A study is reported testing two hypotheses about a close parallel relation between indicative conditionals, if A then B , and conditional bets, I bet you that if A then B . The first is that both the indicative conditional and the conditional bet are related to the conditional probability, P(B|A). The second is that de Finetti's three-valued truth table has psychological reality for both types of conditional— true , false , or void for indicative conditionals and win , lose (...) , or void for conditional bets. The participants were presented with an array of chips in two different colours and two different shapes, and an indicative conditional or a conditional bet about a random chip. They had to make judgements in two conditions: either about the chances of making the indicative conditional true or false or about the chances of winning or losing the conditional bet. The observed distributions of responses in the two conditions were generally related to the conditional probability, supporting the first hypothesis. In addition, a majority of participants in further conditions chose the third option, “void”, when the antecedent of the conditional was false, supporting the second hypothesis. (shrink)

This paper argues that the interest-relativity of knowledge cannot be explained by the interest-relativity of belief. The discussion starts with an argument that knowledge plays a key pair of roles in decision theory. It is then argued that knowledge cannot play that role unless knowledge is interest-relative. The theory of the interest-relativity of belief is reviewed and revised. That theory can explain some of the cases that are used to suggest knowledge is interest-relative. But it can’t explain some cases involving (...) ignorance, or mistake, about the odds at which a bet is offered. The paper ends with an argument that these cases require positing interest-relative defeaters, which affect whether an agent knows something without affecting whether she believes it, or is justified in believing it. (shrink)

If an agent believes that the probability of E being true is 1/2, should she accept a bet on E at even odds or better? Yes, but only given certain conditions. This paper is about what those conditions are. In particular, we think that there is a condition that has been overlooked so far in the literature. We discovered it in response to a paper by Hitchcock (2004) in which he argues for the 1/3 answer to the Sleeping Beauty problem. (...) Hitchcock argues that this credence follows from calculating her fair betting odds, plus the assumption that Sleeping Beauty’s credences should track her fair betting odds. We will show that this last assumption is false. Sleeping Beauty’s credences should not follow her fair betting odds due to a peculiar feature of her epistemic situation. (shrink)

In this paper, I examine two major challenges to epistemic theories of democracy: “the authority dilemma” and “the epistemic gamble.” The first is a conceptual challenge, suggesting that epistemic democracy is inherently self-undermining. The second is a normative challenge, asserting that the case for democracy should not rely on precarious epistemic grounds. I argue that both challenges fail. Thus, epistemic theories of democracy escape two of the most popular objections to this view.

According to the preference-centric approach to understanding partial belief, the connection between partial beliefs and preferences is key to understanding what partial beliefs are and how they’re measured. As Ramsey put it, the ‘degree of a belief is a causal property of it, which we can express vaguely as the extent to which we are prepared to act on it’ The Foundations of Mathematics and Other Logical Essays, Routledge, Oxon, pp 156–198, 1931). But this idea is not as popular as (...) it once was. Nowadays, the preference-centric approach is frequently dismissed out-of-hand as behaviouristic, unpalatably anti-realist, and/or prone to devastating counterexamples. Cases like Eriksson and Hájek’s :183–213, 2007) preferenceless Zen monk and Christensen’s :356–376, 2001) other roles argument have suggested to many that any account of partial belief that ties them too closely to preferences is irretrievably flawed. In this paper I provide a defence of preference-centric accounts of partial belief. (shrink)

If an agent believes that the probability of E being true is 1/2, should she accept a bet on E at even odds or better? Yes, but only given certain conditions. This paper is about what those conditions are. In particular, we think that there is a condition that has been overlooked so far in the literature. We discovered it in response to a paper by Hitchcock (2004) in which he argues for the 1/3 answer to the Sleeping Beauty problem. (...) Hitchcock argues that this credence follows from calculating her fair betting odds, plus the assumption that Sleeping Beauty’s credences should track her fair betting odds. We will show that this last assumption is false. Sleeping Beauty’s credences should not follow her fair betting odds due to a peculiar feature of her epistemic situation. (shrink)

The question of the rationality of conspiratorial belief ¬divides philosophers into mainly two camps. The particularists believe that each conspiracy theory ought to be examined on its own merits. The generalist, by contrast, argues that there is something inherently suspect about conspiracy theories that makes belief in them irrational. Recent empirical findings indicate that conspiratorial thinking is commonplace among ordinary people, which has naturally shifted attention to the particularists. Yet, even the particularist must agree that not all conspiracy belief is (...) rational, in which case she must explain what separates rational from non-rational conspiratorial thinking. In this paper, I contrast three strategies to this end: 1) the probabilistic objectivist, who assesses the objective probability of conspiracies; 2) the subjectivist, who rather focuses on the perspective of the believer, and typically views the decision to believe in a conspiracy as a problem of decision making under risk. Approaches 1) and 2) rely on assessments of the probability of conspiracy which, I argue, limits their applicability. Instead, I explore 3) viewing the problem facing the potential believer as a decision problem under uncertainty about probabilities. I argue, furthermore, that focusing solely on epistemic utilities fails to do justice to the particular character of conspiracy beliefs, which are not exclusively epistemically motivated, and I investigate the rationality of such beliefs under a number of standard decision rules. (shrink)

Basic Emotion Theory, or BET, has dominated the affective sciences for decades (Ekman, 1972, 1992, 1999; Ekman and Davidson, 1994; Griffiths, 2013; Scarantino and Griffiths, 2011). It has been highly influential, driving a number of empirical lines of research (e.g., in the context of facial expression detection, neuroimaging studies and evolutionary psychology). Nevertheless, BET has been criticized by philosophers, leading to calls for it to be jettisoned entirely (Colombetti, 2014; Hufendiek, 2016). This paper defuses those criticisms. In addition, it shows (...) that we have good reason to retain BET. Finally, it reviews and puts to rest worries that BET’s commitment to affect programs renders it outmoded. We propose that, with minor adjustments, BET can avoid such criticisms when conceived under a radically enactive account of emotions. Thus, rather than leaving BET behind, we show how its basic ideas can be revised, refashioned and preserved. Hence, we conclude, our new BET is still a good bet. (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)

Many have argued that a rational agent's attitude towards a proposition may be better represented by a probability range than by a single number. I show that in such cases an agent will have unstable betting behaviour, and so will behave in an unpredictable way. I use this point to argue against a range of responses to the ‘two bets’ argument for sharp probabilities.

Certain kinds of prediction, foreknowledge, and future‐oriented action appear to require settled future truths. But open futurists think that the future is metaphysically unsettled: if it is open whether p is true, then it cannot currently be settled that p is true. So, open futurists—and libertarians who adopt the position—face the objection that their view makes rational action and deliberation impossible. I defuse the epistemic concern: open futurism does not entail obviously counterintuitive epistemic consequences or prevent rational action.

There seems to be widespread agreement that to be responsible for something is to be deserving of certain consequences on account of that thing. Call this the “merited-consequences” conception of responsibility. I think there is something off, or askew, in this conception, though I find it hard to articulate just what it is. The phenomena the merited-consequences conception is trying to capture could be better captured, I think, by noting the characteristic way in which certain minds can rightly matter to (...) other such minds—the way in which certain minds can carry a certain kind of importance, made manifest in certain sorts of responses. Mattering, not meriting, seems to me central. However, since I cannot yet better articulate an alternative, I continue in the merit-consequences framework. I focus on a particular class of consequences: those that are non-voluntary, in a sense explained. The non-voluntariness of these reactions has two important upshots. First, questions about their justification will be complex. Second, they are not well thought of as consequences voluntarily imposed upon the wrongdoer by the responder. By focusing on merited consequences and overlooking non-voluntariness, we risk misunderstanding the significance of moral criticism and of certain reactions to moral failure. (shrink)

Experimental results on the Ellsberg paradox typically reveal behavior that is commonly interpreted as ambiguity aversion. The experiments reported in the current paper find the objective probabilities for drawing a red ball that make subjects indifferent between various risky and uncertain Ellsberg bets. They allow us to examine the predictive power of alternative principles of choice under uncertainty, including the objective maximin and Hurwicz criteria, the sure-thing principle, and the principle of insufficient reason. Contrary to our expectations, the principle of (...) insufficient reason performed substantially better than rival theories in our experiment, with ambiguity aversion appearing only as a secondary phenomenon. (shrink)

In "To Bet The Impossible Bet", Harmon Holcomb III argues: (i) that Pascal's wager is structurally incoherent; (ii) that if it were not thus incoherent, then it would be successful; and (iii) that my earlier critique of Pascal's wager in "On Rescher On Pascal's Wager" is vitiated by its reliance on "logicist" presuppositions. I deny all three claims. If Pascal's wager is "incoherent", this is only because of its invocation of infinite utilities. However, even if infinite utilities are admissible, the (...) wager is defeated by the "many gods" and "many wagers" objections. Moreover, these objections do not rely on mistaken "logicist" presuppositions: atheists and agnostics traditionally and typically hold that they have no more--or at any rate, hardly any more--reason to believe in the traditional Christian God than they have to believe in countless alternative deities. (shrink)

This essay investigates, via the concepts of the philosophy of orientation, Annie Duke’s decision-making theory in "Thinking in Bets" and scrutinizes as to what extent one can universalize the 'orientation skill' of decision-making with regard to our everyday and professional life.

Over the past two decades, gamblers have begun taking mathematics into account more seriously than ever before. While probability theory is the only rigorous theory modeling the uncertainty, even though in idealized conditions, numerical probabilities are viewed not only as mere mathematical information, but also as a decision-making criterion, especially in gambling. This book presents the mathematics underlying the major games of chance and provides a precise account of the odds associated with all gaming events. It begins by explaining in (...) simple terms the meaning of the concept of probability for the layman and goes on to become an enlightening journey through the mathematics of chance, randomness and risk. It then continues with the basics of discrete probability, combinatorics and counting arguments for those interested in the supporting mathematics. These mathematic sections may be skipped by readers who do not have a minimal background in mathematics; these readers can skip directly to the Guide to Numerical Results to pick the odds and recommendations they need for the desired gaming situation. Doing so is possible due to the organization of that chapter, in which the results are listed at the end of each section, mostly in the form of tables. The chapter titled The Mathematics of Games of Chance presents these games not only as a good application field for probability theory, but also in terms of human actions where probability-based strategies can be tried to achieve favorable results. Through suggestive examples, the reader can see what are the experiments, events and probability fields in games of chance and how probability calculus works there. The main portion of this work is a collection of probability results for each type of game. Each game s section is packed with formulas and tables. Each section also contains a description of the game, a classification of the gaming events and the applicable probability calculations. The primary goal of this work is to allow the reader to quickly find the odds for a specific gaming situation, in order to improve his or her betting/gaming decisions. Every type of gaming event is tabulated in a logical, consistent and comprehensive manner. The complete methodology and complete or partial calculations are shown to teach players how to calculate probability for any situation, for every stage of the game for any game. Here, readers can find the real odds, returned by precise mathematical formulas and not by partial simulations that most software uses. Collections of odds are presented, as well as strategic recommendations based on those odds, where necessary, for each type of gaming situation. The book contains much new and original material that has not been published previously and provides great coverage of probabilities for the following games of chance: Dice, Slots, Roulette, Baccarat, Blackjack, Texas Hold em Poker, Lottery and Sport Bets. Most of games of chance are predisposed to probability-based decisions. This is why the approach is not an exclusively statistical one, but analytical: every gaming event is taken as an individual applied probability problem to solve. A special chapter defines the probability-based strategy and mathematically shows why such strategy is theoretically optimal.". (shrink)

Continuing his series of books on the mathematics of gambling, the author shows how a simple-rule game such as roulette is suited to a complex mathematical model whose applications generate improved betting systems that take into account a player's personal playing criteria. The book is both practical and theoretical, but is mainly devoted to the application of theory. About two-thirds of the content is lists of categories and sub-categories of improved betting systems, along with all the parameters that (...) might stand as the main objective criteria in a personal strategy - odds, profits and losses. The work contains new and original material not published before. The mathematical chapter describes complex bets, the profit function, the equivalence between bets and all their properties. All theoretical results are accompanied by suggestive concrete examples and can be followed by anyone with a minimal mathematical background because they involve only basic algebraic skills and set theory basics. The reader may also choose to skip the math and go directly to the sections containing applications, where he or she can pick desired numerical results from tables. The book offers no new so-called winning strategies, although it discusses them from a mathematical point of view. It does, however, offer improved betting systems and helps to organize a player's choices in roulette betting, according to mathematical facts and personal strategies. It is a must-have roulette handbook to be studied before placing your bets on the turn of either a European or American roulette wheel. (shrink)

Many philosophers hold that punishment has an expressive dimension. Advocates of expressive theories have different views about what makes punishment expressive, what kinds of mental states and what kinds of claims are, or legitimately can be expressed in punishment, and to what kind of audience or recipients, if any, punishment might express whatever it expresses. I shall argue that in order to assess the plausibility of an expressivist approach to justifying punishment we need to pay careful attention to whether the (...) things which punishment is supposed to express are aimed at an audience. For the ability of any version of expressivism to withstand two important challenges, which I call the harsh treatment challenge’ and the ‘publicity challenge’ respectively. will depend on the way it answers them. The first of these challenges has received considerable discussion in the literature on expressive theories of punishment; the second considerably less. This is unfortunate. For careful consideration of the publicity challenge should lead us to favor a version of the expressive theory which has been under-discussed: the view on which punishment has an intended audience, and on which the audience is society at large, rather than—as on the most popular version of that view—the criminal. Furthermore, this view turns out to be better equipped to meet the harsh treatment challenge, and to be so precisely because of the way in which it meets the publicity challenge. (shrink)

I describe Maher's utility-based account of theory acceptance, generally approvingly but with a few questions and doubts.

I bet you don’t practice your philosophical intuitions. What’s your excuse? If you think philosophical training improves the reliability of philosophical intuitions, then practicing intuitions should improve them even further. I argue that philosophers’ reluctance to practice their intuitions highlights a tension in the way that they think about the role of intuitions in philosophy.

This paper considers fair betting odds for certain bets that might be placed in the situation discussed in the so-called Sleeping Beauty Problem. This paper examines what Thirders, Halfers, and Double Halfers must say about the odds as determined by various decision theoretic approaches and argues that Thirders and Halfers have difficulties formulating plausible and coherent positions concerning the relevant betting odds. Double Halfers do not face this problem and that is an important consideration in favor of Double (...) Halfers. (shrink)

The Dutch Book Argument for Probabilism assumes Ramsey's Thesis (RT), which purports to determine the prices an agent is rationally required to pay for a bet. Recently, a new objection to Ramsey's Thesis has emerged (Hedden 2013, Wronski & Godziszewski 2017, Wronski 2018)--I call this the Expected Utility Objection. According to this objection, it is Maximise Subjective Expected Utility (MSEU) that determines the prices an agent is required to pay for a bet, and this often disagrees with Ramsey's Thesis. I (...) suggest two responses to Hedden's objection. First, we might be permissive: agents are permitted to pay any price that is required or permitted by RT, and they are permitted to pay any price that is required or permitted by MSEU. This allows us to give a revised version of the Dutch Book Argument for Probabilism, which I call the Permissive Dutch Book Argument. Second, I suggest that even the proponent of the Expected Utility Objection should admit that RT gives the correct answer in certain very limited cases, and I show that, together with MSEU, this very restricted version of RT gives a new pragmatic argument for Probabilism, which I call the Bookless Pragmatic Argument. (shrink)

Jeff Paris proves a generalized Dutch Book theorem. If a belief state is not a generalized probability then one faces ‘sure loss’ books of bets. In Williams I showed that Joyce’s accuracy-domination theorem applies to the same set of generalized probabilities. What is the relationship between these two results? This note shows that both results are easy corollaries of the core result that Paris appeals to in proving his dutch book theorem. We see that every point of accuracy-domination defines a (...) dutch book, but we only have a partial converse. (shrink)

Cryonics is the practice of cryopreserving the bodies or brains of legally dead individuals with the hope that these individuals will be reanimated in the future. A standard argument for cryonics says that cryonics is prudentially justified despite uncertainty about its success because at worst it will leave you no worse off than you otherwise would have been had you not chosen cryonics, and at best it will leave you much better off than you otherwise would have been. Thus, it (...) is a good, no-risk bet; in game-theoretic terms, cryonics is a weakly dominant strategy relative to refraining from utilizing cryonics. I object to this argument for two reasons. First, I argue that there is a practically relevant chance that cryonics will put you into an inescapable and very bad situation. Hence, cryonics is neither a no-risk bet nor a weakly dominant strategy. Second, I argue that the experience of being reanimated and living in the distant future would likely be transformative, and this likelihood undermines your justification for thinking that reanimation would be beneficial to you. I conclude that the standard argument does not show that cryonics is prudentially justified. (shrink)

In this paper we consider conditional random quantities (c.r.q.’s) in the setting of coherence. Based on betting scheme, a c.r.q. X|H is not looked at as a restriction but, in a more extended way, as \({XH + \mathbb{P}(X|H)H^c}\) ; in particular (the indicator of) a conditional event E|H is looked at as EH + P(E|H)H c . This extended notion of c.r.q. allows algebraic developments among c.r.q.’s even if the conditioning events are different; then, for instance, we can give (...) a meaning to the sum X|H + Y|K and we can define the iterated c.r.q. (X|H)|K. We analyze the conjunction of two conditional events, introduced by the authors in a recent work, in the setting of coherence. We show that the conjoined conditional is a conditional random quantity, which may be a conditional event when there are logical dependencies. Moreover, we introduce the negation of the conjunction and by applying De Morgan’s Law we obtain the disjoined conditional. Finally, we give the lower and upper bounds for the conjunction and disjunction of two conditional events, by showing that the usual probabilistic properties continue to hold. (shrink)

In this paper I present a new way of understanding Dutch Book Arguments: the idea is that an agent is shown to be incoherent iff he would accept as fair a set of bets that would result in a loss under any interpretation of the claims involved. This draws on a standard definition of logical inconsistency. On this new understanding, the Dutch Book Arguments for the probability axioms go through, but the Dutch Book Argument for Reflection fails. The question of (...) whether we have a Dutch Book Argument for Conditionalization is left open. (shrink)

Suppose that an altruistic agent who is uncertain between evidential and causal decision theory finds herself in a situation where these theories give conflicting verdicts. We argue that even if she has significantly higher credence in CDT, she should nevertheless act in accordance with EDT. First, we claim that the appropriate response to normative uncertainty is to hedge one's bets. That is, if the stakes are much higher on one theory than another, and the credences you assign to each of (...) these theories are not very different, then it is appropriate to choose the option that performs best on the high-stakes theory. Second, we show that, given the assumption of altruism, the existence of correlated decision makers will increase the stakes for EDT but leave the stakes for CDT unaffected. Together these two claims imply that whenever there are sufficiently many correlated agents, the appropriate response is to act in accordance with EDT. (shrink)

The linchpin of Williamson (2000)'s radically externalist epistemological program is an argument for the claim that no non-trivial condition is luminous—that no non-trivial condition is such that whenever it obtains, one is in a position to know that it obtains. I argue that Williamson's anti-luminosity argument succeeds only if one assumes that, even in the limit of ideal reflection, the obtaining of the condition in question and one's beliefs about that condition can be radically disjoint from one another. However, no (...) self-respecting defender of the luminosity of the mental would ever make such an assumption. Thus Williamson can only secure his controversial claims in epistemology by taking for granted certain equally controversial claims in the philosophy of mind. What emerges is that the best bet for defending an internalist epistemology against Williamson's attack is to take there to be a tight, intimate connection between (to take one example) our experiences and our beliefs upon reflection about the obtaining of those experiences, or between (to take another example) the rationality of our beliefs and our beliefs upon reflection about the rationality of those beliefs. (shrink)

In earlier work, I predicted that we would probably not be able to determine the colors of the dinosaurs. I lost this epistemic bet against science in dramatic fashion when scientists discovered that it is possible to draw inferences about dinosaur coloration based on the microstructure of fossil feathers (Vinther et al., 2008). This paper is an exercise in philosophical error analysis. I examine this episode with two questions in mind. First, does this case lend any support to epistemic optimism (...) about historical science? Second, under what conditions is it rational to make predictions about what questions scientists will or will not be able answer? In reply to the first question, I argue that the recent work on the colors of the dinosaurs matters less to the debate about the epistemology of historical science than it might seem. In reply to the second question, I argue that it is difficult to specify a policy that would rule out the failed bet without also being too conservative. (shrink)

We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of "essentially Kolmogorovian" probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees of belief are those representable (...) by probability functions from the class appropriate to that logic. Classical Bayesianism, which fixes the logic as classical logic, is only one version of this general approach. Another, which we call Intuitionistic Bayesianism, selects intuitionistic logic as the preferred logic and the associated class of probability functions as the right class of candidate representions of epistemic states (rational allocations of degrees of belief). Various objections to classical Bayesianism are, we argue, best met by passing to intuitionistic Bayesianism—in which the probability functions are taken relative to intuitionistic logic—rather than by adopting a radically non-Kolmogorovian, for example, nonadditive, conception of (or substitute for) probability functions, in spite of the popularity of the latter response among those who have raised these objections. The interest of intuitionistic Bayesianism is further enhanced by the availability of a Dutch Book argument justifying the selection of intuitionistic probability functions as guides to rational betting behavior when due consideration is paid to the fact that bets are settled only when/if the outcome bet on becomes known. (shrink)

Today, in the situation that we call the instanternity of the digital age, the visual aspect of the social (and power) relations is ever more important. The majority of human interactions on the Internet are happening in the field of vision. In this field, human desire follows the scopic drive, which is, according to Freud, expressed in the ambivalence of voyeurism and exhibitionism. This means that voyeurism and exhibitionism are the fundamental mechanisms operating in, and structuring, the digital virtual. This (...) topic, in a broader sense, tackles the inscription of the subject within the digital virtual spectacle, which deals with the relation between the individual’s imaginary and symbolic identification, that is, between the ideal ego and the ego ideal. To a certain extent, this also relates to what has been marked as a »pathological narcissism«. Even if the changes brought about by the digital virtual, as far as the subject is concerned, are not ontological, i.e. they do not concern its relation to being, they do concern its entry into the field of the Other, and can, because they are systemic changes, fundamentally restructure the social fabric. The bet of this article is therefore not only to try to understand the mechanisms driving the formation of subjectivity within the digital virtual, but also to trace their transformative potential. (shrink)

Matti Eklund (2017) has argued that ardent realists face a serious dilemma. Ardent realists believe that there is a mind-independent fact as to which normative concepts we are to use. Eklund claims that the ardent realist cannot explain why this is so without plumping in favor of their own normative concepts or changing the topic. The paper first advances the discussion by clarifying two ways of understanding the question of which normative concepts to choose: a theoretical question about which concepts (...) have the abstract property of being normatively privileged and a further practical question of which concepts we are to choose even granting some concepts are thus privileged. I argue that the ardent realist’s best bet for answering the theoretical question while avoiding Eklund’s dilemma is to provide a real definition of this property. I point out the difficulties for providing such a definition. I then argue that even with an answer to the theoretical question, the ardent realist faces a further dilemma in answering the practical question. In sum, though I see no knock-down argument against ardent realism, it may nonetheless die a death by a thousand cuts. I close by considering a deeper reason for why ardent realism is so difficult to defend: every argument starts somewhere. It is unclear how there can be an Archimedean point that makes no reference to any normative concepts that can nonetheless be employed to convince everyone to adopt ours. I then briefly propose two options for someone still inclined towards realism: (i) accept that our normative concepts are normatively privileged without attempting to explain why this is so, or (ii) be less ardent and accept a perspective-dependent account of normativity. (shrink)

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)

Bernard Williams argues that human mortality is a good thing because living forever would necessarily be intolerably boring. His argument is often attacked for unfoundedly proposing asymmetrical requirements on the desirability of living for mortal and immortal lives. My first aim in this paper is to advance a new interpretation of Williams' argument that avoids these objections, drawing in part on some of his other writings to contextualize it. My second aim is to show how even the best version of (...) his argument only supports a somewhat weaker thesis: it may be possible for some people with certain special psychological features to enjoy an immortal life, but no one has good reason to bet on being such a person. (shrink)

One guide to an argument's significance is the number and variety of refutations it attracts. By this measure, the Dutch book argument has considerable importance.2 Of course this measure alone is not a sure guide to locating arguments deserving of our attention—if a decisive refutation has really been given, we are better off pursuing other topics. But the presence of many and varied counterarguments at least suggests that either the refutations are controversial, or that their target admits of more than (...) one interpretation, or both. The main point of this paper is to focus on a way of understanding the Dutch Book argument (DBA) that avoids many of the well-known criticisms, and to consider how it fares against an important criticism that still remains: the objection that the DBA presupposes value-independence of bets. (shrink)

It has been argued that if the rigidity condition is satisfied, a rational agent operating with uncertain evidence should update her subjective probabilities by Jeffrey conditionalization or else a series of bets resulting in a sure loss could be made against her. We show, however, that even if the rigidity condition is satisfied, it is not always safe to update probability distributions by JC because there exist such sequences of non-misleading uncertain observations where it may be foreseen that an agent (...) who updates her subjective probabilities by JC will end up nearly certain that a false hypothesis is true. We analyze the features of JC that lead to this problem, specify the conditions in which it arises and respond to potential objections. (shrink)

The purpose of this paper is to think about the various methods of attempting to make money in the capital markets (“investing”). I suggest that though running a betting system on a Roulette wheel is silly, running a betting system on the capital markets may be a good idea.

De Finetti would claim that we can make sense of a draw in which each positive integer has equal probability of winning. This requires a uniform probability distribution over the natural numbers, violating countable additivity. Countable additivity thus appears not to be a fundamental constraint on subjective probability. It does, however, seem mandated by Dutch Book arguments similar to those that support the other axioms of the probability calculus as compulsory for subjective interpretations. These two lines of reasoning can be (...) reconciled through a slight generalization of the Dutch Book framework. Countable additivity may indeed be abandoned for de Finetti's lottery, but this poses no serious threat to its adoption in most applications of subjective probability. Introduction The de Finetti lottery Two objections to equiprobability 3.1 The ‘No random mechanism’ argument 3.2 The Dutch Book argument Equiprobability and relative betting quotients The re-labelling paradox 5.1 The paradox 5.2 Resolution: from symmetry to relative probability Beyond the de Finetti lottery. (shrink)

Inner speech is commonly understood as the conscious experience of a voice within the mind. One recurrent theme in the scientific literature is that the phenomenon involves a representation of overt speech, for example, a representation of phonetic properties that result from a copy of speech instructions that were ultimately suppressed. I propose a larger picture that involves some embodied objects and their misperception. I call it “the Body Error Theory,” or BET for short. BET is a form of illusionism, (...) but the particular version I favor is a cross-modal illusion. Newly described here, my hypothesis is that the experience of inner speech arises from a mix of interoception and audition. Specifically, there is the detection of slight but well-confirmed activities in the speech musculature that occur during inner speech, which helps to transform representations of normal but quiet nonverbal sounds that inevitably occur during inner speech, from breathing to background noise, into a mistaken perception of inner speech. Simply put, activities in the speech musculature mix with sounds to create the appearance of speech sounds, which thus explains the “voice within the mind.” I also show how BET’s cross-modal system fits with standard information processing accounts for speech monitoring and how it accommodates the central insights of leading theories of inner speech. In addition, I show how BET is supported by data from experience-sampling surveys and how it can be empirically tested against its rivals. (shrink)

Elon Musk famously predicted that an artificial intelligence superior to the smartest individual human would arrive by the year 2025. In response, Gary Marcus offered Musk a $1 million bet to the effect that he would be proved wrong. In specifying the conditions of this bet (which Musk did not take) Marcus lists the following ‘tasks that ordinary people can perform’ which, he claimed, AI will not be able to perform by the end of 2025. • Reliably drive a car (...) in a novel location that they haven’t previously encountered, even in the face of unusual circumstances like hand lettered signs, without the assistance of other humans. • Learn to ride a mountain bike off-road through forest trails. • Babysit children in an unfamiliar home and keep them safe. • Tend to the physical and psychological needs of an elderly or infirm person. Each of these tasks involves the application of practical or tacit knowledge, or what is also called ‘knowing how’, which is to say knowledge of a sort that is captured not by means of sentences or propositions or explicit rules, but rather through the expertise demonstrated in human actions. The talk addresses the puzzle that nowhere in the AI literature do we find a discussion of knowing how as a feature of human intelligence. (shrink)

We present a minimal pragmatic restriction on the interpretation of the weights in the “Equal Weight View” regarding peer disagreement and show that the view cannot respect it. Based on this result we argue against the view. The restriction is the following one: if an agent, $$\hbox {i}$$ i, assigns an equal or higher weight to another agent, $$\hbox {j}$$ j,, he must be willing—in exchange for a positive and certain payment—to accept an offer to let a completely rational and (...) sympathetic $$\hbox {j}$$ j choose for him whether to accept a bet with positive expected utility. If $$\hbox {i}$$ i assigns a lower weight to $$\hbox {j}$$ j than to himself, he must not be willing to pay any positive price for letting $$\hbox {j}$$ j choose for him. Respecting the constraint entails, we show, that the impact of disagreement on one’s degree of belief is not independent of what the disagreement is discovered to be. (shrink)

Let’s consider the skeptical example of the brain in a vat. It has been pointed out by Crispin Wright (1994) that Putnam's argument does not affect certain cases such as my brain being removed from my skull by a mad scientist and hooked up to a computer. Since Putnam's argument falls flat at least in cases where the brain is first removed from a human body and then hooked up to a computer, I consider the skeptical aspects of the brain-in-a-vat (...) thought experiment below. Let’s consider the following hypotheses: C “I’m a brain in a vat” EC “I’m not a brain in a vat”. It is argued by skeptics that it cannot be proven that we are not brains in a vat. If we assume the skeptical thesis according to which it is impossible to prove that we are not brains in a vat, i.e. there is the impossibility of falsifying C, then the truthfulness of EC implies that both C and EC can not be falsified. On the other hand, the truthfulness of C does not imply the unfalsifiability of EC: for example, the mad scientist mentioned above could decide (perhaps for a sadistic pleasure) to inform us and prove to us that we are brains in a vat; in the latter case the EC hypothesis would be falsified. The truthfulness of EC implies the unfalsifiability of both EC and C. By contrast, the truthfulness of C does not imply the unfalsifiability of EC. The current evidence is that both C and EC are not falsified: the hypothesis EC necessarily implies that both EC and C result not falsified; the hypothesis C does not necessarily imply that both C and EC result not falsified And so, it is more rational to bet on EC rather than on C. (shrink)

Bayesianism is the position that scientific reasoning is probabilistic and that probabilities are adequately interpreted as an agent's actual subjective degrees of belief, measured by her betting behaviour. Confirmation is one important aspect of scientific reasoning. The thesis of this paper is the following: if scientific reasoning is at all probabilistic, the subjective interpretation has to be given up in order to get right confirmation—and thus scientific reasoning in general. The Bayesian approach to scientific reasoning Bayesian confirmation theory The (...) example The less reliable the source of information, the higher the degree of Bayesian confirmation Measure sensitivity A more general version of the problem of old evidence Conditioning on the entailment relation The counterfactual strategy Generalizing the counterfactual strategy The desired result, and a necessary and sufficient condition for it Actual degrees of belief The common knock-down feature, or ‘anything goes’ The problem of prior probabilities. (shrink)

The purpose of this paper is to point the way to the money tree. Currently, almost all investment professionals think that outperformance requires an “edge,” that is, the ability to predict the future to some degree. In this paper, I suggest that money can be made in a 0, or even slightly negative, expected value environment by carefully choosing investment/bet sizes. Philosophical considerations are found mainly in Section 4.

The Apaṇṇaka Sutta, one of the early recorded teachings of the Buddha, contains an argument for accepting the doctrines of karma and rebirth that Buddhist scholars claim anticipates Pascal’s wager. I call this argument the Buddha’s wager. Does it anticipate Pascal’s wager and is it a good bet? Contemporary scholars identify at least four versions of Pascal’s wager in his Pensées. This article demonstrates that the Buddha’s wager anticipates two versions of Pascal’s wager, but not its canonical form. Like Pascal’s (...) wager, the Buddha’s wager presents a decision problem between two opposing theses in an epistemic context that lacks evidence of their truth or falsity. Like Pascal, the Buddha also tries to solve this problem using dominance, superdominance or ‘superduperdominance’ reasoning. The Apaṇṇaka Sutta likely provides the earliest textual example of such reasoning. While the Buddha’s wager does not exhibit the expected utility reasoning of the best-known form of Pascal’s wager, the article suggests a reformulation that parallels Alan Hájek’s (2018) vector-value reformulation. Is it a good bet? This article argues that it is not if this means we are rationally required to accept its recommendation. This is because, while it avoids two of the major objections levelled against Pascal’s wager, it succumbs to one and has at least two problems of its own. (shrink)

“Dutch Book” arguments and references to gambling theorems are typical in the debate between Bayesians and scientists committed to “classical” statistical methods. These arguments have rarely convinced non-Bayesian scientists to abandon certain conventional practices, partially because many scientists feel that gambling theorems have little relevance to their research activities. In other words, scientists “don’t bet.” This article examines one attempt, by Schervish, Seidenfeld, and Kadane, to progress beyond such apparent stalemates by connecting “Dutch Book”–type mathematical results with principles actually endorsed (...) by practicing experimentalists. (shrink)

Experimental philosophers track folk intuitions better than armchair reflection. Yet, many of them are stuck in a controversy: on the one hand they have vividly shown how untrustworthy intuition is. On the other, they depend all their theorising on the intuitions recorded. If intuition is unreliable, though, why does it make it bet- ter to rely on the intuitions of the many? A mistake is not less a mistake if made by many.

Before a fair, indeterministic coin is tossed, Lucky, who is causally isolated from the coin-tossing mechanism, declines to bet on heads. The coin lands heads. The consensus is that the following counterfactual is true: (M:) If Lucky had bet heads, he would have won the bet. It is also widely believed that to rule (M) true, any plausible semantics for counterfactuals must invoke causal independence. But if that’s so, the hope of giving a reductive analysis of causation in terms of (...) counterfactuals is undermined. Here I argue that there is compelling reason to question the assumption that (M) is true. (shrink)

Pascal’s Wager does not exist in a Platonic world of possible gods, abstract probabilities and arbitrary payoffs. Real decision-makers, such as Pascal’s “man of the world” of 1660, face a range of religious options they take to be serious, with fixed probabilities grounded in their evidence, and with utilities that are fixed quantities in actual minds. The many ingenious objections to the Wager dreamed up by philosophers do not apply in such a real decision matrix. In the situation Pascal addresses, (...) the Wager is a good bet. In the situation of a modern Western intellectual, the reasoning of the Wager is still powerful, though the range of options and the actions indicated are not the same as in Pascal’s day. (shrink)

Straipsnio tikslas – atskleisti įrankio (Zeug) ir technikos (Technik) skirtumą M. Heideggerio technikos filosofijoje. Analizuojami skirtumai nurodo pasaulio konstitucijos problematiką. Dasein santykį su įrankiu M. Heideggeris pristatė kaip parankų (Zuhandenheit), o štai santykį su technika įvardijo priešingai. Technika, kylanti iš gamtos mokslų, susaistytų machinacija (Machenschaft), filosofo pristatoma kaip Dasein kūrybines galias nuostatyne (Gestell) slopinanti terpė. Straipsnyje atskleidžiama dvejopa problematika. Pirma, parodomi įrankio ir technikos ontologiniai skirtumai. Antra, atskleidžiamas nuostatyno ontologijos ambivalentiškumas. Nuostatynas M. Heideggeriui nėra tik techniškai orientuoto pasaulio užvaldymo mechanizmas, (...) bet ir „gelbstintis“ pradas. (shrink)