Seventeenth-century “chance combinatorics” was a self-contained theory. It had an objective notion of chance derived from physical devices with chance properties, such as casts of dice, combinatorics to count chances and, to interpret their significance, a rule for converting these counts into fair wagers. It lacked a notion of chance as a measure of belief, a precise way to connect chance counts with frequencies and a way to compare chances across different games. These omissions were not needed for the theory’s (...) interpretation of chance counts: determining which are fair wagers. The theory provided a model for how indefinitenesses could be treated with mathematical precision in a special case and stimulated efforts to seek a broader theory. (shrink)

One of the central criteria for free will is “Could I have done otherwise?” But because of a temporal asymmetry in human choice, the question makes no sense. The question is backward-looking, while human choices are forward-looking. At the time when any choice is actually made, there is as of yet no action to do otherwise. Expectation is the only thing to contradict (do other than). So the ability to do something not expected by the ultimate expecter, Laplace’s demon, is (...) a better criterion for free will. If human action is fundamentally unpredictable, then we have free will. Scientists have studied a form of fundamental unpredictability, known as undecidability. The features that make a system capable of undecidable dynamics have been identified: program-data duality; potential to access an infinite computational medium; and the ability to implement negation. Humans have all three of these features, so we very likely are fundamentally unpredictable, so we have free will. (shrink)

The relationship between consciousness and brain, subject and body, appears today far away from being elucidated. All attempts to reduce consciousness and subject to the brain end up abolishing the subject, i.e., what is evidently most relevant for each one of us. Luigi Giussani proposes a method to investigate human consciousness based on the analysis of oneself personal experience, verifiable by every human being. He is very attentive to avoiding during the experiential analysis interference of prejudices, ideological conceptions, and conjectures. (...) His method remains perfectly coherent and open to all contributions from neuroscience and scientific discoveries. He leaves completely open the major question about the relationship between brain physical-chemical functioning and subjective experience, individual consciousness. A comparison between Giussani’s method and the starting point and the fundamental assumption that lays the basis of various modern neuroscientific conceptions of consciousness is conducted. A discussion about the assumption that stays at the basis of the various neuroscientific currents appears necessary and the method proposed by Giussani may constitute a common and acceptable by everyone background for future development and advances in studying the greatest problem of our culture, the relation between brain and human consciousness. (shrink)

Determinism and unpredictability are compatible since deterministic flows can produce, if sensitive to initial conditions, unpredictable behaviors. Within this perspective, the notion of scenario to chaos transition offers a new form of predictability for the behavior of sensitive to initial condition systems under the variation of a control parameter. In this paper I first shed light on the genesis of this notion, based on a dynamical systems approach and on considerations of structural stability. I then suggest a link to the (...) figure of epigenetic landscape, partially inspired by a dynamical systems perspective, and offering a theoretical framework to apprehend developmental noise. (shrink)

The extravagances of quantum mechanics never fail to enrich daily the debate around natural philosophy. Entanglement, non-locality, collapse, many worlds, many minds, and subjectivism have challenged generations of thinkers. Its approach can perhaps be placed in the stream of quantum logic, in which the “strangeness” of QM is “measured” through the violation of Bell’s inequalities and, from there, attempts an interpretative path that preserves realism yet ends up overturning it, restating the fundamental mechanisms of QM as a logical necessity for (...) a strong realism. (shrink)

Masarykovy a Brentanovy snahy o překonání Humova skepticismu prostřednictvím počtu pravděpodobnosti lze chápat jako svého druhu "třetí cestu" mezi kantovským apriorismem a kapitulací před subtilními Humovými argumenty. U Masaryka je ono snažení součástí jeho projektu nové induktivní logiky, která (v návaznosti na Leibnize) by měla být logickým základem pro "umění vynalézat" (ars inveniendi). Masaryk akceptuje Humovu koncepci analytických soudů, ale zároveň inklinuje i ke koncepci Adolfa Ficka, v souladu s níž mají věty počtu pravděpodobnosti charakter syntetických soudů a priori; kromě (...) toho odkazuje pozoruhodným způsobem k Bernoulliho zákonu velkých čísel. Masarykovy úvahy vedou k závěru, že zákon velkých čísel zaručuje shodu mezi apriorními tvrzeními počtu pravděpodobnosti a empirickou skutečností, což podle Masaryka vyvrací "tresť" Humova skepticismu, spočívající v tvrzení, že rozum a zkušenost se vylučují. Vzhledem k tomu, že hlavním objektem Humovy kritiky byl pojem kauzality, je však nutno konstatovat, že Masarykovo snažení bylo neúspěšné, neboť žádná aplikace počtu pravděpodobnosti, jenž se zabývá náhodnými jevy, nemůže vést k založení kauzálního zákona (pokud tento zákon zahrnuje také tezi uniformity kauzální determinace). (shrink)

Ernst Cassirer’s epistemological trilogy – Substanzbegriff und Funktionsbegriff (1910), Zur Einsteinschen Relativitätstheorie (1921) and Determinismus und Indeterminismus (1937) – is well known to Western scholars, some of whom recently devoted a number of in-depth and interesting studies to Cassirer’s epistemology. Nonetheless, they overlooked aspects of Cassirer’s concept of idealisation and his model of science as found in his last epistemological work: Determinismus und Indeterminismus. In this essay I will consider these two almost disregarded aspects of Cassirer’s epistemology in order to (...) provide a better understanding of his idea of science. (shrink)

Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general.

La métaphysique de Leibniz revue par Wolff est débattue dans la correspondance qu'entretiennent Voltaire et Frédéric, futur Frédéric II. Ce dernier tente d'initier et de convertir Voltaire au wolffisme. Même s'il la prétend remarquable, Voltaire estime peu la méthode wolffienne. Refusant le fidéisme à la Bayle, Frédéric ne se résout pas à renoncer volontairement aux connaissances que l'on peut acquérir par le raisonnement. Selon Voltaire, les vérités métaphysiques demeurent inaccessibles. La seule position défendable s'avère donc être le scepticisme métaphysique. Frédéric (...) l'admet: après avoir étudié les sciences et observé l'esprit des hommes, l'inclination au scepticisme est naturelle. Ainsi, le débat sur les monades a conduit Frédéric à dénier son wolffisme antérieur: il est prêt à devenir le parfait despote pragmatique et réaliste, disciple des Lumières françaises. (shrink)

It is argued that the many-worlds interpretation is by far the best interpretation of quantum mechanics. The key points of this view are viewing the wave functions of worlds in three dimensions and understanding probability through self-locating uncertainty.

In the article ”Against Physicalism-plus-God: How Creation Accounts for Divine Action in the World’, I defined a framework which allows us to make some progress in our understanding of how God acts in the world. In the present article, I apply this framework to the specific question of chance events. I show that chance does not provide an explanation for special divine action. Nevertheless, chance does not hamper God’s ability to act in the world, and creation provides a framework for (...) the understanding of chance, which is akin to what we see in modern science. (shrink)

There are many ontologies of the world or of specific phenomena such as time, matter, space, and quantum mechanics1. However, ontologies of information are rather rare. One of the reasons behind this is that information is most frequently associated with communication and computing, and not with ‘the furniture of the world’. But what would be the nature of an ontology of information? For it to be of significant import it should be amenable to formalization in a logico-grammatical formalism. A candidate (...) ontology satisfying such a requirement can be found in some of the ideas of K. Turek, presented in this paper. Turek outlines the ontology of information conceived of as a part of nature, and provides the ‘missing link’ to the Z axiomatic set theory, offering a proposal for developing a formal ontology of information both in its philosophical and logicogrammatical representations. (shrink)

This paper has the aim of making Johannes von Kries’s masterpiece, Die Principien der Wahrscheinlichkeitsrechnung of 1886, a little more accessible to the modern reader in three modest ways: first, it discusses the historical background to the book ; next, it summarizes the basic elements of von Kries’s approach ; and finally, it examines the so-called “principle of cogent reason” with which von Kries’s name is often identified in the English literature.

The prospects of a causal interpretation of probability are examined. Various accounts both from the history of scientific method and from recent developments in the tradition of the method of arbitrary functions, in particular by Strevens, Rosenthal, and Abrams, are briefly introduced and assessed. I then present a specific account of causal probability with the following features: First, the link between causal probability and a particular account of induction and causation is established, namely eliminative induction and the related difference-making account (...) of causation in the tradition of Bacon, Herschel, and Mill. Second, it is shown how a causal approach is useful beyond applications of the method of arbitrary functions and is able to deal with various shades of both ontic and epistemic probabilities. Furthermore, I clarify the notion of causal symmetry as a central element of an objective version of the principle of indifference and relate probabilistic independence to causal irrelevance. (shrink)

This paper argues that the innovation of an ordering source parameter in the standard Lewis-Kratzer semantics for modals was a mistake, at least for English auxiliaries like ‘ought’, and that a simpler dyadic semantics (as proposed in my earlier work) provides a superior account of normative uses of modals. I programmatically investigate problems arising from (i) instrumental conditionals, (ii) gradability and “weak necessity”, (iii) information-sensitivity, and (iv) conflicts, and show how the simpler semantics provides intuitive solutions given three basic moves: (...) (1) an end-relational analysis of normative modality, (2) a “most” analysis of “weak necessity”, and (3) well-motivated appeals to pragmatics. I conclude with metasemantic observations about the desiderata for a semantics for ‘ought’. (shrink)

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...) of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

In France, as in other European countries, especially Britain and Germany, the nineteenth century was a period of great progress and achievement in science. This would still have been true if Claude Bernard and Louis Pasteur had been the only outstanding French scientists of the nineteenth century, whereas there were, of course, many others apart from an impressive number of brilliant French mathematicians. Nevertheless, although it was a great century for French science there was perhaps something rather disappointing about it, (...) and something rather ingrowing about the attitude of French scientists towards scientific developments in other countries. For example, the French took it hard that the creator of the theory of evolution should have been an Englishman, remembering too late Darwin's predecessor Lamarck, and they certainly were very slow in accepting Darwin's theory of evolution.1 Again, the French may have felt that after the important contributions of French scientists such as Coulomb, Poisson, Biot and, above all, Ampère, the theory of electricity and magnetism which is today principally associated with the names of Faraday and Maxwell should have been created by a Frenchman. Once again this new theory was only accepted very slowly and hesitantly, and even unwillingly, in France—one thinks, for example, of the criticisms levelled at the theory by Pierre Duhem in his “The Aim and Structure of Physical Theory”.2 Of course it might be that if one knew how to weigh properly the various achievements of French scientists in different branches of science one would find that, allowing for her rather static population during the nineteenth century, thetotalcontribution of France compared well with those of Britain and Germany. Nevertheless, in one case at least, that of theoretical physics, there seems to have been an unmistakable failure to live up to the promise of the beginning of the century. The purpose of this paper is to advance possible reasons to explain this failure. (shrink)

Theoretical determinism, as it is usually ascribed to Laplace, is neither verifiable nor falsifiable and has therefore no real content. It is not the same as predictability of actually observable phenomena. On the other hand, predictability is not an abstract principle; rather it is true to a certain degree, depending on the phenomena considered. It can be discussed only by examining the scientific state of affairs. This is done in some detail for classical statistical mechanics. Much of a recently published (...) debate on determinism (Amsterdamski et al. 1990) is thereby obviated. (shrink)

For years, experimental philosophers have attempted to discern whether laypeople find free will compatible with a scientifically deterministic understanding of the universe, yet no consensus has emerged. The present work provides one potential explanation for these discrepant findings: People are strongly motivated to preserve free will and moral responsibility, and thus do not have stable, logically rigorous notions of free will. Seven studies support this hypothesis by demonstrating that a variety of logically irrelevant (but motivationally relevant) features influence compatibilist judgments. (...) In Study 1, participants who were asked to consider the possibility that our universe is deterministic were more compatibilist than those not asked to consider this possibility, suggesting that determinism poses a threat to moral responsibility, which increases compatibilist responding (thus reducing the threat). In Study 2, participants who considered concrete instances of moral behavior found compatibilist free will more sufficient for moral responsibility than participants who were asked about moral responsibility more generally. In Study 3a, the order in which participants read free will and determinism descriptions influenced their compatibilist judgments—and only when the descriptions had moral significance: Participants were more likely to report that determinism was compatible with free will than that free will was compatible with determinism. In Study 3b, participants who read the free will description first (the more compatibilist group) were particularly likely to confess that their beliefs in free will and moral responsibility and their disbelief in determinism influenced their conclusion. In Study 4, participants reduced their compatibilist beliefs after reading a passage that argued that moral responsibility could be preserved even in the absence of free will. Participants also reported that immaterial souls were compatible with scientific determinism, most strongly among immaterial soul believers (Study 5), and evaluated information about the capacities of primates in a biased manner favoring the existence of human free will (Study 6). These results suggest that people do not have one intuition about whether free will is compatible with determinism. Instead, people report that free will is compatible with determinism when desiring to uphold moral responsibility. Recommendations for future work are discussed. (shrink)

I show how classical and quantum physics approach the problem of randomness and probability. Contrary to popular opinions, neither we can prove that classical mechanics is a deterministic theory, nor that quantum mechanics is a nondeterministic one. In other words it is not possible to show that randomness in classical mechanics has a purely epistemic character and that of quantum mechanics an ontic one. Nevertheless, recent developments of quantum theory and increasing experimental possibilities to check its predictions call for returning (...) to the problem of comparing possibilities given by classical and quantum physics to accommodate and prove the existence of a `genuine randomness'. Recent results concerning `amplification of randomness' show that, in certain sense, quantum physics is in fact ‘more random’ that classical and outperforms it in producing a `truly random process'. (shrink)

The primary aim of this chapter is to explain the nature of evidential reasoning, the characteristic difficulties encountered, and the tools to address these difficulties. Our focus is on evidential reasoning in criminal cases. There is an extensive scholarly literature on these topics, and it is a secondary aim of the chapter to provide readers the means to find their way in historical and ongoing debates.

This chapter contains sections titled: Highlights of Past Literature Current Work Future Work.

The essay revisits the puzzle of the ‘passage’ of time in relation to EPR-type measurements and asks what philosophical consequences can be drawn from them. Some argue that the lack of invariance of temporal order in the measurement of a space-like related EPR pair, under relativistic motion, casts serious doubts on the ‘reality’ of the lapse of time. Others argue thatcertain features of quantum mechanics establisha tensed theory of time – understood here as Possibilism or the growing block universe. The (...) paper analyzes the employment of frame-invariant entropic clocks in a relativistic setting and argues that tenselessness does not imply timelessness. But this conclusion does not support a tensed theory of time, which requires a preferred foliation. It is argued that the only reliable inference from the EPR example and the use of entropic clocks is an inference not just to a Leibnizian order of the succession of events but a frame-invariant order according to some selected clocks. (shrink)

In my dissertation I define historical disciplines as disciplines that aim to give a historical interpretation of the evidence. Phylogenetic systematics is a historical discipline and therefore in my definition phylogenies should be thought of as historical interpretations of relationships between taxa.

This paper addresses the question of how we should regard the probability distributions introduced into statistical mechanics. It will be argued that it is problematic to take them either as purely ontic, or purely epistemic. I will propose a third alternative: they are almost objective probabilities, or epistemic chances. The definition of such probabilities involves an interweaving of epistemic and physical considerations, and thus they cannot be classified as either purely epistemic or purely ontic. This conception, it will be argued, (...) resolves some of the puzzles associated with statistical mechanical probabilities: it explains how probabilistic posits introduced on the basis of incomplete knowledge can yield testable predictions, and it also bypasses the problem of disastrous retrodictions, that is, the fact the standard equilibrium measures yield high probability of the system being in equilibrium in the recent past, even when we know otherwise. As the problem does not arise on the conception of probabilities considered here, there is no need to invoke a Past Hypothesis as a special posit to avoid it. (shrink)

The anti-causal prophecies of last century have been disproved. Causality is neither a ‘relic of a bygone’ nor ‘another fetish of modern science’; it still occupies a large part of the current debate in philosophy and the sciences. This investigation into causal modelling presents the rationale of causality, i.e. the notion that guides causal reasoning in causal modelling. It is argued that causal models are regimented by a rationale of variation, nor of regularity neither invariance, thus breaking down the dominant (...) Human paradigm. The notion of variation is shown to be embedded in the scheme of reasoning behind various causal models: e.g. Rubin’s model, contingency tables, and multilevel analysis. It is also shown to be latent – yet fundamental – in many philosophical accounts. Moreover, it has significant consequences for methodological issues: the warranty of the causal interpretation of causal models, the levels of causation, the characterisation of mechanisms, and the interpretation of probability. This book offers a novel philosophical and methodological approach to causal reasoning in causal modelling and provides the reader with the tools to be up to date about various issues causality rises in social science. (shrink)

There are three main kinds of causal connections between two events: the transfer of energy, the transfer of information and the triggering of the transfer of one of them or both. There are also other kinds of causal connections.

I argue here for a number of ways that modern computational science requires a change in the way we represent the relationship between theory and applications. It requires a switch away from logical reconstruction of theories in order to take surface mathematical syntax seriously. In addition, syntactically different versions of the same theory have important differences for applications, and this shows that the semantic account of theories is inappropriate for some purposes. I also argue against formalist approaches in the philosophy (...) of science and for a greater role for perceptual knowledge rather than propositional knowledge in scientific empiricism. (shrink)

The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference (...) class problem. Other versions of these interpretations apparently evade the problem. But I contend that they are all “no-theory” theories of probability - accounts that leave quite obscure why probability should function as a guide to life, a suitable basis for rational inference and action. The reference class problem besets those theories that are genuinely informative and that plausibly constrain our inductive reasonings and decisions. I distinguish a “metaphysical” and an “epistemological” reference class problem. I submit that we can dissolve the former problem by recognizing that probability is fundamentally a two-place notion: conditional probability is the proper primitive of probability theory. However, I concede that the epistemological problem remains. (shrink)

This paper investigates the kind of empiricism combined with an operationalist perspective that, in the first decades of our Century, gave rise to a turning point in theoretical physics and in probability theory. While quantum mechanics was taking shape, the classical (Laplacian) interpretation of probability gave way to two divergent perspectives: frequentism and subjectivism. Frequentism gained wide acceptance among theoretical physicists. Subjectivism, on the other hand, was never held to be a serious candidate for application to physical theories, despite the (...) fact that its philosophical back-ground strongly resembles that underlying quantum mechanics, at least according to the Copenhagen interpretation. The reasons for this are explored. (shrink)

It is natural for humans to judge the outcome of a decision under uncertainty as a percentage of an ex-post optimal performance. We propose a robust decision-making framework based on a relative performance index. It is shown that if the decision maker’s preferences satisfy quasisupermodularity, single-crossing, and a nondecreasing log-differences property, the worst-case relative performance index can be represented as the lower envelope of two extremal performance ratios. The latter is used to characterize the agent’s optimal robust decision, which has (...) implications both computationally and for obtaining closed-form solutions. We illustrate our results in an application which compares the performance of relative robustness to solutions that optimize worst-case payoffs, maximum absolute regret, and expected payoffs under a Laplacian prior. (shrink)

Justified by spectacular achievements facilitated through applied deep learning methodology, the “Everything is possible” view dominates this new hour in the “boom and bust” curve of AI performance. The optimistic view collides head on with the “It is not possible”—ascertainments often originating in a skewed understanding of both AI and medicine. The meaning of the conflicting views can be assessed only by addressing the nature of medicine. Specifically: Which part of medicine, if any, can and should be entrusted to AI—now (...) or at some moment in the future? AI or not, medicine should incorporate the anticipation perspective in providing care. (shrink)

From the very beginning of ancient Greek philosophy up to the present day a puzzling correlation is found between rationality and reality. In this study this relation is examined with emphasis on the philosophical tradition of Aristotle and Aquinas. A comparison is made with the virtual reality created by computers and actual reality of our universe. The view expressed in the scientific neopositivism of Jordan and Mach is found to be an adequate approach to avoid contradictions in the interpretation of (...) modern physics. A challenging hypothesis is made by updating the Laplacian Demon by a powerful creative intellect in line with Judeo-Christian tradition. With this hypothesis a new light is shed on several fundamental issues in modern science. (shrink)

In this essay we argue that the notion of machine necessarily includes its being designed for a purpose. Therefore, being a mechanical system is not enough for being a machine. Since the experimental scientific method excludes any consideration of finality on methodological grounds, it is then also insufficient to fully understand what machines are. Instead in order to understand a machine it is first required to understand its purpose, along with its structure, in clear parallel with Aristotle’s final and formal (...) causes. Obviously, purpose and structure are not machine components that can physically interact with other components; nonetheless they are essential to understanding their operation. This casts an interesting light on the relationship between mind and body: for just as an artifact’s finality and structure explain its operation, so also consciousness is the explanation—not the efficient cause—of specifically human behavior. What machines and human beings have in common is that, in order to understand them, it is necessary to appeal to the principle of finality. Yet while finality is given and extrinsic in the case of machines, we human beings are characterized by the ability to self-propose our own ends. Since the principle of finality is essential to understanding the production of machines, the traditional view in modern Western philosophy that finality lies beyond the scope of objective/scientific knowledge should be rectified to allow for a genuine science of the artificial. We think a correct understanding of final causality will overcome current resistance to this principle. (shrink)

The article presents, develops, and defends a non-reductionist model of the generation of knowledge from multiple testimonies. It distinguishes the generation of knowledge from multiple testimonies from the transmission of knowledge by a single testimony. The reiteration of the generation of knowledge from multiple testimonies generates social knowledge.Critical examination of the literature about the coherence of multiple testimonies, their reliability, and independence argues in particular against conditional and causal interpretations and attempts to overcome the limitations of exclusively conceptual and formal (...) epistemologies. Instead, the article introduces an analysis of the generation of knowledge from multiple testimonies in terms of tracing information flows. The article presents a new three-stage modular model of knowledge generation from multiple testimonies that fits the actual veritistic best practices of institutionally embedded professionals like intelligence analysts, detectives, investigat.. (shrink)

The metamathematical tradition, tracing back to Hilbert, employs syntactic modeling to study the methods of contemporary mathematics. A central goal has been, in particular, to explore the extent to which infinitary methods can be understood in computational or otherwise explicit terms. Ergodic theory provides rich opportunities for such analysis. Although the field has its origins in seventeenth century dynamics and nineteenth century statistical mechanics, it employs infinitary, nonconstructive, and structural methods that are characteristically modern. At the same time, computational concerns (...) and recent applications to combinatorics and number theory force us to reconsider the constructive character of the theory and its methods. This paper surveys some recent contributions to the metamathematical study of ergodic theory, focusing on the mean and pointwise ergodic theorems and the Furstenberg structure theorem for measure preserving systems. In particular, I characterize the extent to which these theorems are nonconstructive, and explain how proof-theoretic methods can be used to locate their "constructive content.". (shrink)

Inductive reasoning aims at constructing rules and models of general applicability from a restricted set of observations. Induction is a keystone in natural sciences, and it influences diverse application fields such as engineering, medicine and economics. More generally, induction plays a major role in the way humans learn and operate in their everyday life. The level of reliability that a model achieves depends on how informative the observations are relative to the flexibility of the process by which the model is (...) constructed. When the process is articulated so that the model can incorporate descriptive details and subtleties, a large set of informative observations are required to reliably tune the model, whereas models obtained from simple procedures can be tuned with fewer observations. This article introduces the concept of “dominance”, which refers to the situation in which a reduced subset of observations suffices to reconstruct the model. A mathematical framework is presented to quantify the reliability of learning procedures as a function of the size of the subset of dominant observations. Although limited in scope, we believe that our study can contribute to the understanding of some fundamental mechanisms by which knowledge is generated from observations in inductive reasoning. (shrink)

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)

In this paper, a concept of chance is introduced that is compatible with deterministic physical laws, yet does justice to our use of chance-talk in connection with typical games of chance. We take our cue from what Poincaré called "the method of arbitrary functions," and elaborate upon a suggestion made by Savage in connection with this. Comparison is made between this notion of chance, and David Lewis' conception.

This paper presents an overview on the concept of cardinal utility in its relations with the literature since the beginning of the XVIIIth century (Part I); an estimate of the cardinal utility function for its negative values, thus completing the estimate of this function for its positive values given in my 1984 Venice paper (Part II); and finally different applications to the theory of choices in the presence of risk and to the wealth transfer and tax questions (Part III).