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)

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)

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)

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)

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)

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)

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)

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)

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.

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)

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)

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 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.

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.

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

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)

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)

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)

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)

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)

When can a Bayesian investigator select an hypothesis H and design an experiment to make certain that, given the experimental outcome, 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)

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)

This paper (based on joint work with M.J.Schervish and J.B.Kadane) discusses some differences between the received theory of regular conditional distributions, which is the countably additive theory of conditional probability, and a rival theory of conditional probability using the theory of finitely additive probability. The focus of the paper is maximally "improper" conditional probability distributions, where the received theory requires, in effect, that P{a: P(a|a) = 0} = 1. This work builds upon the results of Blackwell and Dubins (1975).

It is a familiar argument that advocates accommodating the so-called paradoxes of decision theory by abandoning the “independence” postulate. After all, if we grant that choice reveals preference, the anomalous choice patterns of the Allais and Ellsberg problems violate postulate P2 of Savage's system. The strategy of making room for new preference patterns by relaxing independence is adopted in each of the following works: Samuelson, Kahneman and Tversky's “Prospect Theory”, Allais and Hagen, Fishburn, Chew and MacCrimmon, McClennen, and in closely (...) argued essays by Machina. (shrink)

This title introduces the concepts of algorithms and sequencing in coding by using relatable real-world examples in the reader's everyday life. Vivid photographs and easy-to-read text aid comprehension for early readers. Features include a table of contents, an infographic, fun facts, Making Connections questions, a glossary, and an index. QR Codes in the book give readers access to book-specific resources to further their learning. Aligned to Common Core Standards and correlated to state standards. Cody Koala is an imprint of Pop!, (...) a division of ABDO. (shrink)

This title introduces the concept of "if this, then that" in coding by using relatable real-world examples. Vivid photographs and easy-to-read text aid comprehension for early readers. Features include an infographic, fun facts, Making Connections questions, a glossary, and an index. QR Codes in the book give readers access to book-specific resources to further their learning.

I will look at and discuss the ideological-subject position of the ‘sympathetic’ slave-owner by employing Žižek ’s specific conception of ideology across two varying slave-narratives. I attempt to uncover how this ideology operates within the social-material reality in the texts Our Nig and Minnie's Sacrifice and the ways that the authors employed tropes in depicting this particular archetypal figure in slave-narratives. These charachter's exhibit an ideology remarkably aligned with Žižek ’s: that a certain non-knowledge of the proper logic of an (...) ideological reality is what sustains it. This suggests not only that such an archetypal figure exists across slave-narratives, but also that they deploy a communal ideology that attempts to conflate unwillingness with inability. They enable the perpetuation of the institution by their unwillingness to reject the economic benefits of slavery, which they conceive of as an inability. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Radicalizing the Local: 60 Linear Miles of Transborder ConflictTeddy Cruz (bio)2008estudio teddy cruzmedium: collage and vinyl wallpaperThe international border between the US and Mexico at the San Diego-Tijuana checkpoint is one of the most trafficked in the world. A 60-linear-mile cross-section—tangential to the border wall—between these two border cities compresses the most dramatic issues currently challenging our normative notions of architecture and urbanism.This transborder “cut” begins 30 miles (...) north of the border, on the periphery of San Diego, and ends 30 miles south of the border. We can find along this section’s trajectory a series of collisions, critical junctures, or conflicts between natural and artificial ecologies, top-down development and bottom-up organization. It is in the midst of many of these metropolitan and territorial sites of conflict where contemporary architectural practice needs to reposition itself.1. Conflict between master-planned gated communities and the natural topography +30 miles / San DiegoTop-down private development has been installing a selfish, oil-hungry sprawl of detached McMansions everywhere, forming massive subdivisions that collide with the natural topography.2. Conflict between large infrastructure and the watershed +28 miles / San DiegoLarge freeway and mall infrastructure runs the length of coastal San Diego, colliding with a natural network of canyons, rivers, and creeks that descend toward the Pacific Ocean.3. Conflict between privatization and everyday life +25 miles / San DiegoThe archipelago of beige tract homes also exacerbates a land use of exclusion, leading to an apartheid of everyday life, as gated communities retreat from the complexities of mixed uses.4. Conflict between military bases and environmental zones +20 miles / San DiegoIronically, the only interruptions along an otherwise continuous sprawl, 30 miles inland from the border, occur as the military bases that dot San Diego’s suburbanization overlap with environmentally protected lands.5. Conflict between the formal and informal +15 miles / San DiegoThe informal densities and economies produced by immigrants yield three-dimensional land use that collides with the one-dimensional zoning that defines suburban tract subdivisions. [End Page 107]6. Conflict between two border cities 0 miles / San Diego-TijuanaThis territorial conflict is currently dramatized by the hardening of the border wall that divides these cities, incrementally transforming San Diego into the world’s largest gated community.7. Conflict between the natural and political +0.5 miles / TijuanaAs the large infrastructure of the Tijuana River clashes with the border wall, a faint yellow line is inscribed on the dry river’s concrete channel to indicate the trajectory of the border. The border checkpoint is exactly at this intersection.8. Conflict between the informal and natural ecologies-10 miles / TijuanaAdjacent to the checkpoint we can find many slums crashing against the border. The wall acts as a powerful dam, containing the density of Tijuana and preventing it from contaminating San Diego’s picturesque sprawl.9. Conflict between factories and emergency housing-15 miles / TijuanaThese American-style, mini-master-planned communities are intertwined with a series of informal communities or slums, and both provide maquiladora factory enclaves with cheap labor.10. Conflict between density and sprawl-20 miles / TijuanaThousands of miniaturized replicas of typical suburban Southern California McMansions are now scattered around the periphery of Tijuana. In recent years, dwellers have radically transformed them into socioeconomic microengines.11. Conflict between two horizons-30 miles / TijuanaAs we reach the sea on the Mexican side, we witness the most dramatic of all territorial collisions across this 60-mile-section of local conflict. Here, the border metal fence finally sinks into the Pacific Ocean. [End Page 108] Click for larger view View full resolution[End Page c1] Click for larger view View full resolution[End Page 2] Click for larger view View full resolution[End Page 12] Click for larger view View full resolution[End Page 22] Click for larger view View full resolution[End Page 32] Click for larger view View full resolution[End Page 42] Click for larger view View full resolution[End Page 52] Click for larger view View full resolution[End Page 62] Click for larger view View full resolution[End Page... (shrink)