According to Humean theories of objective chance, the chances reduce to patterns in the history of occurrent events, such as frequencies. According to non-Humean accounts, the chances are metaphysically fundamental, existing independently of the "Humean Mosaic" of actually-occurring events. It is therefore possible, by the lights of non-Humeanism, for the chances and the frequencies to diverge wildly. Humeans often allege that this undermines the ability of non-Humean accounts of chance to rationalize adherence to David Lewis' Principal Principle (PP), which states (...) that an agent's degrees of belief should match what they take to be the objective chances. In this paper, I propose two approaches to justifying (PP) for non-Humean chance, hence defusing the Humean objection. The first approach justifies (PP) via the role it plays in informing outright beliefs about long-run frequencies. The second approach justifies (PP) by showing that adherence to (PP), even for non-Humean chance, maximizes expected epistemic utility according to the actual objective chance function. I then address an objection to this approach, concerning the alleged circularity of the derivations. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

Spontaneous collapse theories of quantum mechanics turn the usual Schrödinger equation into a stochastic dynamical law. In particular, in this paper, I will focus on the GRW theory. Two philosophical issues that can be raised about GRW concern (i) the ontology of the theory, in particular the nature of the wave function and its role within the theory, and (ii) the interpretation of the objective probabilities involved in the dynamics of the theory. During the last years, it has been claimed (...) that we can take advantage of dispositional properties in order to develop an ontology for GRW theory, and also in order to ground the objective probabilities which are postulated by it. However, in this paper, I will argue that the dispositional interpretations which have been discussed in the literature so far are either flawed or – at best – incomplete. If we want to endorse a dispositional interpretation of GRW theory we thus need an extended account that specifies the precise nature of those properties and which makes also clear how they can correctly ground all the probabilities postulated by the theory. Thus, after having introduced several different kinds of probabilistic dispositions, I will try to fill the gap in the literature by proposing a novel and complete dispositional account of GRW, based on what I call spontaneous weighted multi-track propensities. I claim that such an account can satisfy both of our desiderata. (shrink)

Presentists believe that only present things exist. Their theories, at first glance, seem to offer many admirable features: a simple ontology, and a meaningful, objective status for key temporal phenomena, such as the present moment and the passage of time. So intuitive is this theory that, as John Bigelow puts it, presentism was “believed by everyone...until at least the nineteenth century”. Yet, in the last 200 years presentism has been beset by criticisms from both physicists and metaphysicians. One of the (...) most significant criticisms is that presentists cannot provide an acceptable system of truthmaking. If there is no past, how can there still be truths about the past? In this paper, I introduce a new theory of presentism, which addresses this problem in a novel way: by simply denying that there are any truths about the past. While prima facie an unintuitive position, I will argue that a sensible presentist philosophy of this kind can be described, so long as it is accompanied by an appropriate system of physics. I will also indicate at certain points that adopting presentism could allow us to understand fundamental physics in new, more intuitive ways. By the end of the paper, I hope to not only show that hard presentism is a defensible theory of time, but also that it could offer a number of advantages to the physicist and the philosopher alike. (shrink)

While the notion of chance has been central in discussions over the probabilistic nature of natural selection and genetic drift, its role in the production of variants on which populational sampling takes place has received much less philosophical attention. This article discusses the concept of chance in evolution in the light of contemporary work in evo-devo. We distinguish different levels at which randomness and chance can be defined in this context, and argue that recent research on variability and evolvability demands (...) a causal understanding of variational probabilities under which development acquires a creative, rather than a constraining role in evolution. We then provide a propensity interpretation of variational probabilities that solves a conceptual confusion between causal properties, variational probabilities and extant variation present in the literature, and explore some metaphysical consequences that follow from our interpretation, specifically with regards to the nature of developmental types. (shrink)

The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability.

The aim of the paper is to develop general criteria of argumentative validity and adequacy for probabilistic arguments on the basis of the epistemological approach to argumentation. In this approach, as in most other approaches to argumentation, proabilistic arguments have been neglected somewhat. Nonetheless, criteria for several special types of probabilistic arguments have been developed, in particular by Richard Feldman and Christoph Lumer. In the first part (sects. 2-5) the epistemological basis of probabilistic arguments is discussed. With regard to the (...) philosophical interpretation of probabilities a new subjectivist, epistemic interpretation is proposed, which identifies probabilities with tendencies of evidence (sect. 2). After drawing the conclusions of this interpretation with respect to the syntactic features of the probability concept, e.g. one variable referring to the data base (sect. 3), the justification of basic probabilities (priors) by judgements of relative frequency (sect. 4) and the justification of derivative probabilities by means of the probability calculus are explained (sect. 5). The core of the paper is the definition of '(argumentatively) valid derivative probabilistic arguments', which provides exact conditions for epistemically good probabilistic arguments, together with conditions for the adequate use of such arguments for the aim of rationally convincing an addressee (sect. 6). Finally, some measures for improving the applicability of probabilistic reasoning are proposed (sect. 7). (shrink)

Do unknown and unrealized risks of harm diminish an individual’s well-being? The traditional answer is no: that the security of prudential goods benefits an individual only instrumentally or by virtue of their subjective sense of security. Recent work has argued, however, that the security of prudential goods non-instrumentally benefits an individual regardless of whether or not they enjoy subjective security. In this paper, I critically examine three claims about the way in which unknown and unrealized risks of harm might diminish (...) individual well-being: it frustrates a desire to be secure, it frustrates the enjoyment of modally-robust goods, and it undermines the ability to make reasonable plans. Ultimately, I argue that all three of these hypotheses are mistaken, but that they deepen our understanding of the ways in which subjective security is an important constituent of individual well-being. (shrink)

Tässä artikkelissa käsittelen Descartesin ikuisten totuuksien välttämättömyyteen liittyvää ongelmaa. Teoksessa Mietiskelyjä ensimmäisestä filosofiasta (1641–1642) Descartes nostaa esiin käsitteen ikuisista totuuksista, käyttäen esimerkkinään kolmiota. Kolmion muuttumattomaan ja ikuiseen luontoon kuuluu esimerkiksi, että sen kolme kulmaa ovat yhteenlaskettuna 180°. Se on totta kolmiosta, vaikka yhtään yksittäistä kolmiota ei olisi koskaan ollutkaan olemassa. Eräät ajattelemieni asioiden piirteet ovat siis Descartesin mukaan ajattelustani riippumattomia. Ikuisia totuuksia ovat ainakin matemaattiset ja geometriset tosiseikat sekä ristiriidan laki. Samoin Descartesin kuuluisa lause “ajattelen, siis olen” lukeutuu ikuisten totuuksien (...) joukkoon. Descartesin ikuiset totuudet olisivatkin siis loogisesti välttämättömiä. Niillä on kyseinen olemus riippumatta ulkoisten kohteiden olemassaolosta tai siitä, ajattelenko niitä lainkaan. Kuitenkin kirjeenvaihdossaan Descartes pitää itsepintaisesti kiinni käsityksestään, että ikuiset totuudet ovat Jumalan vapaasti luomia ja Jumala olisi voinut luoda ne erilailla. Näin ollen luodut ikuiset totuudet eivät tarkkaan ottaen olisikaan välttämättömiä vaan kontingentteja. Ne voisivat olla myös toisella tavalla. Artikkelin alkuun esittelen Descartesin modaalista metafysiikkaa sekä luotujen ikuisten totuuksien kontingenttiudesta seuraavia tulkinnallisia vaikeuksia. Tämän jälkeen pureudun kolmeen erilaiseen ratkaisuyritykseen kommentaarikirjallisuudessa (Frankfurt 1977; Curley 1984 & Bennett 1994) ja osoitan, miksi ne eivät riitä vastaamaan ongelmaan. Lopussa vedän johtopäätöksiä ja luonnostelen mahdollisen ratkaisun. (shrink)

This paper seeks to recover the function of universal history, which was to place particulars into relation with universals. By the 20th century universal history was largely discredited because of an idealism that served to lend epistemic coherence to the overwhelming complexity arising from universal history's comprehensive scope. Idealism also attempted to account for history's being "open"--for the human ability to transcend circumstance. The paper attempts to recover these virtues without the idealism by defining universal history not by its scope (...) but rather as a scientific method that provides an understanding of any kind of historical process, be it physical, biological or human. While this method is not new, it is in need of a development that offers a more robust historiography and warrant as a liberating historical consciousness. The first section constructs an ontology of process by defining matter as ontic probabilities rather than as closed entities. This is lent warrant in the next section through an appeal to contemporary physical science. The resulting conceptual frame and method is applied to the physical domain of existents, to the biological domain of social being and finally to the human domain of species being. It is then used to account for the emergence of human history's initial stage--the Archaic Socio-Economic Formation and for history' stadial trajectory--its alternation of evolution and revolution. (shrink)

This paper reviews four attempts throughout the history of quantum mechanics to explicitly employ dispositional notions in order to solve the quantum paradoxes, namely: Margenau's latencies, Heisenberg's potentialities, Maxwell's propensitons, and the recent selective propensities interpretation of quantum mechanics. Difficulties and challenges are raised for all of them, and it is concluded that the selective propensities approach nicely encompasses the virtues of its predecessors. Finally, some strategies are discussed for reading similar dispositional notions into two other well-known interpretations of quantum (...) mechanics, namely the GRW interpretation and Bohmian mechanics. (shrink)

Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: inferential probability, ensemble probability, and propensity. Class is the basis of inductive logic; deals with the frequencies of events in repeatable experiments; describes (...) a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge. (shrink)

One finds intertwined with ideas at the core of evolutionary theory claims about frequencies in counterfactual and infinitely large populations of organisms, as well as in sets of populations of organisms. One also finds claims about frequencies in counterfactual and infinitely large populations—of events—at the core of an answer to a question concerning the foundations of evolutionary theory. The question is this: To what do the numerical probabilities found throughout evolutionary theory correspond? The answer in question says that evolutionary probabilities (...) are “hypothetical frequencies” (including what are sometimes called “long-run frequencies” and “long-run propensities”). In this paper, I review two arguments against hypothetical frequencies. The arguments have implications for the interpretation of evolutionary probabilities, but more importantly, they seem to raise problems for biologists’ claims about frequencies in counterfactual or infinite populations of organisms and sets of populations of organisms. I argue that when properly understood, claims about frequencies in large and infinite populations of organisms and sets of populations are not threatened by the arguments. Seeing why gives us a clearer understanding of the nature of counterfactual and infinite population claims and probability in evolutionary theory. (shrink)

This volume focuses on various questions concerning the interpretation of probability and probabilistic reasoning in biology and physics. It is inspired by the idea that philosophers of biology and philosophers of physics who work on the foundations of their disciplines encounter similar questions and problems concerning the role and application of probability, and that interaction between the two communities will be both interesting and fruitful. In this introduction we present the background to the main questions that the volume focuses on (...) and summarize the highlights of the individual contributions. (shrink)

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

Bayes’ rule shows how one might rationally change one’s beliefs in the light of evidence. It is the foundation of a statistical method called Bayesianism. In health care research, Bayesianism has its advocates but the dominant statistical method is frequentism. There are at least two important philosophical differences between these methods. First, Bayesianism takes a subjectivist view of probability (i.e. that probability scores are statements of subjective belief, not objective fact) whilst frequentism takes an objectivist view. Second, Bayesianism is explicitly (...) inductive (i.e. it shows how we may induce views about the world based on partial data from it) whereas frequentism is at least compatible with non-inductive views of scientific method, particularly the critical realism of Popper. Popper and others detail significant problems with induction. Frequentism’s apparent ability to avoid these, plus its ability to give a seemingly more scientific and objective take on probability, lies behind its philosophical appeal to health care researchers. However, there are also significant problems with frequentism, particularly its inability to assign probability scores to single events. Popper thus proposed an alternative objectivist view of probability, called propensity theory, which he allies to a theory of corroboration; but this too has significant problems, in particular, it may not successfully avoid induction. If this is so then Bayesianism might be philosophically the strongest of the statistical approaches. The article sets out a number of its philosophical and methodological attractions. Finally, it outlines a way in which critical realism and Bayesianism might work together. (shrink)

The problem of philosophical skepticism relates to the difficulty involved in underwriting the claim that we know anything of spatio-temporal reality. It is often claimed, in fact, that proper philosophical scrutiny reveals quite the opposite from what common sense suggests. Knowledge of external reality is thought to be even quite obviously denied to us as a result of the alleged fact that we all fail to know that certain skeptical scenarios do not obtain. A skeptical scenario is one in which (...) we have neurological occurrences just like any normal situation in which we actually perceive spatio-temporal objects, but where we are deceived in some sense as a result of the manipulation of our brains from some outside source. In this work I attempt to address the problem of philosophical skepticism by claiming that most of us are able to come to know plenty about external reality, since we can come to realize that a certain philosophical theory of perception is correct. The theory I have in mind is what I call a non-cognitive theory of perception. According to this view, perceptual experience is defined by continuous, sensitive behavioral interaction with spatio-temporal objects of the appropriate size, shape, hardness, speed, etc. Knowing that this theory of perception is correct is equivalent to knowing that we know plenty about external reality. This is ultimately because by knowing that a non-cognitive theory of perception is true, we know that any skeptical scenario must fail to obtain. The structure of the work proceeds by first discussing the significance of the problem of philosophical skepticism in some detail. Chapter 1 lays out how the problem does indeed forcefully arise if it is conceded that we fail to know that the skeptical scenarios fail to obtain. Chapter 2 develops the sort of view of our epistemological situation that falls out of accepting without qualification that the problem exists. Chapter 3 examines and criticizes certain popular responses to the skeptical problem. The main goal of these first three preliminary chapters is to indicate that once it is admitted that we fail to know that the skeptical scenarios fail to obtain, the problem of philosophical skepticism forcefully presents itself. Chapter 4, however, attacks the idea that we fail to know that the skeptical scenarios fail to obtain. In this chapter I argue that this idea is wedded to the position that a certain theory of perception is correct. The theory in question is what I call a conjunctive theory of veridical experience. According to this view, normal experience of spatio-temporal objects occurs when a subject has a certain perceptual experience, and that experience also happens to match up with and/or be satisfied by what is really the case. Only when a theory of this sort is assumed, I argue, is the claim that we fail to know that the skeptical scenarios fail to obtain found to be obvious. In chapter 5 I argue that, in fact, a non-cognitive theory, rather than a conjunctive theory, is the correct view to maintain. In the final chapter 6 I develop the epistemological position that falls out of accepting a non-cognitive theory. (shrink)

This article explores the connection between objective chance and the randomness of a sequence of outcomes. Discussion is focussed around the claim that something happens by chance iff it is random. This claim is subject to many objections. Attempts to save it by providing alternative theories of chance and randomness, involving indeterminism, unpredictability, and reductionism about chance, are canvassed. The article is largely expository, with particular attention being paid to the details of algorithmic randomness, a topic relatively unfamiliar to philosophers.

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)

This paper investigates the relations between causality and propensity. Aparticular version of the propensity theory of probability is introduced, and it is argued that propensities in this sense are not causes. Some conclusions regarding propensities can, however, be inferred from causal statements, but these hold only under restrictive conditions which prevent cause being defined in terms of propensity. The notion of a Bayesian propensity network is introduced, and the relations between such networks and causal networks is investigated. It is argued (...) that causal networks cannot be identified with Bayesian propensity networks, but that causal networks can be a valuable heuristic guide for the construction of Bayesian propensity networks. (shrink)

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

We offer a novel theory of information that differs from traditional accounts in two respects: (i) it explains information in terms of counterfactuals rather than conditional probabilities, and (ii) it does not make essential reference to doxastic states of subjects, and consequently allows for the sort of objective, reductive explanations of various notions in epistemology and philosophy of mind that many have wanted from an account of information.

These are the introduction chapters to the forthcoming collection of essays published by Springer (Synthese Library) and entitled Probabilities, Causes and Propensities in Physics.

I review five explicit attempts throughout the history of quantum mechanics to invoke dispositional notions in order to solve the quantum paradoxes, namely: Margenau’s latencies, Heisenberg’s potentialities, Popper’s propensity interpretation of probability, Nick Maxwell’s propensitons, and the recent selective propensities interpretation of quantum mechanics. I raise difficulties and challenges for all of them, but conclude that the selective propensities approach nicely encompasses the virtues of its predecessors. I elaborate on some of the properties of the type of propensities that I (...) claim to be successful for quantum mechanics, and finish by briefly sketching out ways in which similar notions can be read into some of the other well-known interpretations of quantum mechanics. (shrink)

There are two central questions concerning probability. First, what are its formal features? That is a mathematical question, to which there is a standard, widely (though not universally) agreed upon answer. This answer is reviewed in the next section. Second, what sorts of things are probabilities---what, that is, is the subject matter of probability theory? This is a philosophical question, and while the mathematical theory of probability certainly bears on it, the answer must come from elsewhere. To see why, observe (...) that there are many things in the world that have the mathematical structure of probabilities---the set of measurable regions on the surface of a table, for example---but that one would never mistake for being probabilities. So probability is distinguished by more than just its formal characteristics. The bulk of this essay will be taken up with the central question of what this “more” might be. (shrink)

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)

The concept of probability seems to have been inexplicable since its invention in the seventeenth century. In its use in science, probability is closely related with relative frequency. So the task seems to be interpreting that relation. In this paper, we start with predicted relative frequency and show that its structure is the same as that of probability. I propose to call that the ‘prediction interpretation’ of probability. The consequences of that definition are discussed. The “ladder”-structure of the probability calculus (...) is analyzed. The expectation of the relative frequency is shown to be equal to the predicted relative frequency. Probability is shown to be the most general empirically testable prediction. (shrink)

David Lewis'sPrincipal Principle states that our credence in a single case follows from the general probability of all such cases. Against this stands the Challenge Argument – to show that the inference is justified. Recent law-to-chance, Bayesian, and propensity theories of probability take up the challenge – but, I argue, fall short. Rather, we should understand propensity via Aristotle's analysis of spontaneity and probabilistic reasoning via theAnti-PPand the practice ofbundling one offs, where forced bad-odds one offsilluminate how extensive a role (...) luck plays in our lives. (shrink)

The paper investigates possible readings of the later Heisenberg's remarks on the nature of quantum states. It discusses, in particular, whether Heisenberg should be seen as a proponent of the epistemic conception of states – the view that quantum states are not descriptions of quantum systems but rather reflect the state assigning observers' epistemic relations to these systems. On the one hand, it seems plausible that Heisenberg subscribes to that view, given how he defends the notorious "collapse of the wave (...) function" by relating it to a sudden change in the epistemic situation of the observer registering a measured result. On the other hand, his remarks on quantum probabilities as "potentia" or "objective tendencies" are difficult to reconcile with such a reading. The accounts that are attributed to Heisenberg by the different possible readings considered are subjected to closer scrutiny; at the same time, their respective virtues and problems are discussed. _German_ Diese Arbeit untersucht mögliche Lesarten von Heisenbergs späten Bemerkungen über die Natur von Quantenzuständen. Insbesondere wird die Frage diskutiert, ob Heisenberg als Vertreter der epistemischen Auffassung von Quantenzuständen gelten kann – der Idee, dass Quantenzustände nicht Beschreibungen der objektiven Eigenschaften von Quantensystemen sind sondern die epistemischen Beziehungen von Beobachtern zu diesen Systemen widerspiegeln. Einerseits erscheint es plausibel, dass Heisenberg dieser Sichtweise zustimmt, wenn man sich ansieht, wie er den berüchtigten,,Kollaps der Wellenfunktion" verteidigt, indem er ihn mit einer plötzlichen Änderung in der Kenntnis des ein Messergebnis registrierenden Beobachters in Zusammenhang bringt. Andererseits sind seine Bemerkungen über quantenmechanische Wahrscheinlichkeiten als,,Potentia" oder,,objektive Tendenzen" mit einer solchen Lesart nur schwer in Einklang zu bringen. Die Positionen, die Heisenberg den verschiedenen möglichen Lesarten zufolge vertritt, werden eingehenden Untersuchungen unterzogen; gleichzeitig werden ihre jeweiligen Vorzüge und Probleme diskutiert. (shrink)

Kolmogorov''s axiomatization of probability includes the familiarratio formula for conditional probability: 0).$$ " align="middle" border="0">.

Probability theory is important because of its relevance for decision making, which also means: its relevance for the single case. The propensity theory of objective probability, which addresses the single case, is subject to two problems: Humphreys’ problem of inverse probabilities and the problem of the reference class. The paper solves both problems by restating the propensity theory using (an objectivist version of) Pearl’s approach to causality and probability, and by applying a decision-theoretic perspective. Contrary to a widely held view, (...) decision making on the basis of given propensities can proceed without a subjective-probability supplement to propensities. (shrink)

"Chance" crops up all over philosophy, and in many other areas. It is often assumed -- without argument -- that chances are probabilities. I explore the extent to which this assumption is really sanctioned by what we understand by the concept of chance.

Natural information refers to the information carried by natural signs such as that smoke is thought to carry natural information about fire. A number of influential philosophers have argued that natural information can also be utilized in a theory of mental content. The most widely discussed account of natural information holds that it results from an extremely strong relation between sign and signified. Critics have responded that it is doubtful that there are many strong relations of this sort in the (...) natural world due to variability between signs and signified. In light of this observation, a promising suggestion is that much of the interesting natural information carried by natural signs is really information with a probabilistic content. However, Dretske’s theory cannot account for this information because it would require implausible second order objective probabilities. Given the most plausible understanding of the probabilities involved here, I argue that it is only sequences of traditional natural signs that carry this probabilistic information. Several implications of this idea will be explored. (shrink)

Concrete Causation centers about theories of causation, their interpretation, and their embedding in metaphysical-ontological questions, as well as the application of such theories in the context of science and decision theory. The dissertation is divided into four chapters, that firstly undertake the historical-systematic localization of central problems (chapter 1) to then give a rendition of the concepts and the formalisms underlying David Lewis' and Judea Pearl's theories (chapter 2). After philosophically motivated conceptual deliberations Pearl's mathematical-technical framework is drawn on for (...) an epistemic interpretation and for emphasizing the knowledge-organizing aspect of causality in an extension of the interventionist Bayes net account of causation (chapter 3). Integrating causal and non-causal knowledge in unified structures ultimately leads to an approach towards solving problems of (causal) decision theory and at the same time facilitates the representation of logical-mathematical, synonymical, as well as reductive relationships in efficiently structured, operational nets of belief propagation (chapter 4). (shrink)

Popper’s introduction of ‘‘propensity’’ was intended to provide a solid conceptual foundation for objective single-case probabilities. By considering the partly opposed contributions of Humphreys and Miller and Salmon, it is argued that when properly understood, propensities can in fact be understood as objective single-case causal probabilities of transitions between concrete events. The chief claim is that propensities are well-explicated by describing how they fit into the existing formal theory of branching space-times, which is simultaneously indeterministic and causal. Several problematic examples, (...) some commonsense and some quantum-mechanical, are used to make clear the advantages of invoking branching space-times theory in coming to understand propensities. (shrink)

Single-case and long-run propensity theories are among the main objective interpretations of probability. There have been various objections to these theories, e.g. that it is difficult to explain why propensities should satisfy the probability axioms and, worse, that propensities are at odds with these axioms, that the explication of propensities is circular and accordingly not informative, and that single-case propensities are metaphysical and accordingly non-scientific. We consider various propensity theories of probability and their prospects in light of these objections. We (...) argue that while propensity theories face challenges, these challenges do not undermine their validity as prospective interpretations of probability in science. (shrink)

Four interpretations of single-case conditional propensities are described and it is shown that for each a version of what has been called ‘Humphreys' Paradox’ remains, despite the clarifying work of Gillies, McCurdy and Miller. This entails that propensities cannot be a satisfactory interpretation of standard probability theory. Introduction The basic issue The formal paradox Values of conditional propensities Interpretations of propensities McCurdy's response Miller's response Other possibilities 8.1 Temporal evolution 8.2 Renormalization 8.3 Causal influence Propensities to generate frequencies Conclusion.

We review the question of whether objective chances are compatible with determinism. We first outline what we mean by chance and what we mean by determinism. We then look at the alleged incompatibility between those concepts. Finally, we look at some ways that one might attempt to overcome the incompatibility.

If chances are propensities, what reason do we have to expect them to be probabilities? I will offer a new answer to this question. It comes in two parts. First, I will defend an accuracy-centred account of what it is for a causal system to have precise propensities in the first place. Second, I will prove that, given some pretty weak assumptions about the nature of comparative causal dispositions, and some fairly standard assumptions about reasonable measures of inaccuracy, propensities must (...) be probabilities. (shrink)

: This paper outlines a genuinely pragmatist conception of propensity, and defends it against common objections to the propensity interpretation of probability, prominently Humphreys’ paradox. The paper reviews the paradox and identifies one of its key assumptions, the identity thesis, according to which propensities are probabilities. The identity thesis is also involved in empiricist propensity interpretations deriving from Popper’s influential original proposal, and makes such interpretations untenable. As an alternative, I urge a return to Charles Peirce’s original insights on probabilistic (...) dispositions, and offer a reconstructed version of his pragmatist conception, which rejects the identity thesis. – Correspondence to: [email protected]. (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.

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)

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)

Russell’s theory of desire in _The Analysis of_ Mind is subject to a seemingly overwhelming objection, apparently stated first by Wittgenstein and subsequently elaborated even more compellingly by Anthony Kenny. The puzzle is that, before he became a neutral monist, Russell had used essentially the same argument as part of a critique of William James’s theory of knowledge. Since Russell had already formulated the argument as part of his case against generally naturalistic, and specifically neutral monist, theories of propositional attitudes, (...) why did he think his own neutral monist theory of desire was exempt? I canvass various suggestions, but argue that none of them are effective. (shrink)

In this article, the epistemological interpretation of the relationship between concepts of relativism, beliefs, and probability ensures a defense of two theses, namely, (i) epistemic relativism refers to attitudes that depend on the repetition and anchoring of probabilistic beliefs, and (ii) Popper’s propensity interpretation of probability discloses the connections between relativity, probability, and collective subjectivity. The propensity interpretation brings a framework for describing the role of collective subjectivity in epistemic systems. This approach, as an acceptable epistemological stance, is related to (...) the variability of anchored collective beliefs. The repetition and anchoring of subjective probabilistic beliefs becomes a relative reference frame for evaluating the elements of knowledge. With this in mind, each particular way of considering probability indicates a manner of distinguishing epistemic systems. In epistemic systems, the statements are collective points of view expressed in the form ‘p is justified when belief in p is probably reliable.’ The statements can be accurate in a particular epistemic system but inaccurate in other systems. As a result, by avoiding the ‘all statements must be true or false’ requirement, each proponent of a certain epistemic system can build a probabilistic picture of the world. In this picture, not every statement needs to be ‘true’ when and if the statement expresses a collective point of view that has a propensity to be reliable and justified. (shrink)