In the introduction to Probabilistic Metaphysics, Patrick Suppes declares his intention to refute each of five central tenets of “neotraditional metaphysics”. These tenets run as follows:The future is determined by the past.Every event has a sufficient determinant cause.Knowledge must be grounded in certainty.Scientific knowledge can in principle be made complete.Scientific knowledge and method can in principle be unified.

William James and Alfred North Whitehead strongly rejected materialism as a metaphysical option. While James lived and wrote only up to the beginning of the revolution in physics that brought to the fore fundamentally different theories such as quantum theory and the special and general theories of relativity, Whitehead, as an accomplished mathematician, was readily conversant with these new developments. Since their respective times, however, much innovation and refinement of theories in physics and other natural sciences has taken place. With (...) these later developments, conceptions of matter and its capabilities have undergone far-reaching explicit and implicit changes. A consequence of these... (shrink)

I argue that the orthodox account of probabilistic causation, on which probabilistic causes determine the probability of their effects, is inconsistent with certain ontological assumptions implicit in scientific practice. In particular, scientists recognize the possibility that properties of populations can cause the behavior of members of the populations. Such emergent population‐level causation is metaphysically impossible on the orthodoxy.

In classical physics, probabilistic or statistical knowledge has been always related to ignorance or inaccurate subjective knowledge about an actual state of affairs. This idea has been extended to quantum mechanics through a completely incoherent interpretation of the Fermi-Dirac and Bose-Einstein statistics in terms of "strange" quantum particles. This interpretation, naturalized through a widespread "way of speaking" in the physics community, contradicts Born's physical account of Ψ as a "probability wave" which provides statistical information about outcomes that, in fact, (...) cannot be interpreted in terms of 'ignorance about an actual state of affairs'. In the present paper we discuss how the metaphysics of actuality has played an essential role in limiting the possibilities of understating things differently. We propose instead a metaphysical scheme in terms of powers with definite potentia which allows us to consider quantum probability in a new light, namely, as providing objective knowledge about a potential state of affairs. (shrink)

A probabilistic theory of causation is a theory which holds that the central feature of causation is that causes raise the probability of their effects. In this dissertation, I defend Hans Reichenbach's original version of the probabilistic theory of causation, which analyses causal relations in terms of a three place statistical betweenness relation. Unlike most discussions of this theory, I hold that the statistical relation should be taken as a sufficient, but not as a necessary , condition for (...) causal betweenness. With this difference in interpretation, Reichenbach's theory is shown to be immune to all of the criticisms which have been raised against it in the last fifty years. ;Reichenbach's main purpose in defending a probabilistic theory of causation was to use it in giving an analysis of the direction of time. I defend this view, arguing that the arrow of causation is more basic than any of the other arrows of time---metaphysical, psychological or physical. In particular, I argue against the popular view that the direction of time is given by the physical fact that entropy only increases in one direction. I further show that the probabilistic theory of causation is particularly suited to the task of analysing the various arrows of time. In my final chapter, I also suggest that the probabilistic theory of causation may be fruitfully applied to the analysis of some important puzzles in the interpretation of quantum mechanics. (shrink)

In Probabilistic Knowledge Sarah Moss proposes that our credences and subjective probability judgments (SPJs) can constitute knowledge. Mossean probabilistic knowledge is grounded in probabilistic beliefs that are justified, true, and unGettiered. In this paper I aim to address and solve two challenges that arise in the vicinity of the factivity condition for probabilistic knowledge: the factivity challenge and the challenge from probabilistic arguments from ignorance (probabilistic AIs). I argue that while Moss's deflationary solution to (...) the factivity challenge formally works, it leaves us ill-equipped to handle probabilistic AIs. An account of probabilistic knowledge that cannot overcome probabilistic AIs makes knowledge of thoroughly probabilistic contents a rare and unstable phenomenon, at best, or, at worst, impossible. I hold that establishing a metaphysically enriched account of probabilistic truth is therefore mandatory. I go on to develop a truth-conditional approach on probabilistic factivity that is relativistic in its nature and centers on objective chances. I show that while the approach is still compatible with Moss's overall semantics for probabilistic knowledge, it provides us with a simple but forceful answer to probabilistic AIs. (shrink)

The best and most popular argument for probabilism is the accuracy-dominance argument, which purports to show that alethic considerations alone support the view that an agent’s degrees of belief should always obey the axioms of probability. I argue that extant versions of the accuracy-dominance argument face a problem. In order for the mathematics of the argument to function as advertised, we must assume that every omniscient credence function is classically consistent; there can be no worlds in the set of dominance-relevant (...) worlds that obey some other logic. This restriction cannot be motivated on alethic grounds unless we’re also willing to accept that rationality requires belief in every metaphysical necessity, as the distinction between a priori logical necessities and a posteriori metaphysical ones is not an alethic distinction. To justify the restriction to classically consistent worlds, non-alethic motivation is required. And thus, if there is a version of the accuracy-dominance argument in support of probabilism, it isn’t one that is grounded in alethic considerations alone. (shrink)

We present new probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment, called Zλ- and lexλ-entailment, which are parameterized through a value λ ∈ [0,1] that describes the strength of the inheritance of purely probabilistic knowledge. In the special cases of λ = 0 and λ = 1, the notions of Zλ- and lexλ-entailment coincide with probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment that have been recently introduced by the (...) author. We show that the notions of Zλ- and lexλ-entailment have similar properties as their classical counterparts. In particular, they both satisfy the rationality postulates of System P and the property of Rational Monotonicity. Moreover, Zλ-entailment is weaker than lexλ-entailment, and both Zλ- and lexλ-entailment are proper generalizations of their classical counterparts. (shrink)

A probabilistic and counterfactual theory of causality is developed within the framework of branching time. The theory combines ideas developed by James Fetzer, Donald Nute, Patrick Suppes, Ming Xu, John Pollock, David Lewis and Mellor among others.

The paper starts with the distinction between conjunction-of-parts accounts and disjunction-of-possibilities accounts to truthlikeness. In Sect. 3, three distinctions between kinds of truthlikeness measures are introduced: comparative versus numeric t-measures, t-measures for qualitative versus quantitative theories, and t-measures for deterministic versus probabilistic truth. These three kinds of truthlikeness are explicated and developed within a version of conjunctive part accounts based on content elements. The focus lies on measures of probabilistic truthlikeness, that are divided into t-measures for statistical probabilities (...) and single case probabilities. The logical notion of probabilistic truthlikeness can be treated as a subcase of deterministic truthlikeness for quantitative theories. In contrast, the epistemic notion of probabilistic truthlikeness creates genuinely new problems, especially for hypotheses about single case probabilities that are evaluated not by comparison to observed frequencies, but by comparison to the truth values of single event statements. By the method of meta-induction, competing theories about single case probabilities can be aggregated into a combined theory with optimal predictive success and epistemic truthlikeness. (shrink)

In the literature, different frameworks of probabilistic epistemic logic have been proposed. Most of these frameworks define knowledge or belief by relational structure. In this paper, we explore the relationship between probability and belief, based on the Lockean thesis, and adopt neighborhood semantics that defines belief directly using probability. We provide a sound and weakly complete axiomatization for our framework. We also try to explain the lottery paradox by modelling it within our framework. Moreover, the paper presents findings concerning (...) the relationship between knowledge, belief and probability within various frameworks. (shrink)

We study a probabilistic logic based on the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence). We examine probabilistic conditional knowledge bases associated with imprecise probability assessments defined on arbitrary families of conditional events. We introduce a notion of conditional interpretation defined directly in terms of precise probability assessments. We also examine a property of strong satisfiability which is related to the notion of toleration well known in default reasoning. In our framework we (...) give more general definitions of the notions of probabilistic consistency and probabilistic entailment of Adams. We also recall a notion of strict p-consistency and some related results. Moreover, we give new proofs of some results obtained in probabilistic default reasoning. Finally, we examine the relationships between conditional probability rankings and the notions of g-coherence and g-coherent entailment. (shrink)

Hans Reichenbach’s posthumous book The Direction of Time ends somewhere between Socratic aporia and historical irony. Prompted by Feynman’s diagrammatic formulation of quantum electrodynamics, Reichenbach eventually abandoned the delicate balancing between the macroscopic foundation of the direction of time and microscopic descriptions of time order undertaken throughout the previous chapters in favor of an exclusively macroscopic theory that he had vehemently rejected in the 1920s. I analyze Reichenbach’s reasoning against the backdrop of the history of Feynman diagrams and the current (...) practice of particle physics. Building upon the debates about processes and conserved quantities between Wesley Salmon and Phil Dowe in the 1990s, and the exchange between Reichenbach and the gestalt theorist Kurt Lewin during the 1920s about topology and genidentity, I investigate whether the aporia about local time order could be avoided by following a strategy that Reichenbach adopted elsewhere in the book and develop a notion of functional genidentity that captures the practice of present-day elementary particle physics and the fact that Feynman diagrams have to be understood in the context of a complex mathematical description of scattering processes. (shrink)

It seems to be generally accepted that (a) counterfactual conditionals are to be analysed in terms of possible worlds and inter-world relations of similarity and (b) causation is conceptually prior to counterfactuals. I argue here that both (a) and (b) are false. The argument against (a) is not a general metaphysical or epistemological one but simply that, structurally speaking, possible worlds theories are wrong: this is revealed when we try to extend them to cover the case of probabilistic counterfactuals. (...) Indeed a type of counterfactual probability exists which cannot be expressed in possible worlds terms at all. The argument against (b) emerges when we look at the form of an adequate account of both probabilistic and non-probabilistic counterfactuals. I do this by sketching and defending an approach to counterfactuals that, first, invoke a generalized notion of cause as primitive and, secondly, is algorithmic in form: counterfactuals are evaluated algorithmically in terms of other counterfactuals, without vicious circularity. Structures like possible worlds do not play a role either in general truth-conditions or in evaluation. They are simply the wrong sorts of structures. (shrink)

The actualism/possibilism debate in ethics is traditionally formulated in terms of whether true counterfactuals of freedom about the future (true subjunctive conditionals concerning what someone would freely do in the future if they were in certain circumstances) even partly determine an agent's present moral obligations. But the very assumption that there are true counterfactuals of freedom about the future conflicts with the idea that freedom requires a metaphysically open future. We develop probabilism as a solution to the actualism/possibilism debate, a (...) solution that accommodates an open future requirement for freedom. We argue that probabilism resolves the conflicting intuitions that arise between actualists and possibilists and maintains certain distinct advantages over actualism and possibilism. (shrink)

Coherentism in epistemology has long suffered from lack of formal and quantitative explication of the notion of coherence. One might hope that probabilistic accounts of coherence such as those proposed by Lewis, Shogenji, Olsson, Fitelson, and Bovens and Hartmann will finally help solve this problem. This paper shows, however, that those accounts have a serious common problem: the problem of belief individuation. The coherence degree that each of the accounts assigns to an information set (or the verdict it gives (...) as to whether the set is coherent tout court) depends on how beliefs (or propositions) that represent the set are individuated. Indeed, logically equivalent belief sets that represent the same information set can be given drastically different degrees of coherence. This feature clashes with our natural and reasonable expectation that the coherence degree of a belief set does not change unless the believer adds essentially new information to the set or drops old information from it; or, to put it simply, that the believer cannot raise or lower the degree of coherence by purely logical reasoning. None of the accounts in question can adequately deal with coherence once logical inferences get into the picture. Toward the end of the paper, another notion of coherence that takes into account not only the contents but also the origins (or sources) of the relevant beliefs is considered. It is argued that this notion of coherence is of dubious significance, and that it does not help solve the problem of belief individuation. (shrink)

We propose a new model for forming and revising beliefs about unknown probabilities. To go beyond what is known with certainty and represent the agent’s beliefs about probability, we consider a plausibility map, associating to each possible distribution a plausibility ranking. Beliefs are defined as in Belief Revision Theory, in terms of truth in the most plausible worlds. We consider two forms of conditioning or belief update, corresponding to the acquisition of two types of information: learning observable evidence obtained by (...) repeated sampling from the unknown distribution; and learning higher-order information about the distribution. The first changes only the plausibility map, but leaves the given set of possible distributions essentially unchanged; the second rules out some distributions, thus shrinking the set of possibilities, without changing their plausibility ordering.. We look at stability of beliefs under either of these types of learning, defining two related notions, as well as a measure of the verisimilitude of a given plausibility model. We prove a number of convergence results, showing how our agent’s beliefs track the true probability after repeated sampling, and how she eventually gains in a sense knowledge of that true probability. Finally, we sketch the contours of a dynamic doxastic logic for statistical learning. (shrink)

At first glance, every metaphysics of laws can be combined with every ontology of time. In contrast, the paper intends to show that Humeanism requires eternalism and that Power metaphysics must presuppose an existentially dynamical view of temporal existence, i.e. growing block or presentism. The presented arguments turn out to be completely independent of whether the laws of nature are deterministic or probabilistic: the world is non-productive and static or productively dynamical, the future be ‘open’ or not.

It is often argued that if a mentalproperty supervenes on a physical property, then (1)the mental property M ``inherits'''' its causal efficacyfrom the physical property P and (2) the causalefficacy of M reduces to that of P. However, once weunderstand the supervenience thesis and the concept ofcausation probabilistically, it turns out that we caninfer the causal efficacy of M from that of P andvice versa if and only if a certain condition, whichI call the ``line-up'''' thesis, holds. I argue that (...) thesupervenience thesis entails neither this conditionnor its denial. I also argue that even when theline-up thesis holds true, reductionism about thecausal efficacy of the mental property doesn''tfollow. (shrink)

In what follows, I’ll discuss both the metaphysics and the epistemology of supervenience from a probabilistic point of view. The first half of this paper will explore how supervenience claims are related to other issues; these will include the thesis that physics is causally complete, the claim that there are emergent properties, the idea that mental properties are causally efficacious, and the notion that there are scientific laws about supervenient properties that generalize over systems that deploy different physical (...) realizations of the properties in question. The second half will examine the question of how observational evidence can lend support to supervenience claims. This problem turns out to raise some surprisingly deep issues about the nature of hypothesis testing in science. (shrink)

In artificial intelligence (AI), a number of criticisms were raised against the use of probability for dealing with uncertainty. All these criticisms, except what in this article we call the non-adequacy claim, have been eventually confuted. The non-adequacy claim is an exception because, unlike the other criticisms, it is exquisitely philosophical and, possibly for this reason, it was not discussed in the technical literature. A lack of clarity and understanding of this claim had a major impact on AI. Indeed, mostly (...) leaning on this claim, some scientists developed an alternative research direction and, as a result, the AI community split in two schools: a probabilistic and an alternative one. In this article, we argue that the non-adequacy claim has a strongly metaphysical character and, as such, should not be accepted as a conclusive argument against the adequacy of probability. (shrink)

In modern science, the theory of probability is one of the basic tools. Scientists using probability often refer to its objective interpretation. They emphasize that their probabilistic hypotheses concern objective facts, not degrees of belief. Accordingly, the following questions arise: What is the meaning of this type of probabilistic hypothesis? Is the assumption of objectivity necessary? The paper addresses these questions by analyzing objective probability in the context of the scientific debate on determinism. Two types of arguments will (...) be presented. On the one hand, there is the assertion that objective probability can exist only in an indeterministic world. Then, on the other hand — I analyze the assertions of those who believe in the co‑existence of objective probability and determinism. As a result I show that the acceptance of deterministic and indeterministic fields as possible areas where objective probability can occur is extremely problematic. Depending on the chosen area we encounter different types of problems. Therefore, I show that a significant number of these problems are associated with the acceptance of incorrect metaphysical assumptions. And finally, I postulate that the objectivity of probability can be reduced to the epistemic variant. (shrink)

This book develops new forms of logic: Operator Logic, Probabilistic Operator Logic and Quantum Operator Logic. It then proceeds to create a new view of metaphysics, Relativistic Quantum Metaphysics, for physical Reality. It then derives the form of The Standard Model of Elementary Particles. In particular it derives the origin of parity violation, the origin of the Strong interactions, and the origin of its peculiar symmetry. Also developed are new formalisms for Logic that are of interest in (...) themselves. While mathematics is essential in the latter stages of the book it is presented with sufficient text discussion to make what it is doing understandable to the non-mathematical reader. Generally the jargon of Philosophy, Logic and Physics is avoided as much as possible. But the second part of this book is very mathematical of necessity. In it the form of The Standard Model is derived in detail from a fundamental set of principles. (shrink)

Both Representation Theorem Arguments and Dutch Book Arguments support taking probabilistic coherence as an epistemic norm. Both depend on connecting beliefs to preferences, which are not clearly within the epistemic domain. Moreover, these connections are standardly grounded in questionable definitional/metaphysical claims. The paper argues that these definitional/metaphysical claims are insupportable. It offers a way of reconceiving Representation Theorem arguments which avoids the untenable premises. It then develops a parallel approach to Dutch Book Arguments, and compares the results. In each (...) case preferencedefects serve as a diagnostic tool, indicating purely epistemic defects. (shrink)

Standard accounts hold that regularities of behavior must be arbitrary to constitute a convention. Yet, there is growing consensus that conventionality is a graded phenomenon, and that conventions can be more or less natural. I develop an account of natural conventions that distinguishes two basic dimensions of conventional naturalness: a probabilistic dimension and an inherent one. A convention is probabilistically natural if it is likely to emerge in a population of agents, and inherently natural if its content is a (...) regularity that scores high on relevant measures for naturalness. I motivate the proposal on conceptual grounds and then showcase its descriptive benefits by discussing two case studies in language: the tendency towards word-length optimality and the prevalence of shape opacity in spoken language vocabularies. (shrink)

When we see or hear a spontaneous emotional expression, we usually immediately, effortlessly, and often correctly interpret it to mean happiness, sadness, or some other emotion as well as what this emotion is about. How do we do that? In this article, I evaluate how useful the concepts of natural meaning and probabilistic meaning are when it comes to explaining how we and other animals interpret emotional signs displayed without communicative intentions. I argue that Grice’s notion of natural meaning, (...) because it is a factive relation, is too restrictive for this purpose. I then present the notion of probabilistic meaning. The latter seems adequate for analyzing our ability to interpret non-communicative emotional signs, but it faces several difficulties when it comes to analyzing how we and other animals interpret emotional _signals_, i.e. signs that have the function to communicate emotional information. I present three of these difficulties. En passant, I suggest that a teleosemantic notion may be better suited for these challenges. (shrink)

D. M. Armstrong famously claims that deterministic laws of nature are contingent relations between universals and that his account can also be straightforwardly extended to irreducibly probabilistic laws of nature. For the most part, philosophers have neglected to scrutinize Armstrong’s account of probabilistic laws. This is surprising precisely because his own claims about probabilistic laws make it unclear just what he takes them to be. We offer three interpretations of what Armstrong-style probabilistic laws are, and argue (...) that all three interpretations are incompatible either with some feature of Armstrong’s broader metaphysics or with essential features of his account of laws (or both). (shrink)

The world contains not only causes and effects, but also causal relations holding between causes and effects. Because causal relations enter into the structure of the world, their presence has various modal and probabilistic consequences. Causation and “necessary and sufficient conditions” do often go hand in hand. Causation, however, is a robust ingredient within the world itself, whereas modalities and probabilities supervene on the nature of the world as a whole, and on the resulting relations between one possible world (...) and others. Some modalities, therefore, are essentially causal; but causation is not essentially modal.19. (shrink)

Inductive probabilistic reasoning is understood as the application of inference patterns that use statistical background information to assign (subjective) probabilities to single events. The simplest such inference pattern is direct inference: from “70% of As are Bs” and “a is an A” infer that a is a B with probability 0.7. Direct inference is generalized by Jeffrey’s rule and the principle of cross-entropy minimization. To adequately formalize inductive probabilistic reasoning is an interesting topic for artificial intelligence, as an (...) autonomous system acting in a complex environment may have to base its actions on a probabilistic model of its environment, and the probabilities needed to form this model can often be obtained by combining statistical background information with particular observations made, i.e., by inductive probabilistic reasoning. In this paper a formal framework for inductive probabilistic reasoning is developed: syntactically it consists of an extension of the language of first-order predicate logic that allows to express statements about both statistical and subjective probabilities. Semantics for this representation language are developed that give rise to two distinct entailment relations: a relation ⊨ that models strict, probabilistically valid, inferences, and a relation that models inductive probabilistic inferences. The inductive entailment relation is obtained by implementing cross-entropy minimization in a preferred model semantics. A main objective of our approach is to ensure that for both entailment relations complete proof systems exist. This is achieved by allowing probability distributions in our semantic models that use non-standard probability values. A number of results are presented that show that in several important aspects the resulting logic behaves just like a logic based on real-valued probabilities alone. (shrink)

Scoring rules measure the deviation between a credence assignment and reality. Probabilism holds that only those credence assignments that satisfy the axioms of probability are rationally admissible. Accuracy-based arguments for probabilism observe that given certain conditions on a scoring rule, the score of any non-probability is dominated by the score of a probability. The conditions in the arguments we will consider include propriety: the claim that the expected accuracy of _p_ is not beaten by the expected accuracy of any other (...) credence _c_ by the lights of _p_ if _p_ is a probability. I argue that if we think through how a non-probabilist can respond to pragmatic arguments for probabilism, we will expect the non-probabilist to accept a condition _stronger_ than propriety for the same reasons that the probabilist gives for propriety, but this stronger condition is incompatible with the other conditions that the probabilist needs to run the accuracy argument. This makes it unlikely for the probabilist’s argument to be compelling. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Literature 25.2 (2001) 353-356 [Access article in PDF] Book Review The Metaphysical Club The Metaphysical Club, by Louis Menand; xii & 546 pp. New York: Farrar, Straus and Giroux, 2001, $27.00. "They didn't just want to keep the conversation going; they wanted to get to a better place" (p. 440). So much for the most prominent contemporary pragmatist, Richard Rorty, who remains unmentioned except in the acknowledgments. (...) That better place is participatory democracy (a phrase that does not appear in the book), which "means that everyone is equally in the game, but it also means that no one can opt out" (p. 441). The true name of the game is skeptical tolerance. There are no unquestionable duties or inalienable rights, no immutable natural laws, no absolute moral rules, no highest principles, no inherent virtues, no absolute standards, no stasis, no absolutely certain truth. There are no individual destinies, because the social comes before the individual, and the individual is embedded within and cannot exist without society. Scientific knowledge is always probabilistic, not necessarily because nature is indeterministic, but because we can never know enough to calculate its regularities if they exist. To wit, there are no Platonic Ideas or unchanging universals. All is change, nothing that happens is ever repeated, our general ideas and laws of nature are merely tools for getting along in the world. Above all, ideas do not refer to things, only to other ideas. What expedites our thinking is true. What expedites our acting is right. Whenever we act according to principle, rule, or law, we are making a bet that events will turn out the way [End Page 353] we think they will. If we keep this always in mind, we will never succumb to violence or war in the name of belief or principle. Whatever we believe, it could be otherwise. Such is a general summary of pragmatism as it has filtered down to the textbooks. It is (again befittingly) more or less accurate. The can-do American seeks out cash value in practical life.Oliver Wendell Holmes, Jr., William James, Charles Saunders Pierce, and John Dewey crafted the only indigenous philosophy that has so far been produced in America. Its roots are in Laplacean probability theory, Darwinian evolutionism, and Chauncey Wright's indeterminism. While James hoped to save a place for religion (if it works, go with it) and Pierce a place for God (he thought there had to be a designing intelligence to account for order), the pragmatic result is profoundly skeptical and secular. Neither Holmes nor Dewey thought that individuals imbedded in societies had any need of absolutes. Holmes said that people first decide on the basis of experience, then they deduce. Dewey said that people first behave commonsensically, then they rationalize.There is nothing as condensed as the above in Louis Menand's beautiful book on the ideas, personalities, and influence of Holmes, James, Pierce, and Dewey. I know of no clearer exposition of their ideas, and few biographers have made them come so alive. In particular, Menand's coverage of peripheral (but by no means insignificant) figures is very rich. He describes the development of graduate universities in America in detail from their autocratic beginnings to the institution of academic freedom as we know it today. University presidents, trustees, and administrators are presented luxuriously as the villains, and the professors gloriously as the heroes. Menand remarks with slight amazement that society bought the concept that professors were beholden to the public at large and not to the state or private university owners. He could have commented further on the fact that the concept of academic freedom has become virtually irrelevant in today's corporate research universities."It is a remarkable fact about the United States," Menand begins his book, "that it fought a civil war without undergoing a change in its form of government" (p. ix). This is a breathtaking fact, and I don't suppose Menand had any intent to explain it. "The Civil War swept away the slave civilization of the South, but it swept away almost the whole intellectual... (shrink)

Branden Fitelson and Alan Hájek have suggested that it is finally time for a “revolution” in which we jettison Kolmogorov’s axiomatization of probability, and move to an alternative like Popper’s. According to these authors, not only did Kolmogorov fail to give an adequate analysis of conditional probability, he also failed to give an adequate account of another central notion in probability theory: probabilistic independence. This paper defends Kolmogorov, with a focus on this independence charge. I show that Kolmogorov’s sophisticated (...) theory of conditional distributions, advocated by authors such as Kenny Easwaran but often overlooked by philosophers, has the resources to define the notion of independence Fitelson and Hájek seek. I then argue that Kolmogorov’s original definition of independence, once suitably reinterpreted as capturing a slight logical weakening of this notion, is not so problematic after all. Indeed, rather than discarding Kolmogorov’s definition, we should make room for two distinct notions of probabilistic independence, one stronger and one weaker, which play different theoretical roles. (shrink)

This paper constitutes my first attempt publicly to comment on Nancy Cartwright’s philosophy of science. That I have not done this earlier is primarily due to the great similarities in our views on topics where our interests overlap.2 But Cartwright’s work also covers topics I have never seriously considered, such as the use of linear models in economics and the measurement problem in quantum mechanics. Even the subject of probabilistic causation, to which I once contributed, is not one I (...) now feel confident in examining in any detail. I will concentrate, therefore, on her views regarding the nature of scientific theories, laws, models, and causality in general – topics at the forefront of my own current thinking. More specifically still, I will focus on the picture of classical mechanics she presents in The Dappled World (1999). (shrink)

Truthlikeness is a property of a theory or a proposition that represents its closeness to the truth. We start by summarizing Niiniluoto’s proposal of truthlikeness for deterministic laws, which defines truthlikeness as a function of accuracy, and García-Lapeña’s expanded version, which defines truthlikeness for DL as a function of two factors, accuracy and nomicity. Then, we move to develop an appropriate definition of truthlikeness for probabilistic laws based on Niiniluoto’s suggestion to use the Kullback–Leibler divergence to define the distance (...) between a probability law X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X$$\end{document} and the true probability law T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T$$\end{document}. We argue that the Kullback–Leibler divergence seems to be the best of the available probability distances to measure accuracy between PL. However, as in the case of DL, we argue that accuracy represents a necessary but not sufficient condition, as two PL may be equally accurate and still one may imply more true or truthlike consequences, behaviours or true facts about the system than the other. The final proposal defines truthlikeness for PL as a function of two factors, p-accuracy and p-nomicity, in intimate connexion with García-Lapeña’s proposal for DL. (shrink)

This volume sheds new light on the multifarious personality of Bruno de Finetti and his outstanding contributions not only to probability and statistics, but also to economics and philosophy. Rather than focusing on de Finetti's technical work on probability, the essays collected here address the philosophy underpinning all of de Finetti's writings, a view Richard Jeffrey labelled "radical probabilism". Special attention is devoted to de Finetti's ideas on economics, which are inspired by the same philosophical approach, while an effort is (...) made to highlight some lesser known aspects of de Finetti's production. The volume ends with an Appendix on de Finetti's book L'invenzione della verit (The invention of truth), written in 1934 and published in 2006, which contains an extensive presentation of de Finetti's philosophical viewpoint, revolving around the idea that our knowledge is the product of human thought, which in such enterprise is guided by considerations of utility, rather than metaphysical principles. (shrink)

The aim of the paper is to propose an understanding of idealization in terms of Nowak’s unitarian metaphysics. Two natural interpretations of the procedure are critically discussed and rejected as inadequate. The first account of idealization is unable to explain why idealized factors cease to exert influence on the investigated magnitude. The second account of idealization solves this problem but does so at the cost of blurring the distinction between idealization and abstruction. Moreover, it faces the consequence that the (...) process of idealization instead of leading to a sharper understanding of phenomena will normally result in making the picture more and more probabilistic. I propose a third account of idealization in unitarian terms that solves all three problems. (shrink)

To recapitulate, then, for Reichenbach probability is the foundation of both metaphysics and epistemology. Metaphysically, probability is fundamental because it is the probability relations among the sequences of events in the world that gives rise to causality, time, and space. Epistemologically, probability is fundamental because empirical knowledge is simply knowledge of probabilities. Even knowledge of observation sentences is considered to be probabilistic knowledge by Reichenbach (EP, pp. 183–188), because Reichenbach's fallibilism leads him to hold that no observation sentence (...) is absolutely incorrigible, and with the advance of scientific knowledge we need to inquire into the probability that our singular observation judgments may be in error.My aim here has not been to argue that Reichenbach succeeded in his magnificent attempt any more than Carnap succeeded in his. But I hope to have convinced you that is was one of the most magnificent attempts by any empiricist philosopher of this or of any other century, and I believe that the effort to understand it and to master its details will as richly repay us as the much greater effort which has been devoted to the study of Carnap's work has already repayed us. (shrink)