It is commonly remarked, as a curiosity, that Imruʾ al-Qays’s traditional death resembles that of Heracles, but it has never been meaningfully discussed. This article undertakes to do so, arguing for the Greek provenance of his death tradition and discussing the implications of the Islamic construction of a Greek death for “the greatest Arab poet.” One implication involves his biography more generally, which is argued to have originally formed a different kind of narrative serving particular Islamic interests, later adapted to (...) a biographic mold. The second stems from the recognition that the legendary Greek death of Imruʾ al-Qays is neither incidental nor isolated, which suggests that the horizons of Greco-Arabic studies are unduly narrow: alongside the transmission of written scientific texts, there were also oral popular traditions of Greek origin that left a deep imprint on Islamic culture. (shrink)

One of the most remarkable features of the language of early Greek writing is a pervasive rhetorical strategy which consists in personifying objects for the purpose of identifying humans closely associated with them. Such ‘speaking objects’ have no Semitic parallel; how, then, is their conventional status in the Archaic Age to be explained? This article first considers the formulaic language of speaking objects, which is no straightforward transcription of speech, and seeks to explain where it comes from. It then turns (...) to the question of why writers employed the curious strategy of personification by setting it in the broader context of early Greek writing and literature. Variously analogous to herms, slaves and skytalai, speaking objects are shown to have been conceived as messengers acting on behalf of their senders by not speaking in their name. (shrink)

In the longstanding foundational debate whether to require that probability is countably additive, in addition to being finitely additive, those who resist the added condition raise two concerns that we take up in this paper. (1) _Existence_: Settings where no countably additive probability exists though finitely additive probabilities do. (2) _Complete Additivity_: Where reasons for countable additivity don’t stop there. Those reasons entail complete additivity—the (measurable) union of probability 0 sets has probability 0, regardless the cardinality of that union. Then (...) probability distributions are discrete, not continuous. We use Easwaran’s (Easwaran, Thought 2:53–61, 2013) advocacy of the _Comparative_ principle to illustrate these two concerns. Easwaran supports countable additivity, both for numerical probabilities and for finer, qualitative probabilities, by defending a condition he calls the _Comparative_ principle [ \({\mathcal{C}}\) ]. For numerical probabilities, principle \({\mathcal{C}}\) contrasts pairs, P 1 and P 2, defined over a common partition \(\prod\) = {a _i_ : _i_ ∈ I} of measurable events. \({\mathcal{C}}\) requires that no P 1 may be pointwise dominated, i.e., no (finitely additive) probability P 2 exists such that for each _i_ ∈ I, P 2 (a _i_ ) > P 1 (a _i_ ). By design, the cardinality of \(\prod\) is not limited in \({\mathcal{C}}\), which Easwaran asserts is important when arguing that the principle does not require more, or less, than that probability is countably additive. We agree that a numerical probability P satisfies principle \({\mathcal{C}}\) in all partitions just in case P is countably additive. However, we show that for numerical probabilities, by considering the size of the algebra of events to which probability is applied, principle \({\mathcal{C}}\) is subject to each of the above concerns, (1) and (2). Also, Easwaran considers principle \({\mathcal{C}}\) with non-numerical, qualitative probabilities, where a qualitative probability may be finer than an almost agreeing numerical probability P. A qualitative probability is regular if possible events are strictly more likely than impossible events. Easwaran motivates and illustrates regular qualitative probabilities using a continuous, almost agreeing quantitative probability that is uniform on the unit interval. We make explicit the conditions for applying principle \({\mathcal{C}}\) with qualitative probabilities and show that \({\mathcal{C}}\) restricts regular qualitative probabilities to those whose almost agreeing quantitative probabilities are completely additive. For instance, Easwaran’s motivating example of a regular qualitative probability is precluded by principle \({\mathcal{C}}\). (shrink)

When real-valued utilities for outcomes are bounded, or when all variables are simple, it is consistent with expected utility to have preferences defined over probability distributions or lotteries. That is, under such circumstances two variables with a common probability distribution over outcomes – equivalent variables – occupy the same place in a preference ordering. However, if strict preference respects uniform, strict dominance in outcomes between variables, and if indifference between two variables entails indifference between their difference and the status quo, (...) then preferences over rich sets of unbounded variables, such as variables used in the St. Petersburg paradox, cannot preserve indifference between all pairs of equivalent variables. In such circumstances, preference is not a function only of probability and utility for outcomes. Then the preference ordering is not defined in terms of lotteries. (shrink)

We review de Finetti’s two coherence criteria for determinate probabilities: coherence1defined in terms of previsions for a set of events that are undominated by the status quo – previsions immune to a sure-loss – and coherence2 defined in terms of forecasts for events undominated in Brier score by a rival forecast. We propose a criterion of IP-coherence2 based on a generalization of Brier score for IP-forecasts that uses 1-sided, lower and upper, probability forecasts. However, whereas Brier score is a strictly (...) proper scoring rule for eliciting determinate probabilities, we show that there is no real-valuedstrictly proper IP-score. Nonetheless, with respect to either of two decision rules – Γ-maximin or E-admissibility-+-Γ-maximin – we give a lexicographic strictly proper IP-scoring rule that is based on Brier score. (shrink)

Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti and Dubins, subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-­additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than κ. This generalizes our result, where we established that each finite but not countably additive probability has (...) conditional probabilities that fail to be conglomerable in some countable partition. (shrink)

We discuss several features of coherent choice functions—where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the sets of probabilities. (...) We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence using a set of probability/almost-state-independent utility pairs. We give sufficient conditions when a choice function satisfying our axioms is represented by a set of probability/state-independent utility pairs with a common utility. (shrink)

For Savage (1954) as for de Finetti (1974), the existence of subjective (personal) probability is a consequence of the normative theory of preference. (De Finetti achieves the reduction of belief to desire with his generalized Dutch-Book argument for Previsions.) Both Savage and de Finetti rebel against legislating countable additivity for subjective probability. They require merely that probability be finitely additive. Simultaneously, they insist that their theories of preference are weak, accommodating all but self-defeating desires. In this paper we dispute these (...) claims by showing that the following three cannot simultaneously hold: (i) Coherent belief is reducible to rational preference, i.e. the generalized Dutch-Book argument fixes standards of coherence. (ii) Finitely additive probability is coherent. (iii) Admissible preference structures may be free of consequences, i.e. they may lack prizes whose values are robust against all contingencies. (shrink)

The degree of incoherence, when previsions are not made in accordance with a probability measure, is measured by either of two rates at which an incoherent bookie can be made a sure loser. Each bet is considered as an investment from the points of view of both the bookie and a gambler who takes the bet. From each viewpoint, we define an amount invested (or escrowed) for each bet, and the sure loss of incoherent previsions is divided by the escrow (...) to determine the rate of incoherence. Potential applications include the treatment of arbitrage opportunities in financial markets and the degree of incoherence of classical statistical procedures. We illustrate the latter with the example of hypothesis testing at a fixed size. (shrink)

Several axiom systems for preference among acts lead to a unique probability and a state-independent utility such that acts are ranked according to their expected utilities. These axioms have been used as a foundation for Bayesian decision theory and subjective probability calculus. In this article we note that the uniqueness of the probability is relative to the choice of whatcounts as a constant outcome. Although it is sometimes clear what should be considered constant, in many cases there are several possible (...) choices. Each choice can lead to a different "unique" probability and utility. By focusing attention on statedependent utilities, we determine conditions under which a truly unique probability and utility can be determined from an agent's expressed preferences among acts. Suppose that an agent's preference can be represented in terms of a probability P and a utility U.That is, the agent prefers one act to another iff the expected utility of that act is higher than that of the other. There are many other equivalent representations in terms of probabilities Q, which are mutually absolutely continuous with P, and state-dependent utilities V, which differ from U by possibly different positive affine transformations in each state of nature. We describe an example in which there are two different but equivalent state-independent utility representations for the same preference structure. They differ in which acts count as constants. The acts involve receiving different amounts of one or the other of two currencies, and the states are different exchange rates between the currencies. It is easy to see how it would not be possible for constant amounts of both currencies to have simultaneously constant values across the differentstates. Savage (1954, sec. 5.5) discovered a situation in which two seemingly equivalent preference structures are represented by different pairs of probability and utility. He attributed the phenomenon to the construction of a "small world." We show that the small world problem is just another example of two different, but equivalent, representations treating different actsas constants. Finally, we prove a theorem (similar to one of Karni 1985) that shows how to elicit a unique state-dependent utility and does not assume that there are prizes with constant value. To do this, we define a new hypothetical kind of act in which both the prize to be awarded and the state of nature are determined by an auxiliary experiment. (shrink)

It has long been known that the practice of testing all hypotheses at the same level , regardless of the distribution of the data, is not consistent with Bayesian expected utility maximization. According to de Finetti’s “Dutch Book” argument, procedures that are not consistent with expected utility maximization are incoherent and they lead to gambles that are sure to lose no matter what happens. In this paper, we use a method to measure the rate at which incoherent procedures are sure (...) to lose, so that we can distinguish slightly incoherent procedures from grossly incoherent ones. We present an analysis of testing a simple hypothesis against a simple alternative as a case‐study of how the method can work. (shrink)

uniquely into a convex combination of a countably additive probability and a purely finitely additive (PFA) one. The coefficient of the PFA probability..

We investigate differences between a simple Dominance Principle applied to sums of fair prices for variables and dominance applied to sums of forecasts for variables scored by proper scoring rules. In particular, we consider differences when fair prices and forecasts correspond to finitely additive expectations and dominance is applied with infinitely many prices and/or forecasts.

Statistical decision theory, whether based on Bayesian principles or other concepts such as minimax or admissibility, relies on minimizing expected loss or maximizing expected utility. Loss and utility functions are generally treated as unit-less numerical measures of value for consequences. Here, we address the issue of the units in which loss and utility are settled and the implications that those units have on the rankings of potential decisions. When multiple currencies are available for paying the loss, one must take explicit (...) account of which currency is used as well as the exchange rates between the various available currencies. (shrink)

We give an extension of de Finetti’s concept of coherence to unbounded random variables that allows for gambling in the presence of infinite previsions. We present a finitely additive extension of the Daniell integral to unbounded random variables that we believe has advantages over Lebesgue-style integrals in the finitely additive setting. We also give a general version of the Fundamental Theorem of Prevision to deal with conditional previsions and unbounded random variables.

We give necessary and sufficient conditions for a scoring rule to be proper for a quantile if utility is linear, and the distribution is unrestricted. We also give results when the set of distributions is limited, for example, to distributions that have first moments.

Gordon Belot argues that Bayesian theory is epistemologically immodest. In response, we show that the topological conditions that underpin his criticisms of asymptotic Bayesian conditioning are self-defeating. They require extreme a priori credences regarding, for example, the limiting behavior of observed relative frequencies. We offer a different explication of Bayesian modesty using a goal of consensus: rival scientific opinions should be responsive to new facts as a way to resolve their disputes. Also we address Adam Elga’s rebuttal to Belot’s analysis, (...) which focuses attention on the role that the assumption of countable additivity plays in Belot’s criticisms. (shrink)

This important collection of essays is a synthesis of foundational studies in Bayesian decision theory and statistics. An overarching topic of the collection is understanding how the norms for Bayesian decision making should apply in settings with more than one rational decision maker and then tracing out some of the consequences of this turn for Bayesian statistics. There are four principal themes to the collection: cooperative, non-sequential decisions; the representation and measurement of 'partially ordered' preferences; non-cooperative, sequential decisions; and pooling (...) rules and Bayesian dynamics for sets of probabilities. The volume will be particularly valuable to philosophers concerned with decision theory, probability, and statistics, statisticians, mathematicians, and economists. (shrink)

The Sleeping Beauty problem has spawned a debate between “thirders” and “halfers” who draw conflicting conclusions about Sleeping Beauty's credence that a coin lands heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational belief with conditioning. No special handling is used for self-locating beliefs or centered propositions. (...) We also explore what fair prices Sleeping Beauty computes for gambles that she might be offered during the experiment. (shrink)

When can a Bayesian investigator select an hypothesis H and design an experiment (or a sequence of experiments) to make certain that, given the experimental outcome(s), the posterior probability of H will be lower than its prior probability? We report an elementary result which establishes sufficient conditions under which this reasoning to a foregone conclusion cannot occur. Through an example, we discuss how this result extends to the perspective of an onlooker who agrees with the investigator about the statistical model (...) for the data but who holds a different prior probability for the statistical parameters of that model. We consider, specifically, one-sided and two-sided statistical hypotheses involving i.i.d. Normal data with conjugate priors. In a concluding section, using an "improper" prior, we illustrate how the preceding results depend upon the assumption that probability is countably additive. (shrink)

The Sleeping Beauty problem has spawned a debate between “Thirders” and “Halfers” who draw conflicting conclusions about Sleeping Beauty’s credence that a coin lands Heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the Experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational belief with conditioning. No special handling is used for self-locating beliefs or centered propositions. (...) We also explore what fair prices Sleeping Beauty computes for gambles that she might be offered during the Experiment. (shrink)

Experimenters sometimes insist that it is unwise to examine data before determining how to analyze them, as it creates the potential for biased results. I explore the rationale behind this methodological guideline from the standpoint of an error statistical theory of evidence, and I discuss a method of evaluating evidence in some contexts when this predesignation rule has been violated. I illustrate the problem of potential bias, and the method by which it may be addressed, with an example from the (...) search for the top quark. A point in favor of the error statistical theory is its ability, demonstrated here, to explicate such methodological problems and suggest solutions, within the framework of an objective theory of evidence. (shrink)

J. L. Ackrill; VIII*—Aristotle's Definitions of Psuche, Proceedings of the Aristotelian Society, Volume 73, Issue 1, 1 June 1973, Pages 119–134, https://doi.org.

Misconceptions about energy conservation abound due to the gap between physics and secondary school chemistry. This paper surveys this difference and its relevance to the 1690s–2010s Leibnizian argument that mind-body interaction is impossible due to conservation laws. Justifications for energy conservation are partly empirical, such as Joule’s paddle wheel experiment, and partly theoretical, such as Lagrange’s statement in 1811 that energy is conserved if the potential energy does not depend on time. In 1918 Noether generalized results like Lagrange’s and proved (...) a converse: symmetries imply conservation laws and vice versa. Conservation holds if and only if nature is uniform. The rise of field physics during the 1860s–1920s implied that energy is located in particular places and conservation is primordially local: energy cannot disappear in Cambridge and reappear in Lincoln instantaneously or later; neither can it simply disappear in Cambridge or simply appear in Lincoln. A global conservation law can be inferred in some circumstances. Einstein’s General Relativity, which stimulated Noether’s work, is another source of difficulty for conservation laws. As is too rarely realized, the theory admits conserved quantities due to symmetries of the Lagrangian, like other theories. Indeed General Relativity has more symmetries and hence more conserved energies. An argument akin to Leibniz’s finally gets some force. While the mathematics is too advanced for secondary school, the ideas that conservation is tied to uniformities of nature and that energy is in particular places, are accessible. Improved science teaching would serve the truth and enhance the social credibility of science. (shrink)

Research questions in mainstream epistemology often take for granted a cognitive internalist picture of the mind. Perhaps this is unsurprising given the seemingly safe presumptions that knowledge entails belief and that the kind of belief that knowledge entails supervenes exclusively on brainbound cognition. It will be argued here that the most plausible version of the entailment thesis holds just that knowledge entails dispositional belief. However, regardless of whether occurrent belief supervenes only as the cognitive internalist permits, we should reject the (...) idea that dispositional belief supervenes only in cognitive internalist-friendly ways. These observations, taken together, reveal two things: first, that a cognitive internalist picture of the mind is much more dispensable in epistemology than has been assumed and, second, that pursuing questions in extended epistemology need not involve any radical departure from the commitments of more traditional epistemological projects. (shrink)

O objetivo deste ensaio é examinar a proposta de Sandy Goldberg, segundo a qual há divisão de trabalho epistêmico em certos processos de aquisição de conhecimento – ao menos em se tratando de conhecimento testemunhal. Goldberg propõe mostrar a veracidade desta alegação salientando a nossa dependência epistêmica em relação a outros indivíduos, ou mesmo comunidades inteiras. Nós, então, vamos propor o tratamento de um famoso caso tipo-Gettier que, segundo Gilbert Harman, revelaria algumas dimensões sociais do conhecimento. Por fim, nós esperamos (...) tirar algumas lições da explicação oferecida por Goldberg, dentre as quais a mais importante a ser tomada é que, havendo tal divisão de trabalho epistêmico em processos de aquisição de conhecimento, muitas vezes, não são apenas as propriedades epistêmicas do sujeito que determinam a sua posse de conhecimento ou ignorância, de modo que o conhecimento é mais social do que individual em se tratando de uma ampla gama de casos. (shrink)

El objetivo de este artículo es definir la concepción del acto involuntario de Francisco Suárez y mostrarla como un medio que permite comprender y profundizar en su teoría de la acción humana. En esta cuestión, el Doctor Eximio parte de presupuestos elaborados por Tomás de Aquino que amplía y adapta siguiendo sus propias tesis metafísicas y teológicas sobre la relación entre Dios y las creaturas. Mostraremos cómo Suárez vincula el verdadero involuntario con el _simpliciter_, lo forzado, necesario e indeseado, dejando (...) al _secundum quid_ como un acto mixto en el que la libertad y la voluntad, pese a las injerencias externas, no quedan anuladas. Por último, subrayaremos las consecuencias de la definición suareciana de lo involuntario sobre la noción de libertad, haciendo patente que tanto una como otra serían imposibles fuera del marco teórico que él sustenta, caracterizado por la eficiencia humana (y su dependencia de la divinidad) y no por la premoción física. (shrink)

Analogies must be symmetric. If a is like b, then b is like a. So if a has property R, and if R is within the scope of the analogy, then b (probably) has R. However, analogical arguments generally single out, or depend upon, only one of a or b to serve as the basis for the inference. In this respect, analogical arguments are directed by an asymmetry. I defend the importance of this neglected – even when explicitly mentioned – (...) feature in understanding analogical arguments. (shrink)

Ethical consumerism is the thesis that we should let our values determine our consumer purchases. We should purchase items that accord with our values and refrain from buying those that do not. The end goal, for ethical consumerism, is to transform the market through consumer demand. The arm of this movement associated with food choice embraces the slogan “Vote with Your Fork!” As in the more general movement, the idea is that we should let our values dictate our choices. In (...) this paper, I offer a critique of the Vote with Your Fork campaign (hereafter VWYF) that focuses on the agency of individuals. For VWYF to be effective, minimally, individuals must act _intentionally_ when making food choices. In the ideal case, individuals adopt and endorse the values implicit in VWYF and exhibit _autonomous agency_ when they purchase and consume food. The problem, though, is that a number of things can go wrong along the way. I argue that very few of us are in the position to exhibit autonomous agency with respect to our food choices. Because of this, VWYF could very well undermine its own goals. (shrink)

C. A. J. Coady offers to clear up confusion about what terrorism is. His "tactical definition" focuses on terrorist acts as violent attacks upon non-combatants. He discusses what it means to be a non-combatant, considers various philosophical attempts to defend terrorism, and examines the idea of a connection between religion and terrorism.

Even the simplest known living organisms are complex chemical processing systems. But how sophisticated is the behaviour that arises from this? We present a framework in which even bacteria can be identified as capable of representing information in arbitrary signal molecules, to facilitate altering their behaviour to optimise their food supplies, for example. Known asion/Representation theory, this framework makes precise the relationship between physical systems and abstract concepts. Originally developed to answer the question of when a physical system is computing, (...) AR theory naturally extends to the realm of biological systems to bring clarity to questions of computation at the cellular level. (shrink)