The aim of this paper is to introduce a new member of the family of the modal interpretations of quantum mechanics. In this modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the property-ascription rule that selects the definite-valued observables whose possible values become actual. We show that this interpretation is effective for solving the measurement problem, both in its ideal and its non-ideal versions, and we argue for the physical relevance of the property-ascription rule by (...) applying it to well-known physical situations. Moreover, we explain how this interpretation supplies a description of the elemental categories of the ontology referred to by the theory, where quantum systems turn out to be bundles of possible properties. (shrink)

We argue that probability mistakes indicate that at least some of us often do not adequately possess the concept of probability (and its cognates) and that the digital dissemination of such misinfo...

In this article, I aim at showing how powers may ground different types of probability in the universe. In Section 1 I single out several dimensions along which the probability of something can be determined. Each of such dimensions can be further specified at the type-level or at the token-level. In Section 2 I introduce some metaphysical assumptions about powers. In Section 3 I show how powers can ground single-case probabilities and frequency-probabilities in a deterministic setting. Later on, in Section (...) 4, I move to a theoretical framework where the falsity of determinism is assumed. Within such a framework, I first argue that some probabilities are grounded on basic powers. Moreover, in Section 5, I introduce tendencies and suggest that they are endowed with specific degrees of activation that may change over time. Such degrees explain why tendencies are more likely to be activated than non-activated, or vice versa. In Section 6 I compare my account of tendencies with other accounts. Finally, in Section 7, I anticipate some general objections against my account – objections that it shares with propensity-accounts of probability – and against degrees of activation of tendencies. (shrink)

GRW Theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as either single (...) case propensities or Humean objective chances. Although single case propensities have some intuitive appeal in the context of GRW theory, on balance it seems that Humean objective chances are preferable on conceptual grounds because single case propensities suffer from various well know problems such as unlimited frequency tolerance and lack of a rationalisation of the principal principle. (shrink)

The proposition that Tweety is a bird coheres better with the proposition that Tweety has wings than with the proposition that Tweety cannot fly. This relationship of contrastive coherence is the focus of the present paper. Based on recent work in formal epistemology we consider various possibilities to model this relationship by means of probability theory. In a second step we consider different applications of these models. Among others, we offer a coherentist interpretation of the conjunction fallacy.

This paper outlines a theory and computer implementation of causal meanings and reasoning. The meanings depend on possibilities, and there are four weak causal relations: A causes B, A prevents B, A allows B, and A allows not‐B, and two stronger relations of cause and prevention. Thus, A causes B corresponds to three possibilities: A and B, not‐A and B, and not‐A and not‐B, with the temporal constraint that B does not precede A; and the stronger relation conveys only the (...) first and last of these possibilities. Individuals represent these relations in mental models of what is true in the various possibilities. The theory predicts a number of phenomena, and, contrary to many accounts, it implies that the meaning of causation is not probabilistic, differs from the meaning of enabling conditions, and does not depend on causal powers or mechanisms. The theory also implies that causal deductions do not depend on schemas or rules. (shrink)

By “Propensities” I mean the kind of probabilities that figure in laws of nature. Propensities might be (i) relative frequencies, finite or long run, de facto or modalized, or (ii) reflections of our epistemic probabilities or (iii) sui generus theoretical notions. I believe that the whole family of relative frequency proposals (i) are inadequate. As an alternative I wish to suggest (ii) an epistemic account of propensities and of nomic force in general, in the spirit of Hume, Mill, DeFinetti, Ayer, (...) Suppes and Jeffrey. Whether accounts of the third kind differ in substance or in name only from the sort of account that I am proposing is a nice question, to which. I will devote some brief closing remarks. (shrink)

We attempt to make superdeterminism more intuitive, notably by simulating a deterministic model system, a billiard game. In this system an initial ‘bang’ correlates all events, just as in the superdeterministic universe. We introduce the notions of ‘strong’ and ‘soft’ superdeterminism, in order to clarify debates in the literature. Based on the analogy with billiards, we show that superdeterministic correlations may exist as a matter of principle, but be undetectable for all practical purposes. Even if inaccessible, such strong-superdeterministic correlations can (...) explain why soft-, or effective, superdeterministic theories can be built. We counter classic objections to superdeterminism such as the claim that it would be at odds with the scientific method, and with the construction of new theories. Finally, we show that probability theory, as a physical theory, indicates that superdeterminism has a greater explanatory power than its competitors: it can coherently answer questions from probability theory for which other positions remain powerless. Since probability theory is, in a sense, the most unifying physics theory (all physical systems comply with it), this argument confers considerable weight. (shrink)

Ranging from Alan Turing’s seminal 1936 paper to the latest work on Kolmogorov complexity and linear logic, this comprehensive new work clarifies the relationship between computability on the one hand and constructivity on the other. The authors argue that even though constructivists have largely shed Brouwer’s solipsistic attitude to logic, there remain points of disagreement to this day. Focusing on the growing pains computability experienced as it was forced to address the demands of rapidly expanding applications, the content maps the (...) developments following Turing’s ground-breaking linkage of computation and the machine, the resulting birth of complexity theory, the innovations of Kolmogorov complexity and resolving the dissonances between proof theoretical semantics and canonical proof feasibility. Finally, it explores one of the most fundamental questions concerning the interface between constructivity and computability: whether the theory of recursive functions is needed for a rigorous development of constructive mathematics. This volume contributes to the unity of science by overcoming disunities rather than offering an overarching framework. It posits that computability’s adoption of a classical, ontological point of view kept these imperatives separated. In studying the relationship between the two, it is a vital step forward in overcoming the disagreements and misunderstandings which stand in the way of a unifying view of logic. (shrink)

I analyse critically what I regard as the most accomplished empiricist account of propensities, namely the long run propensity theory developed by Donald Gillies . Empiricist accounts are distinguished by their commitment to the ‘identity thesis’: the identification of propensities and objective probabilities. These theories are intended, in the tradition of Karl Popper’s influential proposal, to provide an interpretation of probability that renders probability statements directly testable by experiment. I argue that the commitment to the identity thesis leaves empiricist theories, (...) including Gillies’ version, vulnerable to a variant of what is known as Humphreys’ paradox. I suggest that the tension may be resolved only by abandoning the identity thesis, and by adopting instead an understanding of propensities as explanatory properties of chancy objects. (shrink)

In a recent paper [e-print quant-ph/0101012], Hardy has given a derivation of “quantum theory from five reasonable axioms.” Here we show that Hardy's first axiom, which identifies probability with limiting frequency in an ensemble, is not necessary for his derivation. By reformulating Hardy's assumptions, and modifying a part of his proof, in terms of Bayesian probabilities, we show that his work can be easily reconciled with a Bayesian interpretation of quantum probability.

Epistemic conservatism is the thesis that the mere holding of a belief confers some positive epistemic status on its content. Conservatism is widely criticized on the grounds that it conflicts with the main goal in epistemology to believe truths and disbelieve falsehoods. In this paper I argue for conservatism and defend it from objections. First, I argue that the objection to conservatism from the truth goal in epistemology fails. Second, I develop and defend an argument for conservatism from the perspectival (...) character of the truth goal. Finally, I examine several forceful challenges to conservatism and argue that these challenges are unsuccessful. The first challenge is that conservatism implies the propriety of assertions like ‘I believe p and this is part of my justification for it’. The second challenge argues that conservatism wrongly implies that the identity of an epistemic agent is relevant to the main goal of believing truths and disbelieving falsehoods. The last two challenges I consider are the ‘extra boost’ objection and the conversion objection. Each of these objections helps to clarify the nature of the conservative thesis. The upshot of the paper is that conservatism is an important and viable epistemological thesis. (shrink)

This paper is an extended review of the book Error and Inference, edited by Deborah Mayo and Aris Spanos, about their frequentist and philosophical perspective on testing of hypothesis and on the criticisms of alternatives like the Bayesian approach.

Recently I posted a paper entitled “External observer reflections on QBism”. As any external observer, I was not able to reflect all features of QBism properly. The comments I received from one of QBism’s creators, C. A. Fuchs, were very valuable to me in better understanding the views of QBists. Some of QBism’s features are very delicate and extracting them from articles of QBists is not a simple task. Therefore, I hope that the second portion of my reflections on QBism (...) might be interesting and useful for other experts in quantum foundations and quantum information theory. In the present paper I correct some of my earlier posted critical comments on QBism. At the same time, other critical comments gained new validation through my recent deeper understanding of QBists views on a number of problems. (shrink)

The corpus of physical theory is a paradigm of knowledge. The evolution of modern physical theory constitutes the clearest exemplar of the growth of knowledge. If the development of physical theory does not constitute an example of progress and growth in what we know about the Universe nothing does. So anyone interested in the theory of knowledge must be interested consequently in the evolution and content of physical theory. Crucial to the conception of physics as a paradigm of knowledge is (...) the way in which physical theory provides explanations of a vast diversity of natural phenomena on the basis of a very few fundamental principles. A central problem for the epistemologist is therefore what is theoretical explanation in physics? Here we can get good insight from what Redhead has said. Indeed one could agree with almost everything Redhead says and simply endorse much of his careful and extensive defence of the covering law account of explanation in the physical sciences at least as an ideal. However I shall, I fear, try the reader's patience by extending some of the considerations he introduced and raising those issues where we disagree, especially in the important area of statistical explanation. (shrink)

A complete calculus of inductive inference captures the totality of facts about inductive support within some domain of propositions as relations or theorems within the calculus. It is demonstrated that there can be no complete, non-trivial calculus of inductive inference.

The goal of this paper is to provide a detailed reading of John Venn's Logic of Chance as a work of logic or, more specifically, as a specific portion of the general system of so-called ‘material’ logic developed in his Principles of Empirical or Inductive Logic and to discuss it against the background of his Boolean-inspired views on the connection between logic and mathematics. It is by means of this situating of Venn 1866 [The Logic of Chance. An Essay on (...) the Foundations and Province of the Theory of Probability. With Especial Reference to Its Application to Moral and Social Science, London: Macmillan] within the entirety of his oeuvre that it becomes both possible to revisit and necessary to re-articulate its place in the history of the frequency interpretation of probability. For it is clear that if Venn's approach to logic not only allowed him to establish its foundations on the basis of a process of idealization and define it as consisting of so-called hypothetical infinite series, bu.. (shrink)

Popper's writings cover a remarkably wide range of subjects. The spectrum runs from Plato's theory of politics to the foundations of quantum mechanics. Yet even amidst this variety the philosophy of probability occupies a prominent place. David Miller once pointed out to me that more than half of Popper's The Logic of Scientific Discovery is taken up with discussions of probability. I checked this claim using the 1972 6th revised impression of The Logic of Scientific Discovery , and found that (...) of the approximately 450 pages of text, approximately 250 are to do with probability. Thus Miller's claim is amply justified. It seems indeed that the philosophy of probability was one of Popper's favourite subjects, and, as we shall see, Popper certainly enriched the field with several striking innovations. In this area, as in others, Popper held very definite views, and criticized his opponents in no uncertain terms. Popper was an objectivist and anti-Bayesian, and his criticisms were directed against subjectivism and Bayesianism. (shrink)

This paper offers a metaphysics of physical probability in (or if you prefer, truth conditions for probabilistic claims about) deterministic systems based on an approach to the explanation of probabilistic patterns in deterministic systems called the method of arbitrary functions. Much of the appeal of the method is its promise to provide an account of physical probability on which probability assignments have the ability to support counterfactuals about frequencies. It is argued that the eponymous arbitrary functions are of little philosophical (...) use, but that they can be substituted for facts about frequencies without losing the ability to provide counterfactual support. The result is an account of probability in deterministic systems that has a “propensity-like” look and feel, yet which requires no supplement to the standard modern empiricist tool kit of particular matters of fact and principles of physical dynamics. (shrink)

The weather report says that the chance of a hurricane arriving later today is 90%. Forewarned is forearmed: expecting a hurricane, before leaving home you pack your hurricane lantern.

Ultimately, the only good reason for restricting the freedom of responsible adults is to protect other people's freedom, to increase the overall enjoyment of freedom.

In order to comprehend the world around us and construct explaining theories for this purpose, we need a conception of physical probability, since we come across many (apparently) probabilistic phenomena in our world. But how should we understand objective probability claims? Since pure frequency approaches of probability are not appropriate, we have to use a single case propensity interpretation. Unfortunately, many philosophers believe that this understanding of probability is burdened with significant difficulties. My main aim is to show that we (...) can treat propensity as a theoretical concept that exhibits many similarities to other theoretical concepts, and its difficulties are not insuperable if we make explicit some general presuppositions of scientific practice and apply them to propensities. At least this is true if we formulate the right bridge principle for propensity and rely on further methodological rules in dealing with propensity assertions to make them empirically testable. (shrink)

Gillies introduced a propensity interpretation of probability which is linked to experience by a falsifying rule for probability statements. The present paper argues that general statistical tests should qualify as falsification rules. The ‘goodness-of-fit paradox’ is introduced: the confirmation of a probability model by a test refutes the model's validity. An example is given in which an independence test introduces dependence. Several possibilities to interpret the paradox and to deal with it are discussed. It is concluded that the propensity interpretation (...) properly reflects statistical practice, but it is not as objective as some adherents claim. (shrink)

The purpose of this paper is to discuss the role of financial practice in the development of mathematics as applied in human judgement. The basis of the paper is in historical research from the 1990s that argues that the monetisation of western commerce, which abstracted value into quantified price, was synthesised with scholastic analysis resulting in a “mathematical mechanistic world picture” that led to the widespread use of mathematics in science from the seventeenth century. An aspect of this process was (...) the quantification of chance that led to the development of mathematical probability, the branch of mathematics most relevant to judgement and the focus of this paper. Ideas from this historical research are related to the fundamental theorem of asset pricing, the foundational theory of contemporary financial mathematics. The paper observes that vestiges of medieval scholastic attitudes to financial ethics can be discerned in the FTAP, offering a novel interpretation of the mathematical theorem. The paper then considers the Dutch book argument, the most popular justification for subjective probability. The paper’s main contribution is in describing the significance of financial practice in validating the DBA and the paper explains how the FTAP addresses some criticisms of how the DBA represents beliefs. The conclusions emphasise the distinction between pure and practical reasoning and that this should be mirrored in a distinction between the mathematics of physica and practica. This point is important as mathematics is becoming more widespread in modelling, and directing, social systems. (shrink)

The aim of this article is to assess the impact of Big Data technologies for insurance ratemaking, with a special focus on motor products.The first part shows how statistics and insurance mechanisms adopted the same aggregate viewpoint. It made visible regularities that were invisible at the individual level, further supporting the classificatory approach of insurance and the assumption that all members of a class are identical risks. The second part focuses on the reversal of perspective currently occurring in data analysis (...) with predictive analytics, and how this conceptually contradicts the collective basis of insurance. The tremendous volume of data and the personalization promise through accurate individual prediction indeed deeply shakes the homogeneity hypothesis behind pooling. The third part attempts to assess the extent of this shift in motor insurance. Onboard devices that collect continuous driving behavioural data could import this new paradigm into these products. An examination of the current state of research on models with telematics data shows however that the epistemological leap, for now, has not happened. (shrink)

One of the first to criticize the verifiability theory of meaning embraced by logical empiricists, Reichenbach ties the significance of scientific statements to their predictive character, which offers the condition for their testability. While identifying prediction as the task of scientific knowledge, Reichenbach assigns induction a pivotal role, and regards the theory of knowledge as a theory of prediction based on induction. Reichenbach's inductivism is grounded on the frequency notion of probability, of which he prompts a more flexible version than (...) that of Richard von Mises. Unlike von Mises, Reichenbach attempts to account for single case probabilities, and entertains a restricted notion of randomness, more suitable for practical purposes. Moreover, Reichenbach developed a theory of induction, absent from von Mises's perspective, and argued for the justification of induction. This article outlines the main traits of Reichenbach's inductivism, with special reference to his book Experience and prediction. (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)

The ArgumentThis paper analyzes the complex and many-layered interrelation between the realization of the inevitable limits of precision in the experimental domain, the emerging quantum theory, and empirically oriented philosophy in the years 1925–1935. In contrast to the usual historical presentation of Heisenberg's uncertainty principle as a purely theoretical achievement, this work discloses the experimental roots of Heisenberg's contribution. In addition, this paper argues that the positivistic philosophy of elimination of unobservables was not used as a guiding principle in the (...) emergence of the new quantum theory, but rather mostly as a post facto justification. The case of P. W. Bridgman, analyzed in this paper, demonstrates how inconclusive operationalistic arguments are, when used as a possible heuristic aid for future discoveries. A large part of this paper is devoted to the evolution of Bridgman's views, and his skeptical reassessment of operationalism and of the very notion of scientific truth. (shrink)