Hume: Philosophy of Probability

In this paper, I examine Hume’s account of an important class of causal belief which he calls “general rules”. I argue that he understands general rules, like all causal beliefs, as lively ideas which are habitually associated with our impressions or memories. However, I argue, he believes that they are unlike any reflectively produced causal beliefs in that they are produced quickly and automatically, such that they occur independently of any other processes of reasoning. Given this, I argue, Hume appears (...) to understand general rules as relatively simple beliefs, expressible only via generic sentences, like “birds lay eggs”. (shrink)

The Heythrop Journal, Volume 63, Issue 4, Page 547-552, July 2022.

This paper examines Hume’s formulations and uses of the conceivability principle and the inconceivability principle. In Hume’s works, we identify different versions of CP and ICP, including proper CP, proper ICP, the weak versions of CP and ICP, the epistemic versions of CP and ICP, and show that Hume not only expresses ICP, but also really maintains it. Assuming an axiomatic characterization of modalities, we argue that if there is a sharp distinction between levels of modalities, then Hume’s conceivability arguments (...) do not hold. But, in a rather different way, we also argue that if Hume’s conceivability arguments hold, then there should be no distinction between levels of modalities. Finally, we argue that after Hume, there are lots of endeavors in logic and philosophy to distinguish different levels of modalities, and to accept new concepts of necessity other than logical necessity. (shrink)

Classical statistical mechanics posits probabilities for various events to occur, and these probabilities seem to be objective chances. This does not seem to sit well with the fact that the theory’s time evolution is deterministic. We argue that the tension between the two is only apparent. We present a theory of Humean objective chance and show that chances thus understood are compatible with underlying determinism and provide an interpretation of the probabilities we find in Boltzmannian statistical mechanics.

In an illuminating article, Claus Beisbart argues that the recently-popular thesis that the probabilities of statistical mechanics (SM) are Best System chances runs into a serious obstacle: there is no one axiomatization of SM that is robustly best, as judged by the theoretical virtues of simplicity, strength, and fit. Beisbart takes this 'no clear winner' result to imply that the probabilities yielded by the competing axiomatizations simply fail to count as Best System chances. In this reply, we express sympathy for (...) the 'no clear winner' thesis. However, we argue that an importantly different moral should be drawn from this. We contend that the implication for Humean chances is not that there are no SM chances, but rather that SM chances fail to be sharp. (shrink)

John Arbuthnot's celebrated but flawed paper in the Philosophical Transactions of 1711-12 is a philosophically and historically plausible target of Hume's probability theory. Arbuthnot argues for providential design rather than chance as a cause of the annual birth ratio, and the paper was championed as a successful extension of the new calculations of the value of wagers in games of chance to wagers about natural and social phenomena. Arbuthnot replaces the earlier anti-Epicurean notion of chance with the equiprobability assumption of (...) Huygens's mathematics of games of chance, and misrepresents the birth ratio data to rule out chance in favour of design. The probability sections of Hume's Treatise taken together correct the equiprobability assumption and its extension to other kinds of phenomena in the estimation of wagers or expectations about particular events. Hume's probability theory demonstrates the flaw in this version of the design argument. (shrink)

Hume appeals to different kinds of certainties and necessities in the Treatise. He contrasts the certainty that arises from intuition and demonstrative reasoning with the certainty that arises from causal reasoning. He denies that the causal maxim is absolutely or metaphysically necessary, but he nonetheless takes the causal maxim and ‘proofs’ to be necessary. The focus of this paper is the certainty and necessity involved in Hume’s concept of knowledge. I defend the view that intuitive certainty, in particular, is certainty (...) of the invariability or necessity of relations between ideas. Against David Owen and Helen Beebee, I argue that the certainty involved in intuition depends on the activity of the mind. I argue, further, that understanding this activity helps us understand more clearly one of Hume’s most important theses, namely that experience is the source of a distinct kind of certainty and of necessity. (shrink)

This paper defends a Bayesian approach to confirming a miracle against Jordan Howard Sobel’s recent novel interpretation of Hume’s criticisms. In his book, ’Logic and Theism’, Sobel offers an intriguing and original way to apply Hume’s criticisms against the possibility of having sufficient evidence to confirm a miracle. The key idea behind Sobel’s approach is to employ infinitesimal probabilities to neutralize the cumulative effects of positive evidence for any miracle. This paper aims to undermine Sobel’s use of infinitesimal probabilities to (...) block a Bayesian approach to confirming a miracle. (shrink)

The theorem of convergence of opinions is an important theorem in the subjective theory of probability.It demonstrates that the subjectivity of a prior probability will be substituted with the objectivity of a posterior probability as evidences increase.The theorem of convergence of opinions is regarded as the dynamic principle of rationality concerning the subjective probability,and therefore is used to resolve Hume's problem,i.e.,the problem of inductive rationality.However,Hacking convincingly argues that the theorem of convergence of opinions is not about the convergence of a (...) posterior probability Pre(h),but about the convergence of a conditional probability Pr(h/e).The subjective theory of probability implies a tacit acceptance of an equation that is Pre(h)=Pr(h/e),usually called "the rule of conditionalisation".Thus,the problem of rationality of induction is converted into one concerning the rule of conditionalisation.In this paper a new principle of rationality(the principle of minimum number of initial probabilities)is put forward,which,in combination with the concept of "local rationality",offers a justification for the rule of conditionalisation. (shrink)

This paper contends that the first argument of Hume's "Of scepticism with regard to reason" entails that humans have no knowledge as Hume understands knowledge. In defending this claim, we also see how Hume's argument anticipates an important aspect of an extremely influential 20th century development: the collapse of the analytic/synthetic distinction.

We must rethink our assessment of Hume’s theory of probabilistic inference. Hume scholars have traditionally dismissed his naturalistic explanation of how we make inferences under conditions of uncertainty; however, psychological experiments and computer models from cognitive science provide substantial support for Hume’s account. Hume’s theory of probabilistic inference is far from obsolete or outdated; on the contrary, it stands at the leading edge of our contemporary science of the mind.

The topic and methods of David Hume’s "Of Miracles" resemble his historiographical more than his philosophical works. Unfortunately, Hume and his critics and apologists have shared the prescientific, indeed ahistorical, limitations of Hume’s original historical investigations. I demonstrate the advantages of the critical methodological approach to testimonies, developed initially by German biblical critics in the late eighteenth century, to a priori discussions of miracles. Any future discussion of miracles and Hume must use the critical method to improve the quality and (...) relevance of the debate. (edited). (shrink)

The most important theories in fundamental physics, quantum mechanics and statistical mechanics, posit objective probabilities or chances. As important as chance is there is little agreement about what it is. The usual “interpretations of probability” give very different accounts of chance and there is disagreement concerning which, if any, is capable of accounting for its role in physics. David Lewis has contributed enormously to improving this situation. In his classic paper “A Subjectivist's Guide to Objective Chance” he described a framework (...) for representing single case objective chances, showed how they are connected to subjective credences, and sketched a novel account what they are within his Humean account of scientific laws. Here I will describe these contributions and add a little to them. (shrink)

In this significant contribution to the history of logic and exemplary work of contextual exegesis, David Owen shows that the early modern conception of reasoning was radically different from our own and applies this insight to the interpretation of Hume. We take the conclusions of deductive arguments to be entailed by premises in virtue of the form of those arguments. But early modern philosophers had a non-formal view of reasoning, dictated by the “way of ideas.” Owen maintains that we must (...) read Hume with this early modern conception of reasoning in mind if we are to understand his views on induction, scepticism with regard to reason, and the warrant for belief. (shrink)

Marc Lange has criticized my assertion that relative to a Bayesian conception of inductive reasoning, Hume's argument for inductive scepticism cannot be run. I reply that the way in which Lange suggests one should run the Humean argument in a Bayesian framework ignores the fact that in Bayesian models of learning from experience, the domain of an agent's probability measure is exogenously determined. I also show that Lange is incorrect to equate probability distributions which 'support inductive inferences' with probability distributions (...) which assign probability to contingent propositions/events. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume Studies Volume 28, Number 1, April 2002, pp. 113-130 Bayesianism, Analogy, and Hume's Dialogues concerning Natural Religion SALLY FERGUSON Introduction Analyses of the argument from design in Hume's Dialogues concerning Natural Religion have generally treated that argument as an example of reasoning by analogy.1 In this paper I examine whether it is in accord with Hume's thinking about the argument to subsume the version of it given in (...) the Dialogues under the model of probabilistic reasoning offered by Bayes's theorem. Wesley Salmon attempted this project in 1978.2 In related projects, David Owen3 as well as Philip Dawid and Donald Gillies4 have more recently attempted to construct Bayesian analyses of Hume's argument concerning testimony in "Of Miracles." I want to be careful at this stage to note exactly what I will claim. It is not that Bayesian reasoning sheds no light on the argument from design, or on arguments concerning testimony. All of the analyses mentioned above are beneficial in that they have been able to expose subtleties in these arguments that had previously gone unnoticed. Salmon's paper, in particular, contributes nicely to an understanding of just how the design argument may function in relation to contemporary scientific reasoning. In this paper I argue that, nonetheless, the attempt to apply Bayesian reasoning to the argument as presented in the Dialogues is not well supported as a reconstruction of Hume's own approach to the argument from design. Sally Ferguson is Assistant Professor of Philosophy, University of West Florida, UOOO University Parkway, Pensacola, FL 32514, USA. e-mail: [email protected] 114 Sally Ferguson There are two stages to my treatment of the issue. I begin by considering how much Hume knew of Bayes's theorem, and what consequence that knowledge might have had on his treatment of the argument in the Dialogues. This discussion includes a consideration of exactly what has been claimed by other authors on this subject, including what some have argued concerning Hume's reasonings in "Of Miracles," section 10 of An Enquiry concerning Human Understanding. I conclude that, based on the historical data, there is little reason to think of Hume's approach to the argument from design as anything more than proto-Bayesian at best. I then argue further, through a close textual analysis of the Dialogues, that there are good reasons for not treating Hume's reasoning there as even proto-Bayesian. In the end, the benefits that have been claimed for that approach, in terms of exposing both the subtleties of the argument and of Hume's reasoning about it, can equally well be derived from a careful analysis of the argument under a model of analogical reasoning, without need of Bayes's theorem. Section One Perhaps one might think that there is not much use for a consideration of the question whether Hume himself conceived of any of his arguments along specifically Bayesian lines. As Gower argues,5 Hume's knowledge of mathematics in general was fairly limited, and Bayes's theorem was not well known even up until Hume's death. It is important, therefore, for me to establish that there have not only been those who thought that Bayesian reasoning illuminates the arguments Hume gave, but also his own thinking about those arguments. It is also important for me to establish that it is not obvious that knowledge of Bayes's theorem did not affect Hume's reasonings. Each of these points will be addressed in the following. As to the first point, the claims of some authors on the subject are ambiguous. Dawid and Gillie, for example, make no statement to the effect that the probabilities involved in Bayes's theorem were in fact examined in "Of Miracles," nor do they attempt to produce any passages from Hume in support of that view. Thus it would be assumed that they see their attempt not as an attempt to provide an analysis that represents Hume's own approach to the argument, but rather simply as one that provides an illuminating method of analysis and support for an argument that Hume happened to give. Indeed, their conclusion, to the effect that a... (shrink)

The foremost advocate of Baconian probability, L. J. Cohen, has credited Hume for being the first to explicitly recognize that there is an important kind of probability which does not fit into the framework afforded by the calculus of chance, a recognition that is evident in Hume's distinction between analogical probability and probabilities arising from chance or cause. This essay defends Hume's account of the credibility of testimony, including his notorious argument against the credibility of testimony to miracles, in light (...) of this insight. (shrink)

Comienzo este artículo mostrando que las teorías neohumeanas de la causalidad probabilista basadas en la noción de relevancia estadlstica (como la teoria de Suppes, 1970) se encuentran con múltiples e insuperables dificultades. Luego analizo brevemente algunas versiones de la causalidad probabilista que relativizan o prescinden de dicha noción: la de Cartwright, que postula la existencia de capacidades causales, y las de Salmon y Dowe, quienes, aunque se proponen no abandonar el suelo humeano, creen necesario introducir una ontología de propensiones. Y (...) concluyo que el análisis de estas versiones demuestra que la causalidad probabilista constituye un nuevo y serio obstáculo para el enfoque humeano o neohumeano de la causalidad.In this paper I first show that the neohumean theories of probabilistic causality based on the notion of statistical relevance (as that of Suppes, 1970) run into many and unsolvable difficulties. Then I briefty analyze some accounts of probabilistic causality which relativize or avoid this notion: the Cartwright’s account, claiming the existence of causal capacities, and those of Salmon and Dowe, though trying to remain on a Humean ground, believe that the introduction of an ontology of propensities is required. I finally conclude that the analysis of these accounts shows that probabilistic causality constitutes a new and serious obstacle to the Humean or neohumean view of causality. (shrink)

Hume's argument concerning miracles is interpreted by making approximations to terms in Bayes's theorem. This formulation is then used to analyse the impact of multiple testimony. Individual testimonies which are ‘non-miraculous’ in Hume's sense can in principle be accumulated to yield a high probability both for the occurrence of a single miracle and for the occurrence of at least one of a set of miracles. Conditions are given under which testimony for miracles may provide support for the existence of God.

This paper presents a new account of Hume’s “probability of causes”. There are two main results attained in this investigation. The first, and perhaps the most significant, is that Hume developed – albeit informally – an essentially sound system of probabilistic inductive logic that turns out to be a powerful forerunner of Carnap’s systems. The Humean set of principles include, along with rules that turn out to be new for us, well known Carnapian principles, such as the axioms of semiregularity, (...) symmetry with respect to individuals (exchangeability), predictive irrelevance and positive instantial relevance. The second result is that Hume developed an original conception of probability, which is subjective in character, although it differs from contemporary personalistic views because it includes constraints that are additional to simple consistency and do not vary between different persons. The final section is a response to Gower’s thesis, by which Hume’s probability of causes is essentially non-Bayesian in character. It is argued that, on closer examination, Gower’s reading of the relevant passages is untenable and that, on the contrary, they are in accordance with the Bayesian reconstruction presented in this paper. (shrink)

Bayesian analyses are prominent among recent and allegedly novel interpretations of Hume’s argument against the justified belief in miracles. However, since there is no consensus on just what Hume’s argument is any Bayesian analysis will beg crucial issues of interpretation. Apart from independent philosophical arguments—arguments that would undermine the relevance of a Bayesian analysis to the question of the credibility of reports of the miraculous—no such analysis can, in principle, prove that no testimony can (or cannot) establish the credibility of (...) a miracle. Bayesian analyses of Hume’s argument are not analyses of Hume’s argument at all—but superfluous representations of it. (shrink)

At the beginning of his section “Of Miracles,” Hume mentions an argument of Dr. Tillotson. The doctrine of “the real presence” seems contradicted by our senses. We see a piece of bread, but are asked to believe it consists in the substance of the body of Christ.

Recent attempts to cast Hume’s argument against miracles in a Bayesian form are examined. It is shown how the Bayesian apparatus does serve to clarify the structure and substance of Hume’s argument. But the apparatus does not underwrite Hume’s various claims, such as that no testimony serves to establish the credibility of a miracle; indeed, the Bayesian analysis reveals various conditions under which it would be reasonable to reject the more interesting of Hume’s claims.

Hume’s main argument against rational belief in miracles might seem to rule out rational belief in other antecedently improbable occurrences as well--for example, a certain person’s having won the lottery. Dorothy Coleman has recently defended Hume against the lottery counterexample, invoking Hume’s distinction between probability of chances and probability of causes. I argue that Coleman’s defence fails.

In lieu of an abstract, here is a brief excerpt of the content:The Logic of Probabilities in Hume's Argument against Miracles Fred Wilson The position is often stated that Hume's discussion of miracles is inconsistent with his views on the logical or ontological status oflaws ofnature and with his more general scepticism. Broad, for one, has so argued.1 Hume's views on induction are assumed to go somethinglike this. Any attempt to demonstrate knowledge ofmatters offact presupposes causal reasoning, but the latter (...) is based not on any perception of necessary connections, but on an unreasoned expectation that because events have been constantly conjoined in the past they will be constantly conjoined in the future. The fact that our past experience gives rise to certain expectations provides absolutely no reason to think that these expectations will be fulfilled. But this is forgotten as soon as he turns to the topic of miracles where the argument requires certain assumptions about laws of nature. Here he claims that the laws of nature arebased upon afirm andunalterable experience and dismisses what he apparently admits to be strong evidence for miracles on the basis of the claim that such events are absolutely impossible. The inconsistency between the discussion of miracles and the earlier discussions of induction and causality is clear. Nonetheless, there is a certain implausibility to this claim that makes it a difficult one to entertain seriously, since it is unlikely that a philosopher as careful as Hume would have failed to recognize the inconsistency if it existed. What I propose here to argue is that there is in fact no inconsistency, and that this becomes clear once one places the discussion ofmiracles in the broader context ofthe overall argument ofthe first Enquiry. In particular, the charge ofinconsistency disappears once one eliminates the caricature ofHume's views on causal reasoning upon which it rests. To come to grips with the discussion of miracles in Hume it is necessary to place that discussion in its historical context. In the generally empiricist atmosphere that developed in Britain following the mid-seventeenth century civil wars, the general defence of the reasonableness of Christianity consisted of two parts. First, it washeldthatrational argument, whether causal or teleological orboth, could yield a reasonable belief that a deity ofa more or less traditional sort existed. Then, second, in order to establish further that Jesus was the Son ofGod it was held that one could rely upon a chain oftestimony Volume XV Number 2 255 FRED WILSON leading back from the present to the past to infer the existence of miracles testifying to the divinity ofJesus. Hume attacks this second inference in the essay on miracles andthe first in the essay that follows in the Enquiries on God's particular providence (the themes of which are developed more fully in the Dialogues on Natural Religion). Given the central place that the appeal to miracles held in Christian apologetics in the 17th and 18th centuries, Hume's systematic attack on the argument from miracles constituted a clear attack on Christianity. To be sure, Hume's argument would never have persuaded JohnWesley, but that would hardly have surprised Hume himself, nor should it surprise us: those in the grips of religious enthusiasm, whether it be John Wesley or Jimmy Swaggart, will hardly be persuaded by rational argument, however much it is still true that they ought to be persuaded by it. The appeal to miracles tojustify specifically Christian beliefs had a long history. One can find it already in the late Roman period in Eusebius. Muslim thinkers were to challenge this traditional defence by arguing that chains oftestimony become more unreliable the longer they become. As for their own Islamic beliefs, these they admitted had also to be justified by an appeal to miracles, but there was, it was claimed, a unique self-justifying miracle in the Koran, the specially revealed Word of God. The critical theme of the Muslim apologists, that the longer a chain of testimony the less assurance it gives of the fact that a miracle had occurred, was developed in Britain in the 17th and 18th centuries.6 It seems to have been introduced by the Oxford orientalist Edward Pocock who had discovered this line of Muslim apologetics while... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:328 HUME, MIRACLES AND LOTTERIES This paper addresses recent criticisms of Hume's skepticism with regard to miracles, by 1 2 Sorensen and Hambourger who argue that there are counterexamples, illustrated by lotteries, to Hume's account of how the truth of reports of improbable events (either first or second hand) must be evaluated. They believe these counterexamples are sufficient to prove that Hume's argument against the believability of miracles, defined (...) as violations of laws of nature caused by God, is unsound. Their arguments merit consideration not only in their own right but also on the basis of historical precedent, since they have in common an assumption that is found in Butler's criticism of Hume's predecessors in this debate. The bulk of my paper deals with Hambourger, who presents the most detailed version of the 'Butler' criticism. Sorensen's version can be answered in light of the evaluation of Hambourger 's argument. Hume's Argument Hume's argument is not against the possibility of miracles but against the possibility that it could ever be reasonable to believe a miracle 4 had occurred. His argument can be summed up as follows: in judging the credibility of a report of an improbable event, the probability of the event must be weighed against the probability that the report could be mistaken. The probability of an event is determined by the degree to which it conforms to known laws of nature. Laws of nature are formulated on the basis of uniform experience. Assuming that a miracle is a violation of laws of nature, any judgment that an event is miraculous presupposes a 329 judgment that there exists a uniform pattern of causation to which it is opposed, which pattern would constitute empirical proof against the miracle's occurrence. Testimony, on the other hand, is shown by experience not to be uniformly reliable. Consequently, no report of a miracle will have credibility since there will always be a uniform experience that is full proof against it, which therefore outweighs whatever merits testimony may have. In Hume's words, [N]o testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavors to establish.... When anyone tells me, that he saw a dead man restored to life, I immediately consider with myself, whether it be more probable, that this person should either deceive or be deceived, or that the fact, which he relates, should really have happened.... If the falsehood of his testimony would be more miraculous, than the event which he relates; then, and not till- then, can he pretend to command my belief or opinion (E 115-116). Hambourger 's Criticism Hambourger maintains that Hume's argument depends on a principle which he calls the "principle of relative likelihood." He restates this principle as follows: Suppose that someone or, perhaps, a group of people testify to the truth of a proposition P that, considered by itself, is improbable. Then to evaluate the testimony, one must weight (sic) the probability that P is true against the probability that the informants are lying or mistaken. If it is more likely that P is true than that the informants are lying or mistaken, then, on balance, the 330 testimony renders P more likely than not, and it may be reasonable for one to believe that P. However, if it is as likely, or even more likely, that the informants are lying or mistaken than it is that P is true, then, on balance, the testimony does not render P more likely true than false, and it would not be,reasonable for one to believe that P. As a counterexample to this principle, Hambourger asks us to suppose that a lottery is held in which there are one million entrants, each of whom has a one in a million chance of winning, and that a reliable newspaper, the New York Times, reports that the winner of the lottery is Smith. He further asks us to suppose that the Times errs only once out of every 10,000 times. Thus, the probability that the Times ' report is wrong is... (shrink)

Hume’s celebrated argument concerning miracles, and an 18th century criticism of it put forward by Richard Price, is here interpreted in terms of the modern controversy over the base-rate fallacy. When considering to what degree we should trust a witness, should we or should we not take into account the prior probability of the event reported? The reliability of the witness (’Pr’(says e/e)) is distinguished from the credibility of the testimony (’Pr’(e/says e)), and it is argued that Hume, as a (...) good proto-Bayesian, argued that the credibility of the testimony should be calculated in terms of both the reliability of the witness and the prior probability of the event reported. (shrink)

A BAYESIAN ARTICULATION OF HUME’S VIEWS IS OFFERED BASED ON A FORM OF THE BAYES-LAPLACE THEOREM THAT IS SUPERFICIALLY LIKE A FORMULA OF CONDORCET’S. INFINITESIMAL PROBABILITIES ARE EMPLOYED FOR MIRACLES AGAINST WHICH THERE ARE ’PROOFS’ THAT ARE NOT OPPOSED BY ’PROOFS’. OBJECTIONS MADE BY RICHARD PRICE ARE DEALT WITH, AND RECENT EXPERIMENTS CONDUCTED BY AMOS TVERSKY AND DANIEL KAHNEMAN ARE CONSIDERED IN WHICH PERSONS TEND TO DISCOUNT PRIOR IMPROBABILITIES WHEN ASSESSING REPORTS OF WITNESSES.

In lieu of an abstract, here is a brief excerpt of the content:125, HUME'S PROBABILITY ARGUMENT OF?,??,? In the Treatise,?,??,?, Hume presents an follows:' argument which, in the barest of outlines, goes as 1 (Pl) Every proposition has a probability less than one. (P2) If reason were the basis of our beliefs, then we would have no beliefs. (follows from (Pl)) (P3) We in fact do have beliefs. Hence, (P4) Reason is not the basis of our beliefs. The argument has (...) not been particularly well received. D. C. Stove, for example, refers to it as being "not merely defective, but one of the worst 2 arguments ever to impose itself on a man of genius." While not everyone is as unsympathetic as Stove, it nonetheless is difficult to find commentators favorably disposed toward the argument. Various sections of the Treatise are notoriously unclear.?,??,? is such a section; as such, it is difficult to say just what Hume intended his argument to be. My contention in the present paper is that there are two reasonable ways of reconstructing Hume's argument, both consistent with what Hume writes in?,??,?. The first reconstruction is clearly unsound; the second reconstruction fares somewhat better. In particular, my contention will be that this second reconstruction, if not sound, is at least valid 4 and contains no obviously false premises. Allow me to make some preliminary comments before presenting these reconstructions. The reconstructions to follow will primarily be concerned with premise (P2) above; in particular, the 126. reconstructions will focus on how Hume can claim that (P2) follows from (Pl). Premise (Pl) is a common 5 sceptical claim, not obviously false, and certainly not unique to Hume. As such, it strikes me that the more interesting part of the argument is Hume's claim that (P2) follows from (Pl), and such will be the focus of the reconstructions (although (Pl) will be discussed toward the end of this paper). Concerning (P2), why does Hume think this follows from (Pl)? His reasoning is contained in the following passage; Having thus found in every probability, beside the original uncertainty inherent in the subject, a new uncertainty deriv'd from the weakness of that faculty, which judges, and having adjusted these two together, we are oblig'd by our reason to add a new doubt deriv'd from the possibility of error in the estimation we make of the truth and fidelity of our faculties. This is a doubt, which immediately occurs to us, and of which, if we wou'd closely pursue our reason, we cannot avoid giving a decision. But this decision, tho' it shou'd be favourable to our preceeding judgment, being founded only on probability, must weaken still further our first evidence, and must itself be weaken'd by a fourth doubt of the same kind, and so on in infinitum; till at last there remain nothing of the original probability, however great we may suppose it to have been, and however small the diminution by every new uncertainty. No finite object can subsist under a decrease repeated in infinitum; and even the vastest quantity, which can enter into human imagination, must in this manner be reduc'd to nothing. (T182) Not for nothing did I claim that this section of the Treatise is unclear. At best, I can discern only the outline of Hume's reasoning, which seems to go as follows: first, when we assign a probability to some 127, proposition, reason dictates that we re-evaluate this probability. In particular, reason dictates that we "add a new doubt deriv'd from the possibility of error in the estimation we make of the truth and fidelity of our faculties." Note that Hume never specifies the object of this 'new doubt.' He might mean a) that our doubt concerns whether the probability we assigned the proposition is correct, or b) that our doubt concerns the evidence on which we based the assignment of that probability. Whatever the case, this 'new doubt' must "weaken still further our first evidence," presumably resulting in a lowering of the probability we originally assigned to the proposition. We then repeat this doubting process, adding new doubts of the same kind in infinitum, "till at last there remain nothing of the original... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:137. PROBABILITY IN HUME'S SCIENCE OF MAN This paper is an attempt to make sense of a fragment of Hume's positive philosophy, namely his theory of how we apportion belief on the basis of ambiguous evidence. The topic is one that has received little critical attention from philosophers. One reason for this neglect is the belief that Hume's discussion of probable reasoning is not addressed to philosophical questions, but (...) rather is concerned merely to give a psychological theory of why we tend to make the inferences we do. Another is the view that Hume's psychology of probability is too obscure to merit serious study. I hope to show, however, that Hume's discussion of probable reasoning contains more philosophy, and more interesting psychology, than the prevalence of these attitudes would suggest. The main philosophical content that I see in Hume's account of probable reasoning is that it embodies a certain theory of belief, worked out in some detail. Here the central notion is the "belief-feeling", vivacity. After an initial discussion of Hume's use of this notion, I hazard the opinion that vivacities are related to probabilities by a simple subtraction formula (§1). The investigation of Hume's account of probable inference (§2) gives strong grounds for thinking that this conjecture is indeed correct. Finally, an examination of what Hume says about the influence of probability on the passions unearths a bold theory of the specific psychological mechanism by which the subtraction of probabilities is effected (§3).§1 Degrees of belief Hume's philosophy makes heavy use of the quality of perceptions which he referred to variously as "force", "liveliness", "violence", "vivacity", "strength", "firmness" and so on. As the variety of these terms indicates, Hume was not entirely happy with any of them. He says it is 138. impossible by words to describe this feeling, which every 2 one must be conscious of in his own breast (A19). But we need to use some word, and rather than emulate Hume's diverse usage it will be convenient to adhere uniformly to the single term 'vivacity'. The first use to which Hume puts vivacity is in distinguishing impressions from ideas. Intuitively, impressions are either sensations, passions or emotions, whereas ideas are the perceptions involved in thinking or reasoning. And Hume maintains that we can distinguish these two kinds of perceptions by their differing degrees of vivacity: all impressions have greater vivacity than any idea. Apparently Hume thinks that the difference in vivacity between impressions and ideas is normally quite considerable, although in a few instances there is only a small differential (T2). Vivacity is again used by Hume to distinguish between belief and conception. Although to have an idea of God, say, is not the same thing as to believe in God, Hume argues that what distinguishes the latter is only the manner of conception. In belief, the idea feels different to an idea that is entertained incredulously. And this difference in feeling is identified by Hume with a difference in vivacity (T96).3 In general, Hume thinks of beliefs as being ideas, not impressions (T86 being an exception). This is the natural view, if one thinks of the distinction between impressions and ideas as a distinction between feeling and thinking (T2, A9 ). What distinguishes beliefs then is a somewhat intermediate vivacity, inferior to the vivacity of an impression but superior to the vivacity of a mere conception. A third use to which Hume puts vivacity is in making the distinction between memory and other beliefs. Just as beliefs are distinguished from other conceptions by their greater vivacity, so likewise memories are distinguished from other beliefs by their greater vivacity (T153). 139. Each of these three applications of vivacity seems to be implausib^e. Introspection inevitably suggests that impressions are not always more vivacious or forceful, or whatever, than ideas. Similarly it seems that our beliefs, and even our memories, are often less vivid than our fancies, contrary to what Hume claims. A considerable part of Hume's appendix to the Treatise is concerned with such objections. Hume appears to allow that what we would naturally call the vivacity of ideas is not a quality... (shrink)

The bulk of this book is the second series of John Dewey Lectures, delivered by Professor Ayer in April 1970. To this, Ayer has added a criticism of Roy Harred’s purported refutation of Hume and a chapter about "non-truth-functional" conditionals that rounds out the lectures. Leaving Harred aside, this book provides an elegant, concise, and up-to-date introduction to the problem of induction and related issues concerning probability. Hume is here vindicated. Beginning by giving what may be the best, updated paraphrase (...) of Hume’s negative argument about causal judgments, Ayer explicates the subsumed atomicity, the denial of natural necessity, and the claimed vacuity or circularity of introducing the "uniformity of nature." Ayer goes on to distinguish a priori or logical probabilities, statistical or frequency judgments, and credibility or ground floor inductive judgments, and he summarily argues that the admissibility of the first two forms of judgment, properly understood, provides no real justification for credibility judgments, which, though not defined as subjective, turn out to need some support from our decision to project and therefore entrench certain predicates, or take as lawlike certain generalizations, rather than others. Ayer here includes a very clear explication and criticism of Carnap’s way out in the Logical Concept of Probability, and elsewhere. Ayer acutely summarizes and discusses the Hempel and Goodman paradoxes, taking a position substantially in agreement with Quine and Goodman, and welds this discussion into a Humean conclusion: "In a certain sense cases are what we choose them to be. We do not decide what facts habitually go together but we do decide what combinations are to be imaginatively projected. The despised savages who beat gongs at solar eclipses to summon back the sun are not making any factual error. It is a true generalization that whenever they beat the gongs the sun does shine again, and if they always keep up the ceremony, it is also a true generalization that the sun comes out again only when they beat the gongs. If we despise them, it is because they tell a fictional story about what would happen if they did not beat the gongs, which we do not accept. They see what goes on as well as we do; it is just that we have a different and, we think, a better idea of the way the world works." To say all this is just, of course, to summarize and refurbish Hume’s position on causality. But to do that has two very real values now: 1) It underlines and exposes the epistemic basis of the position taken by Hume’s heirs; 2) It makes clear what are the departures required if one is to differ in substance from Hume and Ayer.—J. L. (shrink)

This book aims to discuss probability and David Hume's inductive scepticism. For the sceptical view which he took of inductive inference, Hume only ever gave one argument. That argument is the sole subject-matter of this book. The book is divided into three parts. Part one presents some remarks on probability. Part two identifies Hume's argument for inductive scepticism. Finally, the third part evaluates Hume's argument for inductive scepticism. Hume's argument that induction must be either deductively valid or circular because based (...) on experience neglects the possibility that it is an argument of non-deductive logic (logical probability, in the sense of Keynes). (shrink)

The overall aim of this thesis is to understand Hume’s famous argument concerning induction, and to appraise its success in establishing its conclusion. The thesis accordingly falls into two main parts, the first being concerned with analysis and interpretation of the argument itself, and the second with investigation of possible responses to it. Naturally the argument’s interpretation strongly constrains the range of possible replies, and indeed the results of Part I indicate that the only kind of strategy which stands much (...) prospect of defeating Hume’s argument is one based on a priori probabilistic reasoning – hence the overwhelming majority of Part II is devoted to a thorough investigation of this approach. (shrink)

The centrepiece of Earman’s provocatively titled book Hume’s Abject Failure: The Argument against Miracles is a probabilistic interpretation of Hume’s famous ‘maxim’ concerning the credibility of miracle reports, followed by a trenchant critique of the maxim when thus interpreted. He argues that the first part of this maxim, once its obscurity is removed, is simply trivial, while the second part is nonsensical. His subsequent discussion culminates with a forthright challenge to any would-be defender of Hume to ‘point to some thesis (...) which is both philosophically interesting and which Hume has made plausible’. My main aim here is to answer this challenge, by demonstrating a preferable interpretation of Hume’s maxim, according to which its first half is both plausible and non-trivial, while its second half sketches a useful, albeit approximate, corollary. I conclude by contesting Earman’s negative views on the originality and philosophical significance of Hume’s justly famous essay. (shrink)