Recent literature in philosophy of science has addressed purported notions of explanatory virtues—‘explanatory power’, ‘unification’, and ‘coherence’. In each case, a probabilistic relation between a theory and data is said to measure the power of an explanation, or degree of unification, or degree of coherence. This essay argues that the measures do not capture cases that are paradigms of scientific explanation, that the available psychological evidence indicates that the measures do not capture judgements of explanatory power, and, finally, that the (...) measures do not provide useful methods for selecting hypotheses. 1. Introduction2. Some Proposed Measures of Explanatory Virtues3. Descriptive Inadequacy3.1 Excellent but false explanations3.2 Causal explanation4. Psychological Inadequacy5. Finding the Truth6. Conclusion. (shrink)

This book offers a concise survey of basic probability theory from a thoroughly subjective point of view whereby probability is a mode of judgment. Written by one of the greatest figures in the field of probability theory, the book is both a summation and synthesis of a lifetime of wrestling with these problems and issues. After an introduction to basic probability theory, there are chapters on scientific hypothesis-testing, on changing your mind in response to generally uncertain (...) observations, on expectations of the values of random variables, on de Finetti's dissolution of the so-called problem of induction, and on decision theory. (shrink)

Classic work by one of the most brilliant figures in post-war analytic philosophy.

Probabilities figure centrally in much of the literature on the semantics of conditionals. I find this surprising: it accords a special status to conditionals that other parts of language apparently do not share. I critically discuss two notable ‘probabilities first’ accounts of counterfactuals, due to Edgington and Leitgeb. According to Edgington, counterfactuals lack truth values but have probabilities. I argue that this combination gives rise to a number of problems. According to Leitgeb, counterfactuals have truth conditions-roughly, a counterfactual is true (...) when the corresponding conditional chance is sufficiently high. I argue that problems arise from the disparity between truth and high chance, between approximate truth and high chance, and from counterfactuals for which the corresponding conditional chances are undefined. However, Edgington, Leitgeb and I can unite in opposition to Stalnaker and Lewis-style ‘similarity’ accounts of counterfactuals. (shrink)

This paper continues our work on a coherence-based probability semantics for Aristotelian syllogisms (Gilio, Pfeifer, and Sanfilippo, 2016; Pfeifer and Sanfilippo, 2018) by studying Figure III under coherence. We interpret the syllogistic sentence types by suitable conditional probability assessments. Since the probabilistic inference of P|S from the premise set {.

This paper engages with a specific problem concerning the relationship between descriptive and normative claims. Namely, if we understand that descriptive claims frequently contain normative assertions, and vice versa, how then do we interpret the traditionally rigid distinction that is made between the two, as ’Hume’s law’ or Moore’s ’naturalistic fallacy’ argument offered. In particular, Kripke’s interpretation of Wittgenstein’s ’rule-following paradox’ is specially focused upon in order to re-consider the rigid distinction. As such, the paper argues that if descriptive and (...) normative claims are not mutually exclusive, then we need a new framework with which to understand this relationship. In this regard, the paper borrows from concerns with vagueness, particularly using a degree-theoretic approach in terms of subjective probability, in an attempt to graphically figure out these differences. Consequently, the paper tentatively proposes the hyperbola model in which degrees of normativity and degrees of descriptivity could be expressed and measured. It is hoped, as a result, that this tentative proposal will contribute to deepening the debate on vagueness in general. (shrink)

We present a coherence-based probability semantics for (categorical) Aristotelian syllogisms. For framing the Aristotelian syllogisms as probabilistic inferences, we interpret basic syllogistic sentence types A, E, I, O by suitable precise and imprecise conditional probability assessments. Then, we define validity of probabilistic inferences and probabilistic notions of the existential import which is required, for the validity of the syllogisms. Based on a generalization of de Finetti's fundamental theorem to conditional probability, we investigate the coherent probability propagation (...) rules of argument forms of the syllogistic Figures I, II, and III, respectively. These results allow to show, for all three Figures, that each traditionally valid syllogism is also valid in our coherence-based probability semantics. Moreover, we interpret the basic syllogistic sentence types by suitable defaults and negated defaults. Thereby, we build a knowledge bridge from our probability semantics of Aristotelian syllogisms to nonmonotonic reasoning. Finally, we show how the proposed semantics can be used to analyze syllogisms involving generalized quantifiers. (shrink)

Classic work by one of the most brilliant figures in post-war analytic philosophy.

Logic is a central and highly useful part of philosophy. Its value is particularly evident when it comes to keeping our thinking about disjunctive probabilities clear. Because of the two meanings of “or”, logic can show how the likelihood of a disjunction being true can be determined quite easily. To gauge the chance that one of two or more exclusive alternatives is true, one need only sum up their respective likelihoods. And to know the chance that at least one of (...) two or more compatible alternatives is true, one simply has to figure the chance that it is false that all of them are false! (shrink)

At the end of the fifth century B.C.E., the character of Odysseus was scorned by most of the Athenians: he illustrated the archetype of the demagogic, unscrupulous and ambitious politicians that had led Athens to its doom. Against this common doxa, the most important disciples of Socrates (Antisthenes, Plato, Xenophon) rehabilitate the hero and admire his temperance and his courage. But it is most surprising to see that, in spite of Odysseus' lies and deceit, these philosophers, who condemn steadfastly the (...) sophists' deceptions, praise his rhetorical ability, his polutropia. The word polutropia is ambiguous: for Antisthenes, it means either "diversity of styles and discourses" or "diversity of dispositions, characters, or souls". It is argued that the same distinction is implicitly at work in Plato's Hippias Minor, where Socrates defends Odysseus' polutropia against the pseudo "simplicity" of Hippias' favourite hero, Achilles. However, whereas Antisthenes tries to clarify these different meanings, Plato's Socrates exploits the ambiguity to confuse his interlocutor. Such a distinction sheds a new light on the Hippias Minor: Odysseus is polutropos in the first (positive) sense, while the simplicity of Achilles should be understood as a bad kind of polutropia. It provides an explanation for the first paradoxical thesis of the dialogue which many commentators do not admit as an expression of the true Socratic view, on the ground of its supposed immorality: that he who voluntary deceives is better than he who errs, for falsehood is, in one case, only in words, while in the other, it is falsehood in the soul itself. It is thus proposed that Odysseus' skill in adapting his logos to his hearers was probably a model for Socrates himself. The analogy between the hero and Socrates is especially clear in Plato's dialogues, which show the philosopher in an Odyssey for knowledge. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 38.2 (2000) 221-238 [Access article in PDF] Hume's Iterative Probability Argument: A Pernicious Reductio Kevin Meeker University of South Alabama In this essay I want to look afresh at David Hume's iterative probability argument, found in the section entitled "Of Scepticism with regard to Reason" in his A Treatise of Human Nature.1 Interestingly enough, after years of comparative neglect,2 this argument (...) has been basking in the glow of scholarly sunshine lately.3 But to what can we attribute its extended hiatus? The convergence of three major factors seems responsible. First, philosophers have oftentimes flung this argument into the ocean of obscurity because of its perceived inadequacies.4 Second, and on a related note, many assume that Hume himself permitted this argument to drown because it never resurfaces again in his writings. Most suspiciously, Hume's Enquiry Concerning Human Understanding, which is his popular (and preferred) presentation of the epistemological sections [End Page 221] of the Treatise, does not contain this argument.5 Last, but certainly not least, for a long time this argument sat uncomfortably with the naturalist interpretation of Hume6 that has gained ascendancy in the twentieth century. For prior to this century, Hume was almost unanimously regarded as a sceptic. Despite a few waves from those who interpreted Hume as a logical positivist earlier in this century, Norman Kemp Smith charted a new course for Humean interpretations with his emphasis on Hume's naturalism.7 And this is the current according to which most Hume interpreters set their sails today.Because the naturalist reading of Hume relies so heavily on the system he attempts to set forth in the Treatise, though, naturalists have come to see the importance of reading this argument in a naturalistically acceptable way. William E. Morris best expresses the significance of this argument from a naturalistic perspective in the following manner: If we ever are to understand Hume's view of the role of reason, it stands to reason that we should first figure out how to integrate "Of scepticism with regard to reason" into the picture. Only then will we be ready to move to a consideration of Hume's positive views about reason. These views are the least understood of any of Hume's doctrines. Gaining an adequate understanding of them is both the most pressing and the most difficult problem facing Hume studies today.8While I agree with Morris about the importance of getting a clear understanding of the reasoning of I, iv, 1, I will argue that a correct reading of this section reveals the implausibility of major naturalistic interpretations of Hume.This paper has four major sections. In the first important section, I will highlight the crucial aspects of the iterative argument that will be the focus of this paper and deal with a preliminary but important interpretive issue. In the second section, I will briefly look at Annette Baier's naturalistic reading of Hume's philosophy to show how this particular passage bears on broader [End Page 222] interpretive issues. The third main section will focus on explicating Morris' similar but more detailed interpretation. Finally in the last part I will show that while it is legitimate to characterize the argument here as a reductio (as Baier and Morris both do), the argument still yields, contrary to what naturalists have recently suggested, a very sceptical conclusion. 1. The Arguments of Section I, IV, 1 of the TreatiseHume's "Of Scepticism with regard to Reason" contains at least two important arguments. While Hume agrees that knowledge involves certainty (whereas beliefs based on probability are by their very nature uncertain9 ), the conclusion of his first argument is that "all knowledge resolves itself into probability" (Treatise, 181). His point here is simply that all of our beliefs are fallible. That is, nothing is absolutely certain; thus none of our beliefs attain the exalted status of certain knowledge. But once this consequence of our fallibility is recognized, he then argues roughly that the probability that any particular belief... (shrink)

At the end of the fifth century B.C.E., the character of Odysseus was scorned by most of the Athenians: he illustrated the archetype of the demagogic, unscrupulous and ambitious politicians that had led Athens to its doom. Against this common doxa, the most important disciples of Socrates (Antisthenes, Plato, Xenophon) rehabilitate the hero and admire his temperance and his courage. But it is most surprising to see that, in spite of Odysseus' lies and deceit, these philosophers, who condemn steadfastly the (...) sophists' deceptions, praise his rhetorical ability, his polutropia. The word polutropia is ambiguous: for Antisthenes, it means either "diversity of styles and discourses" or "diversity of dispositions, characters, or souls". It is argued that the same distinction is implicitly at work in Plato's Hippias Minor, where Socrates defends Odysseus' polutropia against the pseudo "simplicity" of Hippias' favourite hero, Achilles. However, whereas Antisthenes tries to clarify these different meanings, Plato's Socrates exploits the ambiguity to confuse his interlocutor. Such a distinction sheds a new light on the Hippias Minor: Odysseus is polutropos in the first (positive) sense, while the simplicity of Achilles should be understood as a bad kind of polutropia. It provides an explanation for the first paradoxical thesis of the dialogue which many commentators do not admit as an expression of the true Socratic view, on the ground of its supposed immorality: that he who voluntary deceives is better than he who errs, for falsehood is, in one case, only in words, while in the other, it is falsehood in the soul itself. It is thus proposed that Odysseus' skill in adapting his logos to his hearers was probably a model for Socrates himself. The analogy between the hero and Socrates is especially clear in Plato's dialogues, which show the philosopher in an Odyssey for knowledge. (shrink)

La dialectique est une des notions les plus recurrentes de la tradition philosophique, que les differents siecles invoquent, soit pour s'en reclamer, soit pour s'en distancier. Chez Platon, elle conquiert ses lettres de noblesse en etant promue au statut de science supreme, mais chez Aristote, elle redevient ce qu'elle etait avant la Republique, un art du dialogue, de la decouverte a tatons de la verite, une methode de raisonnement sur des premisses simplement probables, qui fraie la voie a la saisie (...) de la verite, qui defend les principes du savoir contre les objections possibles mais qui ne peut pretendre au statut apodictique de la science. Ce differend originaire sur le statut et la portee va se diffracter au cours de l'histoire en une multiplicite impressionnante de figures qui sont autant de sources d'inspiration ou de repoussoirs pour les productions philosophiques ulterieures. Mais par dela les differences et les oppositions dans la conception de la dialectique, n'y a-t-il pas moyen de degager des lignes de convergence, des caracteristiques communes? C'est le pari qu'ont tente les participants d'un colloque tenu a Louvain-la-Neuve en 2007, consacre a la dialectique. Le present volume reprend une serie de contributions qui y ont ete presentees et discutees. Il couvre les differentes periodes de l'histoire de la philosophie, depuis Platon jusqu'au XXe siecle, et aborde la question dans des aires philosophiques variees. A l'heure ou notre monde prend toujours davantage conscience de la necessite de changer le paradigme en vigueur au sujet de la rationalite, la dialectique, avec son approche necessairement modeste de la totalite, avec sa dimension pratique, bien mise en evidence dans les diverses contributions, et avec son ouverture constitutive a l'alterite, se revele comme une voie feconde pour frayer la route de l'avenir. (shrink)

Aristotle divided arguments that persuade into the rhetorical (which happen to persuade), the dialectical (which are strong so ought to persuade to some degree) and the demonstrative (which must persuade if rightly understood). Dialectical arguments were long neglected, partly because Aristotle did not write a book about them. But in the sixteenth and seventeenth century late scholastic authors such as Medina, Cano and Soto developed a sound theory of probable arguments, those that have logical and not merely psychological force but (...) fall short of demonstration. Informed by late medieval treatments of the law of evidence and problems in moral theology and aleatory contracts, they considered the reasons that could render legal, moral, theological, commercial and historical arguments strong though not demonstrative. At the same time, demonstrative arguments became better understood as Galileo and other figures of the Scientific Revolution used mathematical proof in arguments in physics. Galileo moved both dialectical and demonstrative arguments into mathematical territory. (shrink)

A new direction in philosophy Between 1920 and 1940 logical empiricism reset the direction of philosophy of science and much of the rest of Anglo-American philosophy. It began as a relatively organized movement centered on the Vienna Circle, and like-minded philosophers elsewhere, especially in Berlin. As Europe drifted into the Nazi era, several important figures, especially Carnap and Neurath, also found common ground in their liberal politics and radical social agenda. Together, the logical empiricists set out to reform traditional philosophy (...) with a new set of doctrines more firmly grounded in logic and science. Criticism and decline Because of Nazi persecution, most of the European adherents of logical empiricism moved to the United States in the late 1930s. During the 1940s, many of their most cherished tenets became targets of criticism from outsiders as well as from within their own ranks. Philosophers of science in the late 1950s and 1960s rejected logical empiricism and, starting in the 1970s, presented such alternative programs such as scientific realism with evolutionary epistemology. A resurgence of interest During the early 1980s, philosophers and historians of philosophy began to study logical empiricism as an important movement. Unlike their predecessors in the 1960s-for whom the debate over logical empiricism now seems to have been largely motivated by professional politics-these philosopher no longer have to take positions for or against logical empiricism. The result has been a more balanced view of that movement, its achievements, its failures, and its influence. Hard-to-find core writings now available This collection makes available a selection of the most influential and representative writings of the logical empiricists, important contemporary criticisms of their doctrines, their responses, as well as the recent reappraisals. Introductions to each volume examine the articles in historical context and provide importantbackground information that is vital to a full understanding of the issues discussed. They outline prevalent trends, identifying leading figures and summarize their positions and reasoning, as well as those of opposing thinkers. (shrink)

Wittgenstein was not only an inspirational figure for Schlick but also contributed to scientific philosophy as Neurath demanded. His verificationism is one instance of this, but it is also shown in his treatment of probability (where his ideas were developed further by Waismann). Wittgenstein revived Bolzano's logical interpretation of probability, anticipating Carnap and many moderns. He construed laws of nature as hypotheses that we had to assume. It is the general form of these hypotheses (what he later called (...) a worldview) and not (pace von Wright) relative frequency that provides the basis for judgements of probability. (shrink)

At the end of the fifth century B.C.E., the character of Odysseus was scorned by most of the Athenians: he illustrated the archetype of the demagogic, unscrupulous and ambitious politicians that had led Athens to its doom. Against this common doxa, the most important disciples of Socrates (Antisthenes, Plato, Xenophon) rehabilitate the hero and admire his temperance and his courage. But it is most surprising to see that, in spite of Odysseus' lies and deceit, these philosophers, who condemn steadfastly the (...) sophists' deceptions, praise his rhetorical ability, his polutropia. The word polutropia is ambiguous: for Antisthenes, it means either "diversity of styles and discourses" or "diversity of dispositions, characters, or souls". It is argued that the same distinction is implicitly at work in Plato's Hippias Minor, where Socrates defends Odysseus' polutropia against the pseudo "simplicity" of Hippias' favourite hero, Achilles. However, whereas Antisthenes tries to clarify these different meanings, Plato's Socrates exploits the ambiguity to confuse his interlocutor. Such a distinction sheds a new light on the Hippias Minor: Odysseus is polutropos in the first (positive) sense, while the sim- plicity of Achilles should be understood as a bad kind of polutropia. It provides an explanation for the first paradoxical thesis of the dialogue which many commentators do not admit as an expression of the true Socratic view, on the ground of its supposed immorality: that he who voluntary deceives is better than he who errs, for falsehood is, in one case, only in words, while in the other, it is falsehood in the soul itself. It is thus proposed that Odysseus' skill in adapting his logos to his hearers was probably a model for Socrates himself. The analogy between the hero and Socrates is especially clear in Plato's dialogues, which show the philosopher in an Odyssey for knowledge. (shrink)

Wittgenstein was not only an inspirational figure for Schlick but also contributed to scientific philosophy as Neurath demanded. His verificationism is one instance of this, but it is also shown in his treatment of probability (where his ideas were developed further by Waismann). Wittgenstein revived Bolzano's logical interpretation of probability, anticipating Carnap and many moderns. He construed laws of nature as hypotheses that we had to assume. It is the general form of these hypotheses (what he later called (...) a worldview) and not (pace von Wright) relative frequency that provides the basis for judgements of probability. (shrink)

Wittgenstein was not only an inspirational figure for Schlick but also contributed to scientific philosophy as Neurath demanded. His verificationism is one instance of this, but it is also shown in his treatment of probability (where his ideas were developed further by Waismann). Wittgenstein revived Bolzano's logical interpretation of probability, anticipating Carnap and many moderns. He construed laws of nature as hypotheses that we had to assume. It is the general form of these hypotheses (what he later called (...) a worldview) and not (pace von Wright) relative frequency that provides the basis for judgements of probability. (shrink)

It's an achievement of the last couple of decades that people who work in linguistic semantics and people who work in the philosophy of language have arrived at a friendly, de facto agreement as to their respective job descriptions. The terms of this agreement are that the semanticists do the work and the philosophers do the worrying. The semanticists try to construct actual theories of meaning (or truth theories, or model theories, or whatever) for one or another kind of expression (...) in one or another natural language; for example, they try to figure out how the temperature could be rising compatibly with the substitutivity of identicals. The philosophers, by contrast, keep an eye on the large, foundational issues, such as: what's the relation between sense and denotation; what's the relation between thought and language; whether translation is determinate; and whether life is like a fountain. Every now and then the philosophers and the semanticists are supposed to get together and compare notes on their respective progress. Or lack thereof. (shrink)

Wittgenstein was not only an inspirational figure for Schlick but also contributed to scientific philosophy as Neurath demanded. His verificationism is one instance of this, but it is also shown in his treatment of probability (where his ideas were developed further by Waismann). Wittgenstein revived Bolzano's logical interpretation of probability, anticipating Carnap and many moderns. He construed laws of nature as hypotheses that we had to assume. It is the general form of these hypotheses (what he later called (...) a worldview) and not (pace von Wright) relative frequency that provides the basis for judgements of probability. (shrink)

It's an achievement of the last couple of decades that people who work in linguistic semantics and people who work in the philosophy of language have arrived at a friendly, de facto agreement as to their respective job descriptions. The terms of this agreement are that the semanticists do the work and the philosophers do the worrying. The semanticists try to construct actual theories of meaning (or truth theories, or model theories, or whatever) for one or another kind of expression (...) in one or another natural language; for example, they try to figure out how the temperature could be rising compatibly with the substitutivity of identicals. The philosophers, by contrast, keep an eye on the large, foundational issues, such as: what's the relation between sense and denotation; what's the relation between thought and language; whether translation is determinate; and whether life is like a fountain. Every now and then the philosophers and the semanticists are supposed to get together and compare notes on their respective progress. Or lack thereof. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 38.2 (2000) 221-238 [Access article in PDF] Hume's Iterative Probability Argument: A Pernicious Reductio Kevin Meeker University of South Alabama In this essay I want to look afresh at David Hume's iterative probability argument, found in the section entitled "Of Scepticism with regard to Reason" in his A Treatise of Human Nature.1 Interestingly enough, after years of comparative neglect,2 this argument (...) has been basking in the glow of scholarly sunshine lately.3 But to what can we attribute its extended hiatus? The convergence of three major factors seems responsible. First, philosophers have oftentimes flung this argument into the ocean of obscurity because of its perceived inadequacies.4 Second, and on a related note, many assume that Hume himself permitted this argument to drown because it never resurfaces again in his writings. Most suspiciously, Hume's Enquiry Concerning Human Understanding, which is his popular (and preferred) presentation of the epistemological sections [End Page 221] of the Treatise, does not contain this argument.5 Last, but certainly not least, for a long time this argument sat uncomfortably with the naturalist interpretation of Hume6 that has gained ascendancy in the twentieth century. For prior to this century, Hume was almost unanimously regarded as a sceptic. Despite a few waves from those who interpreted Hume as a logical positivist earlier in this century, Norman Kemp Smith charted a new course for Humean interpretations with his emphasis on Hume's naturalism.7 And this is the current according to which most Hume interpreters set their sails today.Because the naturalist reading of Hume relies so heavily on the system he attempts to set forth in the Treatise, though, naturalists have come to see the importance of reading this argument in a naturalistically acceptable way. William E. Morris best expresses the significance of this argument from a naturalistic perspective in the following manner: If we ever are to understand Hume's view of the role of reason, it stands to reason that we should first figure out how to integrate "Of scepticism with regard to reason" into the picture. Only then will we be ready to move to a consideration of Hume's positive views about reason. These views are the least understood of any of Hume's doctrines. Gaining an adequate understanding of them is both the most pressing and the most difficult problem facing Hume studies today.8While I agree with Morris about the importance of getting a clear understanding of the reasoning of I, iv, 1, I will argue that a correct reading of this section reveals the implausibility of major naturalistic interpretations of Hume.This paper has four major sections. In the first important section, I will highlight the crucial aspects of the iterative argument that will be the focus of this paper and deal with a preliminary but important interpretive issue. In the second section, I will briefly look at Annette Baier's naturalistic reading of Hume's philosophy to show how this particular passage bears on broader [End Page 222] interpretive issues. The third main section will focus on explicating Morris' similar but more detailed interpretation. Finally in the last part I will show that while it is legitimate to characterize the argument here as a reductio (as Baier and Morris both do), the argument still yields, contrary to what naturalists have recently suggested, a very sceptical conclusion. 1. The Arguments of Section I, IV, 1 of the TreatiseHume's "Of Scepticism with regard to Reason" contains at least two important arguments. While Hume agrees that knowledge involves certainty (whereas beliefs based on probability are by their very nature uncertain9 ), the conclusion of his first argument is that "all knowledge resolves itself into probability" (Treatise, 181). His point here is simply that all of our beliefs are fallible. That is, nothing is absolutely certain; thus none of our beliefs attain the exalted status of certain knowledge. But once this consequence of our fallibility is recognized, he then argues roughly that the probability that any particular belief... (shrink)

This article sketches a theory of objective probability focusing on nomic probability, which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the statistical syllogism. It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of (...) induction. The theory of induction is not of the familiar Bayesian variety, but consists of a precise version of the traditional Nicod Principle and its statistical analogues. (shrink)

This article analyzes the role of entropy in Bayesian statistics, focusing on its use as a tool for detection, recognition and validation of eigen-solutions. “Objects as eigen-solutions” is a key metaphor of the cognitive constructivism epistemological framework developed by the philosopher Heinz von Foerster. Special attention is given to some objections to the concepts of probability, statistics and randomization posed by George Spencer-Brown, a figure of great influence in the field of radical constructivism.

Historiography of the development of probability and statistics in the Russian Empire focusses on the contributions of the central figure Pafnutiy Lvovich Chebyshev and his successors. The purpose of this article is to concentrate on an earlier period which culminates with Chebyshev, and specifically on two less-than-well-explored aspects.

This paper is about the differences between probabilities and beliefs and why reasoning should not always conform to probability laws. Probability is defined in terms of urn models from which probability laws can be derived. This means that probabilities are expressed in rational numbers, they suppose the existence of veridical representations and, when viewed as parts of a probability model, they are determined by a restricted set of variables. Moreover, probabilities are subjective, in that they apply (...) to classes of events that have been deemed (by someone) to be equivalent, rather than to unique events. Beliefs on the other hand are multifaceted, interconnected with all other beliefs, and inexpressible in their entirety. It will be argued that there are not sufficient rational numbers to characterise beliefs by probabilities and that the idea of a veridical set of beliefs is questionable. The concept of a complete probability model based on Fisher's notion of identifiable subsets is outlined. It is argued that to be complete a model must be known to be true. This can never be the case because whatever a person supposes to be true must be potentially modifiable in the light of new information. Thus to infer that an individual's probability estimate is biased it is necessary not only to show that the estimate differs from that given by a probability model, but also to assume that this model is complete, and completeness is not empirically verifiable. It follows that probability models and Bayes theorem are not necessarily appropriate standards for people's probability judgements. The quality of a probability model depends on how reasonable it is to treat some existing uncertainty as if it were equivalent to that in a particular urn model and this cannot be determined empirically. Bias can be demonstrated in estimates of proportions of finite populations such as in the false consensus effect. However the modification of beliefs by ad hoc methods like Tversky and Kahneman's heuristics can be justified, even though this results in biased judgements. This is because of pragmatic factors such as the cost of obtaining and taking account of additional information which are not included even in a complete probability model. Finally, an analogy is drawn between probability models and geometric figures. Both idealisations are useful but qualitatively inadequate characterisations of nature. A difference between the two is that the size of any error can be limited in the case of the geometric figure in a way that is not possible in a probability model. (shrink)

A coherence-based probability semantics for categorical syllogisms of Figure I, which have transitive structures, has been proposed recently (Gilio, Pfeifer, & Sanfilippo [15]). We extend this work by studying Figure II under coherence. Camestres is an example of a Figure II syllogism: from Every P is M and No S is M infer No S is P. We interpret these sentences by suitable conditional probability assessments. Since the probabilistic inference of ~????|???? from the premise set {????|????, ~????|????} is (...) not informative, we add ????(????|(????∨????))>0 as a probabilistic constraint (i.e., an “existential import assumption”) to obtain probabilistic informativeness. We show how to propagate the assigned (precise or interval-valued) probabilities to the sequence of conditional events (????|????,~????|????,????|(????∨????)) to the conclusion ~????|???? . Thereby, we give a probabilistic meaning to the other syllogisms of Figure II. Moreover, our semantics also allows for generalizing the traditional syllogisms to new ones involving generalized quantifiers (like Most S are P) and syllogisms in terms of defaults and negated defaults. (shrink)

It is widely assumed that candidates for free, undetermined choices must have objective probabilities prior to their performance. Indeed although this premise figures prominently in a widely discussed argument against libertarianism, few libertarians have called it into question. In this article, I will investigate whether libertarians ought to reject it. I will conclude that doing so should not be tempting to event-causal libertarians or most agent-causal ones, because the added costs outweigh the benefits.

The artist and analytic Kant scholar Adrian Piper has been aptly described as “one of the most important and influential cultural figures of our time. The award-winning work of installation and participatory performance art, Probable Trust Registry: Rules of the Game #1-3, implicitly poses philosophical questions of interest to contractarian philosophy and its critique, including whether through an art installation one can execute a genuine, morally binding commitment to be honest, authentic, and respectful of oneself. Especially for audiences who closely (...) identify with her experiences, Piper’s artwork, like that of other important artists, has powerfully catalytic ethical potential. Motivated by admiration for the artist and a perceived conflictual relationship between women of color and conventional discourses of moral solidarity, I offer three different ways to understand Piper’s Probable Trust Registry. I suggest that Piper’s thought-provoking artwork, which implicitly nods at John Rawls and Charles Mills, can be interpreted as asking its audiences to agree to selections from a menu of rules that, in the alternative, embrace universal moral imperatives, predict future moral integrity, or vow moral integrity. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:New Light from Arabic Sources on Galen and the Fourth Figure of the Syllogism NICHOLAS RESCHER The Problem of the Origin of the Fourth Figure FLYING IN THE FACE of the long-standing tradition--going back in Europe to Renaissance times--which credits Galen of Pergamon with the origination of the fourth syllogistic figure, recent authorities have almost to a man evinced doubt about Galen's claim to this innovation. Heinrieh Scholz speaks (...) of "the Galenian syllogistic figure which has been attributed to him, probably wrongly." i j. W. Stakelum concludes his careful discussion of the matter with the categorical assertion that "Galen did not teach the fourth figure." ~ I. M. Bochenski--following Lukasiewicz (see below)--says that the fourth figure "was only ascribed to Galen by a misunderstanding." : William Kneale (also following Lukasiewicz) writes that "it is easy to see how misunderstanding.., by some Arabian philosopher... could have given rise to the tradition that Galen added a fourth figure to Aristotle's syllogistic theory." 4 The currently received account of the matter is that of Jan Lukasiewicz who, in his book on Aristotle's Syllogistic (1951; 2d ed., 1957), presents the known reports about Galen and the fourth figure as follows (I list them in the order in which they came to light) : 1) Several passages in Averroes' (d. 1198) Middle Commentary on Prior Analytics credit Galen with introducing a fourth figure (ad Anal. Pr. I, 5; I, 8; I, 23). These passages, known in Europe through a Renaissance Latin translation of a Hebrew version, provided the basis upon which Zabarella in his work, De Quarta Syllogismorum Figura (in his Opera [Leiden: 1587], pp. 41-53), popularized the "Galenian figure" in European logic. 2) In 1844 Minoides Mynas published in the Preface to his edition of Galen's EisagSg~ dialektik~ an anonymous Greek fragment (late, perhaps 6th century) which states that certain "later scholars" transformed the indirect moods of the first figure added by Theophrastus and Eudeffms into a new fourth figure, citing Galen as the originator of this doctrine.~ 1Abriss der Geschichte der Logik (Miinster: 1931), trans, into English by K. F. Leidecker, ConciseHistory of Logic (NewYork: 1961);p. 38ofthe Englishversion. "Why 'Galenian' Figure?" The New Scholasticism, XVI (1942),289-296. s Formale Logik (Miinchen-Freiburg:1956; 2nd. ed., 1962), trans, into English by Ivo Thomas, A History of Formal Logic (Notre Dame: 1961);p. 142of the Englishversion. Williamand Martha Kneale, The Developmentof Logic (Oxford: 1962),p. 184. Alsoprinted in Karl Kalbfieisch, ~ber Galen s Einleitung in die Logik, 2~. Supplementband der Jahrbi~cherfi~r klassische Philologie (Leipzig:1897), p. 707. This datum casts some 28 HISTORY OF PHILOSOPHY 3) A Greek fragment was found around 1858 by Karl Prantl in a logical work of the Byzantine scholar Ioannes Italus (llth century) which says that Galen taught the existence of a fourth figure, adding sarcastically that he (Galen) thought thus to appear cleverer than the older logical commentators (presumably Theophrastus and Eudemus are intended), but fell far short.6 4) In 1899 Maximilian Wallies published7 an anonymous Greek scholium (of perhaps the 6th or the 7th century) on Ammonins' commentary on Prior Analytics which states that Galen "says in his Apodictic that there are four figures, because he looks at the compound syllogisms consisting of four terms (i.e., with three premisses )" rather than the simple (three-term, two-premiss) syllogisms of Aristotle. (The scholiast goes on to explain at some length how such compound syllogisms can be sorted into four groups.) It is readily seen that, given these data, two possibilities stand before us: a) Galen did actually invent the traditional fourth figure. Reports (1)-(3) are correct, and the anonymous scholiast of (4) was put on the wrong track by the fact that Galen also said that compound syllogisms of four terms can be classed into four groups. b) Galen did not invent the traditional fourth figure. Only after his time when once the indirect moods of the first figure had--somehow--become systematized into a separate "figure," was this credited to Galen by a mistake along the lines described by the anonymous scholiast. Thus (4) alone is right, and (1)-(3) are mistaken. Which of... (shrink)

Under approval voting, each voter just distinguishes the candidates he approves of from those appearing as unacceptable. The preference approval voting is a hybrid version of the approval voting first introduced by Brams and Sanver The mathematics of preference, choice and order. Springer, Berlin, pp 215–237, 2009). Under PAV, each voter ranks all the candidates and then indicates the ones he approves. In this paper, we provide an analytical representation of the limiting probability that PAV elects the Condorcet winner (...) when she exists in three-candidate elections. We perform our analysis by assuming the assumption of the Extended Impartial Culture. The aim is to measure at which extend PAV performs better than AV both on the propensity of electing the Condorcet winner and on that of the non-election of the Condorcet loser. For this purpose, we also provide an analytical representation of the limiting probability that AV elects the Condorcet winner when she exists in three-candidate elections. Our representation of the limiting probability that AV elects the Condorcet winner is more general than that provided by Diss et al. Handbook on approval voting. Springer, Berlin, pp 255–283, 2010) and it leads to the same figures as the representation provided by Gehrlein and Lepelley. (shrink)

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)

Hans Reichenbach has been not only one of the founding fathers of logical empiricism but also one of the most prominent figures in the philosophy of science of the past century. While some of his ideas continue to be of interest in current philosophical programs, an important part of his early work has been neglected, and some of it has been unavailable to English readers. Among Reichenbach’s overlooked (and untranslated) early works, his doctoral thesis of 1915, The Concept of (...) class='Hi'>Probability in the Mathematical Representation of Reality, deserves special attention, both for the topics covered and for its significance for a proper understanding of his intellectual trajectory. This volume anticipates most of the fundamental themes of his later philosophy. In particular, it addresses the issue of the application of probability statements to reality, as well as the relationship between probability and causality—questions that have been at the core of his research throughout his life. (shrink)

Contents \t\t\t\t\t \tTRANSLATOR'S INTRODUCTION \t\t1 \t \tNOTE ON THE TRANSLATION \t\t39 \t OBSERVATIONS ON THE FEELING OF THE BEAUTIFUL AND SUBLIME \t\t\t\t\t \tSECTION ONE: \t\t\t\t \t\tOf the Distinct Objects of the Feeling of the Beautiful and Sublime \t\t45 \tSECTION TWO: \t\t\t\t \t\tOf the Attributes of the Beautiful and Sublime.

The religious history of Bremen includes many impressive figures. Probably the most enigmatic figure of Bremen's church life around 1900 was the pastor at St. Martini, Albert Kalthoff. However, his impact reached beyond the borders of local religious history: He was important for the history of the Protestant culture of piety as well as for a religious historical analysis of reform attempts within Protestantism in Imperial Germany. Kalthoff was part of the leftist reform movement within German Protestantism. Furthermore, he can (...) be said to have had certain sympathies for the free thinker movement. This article wants to situate Kalthoff and his public works and goals in religious history with regard to the religious-confessional, cultural-religious, and cultural-political tendencies of his time. His example delineates the contours of a transitional space between Protestantism and the free thinker movement. (shrink)

Ockham's razor, the principle of parsimony, states that simpler theories are better than theories that are more complex. It has a history dating back to Aristotle and it plays an important role in current physics, biology, and psychology. The razor also gets used outside of science - in everyday life and in philosophy. This book evaluates the principle and discusses its many applications. Fascinating examples from different domains provide a rich basis for contemplating the principle's promises and perils. It is (...) obvious that simpler theories are beautiful and easy to understand; the hard problem is to figure out why the simplicity of a theory should be relevant to saying what the world is like. In this book, the ABCs of probability theory are succinctly developed and put to work to describe two 'parsimony paradigms' within which this problem can be solved. (shrink)

This article provides a basic general introduction to Ramus, and evaluates his role in the history of logic and rhetoric, especially with relation to the study of argumentation. The author agrees with Ong and other historians of logic that Ramus is not to be taken seriously as a logician, and that his undoubted importance in the history of ideas is to be found elsewhere.Ramus advocates a belief in nature, experience and reason, and rejects the reliance on the authority of ancient (...) philosophers, above all Aristotle, though ‘experience’ does not mean scientific experiment and, paradoxically, includes the example of great philosophers and writers. In the end Ramus is seen as responsible for substituting for ancient classical rhetoric an entirely ornamental rhetoric of figures which was to take over education (with the exception of the Jesuit schools) almost until our own day. This curtailing and diminishing of rhetoric is seen as a degeneration. Ancient five-part rhetoric had been concerned with convincing and persuading: Aristotle distinguished the analytic, scientific reasoning of logic, from dialectic which was based on opinion and probability and had close links with rhetoric; by the time of Cicero and Quintilian, who addressed themselves to jurists and politicians, logic has given way to dialectic. In the Middle Ages and the Renaissance the two become assimilated; the evolution of this is traced here through the thirteenth-century Summulae logicales of Peter of Spain to the fifteenth-century German humanist logician Rudolph Agricola, who influenced Ramus partly through the intermediary of Johann Sturm. Ramus took over their topical theories but restricted them to logic/dialectic, and left rhetoric with little more than tropes and figures. He believed that there was only one method for teaching all the arts, and one dialectic common to them all. The distinction between analytical and dialectical has disappeared, with far-reaching consequences for the study of argumentation. Over the centuries logic has lost its connection with controversy and persuasion. With the development of the post-Cartesian, post-Baconian emphasis on the clarity of scientific discourse, and the mid-nineteenth-century interest in mathematical and formal logic, the process was complete. Argumentation, or the ‘new rhetoric’, aims to fill the gap thus created. (shrink)