Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand’s chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum sized state spaces. Articulating the nature of such spaces involves some deep mathematics and that is perhaps why the recent literature on Bertrand’s Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication. At the same time, the (...) philosophy of probability has been left out. In particular, left out entirely are the philosophical ground of the principle of indifference, the nature of the principle itself, the stringent constraint this places on the mathematical representation of the principle needed for its application to continuum sized event spaces, and what these entail for rigour in developing the paradox itself. This book puts the philosophy and its entailments back in and in so doing casts a new light on the paradox, giving original analyses of the paradox, its possible solutions, the source of the paradox, the philosophical errors we make in attempting to solve it and what the paradox proves for the philosophy of probability. The book finishes with the author’s proposed solution—a solution in the spirit of Bertrand’s, indeed—in which an epistemic principle more general than the principle of indifference offers a principled restriction of the domain of the principle of indifference. (shrink)

The Indifference Principle, its Paradoxes and Kolmogorov's Probability Space.

In a recent article, William C. Roach offers a presuppositional critique, which is inspired by Carl F. H. Henry, of Michael R. Licona’s so-called New Historiographical Approach to defending the resurrection. More precisely, Roach attempts to defend six key theses, namely, that the NHA is an evidentialist approach, the NHA is a deductive argument, the NHA is an insufficient approach, believers and unbelievers share no common ground, the NHA does not embrace a correspondence theory of truth, and the presupposition of (...) divine revelation is necessary for apologetics. We respond to each of Roach’s arguments, respectively. (shrink)

This is a study in the meaning of natural language probability operators, sentential operators such as probably and likely. We ask what sort of formal structure is required to model the logic and semantics of these operators. Along the way we investigate their deep connections to indicative conditionals and epistemic modals, probe their scalar structure, observe their sensitivity to contex- tually salient contrasts, and explore some of their scopal idiosyncrasies.

Epistemic modal operators give rise to something very like, but also very unlike, Moore's paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequence are investigated. The semantics is then extended to probability operators. Some problems and prospects for probabilistic representations of content and context are explored.

This paper develops a critical response to John Beatty’s recent (2006) engagement with Stephen Jay Gould’s claim that evolutionary history is contingent. Beatty identifies two senses of contingency in Gould’s work: an unpredictability sense and a causal dependence sense. He denies that Gould associates contingency with stochastic phenomena, such as drift. In reply to Beatty, this paper develops two main claims. The first is an interpretive claim: Gould really thinks of contingency has having to do with stochastic effects at the (...) level of macroevolution, and in particular with unbiased species sorting. This notion of contingency as macro-level stochasticity incorporates both the causal dependence and the unpredictability senses of contingency. The second claim is more substantive: Recent attempts by other scientists to put Gould’s claim to the test fail to engage with the hypothesis that species sorting sometimes resembles a lottery. Gould’s claim that random sorting is a significant macroevolutionary phenomenon remains an intriguing and largely untested live hypothesis about evolution. (shrink)

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

Many philosophers have argued that an event is lucky for an agent only if it was suitably improbable, but there is considerable disagreement about how to understand this improbability condition. This paper argues for a hitherto overlooked construal of the improbability condition in terms of the lucky agent’s epistemic situation. According to the proposed account, an event is lucky for an agent only if the agent was not in a position to know that the event would occur. It is also (...) explored whether this new account threatens the anti- luck program in epistemology. It is argued that although not detrimental to the anti- luck program, the epistemic account of luck sets certain important limits to its scope and feasibility. (shrink)

Information, entropy, probability: these three terms are closely interconnected in the prevalent understanding of statistical mechanics, both when this field is taught to students at an introductory level and in advanced research into the field’s foundations. This paper examines the interconnection between these three notions in light of recent research in the foundations of statistical mechanics. It disentangles these concepts and highlights their differences, at the same time explaining why they came to be so closely linked in the literature. In (...) the literature the term ‘information’ is often linked to entropy and probability in discussions of Maxwell’s Demon and its attempted exorcism by the Landauer-Bennett thesis, and in analyses of the spin echo experiments. The direction taken in the present paper is a different one. Here we discuss the statistical mechanical underpinning of the notions of probability and entropy, and this constructive approach shows that information plays no fundamental role in these concepts, although it can be conveniently used in a sense that we shall specify. (shrink)

Precautionary Principles are often said to be appropriate for decision-making in contexts of uncertainty such as climate policy. Contexts of uncertainty are contrasted to contexts of risk depending on whether we have probabilities or not. Against this view, I argue that the risk-uncertainty distinction is practically irrelevant. I start by noting that the history of the distinction between risk and uncertainty is more varied than is sometimes assumed. In order to examine the distinction, I unpack the idea of having probabilities, (...) in particular by distinguishing three interpretations of probability: objective, epistemic, and subjective probability. I then claim that if we are concerned with whether we have probabilities at all—regardless of how low their epistemic credentials are—then we almost always have probabilities for policy-making. The reason is that subjective and epistemic probability are the relevant interpretations of probability and we almost always have subjective and epistemic probabilities. In contrast, if we are only concerned with probabilities that have sufficiently high epistemic credentials, then we obviously do not always have probabilities. Climate policy, for example, would then be a case of decision-making under uncertainty. But, so I argue, we should not dismiss probabilities with low epistemic credentials. Rather, when they are the best available probabilities our decision principles should make use of them. And, since they are almost always available, the risk-uncertainty distinction remains irrelevant. (shrink)

Although recent epistemology has been marked by several prominent disagreements – e.g., between foundationalists and coherentists, internalists and externalists – there has been widespread agreement that some form of fallibilism must be correct. According to a rough formulation of this view, it is possible for a subject to have knowledge even in cases where the justification or grounding for the knowledge is compatible with the subject’s being mistaken. In this paper, I examine the motivation for fallibilism before providing a fully (...) general account of the view. I conclude by looking at the two major difficulties for fallibilism: the Gettier problem and the lottery paradox. (shrink)

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

While there is no universal logic of induction, the probability calculus succeeds as a logic of induction in many contexts through its use of several notions concerning inductive inference. They include Addition, through which low probabilities represent disbelief as opposed to ignorance; and Bayes property, which commits the calculus to a ‘refute and rescale’ dynamics for incorporating new evidence. These notions are independent and it is urged that they be employed selectively according to needs of the problem at hand. It (...) is shown that neither is adapted to inductive inference concerning some indeterministic systems. (shrink)

This paper evaluates whether and to what extent modal constraints on knowledge or the semantics of ‘knows’, which make essential reference to what goes on in other possible worlds, can be considered non-epistemic factors with epistemic significance. This is best understood as the question whether modal factors are non-truth-relevant factors that make the difference between true belief and knowledge, or to whether a true belief falls under the extension of ‘knowledge’ in a context, where a factor is truth-relevant with respect (...) to S’s belief that P iff it bears on the probability that P is true. To the extent that these factors are non-epistemic, epistemologies that endorse them—modal epistemologies—stand in conflict with intellectualism. I focus on three modal epistemologies: safety, sensitivity, and David Lewis’s epistemic contextualism. I argue that prima facie, safety and sensitivity allow that non-epistemic changes in a context can shift the closeness ordering on worlds, and in so doing make a difference to whether S knows P, while Lewis’s contextualism allows that non-epistemic changes in a context can shift the relevant domain of not-P possibilities that must be eliminated for ‘S knows P’ to be true in that context. Then to make her theory compatible with intellectualism, the modal epistemologist must say much more about the notion of probability at play in the definition of ‘truth-relevant’. I suggest that either accepting or rejecting that modal epistemologies are intellectualist has significance consequences for debates between pragmatists and purists, which radiate into wider contemporary epistemology. (shrink)

In this paper, I provide an account of epistemic anxiety as an emotional response to epistemic risk: the risk of believing in error. The motivation for this account is threefold. First, it makes epistemic anxiety a species of anxiety, thus rendering psychologically respectable a notion that has heretofore been taken seriously only by epistemologists. Second, it illuminates the relationship between anxiety and risk. It is standard in psychology to conceive of anxiety as a response to risk, but psychologists – very (...) reasonably – have little to say about risk itself, as opposed to risk judgement. In this paper, I specify what risk must be like to be the kind of thing to which anxiety can be a response. Third, my account improves on extant accounts of epistemic anxiety in the literature. It is more fleshed out than Jennifer Nagel’s, which is largely agnostic about the nature of epistemic anxiety, focusing instead on what work it does in our epistemic lives. In offering an account of epistemic anxiety as an emotion, my account explains how it is able to do the epistemological work to which Nagel puts it. My account is also more plausible than Juliette Vazard’s, on which epistemic anxiety is an emotional response to potential threat to one’s practical interests. Vazard’s account cannot distinguish epistemic anxiety from anxiety in general, and also fails to capture all instances of what we want to call epistemic anxiety. My account does better on both counts. (shrink)

I follow Hájek (Synthese 137:273–323, 2003c) by taking objective probability to be a function of two propositional arguments—that is, I take conditional probability as primitive. Writing the objective probability of q given r as P(q, r), I argue that r may be chosen to provide less than a complete and exact description of the world’s history or of its state at any time. It follows that nontrivial objective probabilities are possible in deterministic worlds and about the past. A very simple (...) chance–credence relation is also then natural, namely that reasonable credence equals objective probability. In other words, we should set our actual credence in a proposition equal to the proposition’s objective probability conditional on available background information. One advantage of that approach is that the background information is not subject to an admissibility requirement, as it is in standard formulations of the Principal Principle. Another advantage is that the “undermining” usually thought to follow from Humean supervenience can be avoided. Taking objective probability to be a two-argument function is not merely a technical matter, but provides us with vital flexibility in addressing significant philosophical issues. (shrink)

In this paper, I argue that, other things being equal, simpler arguments are better. In other words, I argue that, other things being equal, it is rational to prefer simpler arguments over less simple ones. I sketch three arguments in support of this claim: an argument from mathematical proofs, an argument from scientific theories, and an argument from the conjunction rule.

This paper makes the case for a wider acceptance of a probabilistic approach to causation in negligence. This acceptance would help to remove much of the incoherence which has come to afflict the English law of personal injury law. This incoherence can also be found in other common law jurisdictions (notably those of the United States, Canada and Australia). Concentrating upon recent UK case law, the argument opposes the contention that ‘naked statistics’ can play no role in establishing causation. The (...) argument is controversial but it can be reduced to three unremarkable grounds: (1) With its acceptance (albeit in certain carefully prescribed circumstances) of liability for a negligently increased risk which has eventuated, the common law has already embraced a probabilistic conception of causation; (2) The English common law already employs a probabilistic (frequentist) approach to identifying coincidences; and (3) With the ‘balance of probabilities’ as the standard of proof in civil cases, the common law has long had a probabilistic (epistemic) concept at its core. Probabilistic approaches (at both the type and token level) are shown to be consistent with laypersons’ understanding of the concepts such as risk, chance, odds and likelihood. Moreover, a wider acceptance of a probabilistic perspective on causation would entail no major challenge to the fundamental aims of tort, viz. deterrence and corrective justice. (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)

Elliott Sober and his defenders think of selection, drift, mutation, and migration as distinct evolutionary forces. This paper exposes an ambiguity in Sober's account of the force of selection: sometimes he appears to equate the force of selection with variation in fitness, sometimes with ‘selection for properties’. Sober's own account of fitness as a property analogous to life-expectancy shows how the two conceptions come apart. Cases where there is selection against variance in offspring number also show that selection and drift (...) cannot be distinguished in the way Sober hopes for. These issues have significance beyond the parochial matter of the coherence of Sober's system. There is no good principled answer to the question of which features of a population should count among the contributors to fitness. This means there is no non-arbitrary account of the nature of selection. (shrink)

Recent literature has paid attention to a demarcation problem for evolutionary debunking arguments. This is the problem of asking in virtue of what regulative metaepistemic norm evolutionary considerations either render a belief justified, or debunk it as unjustified. I examine the so-called ‘Milvian Bridge principle’ A new science of religion, Routledge, New York, 2012; Sloan, McKenny, Eggelson Darwin in the 21st century: nature, humanity, and God, University Press, Notre Dame, 2015)), which offers exactly such a called for regulative metaepistemic norm. (...) The Milvian Bridge principle suggests that the metaepistemic norm is: adaptive reliability for truth of cognitive processes that the existence of corresponding truth-making facts evolutionary theory justifies. I argue that the Milvian Bridge principle is problematic on a number of counts, something that is shown via spiraling ‘companions in guilt arguments’. Finally, I consider ‘the core reductionist objection’ to the critique of the Milvian Bridge principle and offer a response. I conclude that the Milvian Bridge principle is destabilized. (shrink)

We claim that if a complete philosophy of evidence-based practice is intended, then attention to the nature of causation in health science is necessary. We identify how health science currently conceptualises causation by the way it prioritises some research methods over others. We then show how the current understanding of what causation is serves to constrain scientific progress. An alternative account of causation is offered. This is one of dispositionalism. We claim that by understanding causation from a dispositionalist stance, many (...) of the processes within an evidence-based practice framework are better accounted for. Further, some of the problems associated with the health research, e.g. external validity of causal findings, dissolve. (shrink)

In the first part of the paper, three objections to the precautionary principle are outlined: the principle requires some account of how to balance risks of significant harms; the principle focuses on action and ignores the costs of inaction; and the principle threatens epistemic anarchy. I argue that these objections may overlook two distinctive features of precautionary thought: a suspicion of the value of “full scientific certainty”; and a desire to distinguish environmental doings from allowings. In Section 2, I argue (...) that any simple distinction between environmental doings and allowings is untenable. However, I argue that the appeal of such a distinction can be captured within a relational account of environmental equity. In Section 3 I show how the proposed account of environmental justice can generate a justification for distinctively “precautionary” policy-making. (shrink)

According to the Nomological Argument, observed regularities in nature are best explained by an appeal to a supernatural being. A successful explanation must avoid two perils. Some explanations provide too little structure, predicting a universe without regularities. Others provide too much structure, thereby precluding an explanation of certain types of lawlike regularities featured in modern scientific theories. We argue that an explanation based in the creative, intentional action of a supernatural being avoids these two perils whereas leading competitors do not. (...) Although our argument falls short of a full defense, it does suggest that the Nomological Argument is worthy of philosophical attention. (shrink)

The Razor says: do not multiply entities without necessity! The Laser says: do not multiply fundamental entities without necessity! Behind the Laser lies a deep insight. This is a distinction between the costs and the commitments of a theory. According to the Razor, every commitment is a cost. Not so according to the Laser. According to the Laser, derivative entities are an ontological free lunch: that is, they are a commitment without a cost. Jonathan Schaffer (2015) has argued that the (...) Laser should replace the Razor. In Sections 2-4 we shall discuss and argue against Schaffer’s arguments for replacing the Razor with the Laser. Schaffer considers several objections to his views, and in Sections 5-7 we shall argue that Schaffer does not deal successfully with two of them. In Section 8 we shall present a probabilistic argument for the Laser. However, the argument has a limitation and does not support the replacement of the Razor with the Laser. Indeed, it supports only the claim that, given certain assumptions, the multiplication of explanatorily relevant derivative entities does not matter; but, as we argue in the same section, there is an argument that multiplying explanatorily superfluous derivative entities does makes a theory less rationally acceptable. Our conclusion is that the Laser cannot replace the Razor and that derivative entities are not an ontological free lunch. (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)

In this paper I argue for a doctrine I call ?infallibilism?, which I stipulate to mean that If S knows that p, then the epistemic probability of p for S is 1. Some fallibilists will claim that this doctrine should be rejected because it leads to scepticism. Though it's not obvious that infallibilism does lead to scepticism, I argue that we should be willing to accept it even if it does. Infallibilism should be preferred because it has greater explanatory power (...) than fallibilism. In particular, I argue that an infallibilist can easily explain why assertions of ?p, but possibly not-p? (where the ?possibly? is read as referring to epistemic possibility) is infelicitous in terms of the knowledge rule of assertion. But a fallibilist cannot. Furthermore, an infallibilist can explain the infelicity of utterances of ?p, but I don't know that p? and ?p might be true, but I'm not willing to say that for all I know, p is true?, and why when a speaker thinks p is epistemically possible for her, she will agree (if asked) that for all she knows, p is true. The simplest explanation of these facts entails infallibilism. Fallibilists have tried and failed to explain the infelicity of ?p, but I don't know that p?, but have not even attempted to explain the last two facts. I close by considering two facts that seem to pose a problem for infallibilism, and argue that they don't. (shrink)

This paper seeks to determine the significance, if any, of epidemiological evidence to prove the specific causation element of liability in negligence or other relevant torts—in particular, what importance can be attached to a relative risk > 2, where that figure represents a sound causal inference at the general level. The paper discusses increased risk approaches to epidemiological evidence and concludes that they are a last resort. The paper also criticizes the proposal that the probability of causation can be estimated (...) with reference to the RR, such that RR > 2 is necessary and sufficient for causation. It is argued, following arguments by Sander Greenland and others, that RR > 2 is not necessary for proof of specific causation, except under restrictive biological assumptions that are not known to be satisfied for any important disease, and therefore must never be required. However, the paper argues that in some circumstances RR > 2 can be sufficient to prove causation at law. This position is defended against the widely held judicial and academic view that epidemiological evidence must be accompanied by something else, particular to the case at hand, if it is to have probative force for specific causation. It is argued that far from being epistemically irrelevant, to achieve correct and just outcomes it is in fact mandatory to take epidemiological evidence into account in deciding specific causation. Failing to consider such evidence when it is available leads to error and injustice. The conclusion is that in certain circumstances epidemiological evidence of RR > 2 is not necessary to prove specific causation but that it is sufficient. This “sufficiency” is confined to circumstances where there is no other evidence, as a way of getting clear on what the epidemiological evidence says. Once we have worked out what it says, this must be weighed against the other relevant evidence, if there is any. (shrink)

The paper assumes that to be of practical interest process must be understood as physical action that takes place in the world rather than being an idea in the mind. It argues that if an ontology of process is to accommodate actuality, it must be represented in terms of relative probabilities. Folk physics cannot accommodate this, and so the paper appeals to scientific culture because it is an emergent knowledge of the world derived from action in it. Process is represented (...) as a contradictory probability distribution that does not depend on a spatio-temporal frame. An actuality is a probability density that grounds the values of probabilities to constitute their distributions. Because probability is a conserved value, probability distributions are subject to the constraint of symmetry and must be zero-sum. An actuality is locked-in by other actualities to become a zero-sum symmetry of probability values. It is shown that the locking-in of actualities constructs spatio-temporal locality, lends actualities specificity, and makes them a contradiction. Localization is the basis for understanding empirical observation. Because becoming depends on its construction of being, processes exist as trajectories. The historical trajectories of evolution and revolution as well as the non-historical trajectory of strong emergence are how processes are observed to exist. (shrink)

We argue that quantum theory does not allow for a generalization of the notion of classical conditional probability by showing that the probability defined by the Lüders rule, standardly interpreted in the literature as the quantum-mechanical conditionalization rule, cannot be interpreted as such.

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)

ABSTRACTA popular strategy for understanding the probabilities that arise in physics is to interpret them via reductionist accounts of chance—indeed, it is sometimes claimed that such accounts are uniquely well-suited to make sense of the probabilities in classical statistical mechanics. Here it is argued that reductionist accounts of chance carry a steep but unappreciated cost: when applied to physical theories of the relevant type, they inevitably distort the relations of probability that they take as input.

Although Bayesian methods are widely used in phylogenetic systematics today, the foundations of this methodology are still debated among both biologists and philosophers. The Bayesian approach to phylogenetic inference requires the assignment of prior probabilities to phylogenetic trees. As in other applications of Bayesian epistemology, the question of whether there is an objective way to assign these prior probabilities is a contested issue. This paper discusses the strategy of constraining the prior probabilities of phylogenetic trees by means of the Principal (...) Principle. In particular, I discuss a proposal due to Velasco (Biol Philos 23:455–473, 2008) of assigning prior probabilities to tree topologies based on the Yule process. By invoking the Principal Principle I argue that prior probabilities of tree topologies should rather be assigned a weighted mixture of probability distributions based on Pinelis’ (P Roy Soc Lond B Bio 270:1425–1431, 2003) multi-rate branching process including both the Yule distribution and the uniform distribution. However, I argue that this solves the problem of the priors of phylogenetic trees only in a weak form. (shrink)

The paper aims to show that, if S5 is the logic of metaphysical necessity, then no state of affairs in any possible world constitutes any non-trivial evidence for or against the existence of the traditional God. There might well be states of affairs in some worlds describing extraordinary goods and extraordinary evils, but it is false that these states of affairs constitute any (non-trivial) evidence for or against the existence of God. The epistemological and metaphysical consequences for philosophical theology of (...) assuming that S4 or Kσρ is the logic of metaphysical necessity are equally untenable. S4 guarantees that God does not exist if there is the slightest evidence against the existence of God. And Kσρ guarantees that God might survive the loss or acquisition of any essential property at all. (shrink)

According to an infinite frequency principle, it is rational, under certain conditions, to set your credence in an outcome to the limiting frequency of that outcome if the experiment were repeated indefinitely. I argue that most infinite frequency principles are undesirable in at least one of the following ways: accepting the principle would lead you to accept bets with sure losses, the principle gives no guidance in the case of deterministic experiments like coin tosses and the principle relies on a (...) metaphysical property, ‘chanciness’, whose necessary and sufficient conditions are unknown. I show that a frequency principle that is based on the principal principle suffers from problems related to the definition of ‘chance’ or ‘chanciness’, which could lead to all three of the above problems. I introduce a version of the infinite frequency principle that does not rely on a notion of chance or chanciness and does not suffer from any of these problems. (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)

Probability and indeterminism have always been core philosophical themes. This paper aims to contribute to understanding probability and indeterminism in biology. To provide the background for the paper, it will first be argued that an omniscient being would not need the probabilities of evolutionary theory to make predictions about biological processes. However, despite this, one can still be a realist about evolutionary theory, and then the probabilities in evolutionary theory refer to real features of the world. This prompts the question (...) of how to interpret biological probabilities which correspond to real features of the world but are in principle dispensable for predictive purposes. This paper will suggest three possible interpretations. The first interpretation is a propensity interpretation of kinds of systems. It will be argued that backward probabilities in biology do not present a problem for this propensity interpretation. The second interpretation is the frequency interpretation. Third, I will suggest Humean chances are a new interpretation of probability in evolutionary theory. Finally, this paper discusses Sansom’s argument that biological processes are indeterministic because probabilities in evolutionary theory refer to real features of the world. It will be argued that Sansom’s argument is not conclusive, and that the question whether biological processes are deterministic or indeterministic is still with us. (shrink)

In the contemporary philosophical debate about probability, one of the main problems con‐ cerns the relation between objective probability and determinism. Is it possible for objective probability and determinism to co‐exist? this is one of the questions this dispute tries to answer. the scope of discussion is conducted between advocates of a positive answer (com‐ patibilist) and co‐existence opponents (incompatibilist). In the early twentieth century, many logicians also developed topics regarding probability and determinism. One of them was the outstanding Polish (...) logician and philosopher — Jan Łukasiewicz. the general purpose of this paper is to analyse and implement Łukasiewicz’s views regarding determinism and probability in the contemporary eld of this problem. I will try to show the relation between his interpre‐ tations of these concepts and in consequence his attempt to con ont them. As a result of the above analysis, I present some di erent positions (located in the elds of logic and semantics) in the contemporary discourse about the relation between objective probability and determi‐ nism. moreover, I will present Łukasiewicz’s views about this relation and the consequence of these solutions in the eld of logic. (shrink)

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)

The idea that probability is a degree of rational belief seemed too vague for a foundation of a mathematical theory. It was certainly not obvious that degrees of rational belief had to be governed by the probability axioms as used by Laplace and other prestatistical probabilityst. The axioms seemed arbitrary in their interpretation. To eliminate the arbitrariness, the stat- isticians of the early 20th century drastically restricted the possible applications of the probability theory, by insisting that probabilities had to be (...) interpreted as relative frequencies, which obviously satisfied the probability axioms, and so the arbitrariness was removed. But the frequentist approach turned more subjective than the prestatistical approach, because the identifications of outcome spaces, the choices of test statistics, the declarations of what rejection regions are, the choices of null-hypothesis among alternatives, the contradictory choices between sizes and powers etc., depend on thoughts or even whims of the experimenter. Frequentists thus failed to solve the problems that motivated their approach, they even exacerbated them. The subjective Bayesianism of Ramsey and de Finetti did not solve the problems either. Finally Cox provided the missing foundation for probability as a degree of rational belief, which makes the Bayesian probability theory (which is based on this foundation) the best theory of probable inference we have. Hence, it is quite unbelievable that it is not even mentioned in recent philosophy textbooks devoted to the probable inference. The reason could be that it requires fairly sophisticated mathematics. But not even to mention it? We explain the history and prove Cox theorem in a novel way. (shrink)

A common view among nontheists combines the de jure objection that theism is epistemically unacceptable with agnosticism about the de facto objection that theism is false. Following Plantinga, we can call this a “proper” de jure objection—a de jure objection that does not depend on any de facto objection. In his Warranted Christian Belief, Plantinga has produced a general argument against all proper de jure objections. Here I first show that this argument is logically fallacious (it makes subtle probabilistic fallacies (...) disguised by scope ambiguities), and proceed to lay the groundwork for the construction of actual proper de jure objections. (shrink)

The history of the mathematical probability includes two phases: 1) From Pascal and Fermat to Laplace, the theory gained in application fields; 2) In the first half of the 20th Century, two competing axiomatic systems were respectively proposed by von Mises in 1919 and Kolmogorov in 1933. This paper places this historical sketch in the context of the philosophical complexity of the probability concept and explains the resounding success of Kolmogorov’s theory through its ability to avoid direct interpretation. Indeed, unlike (...) experimental sciences, and despite its numerous applications, probability theory cannot be tested per se. Rather it relates to practical matters by means of transition hypotheses or bridging principles that match the structure of practical problems with abstract theory. In this respect probability theory has a very special status among scientific disciplines. (shrink)