Arguments for A "fair" coin has probability 1/2. There is no physical probability attached to the coin, we can cheat on each toss (by sufficient control). My aim: The coin toss is fine-grained deterministic, but coarsgrained random.

Timothy Williamson claimed to prove with a coin-tossing example that hyperreal probabilities cannot save the principle of regularity. A premise of his argument is that two specified infinitary events must be assigned the same probability because, he claims, they are isomorphic. But as has been pointed out, they are not isomorphic. A way of framing Williamson’s argument that does not make it depend on the isomorphism claim is in terms of shifts in Bernoulli processes, the usual mathematical model (...) of sequential coin tossing. But even so framed, the argument still fails. (shrink)

Morgenbesser's Coin is a thought experiment that exemplifies a widespread disposition to infer counterfactual independence from causal independence. I argue that this disposition is mistaken by analysing a closely related thought experiment.

Timothy Williamson has claimed to prove that regularity must fail even in a nonstandard setting, with a counterexample based on tossing a fair coin infinitely many times. I argue that Williamson’s argument is mistaken, and that a corrected version shows that it is not regularity which fails in the non-standard setting but a fundamental property of shifts in Bernoulli processes.

In the literature on the so-called numbers problem, some authors have recently argued that the individualist lottery (IL) avoids the flaws of the proportional lottery. This article first presents two recent defenses of the IL, and then argues that both are implausible if we focus, as we should, strictly on their non-consequentialist aspects. This conclusion holds even if we take account of the fact that the IL is arguably that solution to the numbers problem which best meets the marginal difference (...) criterion. The upshot is that non-consequentialists should toss a coin rather than spin a wheel in conflict cases (if and when they must do either). (shrink)

In the problem of the gambler's ruin, a classic problem in probability theory, a number of gamblers play against each other until all but one of them is “wiped out.” It is shown that this problem is identical to a previously presented formulation of the reduction of the state vector, so that the state vectors in a linear superposition may be regarded as “playing” against each other until all but one of them is “wiped out.” This is a useful part (...) of the description of an objectively real universe represented by a state vector that is a superposition of macroscopically distinguishable states dynamically created by the Hamiltonian and destroyed by the reduction mechanism. (shrink)

Imagine that, through no fault of your own, you nd yourself at the bottom of a deep well. Thugs have picked up an innocent person | call him Bob | and have thrown him down the well. Bob is now falling towards you. If you do nothing, your body will cushion Bob's otherwise lethal fall. This will guarantee his survival, but it will kill you. If you shoot your ray gun, you vaporize and kill Bob, thereby saving your life. Are (...) you morally permitted to shoot your ray gun?Most people believe that self-defence against an innocent threat such as Bob is permissible. Judith Thomson (1991) and Frances Kamm (1987) have tried to justify this widely held belief. Jeff McMahan (2002) and Michael Otsuka (1994) have argued against it. In this paper, I contend that arguments from both sides of the debate mistakenly take the existence of an important asymmetry between Bob and you for granted. That way, they miss how similar Bob and you are, in that both of you happen to nd yourselves, undeservingly and through no fault of your own, in a situation in which you can secure your own survival only if you kill an innocent person. In this paper, I argue that despite certain differences, we are justi ed in focusing on the simliarities between Bob and you, and that you should thus flip a coin to decide who should live (cf. Broome, 1991). By flipping a coin, you ensure that an indivisible good -- continuing one's life -- is distributed as fairly as is possible without wasting it. (shrink)

The Eternal Coin is a fair coin has existed forever, and will exist forever, in a region causally isolated from you. It is tossed every day. How confident should you be that the Coin lands heads today, conditional on (i) the hypothesis that it has landed Heads on every past day, or (ii) the hypothesis that it will land Heads on every future day? I argue for the extremely counterintuitive claim that the correct answer to both questions (...) is 1. (shrink)

A decision maker bets on the outcomes of a sequence of coin-tossings. At the beginning of the game the decision maker can choose one of two coins to play the game. This initial choice is irreversible. The coins can be biased and the player is uncertain about the nature of one (or possibly both) coin(s). If the player is an expected-utility maximizer, her choice of the coin will depend on different elements: the nature of the game (namely, (...) whether she can observe the outcomes of the previous tosses before making her next decision), her utility function, the prior distribution on the bias of the coin. We will show that even a risk averter might optimally choose a riskier coin when learning is allowed. We will express most of our results in the language of stochastic orderings, allowing comparisons that are valid for large classes of utility functions. (shrink)

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)

In a well-known paper, Timothy Williamson claimed to prove with a coin-flipping example that infinitesimal-valued probabilities cannot save the principle of Regularity, because on pain of inconsistency the event ‘all tosses land heads’ must be assigned probability 0, whether the probability function is hyperreal-valued or not. A premise of Williamson’s argument is that two infinitary events in that example must be assigned the same probability because they are isomorphic. It was argued by Howson that the claim of isomorphism fails, (...) but a more radical objection to Williamson’s argument is that it had been, in effect, refuted long before it was published. (shrink)

When facing a choice between saving one person and saving many, some people have argued that fairness requires us to decide without aggregating numbers; rather we should decide by coin toss or some form of lottery, or alternatively we should straightforwardly save the greater number but justify this in a non-aggregating contractualist way. This paper expands the debate beyond well-known number cases to previously under-considered probability cases, in which not (only) the numbers of people, but (also) the probabilities of (...) success for saving people vary. It is shown that, in these latter cases, both the coin toss and the lottery lead to what is called an awkward conclusion, which makes probabilities count in a problematic way. Attempts to avoid this conclusion are shown to lead into difficulties as well. Finally, it is shown that while the greater number method cannot be justified on contractualist grounds for probability cases, it may be replaced by another decision method which is so justified. This decision method is extensionally equivalent to maximising expected value and seems to be the least problematic way of dealing with probability cases in a non-aggregating manner. (shrink)

Games such as the St. Petersburg game present serious problems for decision theory.1 The St. Petersburg game invokes an unbounded utility function to produce an infinite expectation for playing the game. The problem is usually presented as a clash between decision theory and intuition: most people are not prepared to pay a large finite sum to buy into this game, yet this is precisely what decision theory suggests we ought to do. But there is another problem associated with the St. (...) Petersburg game. The problem is that standard decision theory counsels us to be indifferent between any two actions that have infinite expected utility. So, for example, consider the decision problem of whether to play the St. Petersburg game or a game where every payoff is $1 higher. Let’s call this second game the Petrograd game (it’s the same as St. Petersburg but with a bit of twentieth century inflation). Standard decision theory is indifferent between these two options. Indeed, it might be argued that any intuition that the Petrograd game is better than the St. Petersburg game is a result of misguided and na¨ıve intuitions about infinity.2 But this argument against the intuition in question is misguided. The Petrograd game is clearly better than the St. Petersburg game. And what is more, there is no confusion about infinity involved in thinking this. When the series of coin tosses comes to an end (and it comes to an end with probability 1), no matter how many tails precede the first head, the payoff for the Petrograd game is one dollar higher than the St. Petersburg game. Whatever the outcome, you are better off playing the Petrograd game. Infinity has nothing to do with it. Indeed, a straightforward application of dominance reasoning backs up this line of reasoning.3 Standard decision theory. (shrink)

Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general. _1_ Introduction _2_ The Limits of Classical Probability Theory _2.1_ Classical probability functions _2.2_ Limitations _2.3_ Infinitesimals to the rescue? _3_ NAP Theory _3.1_ First four axioms of NAP _3.2_ Continuity and conditional probability _3.3_ The final axiom of NAP (...) _3.4_ Infinite sums _3.5_ Definition of NAP functions via infinite sums _3.6_ Relation to numerosity theory _4_ Objections and Replies _4.1_ Cantor and the Archimedean property _4.2_ Ticket missing from an infinite lottery _4.3_ Williamson’s infinite sequence of coin tosses _4.4_ Point sets on a circle _4.5_ Easwaran and Pruss _5_ Dividends _5.1_ Measure and utility _5.2_ Regularity and uniformity _5.3_ Credence and chance _5.4_ Conditional probability _6_ General Considerations _6.1_ Non-uniqueness _6.2_ Invariance Appendix. (shrink)

Partial lying denotes the cases where we partially believe something to be false but nevertheless assert it with the intent to deceive the addressee. We investigate how the severity of partial lying may be determined and how partial lies can be classified. We also study how much epistemic damage an agent suffers depending on the level of trust that she invests in the liar and the severity of the lies she is told. Our analysis is based on the results from (...) exploratory computer simulations of an arguably rational Bayesian agent who is trying to determine how biased a coin is while observing the coin tosses and listening to a liar’s misleading predictions about the outcomes. Our results provide an interesting testable hypothesis at the intersection of epistemology and ethics, namely that in the longer term partial lies lead to more epistemic damage than outright lies. (shrink)

It is possible that a fair coin tossed infinitely many times will always land heads. So the probability of such a sequence of outcomes should, intuitively, be positive, albeit miniscule: 0 probability ought to be reserved for impossible events. And, furthermore, since the tosses are independent and the probability of heads (and tails) on a single toss is half, all sequences are equiprobable. But Williamson has adduced an argument that purports to show that our intuitions notwithstanding, the probability of (...) an infinite sequence is 0. In this paper, I rebut his argument.No Abstract. (shrink)

The present study tests a gestalt explanation for the gambler's fallacy which posits that runs in random events will be expected to reverse only when the run is open or ongoing. This is contrasted with the law of small numbers explanation suggesting that people expect random outcomes to balance out generally. Sixty-one university students placed hypothetical guesses and bets on a series of coin tosses. Either heads or tails were dominant . In a closed run condition the run ended (...) prior to the critical trial , and in an open run condition the run remained open . As hypothesised, participants showed the gambler's fallacy in the open run condition, but not in the closed run condition. This difference is not due to differential memory for the outcomes. Men, and people with more previous experience gambling, were also found to be more prone to the gambler's fallacy. It is argued that the gestalt explanation best explains the results. (shrink)

The rejection of an infinitesimal solution to the zero-fit problem by A. Elga ([2004]) does not seem to appreciate the opportunities provided by the use of internal finitely-additive probability measures. Indeed, internal laws of probability can be used to find a satisfactory infinitesimal answer to many zero-fit problems, not only to the one suggested by Elga, but also to the Markov chain (that is, discrete and memory-less) models of reality. Moreover, the generalization of likelihoods that Elga has in mind is (...) not as hopeless as it appears to be in his article. In fact, for many practically important examples, through the use of likelihoods one can succeed in circumventing the zero-fit problem. 1 The Zero-fit Problem on Infinite State Spaces 2 Elga's Critique of the Infinitesimal Approach to the Zero-fit Problem 3 Two Examples for Infinitesimal Solutions to the Zero-fit Problem 4 Mathematical Modelling in Nonstandard Universes? 5 Are Nonstandard Models Unnatural? 6 Likelihoods and Densities A Internal Probability Measures and the Loeb Measure Construction B The (Countable) Coin Tossing Sequence Revisited C Solution to the Zero-fit Problem for a Finite-state Model without Memory D An Additional Note on ‘Integrating over Densities’ E Well-defined Continuous Versions of Density Functions. (shrink)

Popper functions allow one to take conditional probabilities as primitive instead of deriving them from unconditional probabilities via the ratio formula P=P/P. A major advantage of this approach is it allows one to condition on events of zero probability. I will show that under plausible symmetry conditions, Popper functions often fail to do what they were supposed to do. For instance, suppose we want to define the Popper function for an isometrically invariant case in two dimensions and hence require the (...) Popper function to be rotationally invariant and defined on pairs of sets from some algebra that contains at least all countable subsets. Then it turns out that the Popper function trivializes for all finite sets: P=1 for all A ) if B is finite. Likewise, Popper functions invariant under all sequence reflections can’t be defined in a way that models a bidirectionally infinite sequence of independent coin tosses. (shrink)

Argues for the "thirder" solution to the Sleeping Beauty puzzle. The argument turns on an analogy with a variant case, in which a coin-toss on Monday night determines whether one's memories of Monday are permanently erased, or merely suspended in such a way that they will return some time after one wakes up on Tuesday.

Preface -- Acknowledgments -- A note on examples -- 1. The coin toss -- 2. Deviance -- 3. Omission -- 4. Imprecision -- 5. Indirectness -- 6. Figurativeness -- 7. Language play -- 8. THE social media -- 9. The art of language -- 10. The end game -- Epilogue: A clearing revealing an eclipse -- References -- Index.

“Randomized dictatorship,” one of the simplest ways to solve bargaining situations, works as follows: a fair coin toss determines the “dictator”—the player to be given his first-best payoff. The two major bargaining solutions, that of Nash and that of Kalai and Smorodinsky, Pareto-dominate this process. However, whereas the existing literature offers axiomatizations of the Nash solution in which this ex ante domination plays a central role, it does not provide an analogous result for Kalai–Smorodinsky. This paper fills in this (...) gap: a characterization of the latter is obtained by combining the aforementioned domination with three additional axioms: Pareto optimality, individual monotonicity, and a weakened version of the Perles–Maschler super additivity axiom. (shrink)

In the Sleeping Beauty problem, Beauty is uncertain whether the outcome of a certain coin toss was heads or tails. One argument suggests that her degree of belief in heads should be 1/3, while a second suggests that it should be 1/2. Prima facie, the argument for 1/2 appears to be stronger. I offer a diachronic Dutch Book argument in favor of 1/3. Even for those who are not routinely persuaded by diachronic Dutch Book arguments, this one has some (...) important morals. (shrink)

The paper discusses Bayesian convergence when the truth is excluded from the analysis by means of a simple coin-tossing example. In the fair-balance paradox a fair coin is tossed repeatedly. A Bayesian agent, however, holds the a priori view that the coin is either biased towards heads or towards tails. As a result the truth is ignored by the agent. In this scenario the Bayesian approach tends to confirm a false model as the data size goes (...) to infinity. I argue that the fair-balance paradox reveals an unattractive feature of the Bayesian approach to scientific inference and explore a modification of the paradox. (shrink)

When making decisions, people tend to overweigh the impact of losses compared to gains, a phenomenon known as loss aversion. A moderate amount of LA may be adaptive as it is necessary for protecting oneself from danger. However, excessive LA may leave people few opportunities and ultimately lead to suboptimal outcomes. Despite frequent reports of elevated LA in specific populations such as patients with depression, little is known about what psychological characteristics are associated with the tendency of LA. Based on (...) the neurobiological studies of LA, we hypothesized that positive psychological wellbeing may be negatively associated with people's tendency of LA. In the present study, we set out to test this hypothesis in a sample of young adults. We evaluated LA using a decision-making task in which subjects were asked to decide whether to accept or reject a series of coin-toss gambles. Our results revealed that individuals with more advanced personal growth as assessed by the Ryff's Psychological Well-being Inventory showed reduced LA. To our knowledge, this is the first report demonstrating an association between positive psychological wellbeing and LA. These findings suggest that personal growth might be employed as interventional targets for correcting excessive LA in vulnerable populations. (shrink)

This article is an attempt to use the insights of objective probability theory to solve the Sleeping Beauty problem. The approach is to develop a partial theory of direct inference and then apply that partial theory to the problem. One of the crucial components of the partial theory is the thesis that expected indefinite probabilities provide a reliable basis for direct inference. The article relies heavily on recent work by Paul D. Thorn to defend that thesis. The article’s primary conclusion (...) is that Beauty can by way of a justifiable direct inference from a statement of expected indefinite probability reach the conclusion that the epistemic probability that the relevant coin toss lands heads is 1/3. The article also provides an account of why the self-locating information that Beauty acquires on Monday is evidentially relevant to the question of whether the coin toss lands heads or tails. (shrink)

On the face of it ‘deterministic chance’ is an oxymoron: either an event is chancy or deterministic, but not both. Nevertheless, the world is rife with events that seem to be exactly that: chancy and deterministic at once. Simple gambling devices like coins and dice are cases in point. On the one hand they are governed by deterministic laws – the laws of classical mechanics – and hence given the initial condition of, say, a coin toss it is determined (...) whether it will land heads or tails.2 On the other hand, we commonly assign probabilities to the different outcomes a coin toss, and doing so has proven successful in guiding our actions. The same dilemma also emerges in less mundane contexts. Classical statistical mechanics (which is still an important part of modern physics) assigns probabilities to the occurrence of certain events – for instance to the spreading of a gas that is originally confined to the left half of a container – but at the same time assumes that the relevant systems are deterministic. How can this apparent conflict be resolved? (shrink)

Let me regale you with yet another variant of the story of Sleeping Beauty. In this one, the experiment takes place in a room with a skylight, so that Beauty can see what the weather is like outside as soon as she wakes up. The weather can be in any one of n different states on any given day. Beauty regards each of these states as equiprobable; moreover, she takes there to be no correlation between the weather on Monday and (...) the weather on Tuesday, or between the weather on either day and the coin-toss. The rest of the story works as usual: Beauty will be awoken on Monday, after which a coin will be tossed; if it lands Tails, she will be woken again on Tuesday having had her memories of the Monday awakening erased; otherwise, she will stay asleep until Wednesday.1 The weather is the only source of variation in her wakings, so if it should happen that the weather is the same on Monday and Tuesday, her total evidence will be exactly the same on both wakings. (shrink)

To analyse contingent propositions, this paper investigates how branching time structures can be combined with probability theory. In particular, it considers assigning infinitesimal probabilities—available in non-Archimedean probability theory—to individual histories. This allows us to introduce the concept of ‘remote possibility’ as a new modal notion between ‘impossibility’ and ‘appreciable possibility’. The proposal is illustrated by applying it to a future contingent and a historical counterfactual concerning an infinite sequence of coin tosses. The latter is a toy model that is (...) used to illustrate the applicability of the proposal to more realistic physical models. (shrink)

I argue that a crucial point has been overlooked in the debate over the “numbers problem.” The initial arrangement of parties in the problem can be thought of as chancy, and whatever considerations of fairness recommend the reliance on something like a coin toss in approaching this problem equally recommend treating the initial distribution as a kind of lottery. This fact, I suggest, undermines one of the principal arguments against saving the greater number.

The probability that a fair coin tossed yesterday landed heads is either 0 or 1, but the probability that it would land heads was 0.5. In order to account for the latter type of probabilities, past probabilities, a temporal restriction operator is introduced and axiomatically characterized. It is used to construct a representation of conditional past probabilities. The logic of past probabilities turns out to be strictly weaker than the logic of standard probabilities.

It is now commonly held that values play a role in scientific judgment, but many arguments for that conclusion are limited. First, many arguments do not show that values are, strictly speaking, indispensable. The role of values could in principle be filled by a random or arbitrary decision. Second, many arguments concern scientific theories and concepts which have obvious practical consequences, thus suggesting or at least leaving open the possibility that abstruse sciences without such a connection could be value-free. Third, (...) many arguments concern the role values play in inferring from evidence, thus taking evidence as given. This paper argues that these limitations do not hold in general. There are values involved in every scientific judgment. They cannot even conceivably be replaced by a coin toss, they arise as much for exotic as for practical sciences, and they are at issue as much for observation as for explicit inference. (shrink)

In management research, theory testing confronts a paradox described by Meehl in which designing studies with greater methodological rigor puts theories at less risk of falsification. This paradox exists because most management theories make predictions that are merely directional, such as stating that two variables will be positively or negatively related. As methodological rigor increases, the probability that an estimated effect will differ from zero likewise increases, and the likelihood of finding support for a directional prediction boils down to a (...) coin toss. This paradox can be resolved by developing theories with greater precision, such that their propositions predict something more meaningful than deviations from zero. This article evaluates the precision of theories in management research, offers guidelines for making theories more precise, and discusses ways to overcome barriers to the pursuit of theoretical precision. (shrink)

The gambler's fallacy and hot hand were studied in predictions about outcomes of coin tosses. A critical trial occurred when participants made predictions after a “run” of four heads or tails. Participants' attention was manipulated to focus on the person flipping the coin, the coin, or neither (control group) as a possible cause of the run. We also manipulated whether or not there was a change in who tossed the coin. In the control condition the standard (...) reversal was observed (gambler's fallacy); however, when participants focused on the person, and it was that same person who conducted the run and critical coin toss, more people chose in the direction of continuation (hot hand). Directing attention to the person tossing the run seemed to prompt participants to behave as if that individual was “hot” in terms of getting a specific outcome (e.g., heads), as if by sympathetic magic, thus eliminating the gambler's fallacy. (shrink)

Bayesian epistemology has struggled with the problem of regularity: how to deal with events that in classical probability have zero probability. While the cases most discussed in the literature, such as infinite sequences of coin tosses or continuous spinners, do not actually come up in scientific practice, there are cases that do come up in science. I shall argue that these cases can be resolved without leaving the realm of classical probability, by choosing a probability measure that preserves “enough” (...) regularity. This approach also provides a resolution to the McGrew, McGrew and Vestrum normalization problem for the fine-tuning argument. (shrink)

clusions are only probably correct. On the other hand, algorithmic information theory provides a precise mathematical definition of the notion of random or patternless sequence. In this paper we shall describe conditions under which if the sequence of coin tosses in the Solovay– Strassen and Miller–Rabin algorithms is replaced by a sequence of heads and tails that is of maximal algorithmic information content, i.e., has maximal algorithmic randomness, then one obtains an error-free test for primality. These results are only (...) of theoretical interest, since it is a manifestation of the G¨ odel incompleteness phenomenon that it is impossible to “certify” a sequence to be random by means of a proof, even though most sequences have this property. Thus by using certified random sequences one can in principle, but not in practice, convert probabilistic tests for primality into deterministic ones. (shrink)

Jonah N. Schupbach and Jan Sprenger and Vincenzo Crupi and Katya Tentori have recently proposed measures of explanatory power and have shown that they are characterized by certain arguably desirable conditions or axioms. I further examine the properties of these two measures, and a third measure considered by I. J. Good and Timothy McGrew . This third measure also has an axiomatic representation. I consider a simple coin-tossing example in which only the Crupi–Tentori measure does not perform well. (...) The Schupbach–Sprenger and Good–McGrew measures are based on different notions of explanatory power, but both are tenable. 1 Introduction2 Measures of Explanatory Power3 The Schupbach–Sprenger Measure4 The Crupi–Tentori Measure5 The Good–McGrew Measure6 Affirmative versus Comprehensive Explanatory Power7 Coin-Flipping Examples8 Decomposition9 Conclusion. (shrink)

On the face of it ‘deterministic chance’ is an oxymoron: either a process is chancy or deterministic, but not both. Nevertheless, the world is rife with processes that seem to be exactly that: chancy and deterministic at once. Simple gambling devices like coins and dice are cases in point.2 On the one hand they are governed by deterministic laws – the laws of classical mechanics – and hence given the initial condition of, say, a coin it is determined whether (...) it will land heads or tails when tossed.3 On the other hand, we commonly assign probabilities to the different outcomes of a coin toss, and doing so has proven successful in guiding our actions. The same dilemma also emerges in less mundane contexts. Classical statistical mechanics assigns probabilities to the occurrence of certain events – for instance to the spreading of a gas that is originally confined to the left half of a container – but at the same time assumes that the relevant systems are deterministic. How can this apparent conflict be resolved? (shrink)

In this paper I defend the thirder solution to the sleeping beauty problem by considering the credence Beauty ought to have, upon first awakening, that it is Monday. This leads to problems for the double-halfer and halfer but not for the thirder. In the three cases the credences Beauty ought to have, upon first awakening, that it is Monday are 1, 3/4, and 2/3, respectively. The first value is implausible given that Tuesday awakenings are possible. The second is implausible because (...) Beauty's credence in the day of the week is linked to her credence in the result of the coin toss such that evidence to favor Monday over Tuesday is evidence that should affect her credence in the result of the coin toss. This is contrary to the halfers' claim that, upon first awakening, Beauty has no such evidence. However, the credence of 2/3 assigned by the thirder can be independently defended in a way that mirrors the thirders defense of assigning a credence of 1/3 to Heads. Moreover, recognizing the probabilistic connection between Beauty's credences in the days of the week and the results of the coin toss indicates the nature of Beauty's inadmissible information. Beauty's loss of information regarding the day is relevant to the credence she should assign to Heads. (shrink)

It is argued that thirder resolution of the Lewis - Elga controversy about Sleeping Beauty is more clear when the coin toss is replaced by a quantum measurement and the analysis is performed in the framework of the Many-Worlds Interpretation.

The Sleeping Beauty problem—first presented by A. Elga in a philosophical context—has captured much attention. The problem, we contend, is more aptly regarded as a paradox: apparently, there are cases where one ought to change one’s credence in an event’s taking place even though one gains no new information or evidence, or alternatively, one ought to have a credence other than 1/2 in the outcome of a future coin toss even though one knows that the coin is fair. (...) In this paper we argue for two claims. First, that Sleeping Beauty does gain potentially new relevant information upon waking up on Monday. Second, his credence shift is warranted provided it accords with a calculation that is a result of conditionalization on the relevant information: “this day is an experiment waking day” (a day within the experiment on which one is woken up). Since Sleeping Beauty knows what days d could refer to, he can calculate the probability that the referred to waking day is a Monday or a Tuesday providing an adequate resolution of the paradox. (shrink)

John Taurek famously argued that, in ‘conflict cases’, where we are confronted with a smaller and a larger group of individuals, and can choose which group to save from harm, we should toss a coin, rather than saving the larger group. This is primarily because coin-tossing is fairer: it ensures that each individual, regardless of the group to which he or she belongs, has an equal chance of being saved. This article provides a new response to Taurek’s (...) argument. It proposes that there are two possible types of unfairness that have to be avoided in conflict cases, as far as possible: ‘selection unfairness’, which is the unfairness of not giving individuals an equal chance of being saved; and ‘outcome unfairness’, which is the unfairness of not actually saving them, when others are saved. Since saving the greater number generates less outcome unfa-irness than coin-tossing, it is argued that, in many conflict cases, fairness demands that we save the greater number. (shrink)

“Double-halfers” think that throughout the Sleeping Beauty Scenario, Beauty ought to maintain a credence of 1/2 in the proposition that the fair coin toss governing the experimental protocol comes up heads. Titelbaum (2012) introduces a novel variation on the standard scenario, one involving an additional coin toss, and claims that the double-halfer is committed to the absurd and embarrassing result that Beauty’s credence in an indexical proposition concerning the outcome of a future fair coin toss is not (...) 1/2. I argue that there is no reason to regard the credence required by the double-halfer as any less acceptable than the one deemed required by Titelbaum. (shrink)

We conduct experiments to analyze investment behavior in decisions under risk. Subjects can bet on the outcomes of a series of coin tosses themselves, rely on randomized ‘experts’, or choose a risk-free alternative. We observe that subjects who rely on the randomized experts pick those who were successful in the past, showing behavior consistent with the hot hand belief. Obviously the term ‘expert’ suffices to attract some subjects. For those who decide on their own, we find behavior consistent with (...) the gambler’s fallacy, as the frequency of betting on heads (tails) decreases after streaks of heads (tails). (shrink)

Several philosophical problems are based on an analogy between a real situation and a probabilistic model. Such problems are based on urn analogies. The present dissertation aims to describe and implement a methodology oriented towards the resolution of philosophical problems based on an urn analogy. This methodology is based on the use of the n-universes. To this end, I describe first the n-universes in a detailed way. I also discuss the difficulties of the theory of n-universes related to the demultiplication (...) of the criteria and to the relation one/many between the objects and a given criterion. On the one hand, I present an application of the framework of n-universes to the Doomsday argument and to the problems recently appeared in the literature in keeping with the Doomsday argument. My concern is also with showing how the application of the framework of n-universes to several problems and thought experiments related to the Doomsday argument helps clarifying the problem data and making disappear the associated ambiguity. I present then an analysis of the following problems related to the Doomsday argument: the two urn case, God's Coin Toss, the Sleeping Beauty Problem, the Presumptuous Philosopher, Lazy Adam, and the Shooting-Room Paradox. I present lastly a solution to the Doomsday argument, based on a third route, by contrast to two types of solutions classically described. On the other hand, I present an application of the framework of n-universes to Goodman's paradox. I replace first Goodman's statement in the framework of n-universes. I propose then a solution to the paradox, based on a distinction between two different modelizations of Goodman's statement in two structurally different n-universes. (shrink)

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

Translation failure occurs when a treatment shown to be safe and effective in one type of population does not produce the same result in another. We are currently in a crisis involving the translatability of preclinical studies to human populations. Animal trials are no better than a coin toss at predicting the safety and efficacy of drugs in human trials, and the high failure rate of drugs entering human trials suggests that most of the suffering of laboratory animals is (...) futile, creating no commensurate benefit for human patients. Here, I argue that animal ethics committees have a role to play in getting us out of this crisis. Inadequate representation is a known contributor to translation failures and is a matter of both scientific and ethical concern. Ethical review committees have the authority to address it by reprioritising the values already enshrined in their guiding principles. (shrink)

Photo ID 222412412 © US Navy Medicine | Dreamstime.com ABSTRACT In a non-military setting, the answer is clear: it would be unethical to treat someone based on non-medical considerations such as nationality. We argue that Battlefield Triage is a moral tragedy, meaning that it is a situation in which there is no morally blameless decision and that the demands of justice cannot be satisfied. INTRODUCTION Medical resources in an austere environment without quick recourse for resupply or casualty evacuation are often (...) limited. The shortage extends not only to supplies like blood products and drugs, but physicians and other medical personnel. In the midst of a mass casualty scenario, such as a battle that includes intense ground fighting, the medical staff will stretch scarce resources and triage casualties according to specific criteria. Typically, they proceed by providing care for the most severely wounded first, referred to here as conventional triage. At times, though, the staff may reverse the triage so that soldiers with minor wounds can return to the fight. In a mass casualty situation, when medical personnel apply conventional triage and treat casualties from opposing forces, a dilemma may arise. We argue that it can be permissible for military physicians to prioritize their own soldiers over enemy combatants in a mass casualty triage, where reverse triage does not apply. The case we will focus on is as follows: Battlefield Triage: During combat operations on a remote island in the Pacific Ocean, a compatriot soldier and an enemy combatant arrive at the compatriot soldier country’s medical treatment facility. Both have similar gunshot wounds to the abdomen, and they arrive with similar conditions. Both have low oxygen saturation and excessive blood loss. The sole physician only has enough time to stabilize one person. The scenario is brief, and we are aware that medical rules of eligibility will most often dictate how the physician proceeds,[1] but this scenario is useful in setting up the question we focus on in this paper: would it be wrong to favor the stabilization of a soldier just because the soldier is the physician’s compatriot? In other words, can nationality serve as an ethically justified tiebreaker in a situation such as Battlefield Triage?[2] In a non-military setting, the answer is clear: it would be unethical to treat someone based on non-medical considerations such as nationality. The AMA’s Code of Medical Ethics asserts that physicians have “ethical obligations to place patients’ welfare above their self-interest and above obligations to other groups.”[3] The World Medical Association’s Declaration of Tokyo affirms that “no motive, whether personal, collective or political, shall prevail against this higher purpose” of alleviating distress.[4] Physicians are taught early on that triage decisions must be medically indicated and made without consideration of factors such as race, ethnicity, religion, social status, and nationality. They are taught that public trust and obligations of justice grounded in equality demand that only medical indications be considered. But military physicians in a military setting are beholden to obligations, duties, and responsibilities as members of the military, and when these obligations, duties, and responsibilities conflict, as they do in Battlefield Triage, which loyalties win out and why?[5] Critics of partiality on national grounds argue that partiality undermines public trust in medicine and justice because everyone should be treated equally regardless of nationality.[6] Proponents of partiality argue that military obligations supersede equality and that justice requires partiality in such cases.[7] Despite the critics’ disagreement, both agree that there is a morally right, perhaps even blameless, course of action. Drawing on insights from virtue ethics, we argue that Battlefield Triage is a moral tragedy in which justice is unattainable and there is no action without moral cost. The assumption that there is a morally right choice is flawed. We argue that while no decision in this scenario is free from moral blame, there are reasons to favor treating one’s soldiers over enemy combatants. I. The Case Against Partiality There is a common assumption that there is a morally right or just decision in Battlefield Triage. A number of organizations and scholars claim that it is wrong for military physicians to favor their own soldiers on the grounds of nationality or some form of ‘group membership.’ (In a conflict involving service members from multiple nations working as a coalition, a soldier from an allied country may receive the same priority as the US service member due to ‘group membership.’) The World Medical Association’s WMA Declaration of Lisbon on the Rights of the Patient, which was reaffirmed in 2015, posits that, “[i]n circumstances where a choice must be made between potential patients for a particular treatment that is in limited supply, all such patients are entitled to a fair selection procedure for that treatment. That choice must be based on medical criteria and made without discrimination.”[8] This echoes what was set forth in Article 12 of the Geneva Conventions, which states that “[o]nly urgent medical reasons will authorize priority in the order of treatment to be administered.”[9] The argument for impartiality in Battlefield Triage is that every person is morally equal, and equality entails that medical distribution is, “based on a combination of medical need and urgency.”[10] This is in keeping with the bioethical principles that are generally applied.[11] II. The Case for Partiality On the other side, there are arguments that favoritism is the ethically right decision in Battlefield Triage.[12] The argument asserts that members of the military form a morally significant community of friends and participation in these relationships demands partiality. Just as parents have strong ethical duties to their children and not just any children, military personnel have ethical duties to their group, a group that involves an affirmation of mutual aid and support. Some have termed these ‘associative duties. According to Michael Gross, obligations of friendship, care, and solidarity “leave very little room for generally applicable principles of justice that would obligate a medic to treat enemy or non-compatriot wounded ahead of their compatriots.”[13] This is true in Battlefield Triage, but it may also be true even if the enemy’s soldier were more seriously wounded: “the ethics of small group cohesion, largely an ethics of care, mostly replaces the demands of impartial justice.”[14] In a more recent article, Gross explains that preferential treatment is ethically justified based on fighting capability and “the special obligations people owe friends, family, and, no less, comrades-in-arms.”[15] To not show partiality to the US soldier would be morally wrong on the grounds of friendship and mutual care.[16] III. The Moral Tragedy of Battlefield Triage Defenders and critics of Battlefield Triage favoritism based on nationality both frame their position as just or fair. For example, Justin List argues that physicians are “bound to practice medical neutrality,”[17] Marcus Adams denies that physicians “possess special ethical obligations” to enemy combatants because of their profession.[18] These perspectives assume that there is a morally right decision and that justice is attainable. The assumption that there is or can be a morally right Battlefield Triage decision, and we need to put our heads together to figure it out, remains strongly entrenched. However, the facts of the situation should give us pause; there are too many people and too few resources, and this demands a decision-making process that determines who will receive scarce resources. By its very nature, a battlefield triage decision has to be made based on some characteristic or value, a characteristic or value that will inevitably favor some at the expense of others. This is precisely why competing analyses “in the military context struggle to resolve these conflicts satisfactorily.”[19] Drawing on the insights of virtue ethics, we suggest that Battlefield Triage is a moral tragedy. Virtue ethics suggests that morality is about acting virtuously, which is to say that we should do what a virtuous person would do in the situation. Ethics is about figuring out how a just, wise, compassionate, loving, and fair person would act, and then doing that, as one grows in virtue. But life is not always clear cut, and it is possible that virtuous people may find themselves in a moral tragedy, a situation in which, through no fault of one’s own, a person must make a morally objectionable decision. After the action the virtuous person “emerges having done a terrible thing, the very sort of thing that the callous, dishonest, unjust, or in general vicious agent would characteristically do.”[20] Stated differently, a moral tragedy presents a virtuous person with two or more courses of action, all of which have a moral cost.[21] In Battlefield Triage, no matter how the physician goes about deciding, there is going to be defensible concern from those not saved. The fact that there are more people than can be helped fosters competing values in battlefield triage: maximize lives saved, treat people equally, treat the worse off, and support the war effort. Treating people equally may create tension between treating the worse off, maximizing lives saved, and supporting the war effort. Reverse triage is a case in point, as supporting the war effort conflicts with treating the worse off first, as is a fair lottery system since deploying a lottery may not maximize lives saved or support the war effort. There can be reasons why one person is selected over another, to be sure. Yet, there are reasons for making a decision, and that the decision is subject to legitimate moral concern is another. To recognize the moral tragedy of Battlefield Triage is to recognize the impossibility of acting blamelessly in the situation. In this situation, the virtuous military physician is going to have to sacrifice important values such as justice, compassion, and respect for others, even with a defensible criterion in hand. The physician will grieve this sacrifice accordingly. The physician may find her decision difficult or stressful, and rightly so, because of what her circumstances require of her. This kind of moral tragedy results “in actions which betray and violate the rights of persons to whom there may be a strong duty of care. When this happens, it properly triggers an appropriate moral emotion since our moral integrity has been violated and this affects how we think of ourselves and what we have become.”[22] Rather than view her triage decision as the morally superior choice, the virtuous military physician will view her decisions in these circumstances in a different light: it is the least bad option in a terrible situation, and she did something ethically problematic, something that is contrary to her moral character. She deeply regrets the circumstances in which she had to act. IV. Virtue Ethics A virtue ethicist has insight into how one should go about deciding what to do in a moral tragedy, although virtue ethics may not be as helpful as one may hope. The goal of the virtuous military physician in Battlefield Triage is to adopt the best course of action or the action that she feels she ought to do, all things considered. This does not make her choice devoid of serious wrongdoing—a decision must be made, but that does not make it just. The virtuous military physician will approach the situation with courage, responsibility, and insight. She will think about the decision carefully, wisely, and conscientiously; she will weigh the goods and harms of the choices before her, in conjunction with a proper conception of the good life, human worth, and understanding of her obligations to others—including chain of command, fellow soldiers, and the medical community. She is attuned to the value of human life and has a reasonable idea of the various ways her decisions will affect others. She recognizes that she is in this non-ideal situation through no fault of her own: she is not the one fighting in battles; she is serving her country as a physician, whose job it is to save lives, treat everyone justly, and promote military objectives. She regrets the decision she is forced to make in battlefield triage, acting “with immense regret and pain,” Hursthouse explains, “instead of indifferently or gladly.”[23] This is because, no matter what decision is made, the virtuous military physician “does something terrible or horrible,” something she otherwise would not do and is contrary to her values.[24] V. A Resolvable Moral Tragedy Instead of asking whether there is a morally right decision, in which a decision is morally blameless and above reproach, the virtue ethicist asks whether there is a decision with a convincing rationale, knowing that a decision can have a clear rationale but still be morally tragic. It is perfectly reasonable to think that different virtuous persons will arrive at different courses of action: “two virtuous agents, in the same situation,” Hursthouse writes, “may act differently” in irresolvable moral tragedies, in cases in which there is no clear course of action.[25] Because a person must act in a moral tragedy, one goal is to identify reasons for choosing the chosen action. Some decisions are clearly indefensible—treating neither the compatriot soldier nor the enemy combatant in Battlefield Triage would be wrong—and some decisions are more problematic than others. If the military physician selects to treat the soldier because she does not like the enemy combatant’s skin color, such a reason would be deeply problematic. But much of the debate over how to act in a moral tragedy is not over clearly indefensible or problematic criteria. Instead, the literature is largely about different standards or implementations of justice. Some scholars defend nation-impartial triage as right, while others defend nation-aware triage as right, and each argues that the other side is promoting an unjust or otherwise wrong solution to Battlefield Triage. We suggest that Battlefield Triage is a resolvable moral tragedy and that virtue ethics offers convincing reasons to prefer the treatment of the compatriot soldier rather than the enemy combatant on the grounds of national identity. Virtues are integral to living a good life, a flourishing life, but as Aristotle observed long ago, human beings are inherently social, interdependent and interconnected in profound ways.[26] This goes beyond the obvious fact that we need each other to survive day to day (one person makes clothes, another farms, and another makes tools); the claim is that a good or flourishing life depends in large part on one’s social network or community. This is why many of Aristotle’s moral virtues are other facing: justice, friendship, generosity, and magnanimity, to name a few. Courage, a typically self-facing virtue, is understood by Aristotle to be the virtue that regards one’s fear of death in battle, a battle fought on behalf of one’s city.[27] All of this remains true today. Namely, there is an important sense in which our community matters to our lives: it is easier to live a good, flourishing life if one is part of a good, flourishing community. Our community is made up of smaller groups, and it is more accurate to say that we are simultaneous members of different groups within a broader community. A person may be part of a family, friend group, research team, large state university, city, state, and nation. Groups can function well or not, as we all have experienced, and this suggests that there are virtues or excellences that groups can instantiate. Good groups are unified in purpose, with each member doing their duty alongside others for the attainment of that purpose. Good groups manifest solidarity among their members. Although Aristotle does not list solidarity as a virtue, a number of modern-day virtue ethicists have begun examining how group solidarity can be a virtue that contributes to a good or flourishing life.[28] Solidarity is not conceptualized as an individual virtue, a virtue possessed by a person in isolation of others; instead, it is a collective virtue, a virtue that is shared among members of a defined group with particular ends.[29] “A group has solidarity to the extent that its members are disposed to: (1) share values, aims, or goals; (2) care about those values, aims, or goals; (3) act in accordance with those values, aims, or goals; (4) trust the testimony of other group members with respect to those values, aims, and goals; and (5) feel a sense of belonging to the group.”[30] The virtue of collective or group solidarity involves individuals having special concern for each other, shared aims and values, trust, loyalty, and a sense of belonging with these specific others. There is a oneness to the group in the pursuit of a definite goal or purpose, involving mutual support and affirmation of each member. As such, the group has ends and goods above and beyond the good of each individual person. Sometimes solidarity requires personal sacrifice for the collective (for example, a father sacrificing food so his child can eat). The virtue of collective or group solidarity is important to the military and medical community at every level, and for clear reasons. In the military, there is a clear hierarchy of command, unity of purpose and end, mutual trust and support in complex settings, and so on. Soldiers need to know they can count on one another, and solidarity grounds a soldier’s ability to trust others and be assured of mutual aid. In medicine, solidarity maintains self-regulation of the profession, shared values and goals, as well as public support, not to mention that day-to-day operations require physician trust, engagement, and effort toward the ends of clinical care. Physicians need to work together, along with others, in pursuit of health, and disunity is sowed when there is mistrust, selfishness, or disengagement among the healthcare team and organization. Importantly, just as we are all members of various groups and hence may manifest group solidarity in different settings, the virtuous military physician instantiates collective solidarity with both the medical profession and the military. Her dual loyalty contributes to the moral difficulty of acting in Battlefield Triage. The military physician has competing obligations to distinct groups and cannot satisfy all obligations in Battlefield Triage. Solidarity with the military supports the consideration of favoring the soldier for reasons of national identity, whereas solidarity with the medical community does not. Something has to give, which is why it is a moral tragedy. The virtuous military physician, therefore, must weigh the costs of each course of action. To fulfill her obligations to the medical community would require that she does not use nationality and other non-medical considerations in Battlefield Triage. Since the soldier and enemy combatant are equally injured, justice would demand a random process, perhaps a flip of the coin. Although this may satisfy obligations the military physician has to the medical community, this would be costly to the physician’s military group. If word gets out that the physician decides who to treat based on a coin toss, soldiers, families, and citizens may become frustrated and angry. Soldier morale may go down if it becomes known that a coin flip led to the preventable death of a soldier and the saving of an enemy combatant who had killed (or attempted to kill) other soldiers. As Gross highlights, military solidarity involves a mutual aid promise that military personnel promise to help one another.[31] A military physician is part of the military and, as such, is part of the mutual aid promise, which would appear to be violated if the physician flips a coin. Treating a member of one’s own team may be psychologically more beneficial than treating an enemy combatant and may lead to less moral distress.[32] Finally, treating soldiers rather than enemy combatants promotes broader military and social aims, including returning soldiers to health, maintaining unity of purpose, and minimizing community suffering from a soldier’s death. Favoring members of one’s group, that is, triage based on nationality in Battlefield Triage, would fulfill obligations of military group loyalty, which is contrary to the values and duties of medicine. It does not seem as though showing favoritism in this particular situation is very costly to the medical community or general public, but this is because there is recognition that the physician is in the military. Medicine is impartial to non-medical indications partly because of fairness and to promote public trust in medicine. However, Battlefield Triage is unique, as medicine is being practiced in a non-public, wartime setting. In ordinary circumstances, a patient’s identity is irrelevant, and physicians ought not play favorites. Since Battlefield Triage is not an ordinary circumstance, decisions based on patient identity may not undermine public trust in medicine. In addition, it is contestable that fairness in Battlefield Triage requires that no consideration be paid to one’s nationality. Fairness is about giving each person their due, what is owed to them, and the case can be made that soldiers who place themselves in danger for the sake of the common good or a just cause are owed special attention when they suffer harm in the line of duty. In other words, soldiers voluntarily undergo risk to themselves for the greater good, and society owes them for this sacrifice. This plausibly includes preferential treatment in a situation such as Battlefield Triage. So, while the medical community affirms justice demands non-preferential treatment, the military community can affirm the opposite. The demands of fairness are unclear at best or in conflict in this situation: demands of physician justice decry favoritism, while demands of military justice support favoritism. Triage not based on nationality is arguably unfair and triage based on nationality may not undermine public trust, after all. All things considered, there is a clear rationale for favoring nationality-based preferential treatment in Battlefield Triage. Adopting a nationality-based preference in this situation is more defensible than not. This does not make such a decision ethically right or just. Preference based on nationality is the least bad decision, but it is not morally blameless. It involves one in a serious moral wrong, a wrong otherwise avoided and contrary to one’s character. The virtuous military physician is in a situation in which obligations conflict, and we disagree with Gross, who posits that care of fellow soldiers “is important to the near exclusion of all else.”[33] Gross fails to appreciate the collective virtue of solidarity as applied to those in medicine. The military physician has duties to fellow soldiers but also to fellow physicians, to the medical community, and humanity. To favor a soldier on grounds of nationality violates her duties and responsibilities to this latter group. She is involved in a moral tragedy and can only seek the most just action given the circumstances, yet, at least in virtue ethics, the action remains far from blameless. CONCLUSION We argue that Battlefield Triage is a moral tragedy, meaning that it is a situation in which there is no morally blameless decision and that the demands of justice cannot be satisfied. As such, the virtuous military physician incurs a moral cost to acting as she does—there is a moral residue. However, despite being a moral tragedy, there are clear reasons to act in favor of treating one’s own, considering group solidarity. As such, these kinds of tragedies are resolvable: virtuous military physicians should favor treatment of their own, although they would do so with sorrow. - [1] Militaries set forth medical rules of eligibility or guidelines used to determine whether a person qualifies for specific medical interventions or treatments in certain circumstances, and these guidelines are binding for a military physician. For example, despite opposition from medical organizations, militaries have adopted reverse triage guidelines for military physicians to follow. For ethical discussion, see Falzone, Elisabeth, P. Pasquier, C. Hoffmann, O. Barbier, M. Boutonnet, A. Salvadori, A. Jarrassier, J. Renner, B. Malgras, and S. Mérat. "Triage in military settings." Anaesthesia Critical Care & Pain Medicine 36, no. 1 (2017): 43-51. https://doi.org/10.1016/j.accpm.2016.05.004 [2] There are issues that are related to this, including the triage of civilians and allied soldiers. We set related issues aside for purposes of this paper [3] American Medical Association, Code of Medical Ethics: Current Opinions with Annotations, 2004–2005 ed. (Chicago, IL: AMA, 2004), 300. [4] American Medical Association, Code of Medical Ethics: Current Opinions with Annotations, 2004–2005 ed. (Chicago, IL: AMA, 2004), 300. [5] This is termed the “dual loyalty” dilemma in military medicine and has been described at length elsewhere: Institute of Medicine (US) Board on Health Sciences Policy. Military Medical Ethics: Issues regarding Dual Loyalties: Workshop Summary. Washington (DC): National Academies Press (US); 2008. Toward a Framework for Resolving Dual Loyalties. Available from: https://www.ncbi.nlm.nih.gov/books/NBK214853/ [6] See Kenneth G. Swan and K.G. Swan, Jr., “Triage: The Past Revisited,” Military Medicine 161:8 (1996): 448–452. https://doi.org/10.1093/milmed/161.8.448; Jerome A. Singh, “American Physicians and dual loyalty obligations in the ‘war on terror,’” BMC Medical Ethics 4.4 (2003): 1–10. https://doi.org/10.1186/1472-6939-4-4; Beam, Thomas E. "Medical Ethics on the Battlefield." Military Medical Ethics: Sect. IV. Medical ethics in the military. Medical ethics on the battlefield: the crucible of military medical ethics 2 (2003): 369-402; Hereth, Blake. "Health justice for unjust combatants." Journal of Military Ethics 20, no. 1 (2021): 67-81. https://doi.org/10.1080/15027570.2021.1949782. [7] See Adams, Marcus P. "Triage priorities and military physicians." In Physicians at war: The dual-loyalties challenge, pp. 215-236. Dordrecht: Springer Netherlands, 2008. Gross, Michael L. "Comradery, community, and care in military medical ethics." Theoretical medicine and bioethics 32 (2011): 337-350. https://doi.org/10.1007/s11017-011-9189-6. Gross, Michael L. "The limits of impartial medical treatment during armed conflict." In Military medical ethics for the 21st century, pp. 71-84. Routledge, 2016. [8] World Medical Association, WMA Declaration of Lisbon on the Rights of the Patient. 5 December 2022, https://www.wma.net/policies-post/wma-declaration-of-lisbon-on-the-rights-of-the-patient/ [9] Geneva Convention for the Amelioration of the Condition of Wounded, Sick in Armed Forces in the Field. 12 August 1949. https://www.un.org/en/genocideprevention/documents/atrocity-crimes/Doc.30_GC-I-EN.pdf. [10] List, Justin M. "Medical neutrality and political activism: physicians' roles in conflict situations." In Physicians at war: The dual-loyalties challenge, pp. 237-253. Dordrecht: Springer Netherlands, 2008. 240 [11] Beauchamp, T., and J. Childress. 2013. Principles of Biomedical Ethics, 7th ed. Oxford, United Kingdom: Oxford University Press. [12] Adams, Marcus P. "Triage priorities and military physicians." In Physicians at war: The dual-loyalties challenge, pp. 215-236. Dordrecht: Springer Netherlands, 2008. [13] Gross, "Comradery, community, and care in military medical ethics," 347. [14] Gross, “Comradery, community, and care in military medical ethics,” 349. [15] Gross, Michael L. "When medical ethics and military ethics collide." Narrative inquiry in bioethics 13, no. 3 (2023): 199-204. 202 https://dx.doi.org/10.1353/nib.2023.a924191 [16] Our argument draws on virtue ethics, from which care ethics derives, and it is worth clarifying how our argument relates to Gross’s. We do not think that the virtue of friendship grounds triage decisions, for we think it is unlikely that the physician and wounded soldier are friends. Instead, as explained below, we think the collective virtue of group solidarity better captures the moral significance of group loyalty and that Gross would agree with us. But since military physicians are part of distinct groups, with competing obligations, the military physician will be forced to sacrifice a value in battlefield triage cases. In other words, we think Gross downplays the dual group membership of a military physician. [17] List,”Medical neutrality and political activism,” 250. [18] Adams,”Triage priorities and military physicians,” 235. [19] London, Leslie, Leonard S. Rubenstein, Laurel Baldwin-Ragaven, and Adriaan Van Es. "Dual loyalty among military health professionals: human rights and ethics in times of armed conflict." Cambridge Quarterly of Healthcare Ethics 15, no. 4 (2006): 381-391. 383. [20] Hursthouse, R. On Virtue Ethics. OUP 1999. 74 [21] Nussbaum, Martha C. "The costs of tragedy: Some moral limits of cost-benefit analysis." The Journal of Legal Studies 29, no. S2 (2000): 1005-1036, 1007. [22] De Wijze, S. (2005). Tragic-remorse–the anguish of dirty hands. Ethical theory and moral practice, 7(5), 453-471, 457. https://doi.org/10.1007/s10677-005-6836-x [23] Hursthouse, 73 [24] Hursthouse, 81 [25] Hursthouse, 72 [26] Aristotle, Politics 1253a8. Reeve, C. D. C., Indianapolis: Hackett Publishing Co., 2017 [27] Aristotle, Nicomachean Ethics. III.6.114a, 34-35. 2002, Nicomachean Ethics, Christopher Rowe (trans.), Oxford: Oxford University Press [28] Byerly, T. Ryan, and Meghan Byerly. "Collective virtue." The Journal of Value Inquiry 50, no. 1 (2016): 33-50. https://doi.org/10.1007/s10790-015-9484-y; Federico, Veronica. "Conclusion: solidarity as a public virtue." Solidarity as a Public Virtue (2018): 495-542. https://doi.org/10.5771/9783845290058. Rehg, William. "Solidarity and the common good: An analytic framework." Journal of Social Philosophy 38, no. 1 (2007): 7-21. https://doi.org/10.1111/j.1467-9833.2007.00363.x [29] Byerly and Byerly. "Collective virtue." 43 [30] Battaly, Heather. "Solidarity: Virtue or vice?." In Social virtue epistemology, pp. 303-324. Routledge, 2022. 304 [31] Ibid., 2011: 341 [32] It might be thought that displaying altruism by helping an enemy combatant at the expense of one’s fellow soldier may be psychologically satisfiying. For evidence that military physicians find it difficult to treat enemy combatants, see Lundberg, Kristina, Sofia Kjellström, Anders Jonsson, and Lars Sandman. "Experiences of Swedish military medical personnel in combat zones: adapting to competing loyalties." Military medicine 179, no. 8 (2014): 821-826. https://doi.org/10.7205/MILMED-D-14-00038. Lamblin, Antoine, Clément Derkenne, Marion Trousselard, and Marie-Ange Einaudi. "Ethical challenges faced by French military doctors deployed in the Sahel (Operation Barkhane): a qualitative study." BMC Medical Ethics 22 (2021): 1-13. https://doi.org/10.1186/s12910-021-00723-2 [33] Ibid., 2011: 344. (shrink)

In this paper I explore a neglected discussion of vagueness put forward by Wittgenstein in his Philosophical Grammar (1932–34). In this work, unlike Philosophical Investigations (1953), Wittgenstein not only discusses the venerable Sorites paradox but provides a novel conception of vagueness using an analogy with coin tossing and converging intervals. As he sees it, the problematic picture of vagueness arises because we conflate aspects of the functioning of vague concepts with those of non-vague ones. Thus, while we accept (...) that vague concepts have no sharp cut-off points (are boundaryless), we nevertheless retain the idea that we can progress towards the penumbra the way we progress towards the cut-off points of non-vague concepts. As a potential remedy, Wittgenstein's analogy with coin tossing and converging intervals replaces this picture and provides an understanding of the functioning of vague concepts in which no notion of a progression arises. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:332 BOOK REVIEWS toral inventions (such as basic Christian communities), and the religious backgrounds of millions who help to make up the churches, Catholic and Protestant, of the United States. Providence College Providence, RI EDWARD L. CLEARY, O.P. Springs of Action: Understanding Intentional Behavior. By ALFRED R. MELE. New York and Oxford: Oxford University Press, 1992. Pp. 272 + ix. $39.95 (cloth). Alfred Mele's overarching aim in this book (...) is to offer an account of the role of intentions in the explanation of intentional action. He works within the familiar terms of causal theories of action, and is particularly indebted to Donald Davidson. In Part I, Mele borrows a set of theses from Davidson's desire/belief model of intentional action, and in the process of addressing problems associated with these theses, he progressively refines an account of action that understands an agent's reasons to have explanatory force by virtue of being among the causes of action. In Part II, Mele argues that desire/belief models are insufficient as they stand and need to be filled out by recognizing that intentions provide a crucial link between reasons and actions. The discussion begins with the vexed question of how the content of mental states can be relevant to the causal explanation of action. We constantly appeal to our desires, beliefs, plans, and so on (i.e., to various propositional, or intentional, attitudes) in explaining our behavior. But how does, say, my appetite for good wine and my belief that the house chardonnay is such a wine figure in the causal order that brings about my act of ordering a glass of it? Presumably, these intentional states supervene upon certain physical states of my body, and the latter do the causal work of producing wine-ordering behavior. However, there are good reasons to think that, with certain sorts of changes in my history and environment (viz., of the sort described in twin earth thought experiments), these physical states could be the realization of different intentional states. So can a causal theory of action actually accord my desires and beliefs any role in explaining my action? Mele argues that even if we hold (with externalists) that the agent's history and environment help to fix the content of her intentional states, we can nonetheless say that unless the agent had intended what she did, she would not have acted as she did. The behavior is intentional action by virtue of issuing (in the right way) from physical processes BOOK REVIEWS 333 that realize the agent's reasons for acting, and these processes realize these reasons only if the processes have an appropriate causal history. The result is that what we desire, believe, and intend does after all make a systematic difference in what we do. Mele makes some helpful refinements in the standard account of the causal role of desire in intentional action. It has typically been claimed that when an agent's wants compete, the "strongest" of them deter· mines the action; if an agent wants to do A more than anything else that she takes herself to be able to do, then if she acts intentionally she will do A. Mele points out that this general claim must be qualified so as to index desires to times, to accommodate both unsuccessful at· tempts and the agent's estimates of the likelihood of success, and to deal with the complex relations between desires. He explores the way in which agents are able to control the motivational strength of their desires, and he works out a definition of irresistible desire. One of the deepest challenges to the claim that action is caused by what we most desire arises in considering "motivational ties." How, on this account, is intentional action possible when we equally desire each of two incompatible alternatives? An arbitrary decision procedure can be adopted (e.g., a coin toss), but this alone does not en· hance the attractiveness of the randomly selected alternative. Here Mele introduces his thesis about intentions: viz., that intentions have an "executive quality that is not reducible to desire-strength" (p. 72), so that even when there is no preponderant motivation to do A... (shrink)