The Sleeping Beauty Problem attracts so much attention because it connects to a wide variety of unresolved issues in formal epistemology, decision theory, and the philosophy of science. The problem raises unanswered questions concerning relative frequencies, objective chances, the relation between self-locating and non-self-locating information, the relation between self-location and updating, Dutch Books, accuracy arguments, memory loss, indifference principles, the existence of multiple universes, and many-worlds interpretations of quantum mechanics. After stating the problem, this article surveys its connections to all (...) of these areas. (shrink)

The main objective of the paper is to propose a frequentist interpretation of probability in the context of model-based induction, anchored on the Strong Law of Large Numbers (SLLN) and justifiable on empirical grounds. It is argued that the prevailing views in philosophy of science concerning induction and the frequentist interpretation of probability are unduly influenced by enumerative induction, and the von Mises rendering, both of which are at odds with frequentist model-based induction that dominates current practice. The differences between (...) the two perspectives are brought out with a view to defend the model-based frequentist interpretation of probability against certain well-known charges, including [i] the circularity of its definition, [ii] its inability to assign ‘single event’ probabilities, and [iii] its reliance on ‘random samples’. It is argued that charges [i]–[ii] stem from misidentifying the frequentist ‘long-run’ with the von Mises collective. In contrast, the defining characteristic of the long-run metaphor associated with model-based induction is neither its temporal nor its physical dimension, but its repeatability (in principle); an attribute that renders it operational in practice. It is also argued that the notion of a statistical model can easily accommodate non-IID samples, rendering charge [iii] simply misinformed. (shrink)

Philosophical interest in the role of self-locating information in the confirmation of hypotheses has intensified in virtue of the Sleeping Beauty problem. If the correct solution to that problem is 1/3, various attractive views on confirmation and probabilistic reasoning appear to be undermined; and some writers have used the problem as a basis for rejecting some of those views. My interest here is in two such views. One of them is the thesis that self-locating information cannot be evidentially relevant to (...) a non-self-locating hypothesis. The other, a basic tenet of Bayesian confirmation theory, is the thesis that an ideally rational agent updates her credence in a non-self-locating hypothesis in response to new information only by conditionalization. I argue that we can disprove these two theses by way of cases that are much less puzzling than Sleeping Beauty. I present two such cases in this paper. (shrink)

In this paper I argue that it is finally time to move beyond the Nagelian framework and to break new ground in thinking about epistemic reduction in biology. I will do so, not by simply repeating all the old objections that have been raised against Ernest Nagel’s classical model of theory reduction. Rather, I grant that a proponent of Nagel’s approach can handle several of these problems but that, nevertheless, Nagel’s general way of thinking about epistemic reduction in terms of (...) theories and their logical relations is entirely inadequate with respect to what is going on in actual biological research practice. (shrink)

In this paper we discuss the new Tweety puzzle. The original Tweety puzzle was addressed by approaches in non-monotonic logic, which aim to adequately represent the Tweety case, namely that Tweety is a penguin and, thus, an exceptional bird, which cannot fly, although in general birds can fly. The new Tweety puzzle is intended as a challenge for probabilistic theories of epistemic states. In the first part of the paper we argue against monistic Bayesians, who assume that epistemic states can (...) at any given time be adequately described by a single subjective probability function. We show that monistic Bayesians cannot provide an adequate solution to the new Tweety puzzle, because this requires one to refer to a frequency-based probability function. We conclude that monistic Bayesianism cannot be a fully adequate theory of epistemic states. In the second part we describe an empirical study, which provides support for the thesis that monistic Bayesianism is also inadequate as a descriptive theory of cognitive states. In the final part of the paper we criticize Bayesian approaches in cognitive science, insofar as their monistic tendency cannot adequately address the new Tweety puzzle. We, further, argue against monistic Bayesianism in cognitive science by means of a case study. In this case study we show that Oaksford and Chater’s (2007, 2008) model of conditional inference—contrary to the authors’ theoretical position—has to refer also to a frequency-based probability function. (shrink)

There is a tradition, tracing back to Kant, of recasting metaphysical questions as questions about the utility of a conceptual scheme, linguistic framework, or methodological rule for achieving some particular end. Following in this tradition, I propose a ‘means-ends metaphysics ’, in which one rigorously demonstrates the suitability of some conceptual framework for achieving a specified goal. I illustrate this approach using a debate about the nature of events. Specifically, the question is whether the time at which an event occurs (...) is an essential property of that event. I argue that this question is naturally transformed into a question about the methodology of causal modeling. In this new framework, the question concerns what kind of variables to use to represent the effects of potential interventions on a system. This question has a demonstrably correct answer, which sheds new light on the original question. (shrink)

The article begins by describing two longstanding problems associated with direct inference. One problem concerns the role of uninformative frequency statements in inferring probabilities by direct inference. A second problem concerns the role of frequency statements with gerrymandered reference classes. I show that past approaches to the problem associated with uninformative frequency statements yield the wrong conclusions in some cases. I propose a modification of Kyburg’s approach to the problem that yields the right conclusions. Past theories of direct inference have (...) postponed treatment of the problem associated with gerrymandered reference classes by appealing to an unexplicated notion of projectability . I address the lacuna in past theories by introducing criteria for being a relevant statistic . The prescription that only relevant statistics play a role in direct inference corresponds to the sort of projectability constraints envisioned by past theories. (shrink)

In a recent article, Joel Pust argued that direct inference based on reference properties of differing arity are incommensurable, and so direct inference cannot be used to resolve the Sleeping Beauty problem. After discussing the defects of Pust's argument, I offer reasons for thinking that direct inferences based on reference properties of differing arity are commensurable, and that we should prefer direct inferences based on logically stronger reference properties, regardless of arity.

Additionally, the text shows how to develop computationally feasible methods to mesh with this framework.

Reichenbach emphasizes the central importance of prediction, which is—for him—the principal aim of science. This paper offers a critical reconstruction of his concept of prediction, taking into account the different periods of his thought. First, prediction is studied as a key factor in rejecting the positivism of the Vienna Circle. This part of the discussion concentres on the general features of prediction before Experience and Prediction (EP) (section 1). Second, prediction is considered in the context of Reichenbach's disagreements with his (...) contemporaries—Carnap and Popper—(section 2). Pointing out these differences gives an additional basis for understanding how Reichenbach saw “prediction” in the period when EP was written. Third, Reichenbach's theoretical framework of prediction is analysed following EP. This analysis studies the semantical, logical, epistemological and methodological bases of his concept of prediction (section 3). Fourth, Reichenbach's conception of prediction, based on an objectivist interpretation of probabilities, is compared with the perspective on prediction of subjective Bayesians (the present personalists). This comparison (section 4) illustrates Reichenbach's views regarding the links of prediction with probability. Fifth, innovations and elements of continuity after EP are noted which give a more complete picture of Reichenbach's thought on prediction (section 5). This contributes to a comprehensive characterization of his concept of prediction. Finally, there is an assessment of his whole view of the matter and a presentation of the ingredients for a satisfactory alternative (section 6). (shrink)

This paper is about the differences between probabilities and beliefs and why reasoning should not always conform to probability laws. Probability is defined in terms of urn models from which probability laws can be derived. This means that probabilities are expressed in rational numbers, they suppose the existence of veridical representations and, when viewed as parts of a probability model, they are determined by a restricted set of variables. Moreover, probabilities are subjective, in that they apply to classes of events (...) that have been deemed (by someone) to be equivalent, rather than to unique events. Beliefs on the other hand are multifaceted, interconnected with all other beliefs, and inexpressible in their entirety. It will be argued that there are not sufficient rational numbers to characterise beliefs by probabilities and that the idea of a veridical set of beliefs is questionable. The concept of a complete probability model based on Fisher's notion of identifiable subsets is outlined. It is argued that to be complete a model must be known to be true. This can never be the case because whatever a person supposes to be true must be potentially modifiable in the light of new information. Thus to infer that an individual's probability estimate is biased it is necessary not only to show that the estimate differs from that given by a probability model, but also to assume that this model is complete, and completeness is not empirically verifiable. It follows that probability models and Bayes theorem are not necessarily appropriate standards for people's probability judgements. The quality of a probability model depends on how reasonable it is to treat some existing uncertainty as if it were equivalent to that in a particular urn model and this cannot be determined empirically. Bias can be demonstrated in estimates of proportions of finite populations such as in the false consensus effect. However the modification of beliefs by ad hoc methods like Tversky and Kahneman's heuristics can be justified, even though this results in biased judgements. This is because of pragmatic factors such as the cost of obtaining and taking account of additional information which are not included even in a complete probability model. Finally, an analogy is drawn between probability models and geometric figures. Both idealisations are useful but qualitatively inadequate characterisations of nature. A difference between the two is that the size of any error can be limited in the case of the geometric figure in a way that is not possible in a probability model. (shrink)

Starting from the sixties of the past century theory change has become a main concern of philosophy of science. Two of the best known formal accounts of theory change are the post-Popperian theories of verisimilitude (PPV for short) and the AGM theory of belief change (AGM for short). In this paper, we will investigate the conceptual relations between PPV and AGM and, in particular, we will ask whether the AGM rules for theory change are effective means for approaching the truth, (...) i.e., for achieving the cognitive aim of science pointed out by PPV. First, the key ideas of PPV and AGM and their application to a particular kind of propositional theories - the so called "conjunctive propositions" - will be illustrated. Afterwards, we will prove that, as far as conjunctive propositions are concerned, AGM belief change is an effective tool for approaching the truth. (shrink)

One argument for the thirder position on the Sleeping Beauty problem rests on direct inference from objective probabilities. In this paper, I consider a particularly clear version of this argument by John Pollock and his colleagues (The Oscar Seminar 2008). I argue that such a direct inference is defeated by the fact that Beauty has an equally good reason to conclude on the basis of direct inference that the probability of heads is 1/2. Hence, neither thirders nor halfers can find (...) direct support in an appeal to objective probabilities. (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)

To clarify and illuminate the place of probability in science Ellery Eells and James H. Fetzer have brought together some of the most distinguished philosophers ...

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)

This survey presents some of the main principles involved in discovering causal relations. They belong to a large array of possible assumptions and conditions about causal relations, whose various combinations limit the possibilities of acquiring causal knowledge in different ways. How much and in what detail the causal structure can be discovered from what kinds of data depends on the particular set of assumptions one is able to make. The assumptions considered here provide a starting point to explore further the (...) foundations of causal discovery procedures, and how they can be improved. (shrink)

Fleeing from the Nazi regime, along with many German refugees, Hans Reichenbach came to teach at Istanbul University in 1933, accepting the invitation of the Turkish government and stayed in Istanbul until 1938. While much is known about his work and life in Istanbul, the existing literature relies mostly on his letters and works. In this article I try to shed more light on Reichenbach's scholarly activities and personal life by also taking into account the Turkish sources and the academic (...) context in which Reichenbach taught and worked. (shrink)

Some think that issues to do with scientific method are last century's stale debate; Popper was an advocate of methodology, but Kuhn, Feyerabend, and others are alleged to have brought the debate about its status to an end. The papers in this volume show that issues in methodology are still very much alive. Some of the papers reinvestigate issues in the debate over methodology, while others set out new ways in which the debate has developed in the last decade. The (...) book will be of interest to philosophers and scientists alike in the reassessment it provides of earlier debates about method and current directions of research. (shrink)

Several authors have claimed that mechanisms play a vital role in distinguishing between causation and mere correlation in the social sciences. Such claims are sometimes interpreted to mean that without mechanisms, causal inference in social science is impossible. The author agrees with critics of this proposition but explains how the account of how mechanisms aid causal inference can be interpreted in a way that does not depend on it. Nevertheless, he shows that this more charitable version of the account is (...) still unsuccessful as it stands. Consequently, he advances a proposal for shoring up the account, which is founded on the possibility of acquiring knowledge of social mechanisms by linking together norms or practices found in a society. Key Words: causality • social mechanisms • interpretation • anthropology. (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)

This article suggests a ‘best alternative' justification of induction (in the sense of Reichenbach) which is based on meta-induction . The meta-inductivist applies the principle of induction to all competing prediction methods which are accessible to her. It is demonstrated, and illustrated by computer simulations, that there exist meta-inductivistic prediction strategies whose success is approximately optimal among all accessible prediction methods in arbitrary possible worlds, and which dominate the success of every noninductive prediction strategy. The proposed justification of meta-induction is (...) mathematically analytical. It implies, however, an a posteriori justification of object-induction based on the experiences in our world. *Received November 2005; revised March 2008. †To contact the author, please write to: Department of Philosophy, University of Duesseldorf, Universitaetsstrasse 1, Geb. 23.21, Duesseldorf, Germany D-40225; e-mail: [email protected]. (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)

Abstract: According to Laurence BonJour, the problem of induction can be solved by recognizing the a priori necessity that inductive conclusions constitute the best explanations of inductive premises. I defend an interpretation of the key probability claims BonJour makes about inductive premises and show that they are not susceptible to many of the objections that have been lodged against them. I then argue that these purportedly necessary probability claims nevertheless remain deeply problematic and that, as a result, BonJour's proposal fails (...) to provide a satisfactory resolution of the problem of induction. (shrink)

In this paper, we develop an account of the justification thinkers have for employing certain basic belief-forming methods. The guiding idea is inspired by Reichenbach's work on induction. There are certain projects in which thinkers are rationally required to engage. Thinkers are epistemically justified in employing any belief-forming method such that "if it doesn't work, nothing will" for successfully engaging in such a project. We present a detailed account based on this intuitive thought and address objections to it. We conclude (...) by commenting on the implications that our account may have for other important epistemological issues and debates. (shrink)

Cohen and Meskin 2006 recently offered a counterfactual theory of information to replace the standard probabilistic theory of information. They claim that the counterfactual theory fares better than the standard account on three grounds: first, it provides a better framework for explaining information flow properties; second, it requires a less expensive ontology; and third, because it does not refer to doxastic states of the information-receiving organism, it provides an objective basis. In this paper, I show that none of these is (...) really an advantage. Moreover, the counterfactual theory fails to satisfy one of the basic properties of information flow, namely the Conjunction principle. Thus, I conclude, there is no reason to give up the standard probabilistic theory for the counterfactual theory of information. (shrink)

According to principles of probability coordination, such as Miller's Principle or Lewis's Principal Principle, you ought to set your subjective probability for an event equal to what you take to be the objective probability of the event. For example, you should expect events with a very high probability to occur and those with a very low probability not to occur. This paper examines the grounds of such principles. It is argued that any attempt to justify a principle of probability coordination (...) encounters the same difficulties as attempts to justify induction. As a result, no justification can be found. (shrink)

Statistical Learning Theory (e.g., Hastie et al., 2001; Vapnik, 1998, 2000, 2006) is the basic theory behind contemporary machine learning and data-mining. We suggest that the theory provides an excellent framework for philosophical thinking about inductive inference.

According to finite frequentism, the probability of an attribute A in a finite reference class B is the relative frequency of actual occurrences of A within B. I present fifteen arguments against this position.

Known as an upholder of subjectivism, Bruno de finetti (1906-1985) put forward a totally original philosophy of probability. This can be qualified as a combination of empiricism and pragmatism within an entirely coherent antirealistic perspective. The paper aims at clarifying the central features of such a philosophical position, Which is not only incompatible with any perspective based on an objective notion, But cannot be assimilated to other subjective views of probability either.

The logical interpretation of probability, or "objective Bayesianism'' – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine them by symmetry via a "principle of insufficient reason" inevitably leads to paradox. Three replies are advanced: that priors are imprecise or of little weight, so that disagreement about them does not matter, within limits; that it (...) is possible to distinguish reasonable from unreasonable priors on logical grounds; and that in real cases disagreement about priors can usually be explained by differences in the background information. It is argued also that proponents of alternative conceptions of probability, such as frequentists, Bayesians and Popperians, are unable to avoid committing themselves to the basic principles of logical probability. (shrink)

Pettit (2006) argues that deferring to majority testimony is not generally rational: it may lead to inconsistent beliefs. He suggests that “another ... approach will do better”: deferring to supermajority testimony. But this approach may also lead to inconsistencies. In this paper, I describe conditions under which deference to supermajority testimony ensures consistency, and conditions under which it does not. I also introduce the concept of “consistency of degree k”, which is weaker than full consistency by ruling out only “blatant” (...) inconsistencies in an agent’s beliefs while permitting less blatant ones, and show that, while super-majoritarian deference often fails to ensure full consistency, it is a route to consistency in this weaker sense. (shrink)

This paper justifies the inference of probabilities from symmetries. I supply some examples of important and correct inferences of this variety. Two explanations of such inferences -- an explanation based on the Principle of Indifference and a proposal due to Poincaré and Reichenbach -- are considered and rejected. I conclude with my own account, in which the inferences in question are shown to be warranted a posteriori, provided that they are based on symmetries in the mechanisms of chance setups.

David Lewis, Michael Thau, and Ned Hall have recently argued that the Principal Principle—an inferential rule underlying much of our reasoning about probability—is inadequate in certain respects, and that something called the ‘New Principle’ ought to take its place. This paper argues that the Principle Principal need not be discarded. On the contrary, Lewis et al. can get everything they need—including the New Principle—from the intuitions and inferential habits that inspire the Principal Principle itself, while avoiding the problems that originally (...) caused them to abandon that principle. (shrink)

This paper describes the development of theories of scientific explanation since Hempel's earliest models in the 1940ies. It focuses on deductive and probabilistic whyexplanations and their main problems: lawlikeness, explanation-prediction asymmetries, causality, deductive and probabilistic relevance, maximal specifity and homogenity, the height of the probability value. For all of these topic the paper explains the most important approaches as well as their criticism, including the author's own accounts. Three main theses of this paper are: (1) Both deductive and probabilistic explanations (...) are important in science, not reducible to each other. (2) One must distinguish between (cause giving) explanations and (reason giving) justifications and predictions. (3) The adequacy of deductive as well as probabilistic explanations is relative to a pragmatically given background knowledge-which does not exclude, however, the possibility of purely semantic models. (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.

An influential argument for anti-reductionism about testimony, due to CAJ Coady, fails, because it assumes that an inductive global defense of testimony would proceed along effectively behaviorist lines. If we take seriously our wealth of non-testimonially justified folk psychological beliefs, the prospects for inductivism and reductionism look much better.

I consider three aspects in which machine learning and philosophy of science can illuminate each other: methodology, inductive simplicity and theoretical terms. I examine the relations between the two subjects and conclude by claiming these relations to be very close.