The most familiar philosophical conception of objective chance renders determinism incompatible with non-trivial chances. This conception – associated in particular with the work of David Lewis – is not a good fit with our use of the word ‘chance’ and its cognates in ordinary discourse. In this paper we show how a generalized framework for chance can reconcile determinism with non-trivial chances, and provide for a more charitable interpretation of ordinary chance-talk. According to our proposal, variation in an admissible ‘evidence (...) base’ generates a spectrum of different chance functions. Successive coarse-grainings of the evidence base generates a partial ordering of chance functions, with finer trumping coarser if known. We suggest that chance-attributions in ordinary discourse express different chance functions in different contexts, and we sketch a potential contextual mechanism for making particular chance functions salient. The mechanism involves the idea that admissible evidence is available evidence: propositions that could be known. A consequence is that attributions of objective chances inherit the relatively familiar context-sensitivity associated with the modal ‘could’. We show how this context-dependency undermines certain arguments for the incompatibility of chance with determinism. (shrink)

This chapter will review selected aspects of the terrain of discussions about probabilities in statistical mechanics (with no pretensions to exhaustiveness, though the major issues will be touched upon), and will argue for a number of claims. None of the claims to be defended is entirely original, but all deserve emphasis. The first, and least controversial, is that probabilistic notions are needed to make sense of statistical mechanics. The reason for this is the same reason that convinced Maxwell, Gibbs, and (...) Boltzmann that probabilities would be needed, namely, that the second law of thermodynamics, which in its original formulation says that certain processes are impossible, must, on the kinetic theory, be replaced by a weaker formulation according to which what the original version deems impossible is merely improbable. Second is that we ought not take the standard measures invoked in equilibrium statistical mechanics as giving, in any sense, the correct probabilities about microstates of the system. We can settle for a much weaker claim: that the probabilities for outcomes of experiments yielded by the standard distributions are effectively the same as those yielded by any distribution that we should take as a representing probabilities over microstates. Lastly, (and most controversially): in asking about the status of probabilities in statistical mechanics, the familiar dichotomy between epistemic probabilities (credences, or degrees of belief) and ontic (physical) probabilities is insufficient; the concept of probability that is best suited to the needs of statistical mechanics is one that combines epistemic and physical considerations. (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 argues that the technical notion of conditional probability, as given by the ratio analysis, is unsuitable for dealing with our pretheoretical and intuitive understanding of both conditionality and probability. This is an ontological account of conditionals that include an irreducible dispositional connection between the antecedent and consequent conditions and where the conditional has to be treated as an indivisible whole rather than compositional. The relevant type of conditionality is found in some well-defined group of conditional statements. As an (...) alternative, therefore, we briefly offer grounds for what we would call an ontological reading: for both conditionality and conditional probability in general. It is not offered as a fully developed theory of conditionality but can be used, we claim, to explain why calculations according to the RATIO scheme does not coincide with our intuitive notion of conditional probability. What it shows us is that for an understanding of the whole range of conditionals we will need what John Heil (2003), in response to Quine (1953), calls an ontological point of view. (shrink)

A theory of causation with ‘tendencies’ as causal con- nections is proposed. Not, however, as ‘necessary connec- tions’: causes are not sufficient, they do not necessitate their effects. The theory is not an analysis of the concept of causation, but a description of what is the case in typical cases of causation. Therefore it does not strictly contradict any analysis of the concept of causation, not even reduct- ive ones. It would even be supported by a counterfactual or a probabilistic (...) analysis. (shrink)

The idea that perceptual and cognitive systems must incorporate knowledge about the structure of the environment has become a central dogma of cognitive theory. In a Bayesian context, this idea is often realized in terms of “tuning the prior”—widely assumed to mean adjusting prior probabilities so that they match the frequencies of events in the world. This kind of “ecological” tuning has often been held up as an ideal of inference, in fact defining an “ideal observer.” But widespread as this (...) viewpoint is, it directly contradicts Bayesian philosophy of probability, which views probabilities as degrees of belief rather than relative frequencies, and explicitly denies that they are objective characteristics of the world. Moreover, tuning the prior to observed environmental frequencies is subject to overfitting, meaning in this context overtuning to the environment, which leads (ironically) to poor performance in future encounters with the same environment. Whenever there is uncertainty about the environment—which there almost always is—an agent's prior should be biased away from ecological relative frequencies and toward simpler and more entropic priors. (shrink)

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)

The paper provides a new critical perspective on the propensity interpretation of fitness, by investigating its relationship to the propensity interpretation of probability. Two main conclusions are drawn. First, the claim that fitness is a propensity cannot be understood properly: fitness is not a propensity in the sense prescribed by the propensity interpretation of probability. Second, this interpretation of probability is inessential for explanations proposed by the PIF in evolutionary biology. Consequently, interpreting the probabilistic dimension of fitness in terms of (...) propensities is neither a strong motivation in favor of this interpretation, nor a possible target for substantial criticism. (shrink)

In this thesis, I develop a nonreductive and general conception of potentiality, and explore the prospects of a realist account of possibility based on this account of potentiality. Potentialities are properties of individual objects; they include dispositions such as fragility and abilities such as the ability to play the piano. Potentialities are individuated by their manifestation alone. In order to provide a unified account of potentialities, I argue in chapter 2 that dispositions, contrary to philosophical orthodoxy, are best understood in (...) terms only of their manifestations (as disposi- tions to ...), rather than in terms of a stimulus and a manifestation condition (as dispositions to ... if ...). Chapter 3 provides some preliminary motivation for a nonreductive and gen- eral account of potentiality, and chapter 4 develops such an account. The guiding question is how far the notion of potentiality can be extended from the initial ex- amples of familiar dispositions and abilities, and it is argued that it can be extended very far. Various features of potentialities are explored, among them extrinsicality, iterations of potentiality, and the behaviour of potentiality with regard to logical equivalence. In chapter 5, the account is set to work in providing the outlines and a defense of a potentiality-based account of possibility. The basic idea of such an account is that it is possible that p just in case some thing has a potentiality for p. The account is defended against the objection that there may not be enough potential- ities to ground all the possibilities that there are. Finally, in chapter 6, a logic of potentiality is formulated and the logic of possibility derived from it, showing that the potentiality-based account of possibility is formally adequate: it provides pos- sibility with the formal features that modal logicians have studied. I conclude that the proposed account of possibility is a promising research programme. (shrink)

A proposal for an objective interpretation of probability is introduced and discussed: probabilities as deriving from ranges in suitably structured initial-state spaces. Roughly, the probability of an event on a chance trial is the proportion of initial states that lead to the event in question within the space of all possible initial states associated with this type of experiment, provided that the proportion is approximately the same in any not too small subregion of the space. This I would like to (...) call the “natural-range conception” of probability. Providing a substantial alternative to frequency or propensity accounts of probability in a deterministic setting, it is closely related to the so-called “method of arbitrary functions”. It is explicated, confronted with certain problems, and some ideas how these might be overcome are sketched and discussed. (shrink)

Social Epistemology, Volume 25, Issue 2, Page 167-172, April 2011.

This paper investigates the possibiity of developing a fully micro realistic version of elementary quantum mechanics. I argue that it is highly desirable to develop such a version of quantum mechanics, and that the failure of all current versions and interpretations of quantum mechanics to constitute micro realistic theories is at the root of many of the interpretative problems associated with quantum mechanics, in particular the problem of measurement. I put forward a propensity micro realistic version of quantum mechanics, and (...) suggest how it might be possible to discriminate, on expermental grounds, between this theory and other versions of quantum mechanics. (shrink)

In recent years, realism?particularly critical realism?has become an important philosophical and methodological foundation for social science. A key feature is that of natural necessity, but this coexists alongside an acceptance of contingency in the social world. I argue in this paper that there cannot be any natural necessity in the social world, but rather the real nature of the social world is that it is contingent. This need not lead to an abandonment of realism, and indeed I argue that a (...) contingent form of realism allows us to bring ontological probability back into realism. (shrink)

Some have argued that chance and determinism are compatible in order to account for the objectivity of probabilities in theories that are compatible with determinism, like Classical Statistical Mechanics (CSM) and Evolutionary Theory (ET). Contrarily, some have argued that chance and determinism are incompatible, and so such probabilities are subjective. In this paper, I argue that both of these positions are unsatisfactory. I argue that the probabilities of theories like CSM and ET are not chances, but also that they are (...) not subjective probabilities either. Rather, they are a third type of probability, which I call counterfactual probability. The main distinguishing feature of counterfactual-probability is the role it plays in conveying important counterfactual information in explanations. This distinguishes counterfactual probability from chance as a second concept of objective probability. (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)

The paper makes a case for there being causation in the form of causal properties or causal structures in the domain of fundamental physics. That case is built in the first place on an interpretation of quantum theory in terms of state reductions so that there really are both entangled states and classical properties, GRW being the most elaborate physical proposal for such an interpretation. I then argue that the interpretation that goes back to Everett can also be read in (...) a causal manner, the splitting of the world being conceivable as a causal process. Finally, I mention that the way in which general relativity theory conceives the metrical field opens up the way for a causal conception of the metrical properties as well. (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)

Recent discussion of the statistical character of evolutionary theory has centered around two positions: (1) Determinism combined with the claim that the statistical character is eliminable, a subjective interpretation of probability, and instrumentalism; (2) Indeterminism combined with the claim that the statistical character is ineliminable, a propensity interpretation of probability, and realism. I point out some internal problems in these positions and show that the relationship between determinism, eliminability, realism, and the interpretation of probability is more complex than previously assumed (...) in this debate. Furthermore, I take some initial steps towards a more adequate account of the statistical character of evolutionary theory. (shrink)

In 2002 the readers of the scientific magazine 'Physics World' voted Young's double-slit experiment applied to the interference of single electrons to be 'the most beautiful experiment in physics'; this experiment, in truth, had already been carried out 30 years beforehand. The present article aims to re-examine the latter real experiment and put it into its proper historical perspective. Even though the experiment was not afforded the importance it perhaps deserved among philosophers, its philosophical mplications add new arguments to the (...) already far-reaching debate triggered off by the ideal experiment. Within the context of quantum mechanics in particular, the experiment revealed for the first time the importance that ought to be attributed at the empirical level to single-case probability, that is, to the probability of a single electron's reaching the screen. I investigate how the empirical significance of the experimental results comes within the framework of the debate over the propensity interpretation of probability in quantum mechanics. I argue that the experiment, when examined in all its technical details does in fact throw light on the evidence for the propensity, as a physical property, of micro-objects. (shrink)

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)

One controversy about the existence of so called evolutionary forces such as natural selection and random genetic drift concerns the sense in which such “forces” can be said to interact. In this paper I explain how natural selection and random drift can interact. In particular, I show how population-level probabilities can be derived from individual-level probabilities, and explain the sense in which natural selection and drift are embodied in these population-level probabilities. I argue that whatever causal character the individual-level probabilities (...) have is then shared by the population-level probabilities, and that natural selection and random drift then have that same causal character. Moreover, natural selection and drift can then be viewed as two aspects of probability distributions over frequencies in populations of organisms. My characterization of population-level probabilities is largely neutral about what interpretation of probability is required, allowing my approach to support various positions on biological probabilities, including those which give biological probabilities one or another sort of causal character. ‡This paper has benefited from feedback on and discussions of this and earlier work. I want to thank André Ariew, Matt Barker, Lindley Darden, Patrick Forber, Nancy Hall, Mohan Matthen, Samir Okasha, Jeremy Pober, Robert Richardson, Alex Rosenberg, Eric Seidel, Denis Walsh, and Bill Wimsatt. †To contact the author, please write to: Department of Philosophy, University of Alabama at Birmingham, HB 414A, 900 13th Street South, Birmingham, AL 35294-1260; e-mail: [email protected]. (shrink)

In 1958, to refute the argument known as the theoretician's dilemma, Hempel suggested that theoretical terms might be logically indispensable for inductive systematization of observational statements. This thesis, in some form or another, has later been supported by Scheffler, Lehrer, and Tuomela, and opposed by Bohnert, Hooker, Stegmüller, and Cornman. In this paper, a critical survey of this discussion is given. Several different putative definitions of the crucial notion inductive systematization achieved by a theory are discussed by reference to the (...) properties of inductive inference. The consequences of the following differences between deductive and inductive inference are emphasized: the lack of simple transitivity properties (even in a modified sense) of inductive inference, and the failure of the inductive analogue of the converse of The Deduction Theorem. The main conclusions are: (i) Hempel's original thesis may very well be right but his argument for it is unsatisfactory, (ii) theoretical terms can be logically indispensable for a non-Hempelian kind of inductive systematization, relative to both Craigian and Ramseyan elimination, (iii) Lehrer's attempt to prove the indispensability of theoretical terms for inductive-probabilistic systematization is, as a modification of Hempelian kind of inductive-deterministic systematization, unsatisfactory, and (iv) there does not seem to be much hope of escaping the conclusion (ii), if it is true, by extending the Craigian replacement programme along the lines suggested by Cornman. (shrink)

Propensities are presented as a generalization of classical determinism. They describe a physical reality intermediary between Laplacian determinism and pure randomness, such as in quantum mechanics. They are characterized by the fact that their values are determined by the collection of all actual properties. It is argued that they do not satisfy Kolmogorov axioms; other axioms are proposed.

This approach does not define a probability measure by syntactical structures. It reveals a link between modal logic and mathematical probability theory. This is shown (1) by adding an operator (and two further connectives and constants) to a system of lower predicate calculus and (2) regarding the models of that extended system. These models are models of the modal system S₅ (without the Barcan formula), where a usual probability measure is defined on their set of possible worlds. Mathematical probability models (...) can be seen as models of S₅. (shrink)

Objective probability, or objective chance, is the probability of some event occurring in the future independent of what anyone thinks. This paper presents and defends a theory of objective chance. I develop an informal analysis of objective chance, taking the common sense picture underlying our talk about the likelihood of future events as our starting point. A formal semantics is introduced, and I argue that the theory presented satisfies certain criteria of adequacy for a theory of probability.

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

In this paper I put forward a new micro realistic, fundamentally probabilistic, propensiton version of quantum theory. According to this theory, the entities of the quantum domain - electrons, photons, atoms - are neither particles nor fields, but a new kind of fundamentally probabilistic entity, the propensiton - entities which interact with one another probabilistically. This version of quantum theory leaves the Schroedinger equation unchanged, but reinterprets it to specify how propensitons evolve when no probabilistic transitions occur. Probabilisitic transitions occur (...) when new "particles" are created as a result of inelastic interactions. All measurements are just special cases of this. This propensiton version of quantum theory, I argue, solves the wave/particle dilemma, is free of conceptual problems that plague orthodox quantum theory, recovers all the empirical success of orthodox quantum theory, and at the same time yields as yet untested predictions that differ from those of orthodox quantum theory. (shrink)

In this paper I expound an argument which seems to establish that probabilism and special relativity are incompatible. I examine the argument critically, and consider its implications for interpretative problems of quantum theory, and for theoretical physics as a whole.

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)

Several philosophers of science have claimed that the conceptual difficulties of quantum mechanics can be resolved by appealing to a particular interpretation of probability theory. For example, Popper bases his treatment of quantum mechanics on the propensity interpretation of probability, and Margenau bases his treatment of quantum mechanics on the frequency interpretation of probability. The purpose of this paper is (i) to consider and reject such claims, and (ii) to discuss the question of whether the ψ -function refers to an (...) individual system or to an ensemble of systems. (shrink)

I argue that any broadly dispositional analysis of probability will either fail to give an adequate explication of probability, or else will fail to provide an explication that can be gainfully employed elsewhere (for instance, in empirical science or in the regulation of credence). The diversity and number of arguments suggests that there is little prospect of any successful analysis along these lines.

Recent debate on the nature of probabilities in evolutionary biology has focused largely on the propensity interpretation of fitness (PIF), which defines fitness in terms of a conception of probability known as “propensity”. However, proponents of this conception of fitness have misconceived the role of probability in the constitution of fitness. First, discussions of probability and fitness have almost always focused on organism effect probability, the probability that an organism and its environment cause effects. I argue that much of the (...) probability relevant to fitness must be organism circumstance probability, the probability that an organism encounters particular, detailed circumstances within an environment, circumstances which are not the organism’s effects. Second, I argue in favor of the view that organism effect propensities either don’t exist or are not part of the basis of fitness, because they usually have values close to 0 or 1. More generally, I try to show that it is possible to develop a clearer conception of the role of probability in biological processes than earlier discussions have allowed. (shrink)

We propose a model of physics that blends Rovelli’s relational quantum mechanics (RQM) interpretation with the language of finite information quantities (FIQs), defined by Gisin and Del Santo in the spirit of intuitionistic mathematics. We discuss deficiencies of using real numbers to model physical systems in general, and particularly under the RQM interpretation. With this motivation for an alternative mathematical language, we propose the use of FIQs to model the world under the RQM interpretation, wherein we view the propensities that (...) make up a FIQ as quantifications of potential interaction. Under this model, the stable facts, relative facts, and shifting perspectives that make up the relational interpretation correspond to shifting digits and propensities of the FIQs. The model’s predictions agree with those of both classical and quantum physics, and it is indeterministic. We also propose explanations, with examples, for how the propensities of a FIQ are distributed, and how its digits become actualized. This is equivalent to the notion of the measurement problem, and the question of what causes wave function collapse. In short, by stepping through the “new door” opened by the language of FIQs, we attempt to describe the world under the relational interpretation. (shrink)

It is generally assumed that compatibility with special relativity is guaranteed by the invariance of the fundamental equations of quantum physics under Lorentz transformations and the impossibility of transferring energy or information faster than the speed of light. Despite this, various contradictions persist, which make us suspect the solidity of that compatibility. This paper focuses on collapse theories—although they are not the only way of interpreting quantum theory—in order to examine what seems to be insurmountable difficulties we encounter when trying (...) to construct a space–time picture of such typically quantum processes as state vector reduction or the non-separability of entangled systems. The inescapable nature of such difficulties suggests the need to go further in the search for new formulations that surpass our current conceptions of matter and space–time. (shrink)

The article focusses on grey system theory and its methodological foundations. Key topics include: axiomatisation of the concept of grey, comparison of grey systems theory with fuzzy logic and probabilistic approaches, and methodological development of the systems approach in grey data modelling. The article discusses in detail the challenges of defining grey space, grey functions, and their applications in solving the methodological problems of grey systems theory. The differences between grey systems theory and other analytical methodologies are highlighted, paying attention (...) to the specifics of the data and the research context and epistemological perspective. (shrink)

This dissertation looks at a set of interconnected questions concerning the foundations of probability, and gives a series of interconnected answers. At its core is a piece of old-fashioned philosophical analysis, working out what probability is. Or equivalently, investigating the semantic question of what is the meaning of ‘probability’? Like Keynes and Carnap, I say that probability is degree of reasonable belief. This immediately raises an epistemological question, which degrees count as reasonable? To solve that in its full generality would (...) mean the end of human inquiry, so that won’t be attempted here. Rather I will follow tradition and merely investigate which sets of partial beliefs are coherent. -/- The standard answer to this question, what is commonly called the Bayesian answer, says that degrees of belief are coherent iff they form a probability function. I disagree with the way this is usually justified, but subject to an important qualification I accept the answer. The important qualification is that degrees of belief may be imprecise, or vague. Part one of the dissertation, chapters 1 to 6, looks largely at the consequences of this qualification for the semantic and epistemological questions already mentioned. It turns out that when we allow degrees of belief to be imprecise, we can discharge potentially fatal objections to some philosophically attractive theses. Two of these, that probability is degree of reasonable belief and that the probability calculus provides coherence constraints on partial beliefs, have been mentioned. Others include the claim, defended in chapter 4, that chance is probability given total history. -/- As well as these semantic and epistemological questions, studies of the foundations of probability usually include a detailed discussion of decision theory. For reasons set out in chapter 2, I deny we can gain epistemological insights from decision theory. Nevertheless, it is an interesting field to study on its own, and it might be expected that there would be decision theoretic consequences of allowing imprecise degrees of belief. As I show in part two, this expectation seems to be mistaken. Chapter 9 shows that there aren’t interesting consequences of this theory for decision theory proper, and chapters 10 and 11 show that Keynes’s attempt to use imprecision in degrees of belief to derive a distinctive theory of interest rates is unsound. -/- Chapters 7 and 8 provide a link between these two parts. In chapter 7 I look at some previous philosophical investigations into the effects of imprecision. In chapter 8 I develop what I take to be the best competitor to the theory defended here – a constructivist theory of probability. On this view degrees of belief are precise, but the relevant coherence constraint is a constructivist probability calculus. This view is, I think, mistaken, but the calculus has some intrinsic interest, and there are at least enough arguments for it to warrant a chapter-length examination. (shrink)

This article introduces the notion of the directedness of a process, which underlies event causation as well as the persistence of things. Using this notion it investigates what happens in typical cases of active event causation. Causes never necessitate their effects because even non- probabilistic causes can be counteracted.

We propose an interpretation of physics named potentiality realism. This view, which can be applied to classical as well as to quantum physics, regards potentialities (i.e. intrinsic, objective propensities for individual events to obtain) as elements of reality, thereby complementing the actual properties taken by physical variables. This allows one to naturally reconcile realism and fundamental indeterminism in any theoretical framework. We discuss our specific interpretation of propensities, that require them to depart from being probabilities at the formal level, though (...) allowing for statistics and the law of large numbers. This view helps reconcile classical and quantum physics by showing that most of the conceptual problems that are customarily taken to be unique issues of the latter -- such as the measurement problem -- are actually in common to all indeterministic physical theories. (shrink)

We present three experiments using a novel problem in which participants update their estimates of propensities when faced with an uncertain new instance. We examine this using two different causal structures (common cause/common effect) and two different scenarios (agent‐based/mechanical). In the first, participants must update their estimate of the propensity for two warring nations to successfully explode missiles after being told of a new explosion on the border between both nations. In the second, participants must update their estimate of the (...) accuracy of two early warning tests for cancer when they produce conflicting reports about a patient. Across both experiments, we find two modal responses, representing around one‐third of participants each. In the first, “Categorical” response, participants update propensity estimates as if they were certain about the single event, for example, certain that one of the nations was responsible for the latest explosion, or certain about which of the two tests is correct. In the second, “No change” response, participants make no update to their propensity estimates at all. Across the three experiments, the theory is developed and tested that these two responses in fact have a single representation of the problem: because the actual outcome is binary (only one of the nations could have launched the missile; the patient either has cancer or not), these participants believe it is incorrect to update propensities in a graded manner. They therefore operate on a “certainty threshold” basis, whereby, if they are certain enough about the single event, they will make the “Categorical” response, and if they are below this threshold, they will make the “No change” response. Ramifications are considered for the “categorical” response in particular, as this approach produces a positive‐feedback dynamic similar to that seen in the belief polarization/confirmation bias literature. (shrink)

The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems with only one adjustable property cannot carry more than a single message at a time. We demonstrate that this is true for the photons in the double-slit experiment, and that this is what leads to the fundamental limit on measuring the complementary aspect of the photons. Next, we illustrate that systems with a single adjustable property exhibit other quantum (...) behaviors, such as noncommutativity and no-cloning. Finally, we formulate a mathematical theory to describe the dynamics of such systems and derive the standard Hilbert space formalism of quantum mechanics as well as the Born probability rule. Our derivation demonstrates the physical foundation of quantum theory. (shrink)