This eighth book of the author on gambling math presents in accessible terms the cold mathematics behind the sparkling slot machines, either physical or virtual. It contains all the mathematical facts grounding the configuration, functionality, outcome, and profits of the slot games. Therefore, it is not a so-called how-to-win book, but a complete, rigorous mathematical guide for the slot player and also for game producers, being unique in this respect. As it is primarily addressed to the slot player, its goal (...) is to present practical applications of the mathematical models of slot games, in order to provide numerical results that a player can use as criteria for gaming decisions or just as information for any slot game and any predicted winning event. These results are focused on probability and expected value, these being the most important parameters for decisional criteria in slots. The book is packed with plenty of figures, tables, and formulas. The content is organized so that readers can skip the theoretical parts and go picking the practical results (numerical, in tables of values where possible, or ready-to-compute formulas) for the desired situation. The practical results are gathered in the last chapter, titled "Practical Applications and Numerical Results," the largest part of the book, for the most popular categories of slot machines, namely with 3, 5, 9, and 16 reels. Any other category of slot games is covered in the theoretical part of the book, where the general formulas apply not only to existing slot games, but also to possible future slot games of any design and configuration. The author does not just throw the slot mathematics to the audience and run away, but offers an ultimate practical contribution with the chapter "How to estimate the number of stops and the symbol distribution on a reel", a surprise for both players and producers, where one can see that mathematics provides players with some statistical methods as well as methods based on physical measurements for retrieving these missing data. Having these data along with the mathematical results of this book, anyone can generate the PAR sheet of any slot machine. In the last decade, mathematics has been taken more and more seriously into account in gaming, as being the essence that governs the games of chance and the only rigorous tool providing information on optimal play, where possible. For the popular game of slots, mathematics already fulfilled its duty by providing all the data that it can provide and that cannot be found on the display of the slot machines - it is all here in this book. (shrink)

This item was published as 'Appendix 3: An Implication of the k-option Condorcet jury mechanism for the probability of cycles' in List and Goodin (2001) http://eprints.lse.ac.uk/705/. Standard results suggest that the probability of cycles should increase as the number of options increases and also as the number of individuals increases. These results are, however, premised on a so-called "impartial culture" assumption: any logically possible preference ordering is assumed to be as likely to be held by an individual as (...) any other. The present chapter shows, in the three-option case, that given suitably systematic, however slight, deviations from an impartial culture situation, the probability of a cycle converges either to zero (more typically) or to one (less typically) as the number of individuals increases. (shrink)

Taking organs from dead people seems, prima facie, to raise fewer ethical complications than taking organs from other sources. There are, however, serious ethical problems in taking organs from the dead unless there is premortem evidence that this is what the deceased would have wanted, or at least, not have objected to. In this paper we will look at a “strong” opting out policy as proposed by John Harris. We will argue that people can be harmed after their death (...) and that the posthumous removal of organs against their expressed wishes is one form that such harm might take. We also argue that Harris’s claim that we show “equality of concern” between the donor and recipient requires too much. (shrink)

Stanovich & West continue a history of norm-setting that began with deference to reasonable people's opinions, followed by adherence to probability theorems. They return to deference to reasonable people, with aptitude test performance substituting for reasonableness. This allows them to select independently among competing theories, but defines reasoning circularly in terms of aptitude, while aptitude is measured using reasoning.

We studied retrieval-induced forgetting for past or future autobiographical experiences. In the study phase, participants were given cues to remember past autobiographical experiences or to think about experiences that may occur in the future. In both conditions, half of the experiences were positive and half negative. In the retrieval-practice phase, for past and future experiences, participants retrieved either half of the positive or negative experiences using cued recall, or capitals of the world. Retrieval practice produced recall (...) facilitation and enhanced memory for the practised positive and negative past and future experiences. While retrieval practice on positive experiences did not impair the recall of other positive experiences, we found inhibition for negative past and future experiences when participants practised negative experiences. Furthermore, retrieval practice on positive future experiences inhibited negative future experiences. These positivity biases for autobiographical memory may have practical implications for treatment of emotional disorders. (shrink)

Contrary to what is stated in Lemma 7.1 of [8], it is shown that some Boolean algebras of finitary logic admit finitely additive probabilities that are not σ-additive. Consequences of Lemma 7.1 are reconsidered. The concept of a C-σ-additive probability on B (where B and C are Boolean algebras, and $\mathscr{B} \subseteq \mathscr{C}$ ) is introduced, and a generalization of Hahn's extension theorem is proved. This and other results are employed to show that every S̄(L)-σ-additive probability (...) on s̄(L) can be extended (uniquely, under some conditions) to a σ-additive probability on S̄(L), where L belongs to a quite extensive family of first order languages, and S̄(L) and s̄(L) are, respectively, the Boolean algebras of sentences and quantifier free sentences of L. (shrink)

In hisStudy of War, Q. Wright considered a model for the probability of warP during a period ofn crises, and proposed the equationP=1– n, wherep is the probability of war escalating at each individual crisis. This probability measure was formally derived recently by Cioffi -Revilla, using the general theory of political reliability and an interpretation of the n-crises problem as a branching process. Two new, alternate solutions are presented here, one using D. Bernoulli''s St. Petersburg Paradox as (...) an analogue, the other based on the logic of conditional probabilities. Analysis shows that, while Wright''s solution is robust with regard to the general overall behavior ofp andn, some significant qualitative and quantitative differences emerge from the alternative solutions. In particular,P converges to 1 only in a special case and not generally. (shrink)

The particle internal clock conjectured by de Broglie in 1924 was investigated in a channeling experiment using a beam of ∼80 MeV electrons aligned along the 〈110〉 direction of a 1 μm thick silicon crystal. Some of the electrons undergo a rosette motion, in which they interact with a single atomic row. When the electron energy is finely varied, the rate of electron transmission at 0° shows a 8% dip within 0.5% of the resonance energy, 80.874 MeV, for which (...) the frequency of atomic collisions matches the electron’s internal clock frequency. A model is presented to show the compatibility of our data with the de Broglie hypothesis. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:David Hume and the Probability of Miracles Barry Gower 1. Introduction Oflate there have been published several discussions ofDavid Hume's famous essay "Of Miracles" which attempt to make precise the reasoning it contains. This, it turns out, requires the use of certain mathematical rules and theorems of the probability calculus which were unknown to Hume or, indeed, to anyone else when the essay was first published. It (...) is suggested, in particular, that the claims he made can best be understood in the light of a theorem of the probability calculus which we now name after a celebrated eighteenth century probabilist, Thomas Bayes. However, the so-called "Bayesian" interpretation of the argument against miracles misrepresents Hume's reasoning in that the manner in which he expressed his thinking does not fit such an interpretation. Moreover, this error needs to be rectified, not just because it involves a mistaken view about the past but, more importantly, because it obscures the legacy of a different mode of thinking evident in Hume's writing about probabilistic inference which deserves to be recovered. Our thinkingisimpoverishedifcertain presumptions aboutprobability become so entrenched that we have great difficulty in seeing them as anything other than obvious. By imputing them to Hume we overlook their contestability and so lose an opportunity to recapture an alternative way of understanding probabilistic reasoning. As is well known, the argument against miracles, though not published until 1748, had been worked out some twelve or thirteen years earlier during Hume's stay at the Jesuit college of La Fleche, where he wrote most of A Treatise of Human Nature. A chapter entitled "Reasonings concerning Miracles" had been written but, at the last moment, it was suppressed for fear that such an explicit attack on religion would give offence and thus deflect attention from the book's main philosophical aim which was to put an end to controversy. On the other hand, Thomas Bayes's famous memoir on probability was not published until 1764, andit is unlikely that Hume knew ofits existence until Richard Price mentionedit, though without identifyingits author, in an elaborate mathematical footnote to a dissertation containing remarks on the probability of miracles, published in 1767. Had Hume taken the trouble to follow up this reference, he would almost certainly Volume XVI Number 1 17 BARRY GOWER have been either baffled by its mathematics or discouraged by its lack of practical advice. That, at least, seems to have been the reaction of Hume's contemporaries, for apart from Price none of them seems to have paid any attention to the memoir. Even today, when anyone with the slightest acquaintance with probability can recite a version of Bayes's theorem, it is hard to follow the reasoning of the memoir and to appreciate the significance of the ideas it contains. As an historian of statistics has recently said, "Bayes's contemporaries were stymied by the work, and modern readers unwilling to devote many hours to it are likely to gain only a superficial understanding ofit." One paradoxical feature of attributing Bayesianism to Hume concerns the role of Richard Price. His dissertation, which had, it seems, been written some years before it was published — perhaps in the early 1750's — is sharply critical of Hume's argument against miracles. Yet it was Price himself who was responsible for the posthumous publication of Bayes's memoir, and his introduction and commentary clearly express approval of its methods and conclusions. We are, then, faced with the suggestion that Hume, not having heard of Bayes, was applying Bayesian ideas about "inverse" inference to miraculous events, whereas Price, who was not only familiar with but also endorsed Bayes's ideas, preferred a quite different approach to reasoning about miracles and about the credibility of testimony generally. Can Hume really be described as a "better intuitive Bayesian" than Price? Before embracing such aparadoxical conclusion we should consider whether it is really justified by what Hume said about the probability ofmiracles. First, though, some attention needs to be paid to a way ofthinking about probable arguments which does not conform to convention, and which implies a non-Bayesian interpretation of the question about miracles. 2. Jakob Bernoulli and the Combination... (shrink)

Slot machines gained a high popularity despite a specific element that could limit their appeal: non-transparency with respect to mathematical parameters. The PAR sheets, exposing the parameters of the design of slot machines and probabilities associated with the winning combinations are kept secret by game producers, and the lack of data regarding the configuration of a machine prevents people from computing probabilities and other mathematical indicators. In this article, I argue that there is no rational justification for this secrecy (...) by giving two reasons, one psychological and the other mathematical. For the latter, I show that mathematics provides us with some statistical methods of retrieving the missing data, which are essential for the numerical probability computations in slots. The slots case raises the problem of the exposure of the parametric configuration and mathematical facts of any game of chance as an ethical obligation. (shrink)

A recurring theme in discussions about the uncertainties of belief is their connection with the uncertainties of chance. Economists, broadly speaking, fall into two groups on this issue. One holds that beliefs can only be taken to correspond to point probabilities in situations that approximate games of chance. The other holds that beliefs should be treated as point probabilities, entering economics via decision theory and emerging as the parameters of consistent choice. I shall call these the traditional view and (...) the Bayesian view respectively. (shrink)

The problems of access—retrieving linguistic structure from some mental grammar —and disambiguation—choosing among these structures to correctly parse ambiguous linguistic input—are fundamental to language understanding. The literature abounds with psychological results on lexical access, the access of idioms, syntactic rule access, parsing preferences, syntactic disambiguation, and the processing of garden‐path sentences. Unfortunately, it has been difficult to combine models which account for these results to build a general, uniform model of access and disambiguation at the lexical, idiomatic, and (...) syntactic levels. For example, psycholinguistic theories of lexical access and idiom access and parsing theories of syntactic rule access have almost no commonality in methodology or coverage of psycholinguistic data. This article presents a single probabilistic algorithm which models both the access and disambiguation of linguistic knowledge. The algorithm is based on a parallel parser which ranks constructions for access, and interpretations for disambiguation, by their conditional probability. Low‐ranked constructions and interpretations are pruned through beam‐search; this pruning accounts, among other things, for the garden‐path effect. I show that this motivated probabilistic treatment accounts for a wide variety of psycholinguistic results, arguing for a more uniform representation of linguistic knowledge and for the use of probabilistically‐enriched grammars and interpreters as models of human knowledge of and processing of language. (shrink)

Our goal was to test the efficiency and accuracy of a complementary morning report, after recall cue, of an experience made and first described during the night. Twenty participants were awakened 10 min after the onset of the second REM sleep. Upon awakening, on one night they described the dream they just had and on the other night they were presented a 4-min video, then had to describe it. A new description requested in the morning after a recall cue (...) yielded an important amount of new information both for the film and the dreams, and for the film, where the accuracy could be checked, 86% of this new information was accurate. Some aspects of the results pointed to an effect of hypermnesia. In conclusion, the morning additional information after recall cue stems from a good access to the memory of the night experience. (shrink)

I argue against preservationism, the epistemic claim that memories can at most preserve knowledge generated by other basic types of sources. I show how memories can and do generate knowledge that is irreducible to other basic sources of knowledge. In some epistemic contexts, memories are primary basic sources of knowledge; they can generate knowledge by themselves or with trivial assistance from other types of basic sources of knowledge. I outline an ontology of information transmission from events (...) to memory as an alternative to causal theories of memory. I derive from information theory a concept of reliability of memories as the ratio of retrieved information to transmitted information. I distinguish the generation of knowledge from reliable memories from its generation from unreliable memories. Reliable memories can generate new knowledge by forming together narratives and via colligation. Coherent, even unreliable, memories can generate knowledge if they are epistemically independent of each other and the prior probability of the knowledge they generate is sufficiently low or high. Ascertaining the epistemic independence of memories and eliminating possible confounders may be achieved through the generation of knowledge from independent memories in different minds, when memories are primary basic sources of knowledge and the testimonies that report them are trivial. (shrink)

We present a comprehensive empirical evaluation of the ACT‐R–based model of sentence processing developed by Lewis and Vasishth (2005) (LV05). The predictions of the model are compared with the results of a recent meta‐analysis of published reading studies on retrieval interference in reflexive‐/reciprocal‐antecedent and subject–verb dependencies (Jäger, Engelmann, & Vasishth, 2017). The comparison shows that the model has only partial success in explaining the data; and we propose that its prediction space is restricted by oversimplifying assumptions. We then implement (...) a revised model that takes into account differences between individual experimental designs in terms of the prominence of the target and the distractor in memory‐ and context‐dependent cue‐feature associations. The predictions of the original and the revised model are quantitatively compared with the results of the meta‐analysis. Our simulations show that, compared to the original LV05 model, the revised model accounts for the data better. The results suggest that effects of prominence and variable cue‐feature associations need to be considered in the interpretation of existing empirical results and in the design and planning of future experiments. With regard to retrieval interference in sentence processing and to the broader field of psycholinguistic studies, we conclude that well‐specified models in tandem with high‐powered experiments are needed in order to uncover the underlying cognitive processes. (shrink)

The epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object’s weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks (...) what probabilities are not determined in this way—these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the “problem of the priors.”. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Creativity and the Context of NoveltyPete A. Y. GunterAn article might have many virtues: breadth, novel perspective, conceptual background, to name a few. The strongest virtue of Professor Crosby's article is in the sharpening of arguments. In both his book, Novelty, and in the present article, he sharpens arguments which surround the concepts of determinism, novelty, and freedom. The end result is increased clarity; it is also, or so (...) it seems to this writer, the increased plausibility of arguments for novelty and indeterminism.I.It has often been argued that strict determinism (henceforth, determinism) has paradoxical implications. Thus William James protests that it leads inescapably to a "Block Universe": one in which everything is given at once—past, present, and future. In such a world, Crosby points out, nothing can happen at all. But Crosby adds to this a second, crucial point. If determinism is true, he insists, we must give up not only the belief that anything actually happens but also the commonsense belief that cause precedes effect. This result of strict determinism has not been stressed by either its opponents or its proponents.Quite probably, those who have argued for determinism have not reflected on the unpalatable idea that cause does not precede effect. Our ordinary experience exhibits the billiard ball falling into the side pocket after we have hit it with the cue stick. If we dive into a swimming pool, we enter the water dry and then become wet. And, the splash occurs after we separate ourselves from the board. Determinism, however useful in helping us to bring order out of our experience, radically conflicts with fundamental features in nature that lead us to think and examine cause and effect to begin with.There is another respect in which Crosby sharpens our assumptions. Ordinarily [End Page 60] we think of novelty and causality as contradictories. In fact, Crosby insists, they are correlatives. Neither is reducible to the other, nor is either alternative prior to the other. The two together constitute a primordial feature of the universe, such that where in some contexts indeterminism is reduced to a minimum, perhaps an infinitesimal, in others (presumably those in which creativity plays a major role) causality is reduced to a minimum and novelty predominates. Hence philosophy is not saddled with the task of trying to show how novelty can possibly find a place in an exclusively deterministic world. Novelty and determinism are, from the beginning, both present throughout.This viewpoint, if accepted, would obviate any attempt to graft indeterminism into a deterministic universe, so to speak, from without. It would also tend to dissolve the dualisms foisted on us by Descartes and, in another way, by Kant, which radically separate mind (or free will) from matter (or, in Kant's case, "phenomena") on the grounds that the former contains novelty and the latter does not. In Crosby's view some element of novelty is already present in matter. Equally, in his view, "mind" in many, perhaps most, contexts contains a strong element of determinism.There is still a further way of taking Crosby's arguments. It is this. Strict determinists must, he shows, hold that the universe is timeless. Past, present, and future coexist and, literally, nothing happens. It then follows that if one accepts the reality of motion, growth, and dissolution in the world, then in doing so one has decreed the falsehood of strict determinism. It does not (and on Crosby's grounds cannot) follow that there is no determinism in nature. There must, on his grounds, be degrees of causal determinism. But there must also be real novelty. One thus has a transcendental argument, beginning from the simple acceptance of real mobility in the world. That is, "If there is real transformation in the world, then strict determinism must be wrong. There is real transformation in the world. Therefore strict determinism must be wrong." This would make life very hard for the strict determinist, for whom the slightest lapse into a commonsense acceptance of the restless mobility of nature entails the denial of his or her basic thesis.A further argument of Crosby's, however, gives me difficulties. He argues that strict determinism... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Affect Attunement in the Caregiver-Infant Relationship and Across SpeciesExpanding the Ethical Scope of ErosCynthia WillettCompelling glimpses into the ethical capacities of our animal kin reveal new possibilities for ethical relationships encompassing humans with other animal species. Consider the remarkable report of a female bonobo in a British zoo who assists a bird found in her cage by retrieving the fallen bird, and spreading its wings so that (...) this fellow creature might fly away to its freedom. Or the report of a cat in a nursing home who curls up around dying elderly patients, and remains steadily by their side as they, unbeknownst to the medical personnel, pass away.1 Or of a sacred moment of silence by a stream for baboons in East Africa.2 Or of the ethics that spontaneously emerges among wolves at play.3 On the basis of extensive studies, biologist Frans de Waal argues that such anecdotes are far from rare, and that some core elements of moral understanding and compassion occur among a significant range of nonhuman as well as the human animal species. Apes, monkeys, and perhaps all nonhuman animals fail to display a distinctly human capacity for abstract moral reasoning. As de Waal (2006) remarks, it is difficult to tell (173–75). But our furry and feathery kin do without a doubt demonstrate rich elements of ethical response, and they often enough extend their moral concern to creatures beyond their own species. Of course, they will also bite each other’s heads off or eat their own young as well. But this is just to say that animals are neither natural [End Page 111] innocents nor savage brutes. Like us, they belong to what post-Nietzschean philosophers might frame, somewhat ironically, as a postlapsarian world of good and evil.What kind of philosophical approach could account for these postlapsarian genealogies of ethics? Biologists, primatologists, and anthropologists are drawing upon investigations of prosocial behavior to remap the boundaries of ethics, as for example in Isabelle Stengers’s call for cosmopolitical ecologies of relationships (2010, 33). Such a cosmopolitics aims to encompass our kin and kind from diverse species within the ethical boundaries of common worlds. Donna Haraway discovers an opening for Stengers’s ecology of relationships in the intimate encounters among co-evolving species, especially those she calls companion species (2008, 83). She argues, following Derrida, that the abstract reasoning processes of Stoic and Kantian cosmopolitan ethics remain closed to the participation of nonhuman animals as anything more than dependents, failing to observe the ways in which they act as companions, if not moral subjects. But then, what normative force might bind together an ethically attuned biosocial sphere that we as humans co-inhabit with other animal species?To explore this question, this essay takes its cues from well-established research on the responsive, preverbal connection of the human infant and adult caregiver (Bateson 1979; Trevarthen 1984; Stern 1985, 2010; Gibbs 2001, 2010; Hansen 2004; Anderson 2006; Papoulias and Callard 2010; Willett 1995, 2001). To this research we can add new animal studies (Smuts 1999, 2001; Fudge 2002; de Waal 2006, 2009; Bekoff 2007; Molnar 2008; Haraway 2008). These animal studies provide a basis for extending an “ethics of eros” with roots in Luce Irigaray, Michel Foucault, Enrique Dussel, Africana feminism, Freudo-Marxist critical theory, and Plato (for discussions of this tradition, see Bergoffen 1997; Huffer 2009; Willett 2001)—but reconfigured in terms of social bonds across multiple animal species. In this tradition of ethics, the lack of a cognitive-based moral subjectivity that can translate into human terms does not consign nonhuman species to a mute moral status. On the contrary, some more primordial basis for relationship and meaning may weave thin but substantial threads of a postmoral ethics across regions of the biosphere.Given the diverse modes of subjectivity among animal species, and even the lack of what we call a moral subject altogether in many species, neither ordinary modes of empathy nor of moral understanding go very far in forging multispecies social bonds. For this reason, we turn to research on “the attunement of affects” in the infant-caregiver relationship (Stern 1985). As we shall see, this... (shrink)

Recognizing that probability (the Greek doxa) was understood in pre-modern theories as the polar opposite of certainty (episteme), the author of this study elaborates the forms which these polar opposites have taken in some twentieth century writers and then, in greater detail, in the writings of Thomas Aquinas. Profiting from subsequent more sophisticated theories of probability, he examines how Aquinas’s judgments about everything from God to gossip depend on schematizations of the polarity between the systematic and the (...) non-systematic: revelation/reason, science/opinion, saints/philosophers, Aristotle/others. Post-medieval developments have provided the means to discern within Thomas’s thought both a logical theory and a kind of relative frequency theory of probability. The former depends on Aristotle’s theory of demonstration, the latter on his theory of an orderly cosmos; but each as used by Thomas lead to convictions that are sometimes naive, sometimes amusing or even terrifying. (shrink)

In this article I consider five anonymous quotations in Stephanus of Byzantium. The first is very probably an overlooked fragment of early mythography. The other four are much less likely to be early, but theoretically could be and are included for the sake of completeness.

Charles Sanders Peirce wrote the article “The probability of induction” in 1878. It was the fourth article of the series “Illustrations of the Logic of Science” which comprised a total of six articles. According to Peirce, to get a clear idea of the conception of probability, one has ‘to consider what real and sensible difference there is between one degree of probability and another.’ He endorsed what John Venn had called the ‘materialistic view’ of the subject, namely (...) that probability is the proportion of times in which an occurrence of one kind is accompanied by an occurrence of another kind. On the other hand, Peirce recognized the existence of a different interpretation of probability, which was termed by Venn the ‘conceptualistic view’, namely the degree of belief that ought to be attached to a proposition. Peirce’s intent on writing this article seems to be to inquire about the claims of the conceptualists concerning the problem of induction. After reasoning on some examples, he concluded on the impossibility of assigning probability for induction. We show here that the arguments advanced in his article are not sufficient to support such conclusion. Peirce’s thoughts on the probability of induction surely may have influenced statisticians and research scientists of the 20th century in shaping data analysis. (shrink)

According to libertarianism about free will, at least some of the choices we make are free and undetermined. Many libertarians also accept the thesis that, before we make an undetermined choice, there is a nontrivial objective probability that we will make that choice. In the literature on free will, the ascription of objective probabilities is sometimes justified via an “Argument from Motivation,” which adverts to the fact that typically, in situations of choice, we are more motivated to choose (...) some options over others. In this paper, I will examine this argument and I will argue that it is unsound, as one of its premises is at odds with a widely accepted principle governing the evolution of objective probabilities over time. (shrink)

Memory is a single word that refers to a complex and fascinating set of abilities which people and other animals possess that enables them to learn from experience and retain what they learn. In memory, an experience affects the nervous system, leaves a residue or trace, and changes later behavior. Types of memory are tremendously varied; so, too, are the techniques used in cognitive science to investigate them. The aim of the present chapter is to give an overall sense (...) of types of memory as well as of techniques used in the experimental study of memory. The process of remembering will be broken up into two main components: encoding and retrieval. We shall then discuss the factors which determine the effectiveness of each component and some of the ways in which memory both succeeds and fails. (shrink)

In his essay on 'Broad on Induction and Probability' (first published in 1959, reprinted in this volume), Professor G. H. von Wright writes: "If Broad's writings on induction have remained less known than some of his other contributions to philosophy . . . , one reason for this is that Broad never has published a book on the subject. It is very much to be hoped that, for the benefit of future students, Broad's chief papers on induction (...) and probability will be collected in a single volume . . . . " The present volume attempts to perform this service to future students of induction and probability. The suggestion of publishing a volume of this kind in Synthese Library was first made by Professor Donald Davidson, one of the editors of the Library, and was partly prompted by Professor von Wright's statement. In carrying out this suggestion, the editors of Synthese Library have had the generous support of Professor Broad who has among other things supplied a new Addendum to 'The Principles of Problematic Induction' and corrected a number of misprints found in the first printings of this paper. The editors gratefully acknow ledge Professor Broad's help and encouragement. A bibliography of Professor Broad's writings (up to 1959) has been compiled by Dr. C. Lewy and has appeared in P. A. Schilpp, editor, The Philosophy of C. D. Broad (The Library of Living Philosophers), pp. 833-852. (shrink)

Luminance and color are strong and self-sufficient cues to pictorial depth in visual scenes and images. The present study investigates the conditions Under which luminance or color either strengthens or overrides geometric depth cues. We investigated how luminance contrasts associated with color contrast interact with relative height in the visual field, partial occlusion, and interposition in determining the probability that a given figure is perceived as ‘‘nearer’’ than another. Latencies of ‘‘near’’ responses were analyzed to test for (...) effects of attentional selection. Figures in a pair were supported by luminance contrast or isoluminant color contrast and combined with one of the three geometric cues. The results of Experiment 1 show that luminance contrasts associated with hue, when it does not interact with other hues, produces the same effects as achromatic luminance contrasts: The probability of‘‘near’’ increases with luminance contrast while the latencies for ‘‘near’’ responses decrease. Partial occlusion is found to be a strong enough pictorial cue to support a weaker red luminance contrast. Interposition cues lose out against cues of spatial position and partial occlusion. The results of Experiment 2, with isoluminant displays of varying color contrast, reveal that red color contrast on a light background supported by any of the three geometric cues wins over green or white supported by any of the three geometric cues. On a dark background, red color contrast supported by the interposition cue loses out against green or white color contrast supported by partial occlusion. These findings reveal that color is not an independent depth cue, but is strongly influenced by luminance contrast and stimulus geometry. Systematically shorter response latencies for stronger ‘‘near’’ percepts demonstrate that selective visual attention reliably detects the most likely depth cue combination in a given configuration. (shrink)

The Protein Ontology (PRO) web resource provides an integrative framework for protein-centric exploration and enables specific and precise annotation of proteins and protein complexes based on PRO. Functionalities include: browsing, searching and retrieving, terms, displaying selected terms in OBO or OWL format, and supporting URIs. In addition, the PRO website offers multiple ways for the user to request, submit, or modify terms and/or annotation. We will demonstrate the use of these tools for protein research and annotation.

Some philosophers have claimed that it is meaningless or paradoxical to consider the probability of a probability. Others have however argued that second-order probabilities do not pose any particular problem. We side with the latter group. On condition that the relevant distinctions are taken into account, second-order probabilities can be shown to be perfectly consistent. May the same be said of an infinite hierarchy of higher-order probabilities? Is it consistent to speak of a probability of a (...) probability, and of a probability of a probability of a probability, and so on, {\em ad infinitum}? We argue that it is, for it can be shown that there exists an infinite system of probabilities that has a model. In particular, we define a regress of higher-order probabilities that leads to a convergent series which determines an infinite-order probability value. We demonstrate the consistency of the regress by constructing a model based on coin-making machines. (shrink)

This article outlines a theory of naive probability. According to the theory, individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an extensional way: They construct mental models of what is true in the various possibilities. Each model represents an equiprobable alternative unless individuals have beliefs to the contrary, in which case some models will have higher probabilities than others. The probability of an event depends on the proportion of models (...) in which it occurs. The theory predicts several phenomena of reasoning about absolute probabilities, including typical biases. It correctly predicts certain cognitive illusions in inferences about relative probabilities. It accommodates reasoning based on numerical premises, and it explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem. Finally, it dispels some common misconceptions of probabilistic reasoning. (shrink)

Two classes of account have been proposed to explain the memory processes subserving the processing of reflexive-antecedent dependencies. Structure-based accounts assume that the retrieval of the antecedent is guided by syntactic tree-configurational information without considering other kinds of information such as gender marking in the case of English reflexives. By contrast, unconstrained cue-based retrieval assumes that all available information is used for retrieving the antecedent. Similarity-based interference effects from structurally illicit distractors which match a non-structural (...) class='Hi'>retrieval cue have been interpreted as evidence favoring the unconstrained cue-based retrieval account since cue-based retrieval interference from structurally illicit distractors is incompatible with the structure-based account. However, it has been argued that the observed effects do not necessarily reflect interference occurring at the moment of retrieval but might equally well be accounted for by interference occurring already at the stage of encoding or maintaining the antecedent in memory, in which case they cannot be taken as evidence against the structure-based account. We present three experiments (self-paced reading and eye-tracking) on German reflexives and Swedish reflexive and pronominal possessives in which we pit the predictions of encoding interference and cue-based retrieval interference against each other. We could not find any indication that encoding interference affects the processing ease of the reflexive-antecedent dependency formation. Thus, there is no evidence that encoding interference might be the explanation for the interference effects observed in previous work. We therefore conclude that invoking encoding interference may not be a plausible way to reconcile interference effects with a structure-based account of reflexive processing. (shrink)

A. J. Ayer was one of the foremost analytical philosophers of the twentieth century, and was known as a brilliant and engaging speaker. In essays based on his influential Dewey Lectures, Ayer addresses some of the most critical and controversial questions in epistemology and the philosophy of science, examining the nature of inductive reasoning and grappling with the issues that most concerned him as a philosopher. This edition contains revised and expanded versions of the lectures and two additional essays. (...) Ayer begins by considering Hume's formulation of the problem of induction and then explores the inferences on which we base our beliefs in factual matters. In other essays, he defines the three kinds of probability that inform inductive reasoning and examines the various criteria for verifiability and falsifiability. In his extensive introduction, Graham Macdonald discusses the arguments in _Probability and Evidence_, how they relate to Ayer's other works, and their influence in contemporary philosophy. He also provides a brief biographical sketch of Ayer, and includes a bibliography of works about and in response to _Probability and Evidence_. (shrink)

Norms—that is, specifications of what we ought to do—play a critical role in the study of informal argumentation, as they do in studies of judgment, decision-making and reasoning more generally. Specifically, they guide a recurring theme: are people rational? Though rules and standards have been central to the study of reasoning, and behavior more generally, there has been little discussion within psychology about why (or indeed if) they should be considered normative despite the considerable philosophical literature that bears on this (...) topic. In the current paper, we ask what makes something a norm, with consideration both of norms in general and a specific example: norms for informal argumentation. We conclude that it is both possible and desirable to invoke norms for rational argument, and that a Bayesian approach provides solid normative principles with which to do so. (shrink)

Some propositions add more information to bodies of propositions than do others. We start with intuitive considerations on qualitative comparisons of information added . Central to these are considerations bearing on conjunctions and on negations. We find that we can discern two distinct, incompatible, notions of information added. From the comparative notions we pass to quantitative measurement of information added. In this we borrow heavily from the literature on quantitative representations of qualitative, comparative conditional probability. We look at (...) two ways to obtain a quantitative conception of information added. One, the most direct, mirrors Bernard Koopman’s construction of conditional probability: by making a strong structural assumption, it leads to a measure that is, transparently, some function of a function P which is, formally, an assignment of conditional probability (in fact, a Popper function). P reverses the information added order and mislocates the natural zero of the scale so some transformation of this scale is needed but the derivation of P falls out so readily that no particular transformation suggests itself. The Cox–Good–Aczél method assumes the existence of a quantitative measure matching the qualitative relation, and builds on the structural constraints to obtain a measure of information that can be rescaled as, formally, an assignment of conditional probability. A classical result of Cantor’s, subsequently strengthened by Debreu, goes some way towards justifying the assumption of the existence of a quantitative scale. What the two approaches give us is a pointer towards a novel interpretation of probability as a rescaling of a measure of information added. (shrink)

Building on a model first proposed by Gary Johnson, it is hypothesized that religious institutions demanding celibacy and other forms of altruism from members take advantage of human predispositions to favor genetic relatives in order to maintain and reinforce these desired behaviors in non-kin settings. This is accomplished through the institutionalization of practices to manipulate cues through which such relatives are regularly identified. These cues are association, phenotypic similarity, and the use of kin terms. In addition, the (...) age of recruits and their contact with actual kin are factors that relate to kinship recognition and that are similarly manipulated by institutions in order to reinforce altruistic behavior directed toward non-kin. Support for this set of predictions is presented from historical and ethnographic sources on monastic life in Buddhism, Christianity, and Hinduism, as well as Islamic dervish groups, the Essenes, Shakers, and others. Potential implications of the model for understanding the development of religious institutions are preliminarily explored by reviewing Joachim Wach's model of religious developmental stages as well as some of the literature on the relationship between individualism and communalism in incipient religious organizations, in light of the kin-cue manipulation model. (shrink)

Some studies have reported that, under some circumstances, participants sometimes reject the truth of conditional premises and give incorrect uncertain conclusions to MP and MT, despite the standard instructions to assume the truth of the premises. Instructions that emphasise the logical nature of the task, on the other hand, increase the number of valid conclusions to these two inferences. In this paper, we examine two possible explanations for the influence of instructions on the production of valid conclusions: (...) (1) instructions trigger a logical mode of thinking that is appropriate for the task to be solved, and (2) instructions affect the way that retrieved information is used when constructing a mental representation of the premises. In order to compare these two hypothesis, we used conditional causal relations having either many or few disabling conditions (i.e. cases of P and not-Q) and presented them in four different instructional conditions. When presented with the standard instructions to suppose the premises to be true, MP and MT inferences show a relatively low percentage of valid conclusions. However, when the logical nature of the task and the necessity to assume the truth of the premises are emphasised, the number of valid conclusions greatly increases. Also, if disabling conditions are made explicit or generated before the presentation of these logical instructions, the performance on MP and MT is lower than when only the logical instructions are presented. Finally, the instructions had no effect on AC and DA. From these results, we concluded that the instructions had an effect on the use of retrieved information rather than on inducing different modes of thinking. (shrink)

Evolutionary theory (ET) is teeming with probabilities. Probabilities exist at all levels: the level of mutation, the level of microevolution, and the level of macroevolution. This uncontroversial claim raises a number of contentious issues. For example, is the evolutionary process (as opposed to the theory) indeterministic, or is it deterministic? Philosophers of biology have taken different sides on this issue. Millstein (1997) has argued that we are not currently able answer this question, and that even scientific realists ought to remain (...) agnostic concerning the determinism or indeterminism of evolutionary processes. If this argument is correct, it suggests that, whatever we take probabilities in ET to be, they must be consistent with either determinism or indeterminism. This raises some interesting philosophical questions: How should we understand the probabilities used in ET? In other words, what is meant by saying that a certain evolutionary change is more or less probable? Which interpretation of probability is the most appropriate for ET? I argue that the probabilities used in ET are objective in a realist sense, if not in an indeterministic sense. Furthermore, there are a number of interpretations of probability that are objective and would be consistent with ET under determinism or indeterminism. However, I argue that evolutionary probabilities are best understood as propensities of population-level kinds. (shrink)

This paper generalises an argument for probabilism due to Lindley [9]. I extend the argument to a number of non-classical logical settings whose truth-values, seen here as ideal aims for belief, are in the set $\{0,1\}$, and where logical consequence $\models $ is given the “no-drop” characterization. First I will show that, in each of these settings, an agent’s credence can only avoid accuracy-domination if its canonical transform is a (possibly non-classical) probability function. In other words, if an (...) agent values accuracy as the fundamental epistemic virtue, it is a necessary requirement for rationality that her credence have some probabilistic structure. Then I show that for a certain class of reasonable measures of inaccuracy, having such a probabilistic structure is sufficient to avoid accuracy-domination in these non-classical settings. (shrink)

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

Despite its computational elegancy, Jackendoff's proposal to reconcile competing approaches by postulating a parallel architecture for phonological, syntactic, and semantic modules is disappointing. We argue that it is a pragmatic version of the leading module which Jackendoff would probably prefer, but which he does not explicitly acknowledge. This internal conflict leads to several shortcomings and even distortions of information presented in the book.

Beliefs come in degrees, and we often represent those degrees with numbers. We might say, for example, that we are 90% confident in the truth of some scientific hypothesis, or only 30% confident in the success of some risky endeavour. But what do these numbers mean? What, in other words, is the underlying psychological reality to which the numbers correspond? And what constitutes a meaningful difference between numerically distinct representations of belief? In this Element, we discuss the (...) main approaches to the measurement of belief. These fall into two broad categories—epistemic and decision-theoretic—with divergent foundations in the theory of measurement. Epistemic approaches explain the measurement of belief by appeal to relations between belief states themselves, whereas decision-theoretic approaches appeal to relations between beliefs and desires in the production of choice and preferences. -/- (This book is part of the Cambridge Elements in Decision Theory and Philosophy series.). (shrink)

Inductive probability is the logical concept of probability in ordinary language. It is vague but it can be explicated by defining a clear and precise concept that can serve some of the same purposes. This paper presents a general method for doing such an explication and then a particular explication due to Carnap. Common criticisms of Carnap's inductive logic are examined; it is shown that most of them are spurious and the others are not fundamental.

When do probability distribution functions (PDFs) about future climate misrepresent uncertainty? How can we recognise when such misrepresentation occurs and thus avoid it in reasoning about or communicating our uncertainty? And when we should not use a PDF, what should we do instead? In this paper we address these three questions. We start by providing a classification of types of uncertainty and using this classification to illustrate when PDFs misrepresent our uncertainty in a way that may adversely affect decisions. (...) We then discuss when it is reasonable and appropriate to use a PDF to reason about or communicate uncertainty about climate. We consider two perspectives on this issue. On one, which we argue is preferable, available theory and evidence in climate science basically excludes using PDFs to represent our uncertainty. On the other, PDFs can legitimately be provided when resting on appropriate expert judgement and recognition of associated risks. Once we have specified the border between appropriate and inappropriate uses of PDFs, we explore alternatives to their use. We briefly describe two formal alternatives, namely imprecise probabilities and possibilistic distribution functions, as well as informal possibilistic alternatives. We suggest that the possibilistic alternatives are preferable. -/- . (shrink)

The social sciences playa variety of multifaceted roles in the policymaking process. So varied are these roles, indeed, that it is futile to talk in the singular about the use of social science in policymaking, as if there were one constant relationship between two fixed and stable entities. Instead, to address this issue sensibly one must talk in the plural about uses of dif ferent modes of social scientific inquiry for different kinds of policies under various circumstances. In some (...) cases, the influence of social scientific research is direct and tangible, and the connection between the find ings and the policy is easy to see. In other cases, perhaps most, its influence is indirect-one small piece in a larger mosaic of politics, bargaining, and compromise. Occasionally the findings of social scientific studies are explicitly drawn upon by policymakers in the formation, implementation, or evaluation of particular policies. More often, the categories and theoretical models of social science provide a general background orientation within which policymakers concep tualize problems and frame policy options. At times, the in fluence of social scientific work is cognitive and informational in nature; in other instances, policymakers use social science primarily for symbolic and political purposes in order to le gitimate preestablished goals and strategies. Nonetheless, amid this diversity and variety, troubling general questions persistently arise. (shrink)

We express here the statement » The probability of a given b equals r « symbolically by » p = r «. A formal axiomatic calculus can be constructed comprising all the well‐known laws of probability theory. This calculus can be interpreted in various ways. The present paper is a criticism of the subjective interpretation; that is to say, of any interpretation which assumes that probability expresses degrees of incomplete knowledge: a is the statement incompletely known, b (...) is our total knowledge, and p is the degree to which a is entailed by b. The subjective interpretation has often been proposed as an explanation and even a sharpening of the various objective theories . It is shown in the paper that this proposal cannot be realised because the subjective theory cannot lead to results which are compatible with the objective theory. This is due to various reasons, the most important of which is that the objective theory interprets » b « in » p « as a statement of the objective conditions of an experiment and » a « as one of its possible results. The subjective theory on the other hand interprets » b « as our total relevant knowledge which will in general include some knowledge of previous results of the experiment. It is shown that this must lead to incompatibility owing to the fact that this knowledge of previous results must influence the value of the probability.It is shown, in this way, that any probabilistic theory of the process of learning from experience—that is to say, any probabilistic theory of induction—must lead to contradictions.RésuméL'énoncé: » La probabilité de a, si b est donné, est égale à r « est ici exprimé symboliquement par » p = r «. On peut construire un système axiomatique formel qui contient toutes les règles bien connues du calcul des probabilités. Ce calcul formel peut ětre interprété de manières très différentes. L'article contient une critique des interprétations subjectives, c'est‐à‐dire des interprétations qui admettent que la probabilité exprime des degrés de connaissance incomplète: a est un énoncé qu'on ne connaǐt que partiellement, b est notre connaissance totale, et p exprime le degré auquel a est implicitement contenu dans b. L'interprétation subjective a souvent été proposée comme une explication et un renforcement des différentes théories objectives . Dans cet article, l'auteur montre que ce projet n'est pas réalisable, car la théorie subjective mène à des résultats qui contredisent la théorie objective. Plusieurs circonstances sont responsables de cette situation; la plus importante, c'est que la théorie interprète le » b « dans » p « comme une description des conditions objectives d'une expérience . D'autre part, la théorie subjective interprète » b « comme notre savoir total , et ce savoir inclura en général des informations sur les résultats obtenus antérieurement pour cette expérience. L'auteur montre que ce fait conduit à une contradiction entre les deux interprétations, car cette connaissance doit avoir une influence sur la valeur subjective de la probabilité.A l'aide de ce raisonnement, on peut montrer que la théorie des probabilités appliquée au processus inductif tirant une expérience du domaine expérimental conduit à des contradictions.ZusammenfassungDie Aussage » Die Wahrscheinlichkeit von a, wenn b gegeben ist, ist gleich r « wird hier symbolisch durch » p = r « ausgedrückt. Ein formales Axiomensystem kann konstruiert werden, das alle die wohlbekannten Regeln der Wahrscheinlichkeitsrechnung enthält. Dieser formale Kalkül kann in sehr verschiedener Weise interpretiert werden. Der Artikel enthält eine Kritik der subjektiven Interpretationen; das heisst, jener Interpretationen die annehmen, dass die Wahrscheinlichkeit Grade von unvollständigem Wissen ausdrückt: a ist ein Satz der unvollständig gewusst wird, b ist unser Gesamtwissen, und p drückt den Grad aus zu dem a in b implizit enthalten ist. Die subjektive Interpretation wurde oft als eine Erklärung und Verschärfung der verschiedenen objektiven Theorien vorgeschlagen. In dem Artikel wird gezeigt, dass der Vorschlag undurchführbar ist, da die subjektive Theorie zu Resultaten führt, die der objektiven Theorie widersprechen. Verschiedene Umstände tragen zu dieser Situation bei. Der wichtigste dieser Umstände ist, dass die objektive Theorie das » b « in » p « als eine Beschreibung der objektiven Bedingungen eines Experimentes interpretiert . Andererseits interpretiert die subjektive Theorie » b « als unser Gesamtwissen , und dieses wird im allgemeinen Informationen bezüglich früherer Resultate dieses Experiments einschliessen. Es wird gezeigt, dass das zu einem Widerspruch zwischen den Interpretationen führt, da dieses Wissen Einfluss auf den subjektiven Wahrscheinlichkeitswert haben muss.Mit Hilfe dieses Gedankenganges wird gezeigt, dass die Wahrscheinlichkeitstheorie des induktiven Lernens aus der Erfahrung zu Widersprüchen führt. (shrink)

This paper reports an experiment which investigates a possible cognitive antecedent of event-splitting effects (ESEs) experimentally observed by Starmer and Sugden (1993) and Humphrey (1995) – the learning of absolute frequency of event category impacting on the learning of probability of event category – and reveals some evidence that it is responsible for observed ESEs. It is also suggested and empirically substantiated that stripped-down prospect theory will accurately predict ESEs in some decision making tasks, but will not (...) perform well in others. This contention, it is argued, is indicative of fundamental descriptive shortcomings in the economic conception of choice under uncertainty and may entail implications beyond the direct concerns of this paper. (shrink)