, Worsnip (2021) argues that considerations of coherence matter for how we structure deliberation. For him, we should treat incoherent combinations of attitudes as (...) off-limits in deliberation. Some important questions are left unanswered by both camps. What do we mean by considerations of coherence “showing up” in first-personal deliberation? How do we interpret the divide between reasons-responsiveness and coherence? How should we interpret cases in which considerations of coherence interact with other norms or requirements? In this paper, I show how Haack’s (1993) crossword puzzle analogy sheds light on these questions. Also, the crossword puzzle analogy allows us to evaluate Kolodny’s objection and identify promising avenues for future research. (shrink)

While Bayesian models have been applied to an impressive range of cognitive phenomena, methodological challenges have been leveled concerning their role in the program of rational analysis. The focus of the current article is on computational impediments to probabilistic inference and related puzzles about empirical confirmation of these models. The proposal is to rethink the role of Bayesian methods in rational analysis, to adopt an independently motivated notion of rationality appropriate for computationally bounded agents, and to explore broad conditions under (...) which Bayesian agents would be rational. The proposal is illustrated with a characterization of costs inspired by thermodynamics. (shrink)

In his account of probable reasoning, Poincaré used the concept, or at least the language, of conventions. In particular, he claimed that the prior probabilities essential for inverse probable reasoning are determined conventionally. This paper investigates, in the light of Poincaré's well known claim about the conventionality of metric geometry, what this could mean, and how it is related to other views about the determination of prior probabilities. Particular attention is paid to the similarities and differences between Poincaré's conventionalism as (...) it applies to probabilities and de Finetti's subjectivism. The aim of the paper is to suggest that in accounts of the development of ideas about probable reasoning, particularly those customarily described as Bayesian, Poincaré's discussion deserves more attention than it has so far received. (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed (...) by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

Although the concept of uncertainty is as old as Epicurus’s writings, and an excellent quantitative theory, with entropy as the measure of uncertainty having been developed in recent times, there has been little exploration of the qualitative theory. The purpose of the present paper is to give a qualitative axiomatization of uncertainty, in the spirit of the many studies of qualitative comparative probability. The qualitative axioms are fundamentally about the uncertainty of a partition of the probability space of events. Of (...) course, it is common to speak of the uncertainty, or randomness, of a random variable, but only the partition defined by the values of the random variable enter into the definition of uncertainty, not the actual values. It is straightforward to add axioms for decision making following the general line of Savage from the 1950s. Indeed, in the spirit of Epicurus, it is really our intuitive feeling about the uncertainty of the future that motivates much of our thinking about decisions. Here, the distinction between the concepts of probability and uncertainty can be made by citing many familiar examples. Without spelling out the technical details, the axiomatization of qualitative probability with uncertainty as the most important primitive concept, it is possible to raise a different kind of question about bounded rationality. This new question is whether or not one should bound the uncertainty in thinking and investigating any detailed framework of decision making. Discussion of this point is certainly different from the question of bounding rationality by not maximizing expected utility. In practice, we naturally bound uncertainty in our analysis of decision-making problems. As in the case of formulating an alternative for maximizing expected utility, so is the case of rational alternatives to maximizing uncertainty. There are several issues to consider. In the spirit of my other work in qualitative probability, I explore alternatives rather than attempt to give a definitive argument for one single solution. (shrink)

We propose a model for belief which is free of presuppositions. Current models for belief suffer from two difficulties. One is the well known problem of logical omniscience which tends to follow from most models. But a more important one is the fact that most models do not even attempt to answer the question what it means for someone to believe something, and just what it is that is believed. We provide a flexible model which allows us to give meaning (...) to beliefs in general contexts, including the context of animal belief , and of human belief which is expressed in language. (shrink)

Inductive probability is the logical concept of probability in ordinary language. It is vague but it can be explicated by defining a clear and precise concept that can serve some of the same purposes. This paper presents a general method for doing such an explication and then a particular explication due to Carnap. Common criticisms of Carnap's inductive logic are examined; it is shown that most of them are spurious and the others are not fundamental.

Bruno de Finetti's earliest works on the foundations of probability are reviewed. These include the notion of exchangeability and the theory of random processes with independent increments. The latter theory relates to de Finetti's ideas for a probabilistic science more generally. Different aspects of his work are united by his foundational programme for a theory of subjective probabilities.

Bayesian models of human learning are becoming increasingly popular in cognitive science. We argue that their purported confirmation largely relies on a methodology that depends on premises that are inconsistent with the claim that people are Bayesian about learning and inference. Bayesian models in cognitive science derive their appeal from their normative claim that the modeled inference is in some sense rational. Standard accounts of the rationality of Bayesian inference imply predictions that an agent selects the option that maximizes the (...) posterior expected utility. Experimental confirmation of the models, however, has been claimed because of groups of agents that probability match the posterior. Probability matching only constitutes support for the Bayesian claim if additional unobvious and untested (but testable) assumptions are invoked. The alternative strategy of weakening the underlying notion of rationality no longer distinguishes the Bayesian model uniquely. A new account of rationality—either for inference or for decision-making—is required to successfully confirm Bayesian models in cognitive science. (shrink)

The Institute Vienna Circle held a conference in Vienna in 2003, Cambridge and Vienna a?

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 interpretation of the calculus of probability as a logic of partial belief has at least two advantages: it makes the assignment of probabilities plausible in cases where classical frequentist interpretations must find such assignments meaningless, and it gives a clear meaning to partial belief and to consistency of partial belief.

Maher (1992b) advances an objection to dynamic Dutch-book arguments, partly inspired by the discussion in Levi (1987; in particular by Levi's case 2, p. 204). Informally, the objection is that the decision maker will "see the dutch book coming" and consequently refuse to bet, thus escaping the Dutch book. Maher makes this explicit by modeling the decision maker's choices as a sequential decision problem. On this basis he claims that there is a mistake in dynamic coherence arguments. There is really (...) no formal mistake in classical dynamic coherence arguments, but the discussions in Maher and Levi do suggest interesting ways in which the definition of dynamic coherence might be strengthened. Such a strengthened "sequentialized" notion of dynamic coherence is explored here. It so happens that even on the strengthened standards for a Dutch book, the classic dynamic coherence argument for conditioning still goes through. (shrink)

Professor Savage has been candid and generous in stating his interest in philosophy, and the philosophers who have heard him are surely grateful for this. His attitude is very far from that of some competent scientists and mathematicans who purport to clear up the questions which philosophers raise concerning their disciplines by means of a battery of technical results of varying relevance—a procedure which can often be appropriately described as “an abominable snow-job.” However, Professor Savage's generosity places a responsibility on (...) philosophers, since the questions he raises are difficult. (shrink)