Chance and Objective Probability

This paper is a discussion note on Isaacs et al. (2022), who have claimed to offer a new motivation for imprecise probabilities, based on the mathematical phenomenon of non-measurability. In this note, I clarify some consequences of their proposal. In particular, I show that if their proposal is applied to a bounded 3-dimensional space, then they have to reject at least one of the following: (i) If A is at most as probable as B and B is at most as (...) probable as C, then A is at most as probable as C. (ii) Let A ∩ C = B ∩ C = ∅. A is at most as probable as B iff (A ∪ C) is at most as probable as (B ∪ C). But rejecting either statement seems unattractive. (shrink)

Rowe has recently argued that pure risk of harm cannot itself be a harm. I respond to Rowe and argue that given an appropriate understanding of objective probabilities, pure objective risk of harm can itself be a harm.

The inflation of Type I error rates is thought to be one of the causes of the replication crisis. Questionable research practices such as p-hacking are thought to inflate Type I error rates above their nominal level, leading to unexpectedly high levels of false positives in the literature and, consequently, unexpectedly low replication rates. In this article, I offer an alternative view. I argue that questionable and other research practices do not usually inflate relevant Type I error rates. I begin (...) with an introduction to Type I error rates that distinguishes them from theoretical errors. I then illustrate my argument with respect to model misspecification, multiple testing, selective inference, forking paths, exploratory analyses, p-hacking, optional stopping, double dipping, and HARKing. In each case, I demonstrate that relevant Type I error rates are not usually inflated above their nominal level, and in the rare cases that they are, the inflation is easily identified and resolved. I conclude that the replication crisis may be explained, at least in part, by researchers’ misinterpretation of statistical errors and their underestimation of theoretical errors. (shrink)

According to a common judgement, a social planner should often use a lottery to decide which of two people should receive a good. This judgement undermines one of the best-known arguments for utilitarianism, due to John C. Harsanyi, and more generally undermines axiomatic arguments for utilitarianism and similar views. In this paper we ask which combinations of views about (a) the social planner’s attitude to risk and inequality, and (b) the subjects’ attitudes to risk are consistent with the aforementioned judgement. (...) We find that the class of combinations of views that can plausibly accommodate this judgement is quite limited. But one theory does better than others: the theory of chance-sensitive utility. (shrink)

This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called generalized stochastic systems, collectively encompass many important kinds of stochastic processes, including Markov chains and random dynamical systems. This paper then states and proves a new theorem that establishes a precise correspondence between any generalized stochastic system and a unitarily evolving quantum system. This theorem therefore leads to a new formulation of (...) quantum theory, alongside the Hilbert-space, path-integral, and quasiprobability formulations. The theorem also provides a first-principles explanation for why quantum systems are based on the complex numbers, Hilbert spaces, linear-unitary time evolution, and the Born rule. In addition, the theorem suggests that by selecting a suitable Hilbert space, together with an appropriate choice of unitary evolution, one can simulate any generalized stochastic system on a quantum computer, thereby potentially opening up an extensive set of novel applications for quantum computing. (shrink)

This is the outline : I - Quelques étapes aux avancées significatives II - La pensée chrétienne et le hasard d’ignorance III - De quelques difficultés de raisonner sur le probable IV - Téléologie et évolutionnisme V - Où est l’« étage » qui permette de parler d’indépendance ? VI. Qu’y a-t-il à la base de nos concepts d’ordre ? VII - Quelle place pour le hasard ? VIII. Le hasard appréhendé de dos ?

This paper proposes a reinterpretation of the Chinese worldview on equilibrium/nonequilibrium and yin-yang. Important terminologies and concepts that constitute Yijing have correlative aspects with irreversible thermodynamics and quantum reality- instability, nonlinearity, nonequilibrium and temporality. Ilya Prigogine is a Nobel laureate noted for his contribution to dissipative structures and their role in thermodynamic systems far from equilibrium, complexity and irreversibility. His expressions, as argued in this paper, resonate with the principles in Yijing. Thus, this paper attempts to re-state existing interpretations of (...) Yijing’s ideas with reference to science. Understanding Yijing’s terms and concepts must be contextualised to account for its pervasiveness of temporality and the change process. Otherwise, these cardinal concepts may be misconstrued as a hodgepodge of Eastern traditions with no relevance to modern science. This paper concentrates on the fundamental role of indeterminism in nonlinear systems on classical and quantum levels using Yijing’s conceptual framework. It concludes that the dominant ideas in Yijing and ancient Chinese philosophy resonate with the current scientific belief – the end of certainty. Instability, far-from-equilibrium, irreversibility, probability, bifurcation, and self-organisation are intrinsic properties of nature appearing at all levels, from particle, protein folding, and DNA double helix to cosmological scales. Information is the basis of all changes, and the agency of change is the human (‘ren’) with a consciousness existing in the probability space between heaven (‘tian’) and earth (‘di’). Finally, this paper outlines a modelling approach with the self-organising human in the centre between heaven and earth, representing living systems as discrete dynamical systems presented with binary choices (yin-yang). The interplay of yin and yang lines in a hexagram is thought to reflect the changing dynamics of a given situation, and the interpretation of the hexagram is based on the relationships between the yin and yang lines based on informational availability. In this way, the concepts of yin-yang and information causality are central to Yijing's understanding of change and are clarified in this paper. (shrink)

Model of intelligence and new methods to assess IQ. MA thesis in 1998 (Comenius University). Art exhibitions "From Animation" London 2013, "Fading Memory" Weißenohe 2015, TAIF Tokyo 2017. Conferences in Santorini, Daejon 2016, Geneva 2017.

There is widespread excitement in the literature about the method of arbitrary functions: many take it to show that it is from the dynamics of systems that the objectivity of probabilities emerge. In this paper, I differentiate three ways in which a probability function might be objective, and I argue that the method of arbitrary functions cannot help us show that dynamics objectivise probabilities in any of these senses.

L’article de Karl Popper « Indeterminism in Quantum Physics and in Classical Physics » est tombé injustement dans l’oubli. Popper jugeait le déterminisme faux : l’avenir est ouvert. En principe, remplacer la variante de Laplace de la pré-détermination par une prédétermination prévisible permet de rendre scienti-fique, donc réfutable, le déterminisme « scientifique ». Popper a affirmé qu’il l’avait réfuté. Maintenant, un système métaphysique peut avoir une extension – au sens mathématique – qui le rend explicatif et testable. Si une extension (...) existe, alors elle n’est pas unique, et de nombreuses autres extensions alterna-tives existent. La preuve de Popper n’est alors pas concluante. (shrink)

This chapter focuses on the relations between objective probabilities in physical theories at different levels. In general philosophy of probability, it is frequently assumed that a fundamental deterministic theory cannot support probabilistic phenomena at any higher level, or more generally that there cannot be non-trivial probabilities in higher-level theories that are not encoded in probabilities at the lower level. These assumptions face significant challenges from some well-understood physical theories – I focus on statistical mechanics and Bohmian mechanics – where a (...) deterministic description at some lower level gives rise to an effectively probabilistic theory at some higher level; in each case, constraints arising from an objective physical limitation on the acquisition of evidence concerning the lower level plays a crucial role in supporting the higher-level probabilities. (shrink)

Why do we value higher-level scientific explanations if, ultimately, the world is physical? An attractive answer is that physical explanations often cite facts that don’t make a difference to the event in question. I claim that to properly develop this view we need to commit to a type of deterministic chance. And in doing so, we see the theoretical utility of deterministic chance, giving us reason to accept a package of views including deterministic chance.

This paper addresses the question whether future contingents are knowable, that is, whether one can know that things will go a certain way even though it is possible that things will not go that way. First I will consider a long-established view that implies a negative answer, and draw attention to some endemic problems that affect its credibility. Then I will sketch an alternative line of thought that prompts a positive answer: future contingents are knowable, although our epistemic access of (...) them is limited in some important respects. (shrink)

Darwin famously held that his use of the term "chance" in evolutionary theory merely "serves to acknowledge plainly our ignorance of the causes of each particular variation". Is this a tenable view today? Or should we revise our thinking about chance in evolution in light of the more advanced, quantitative models of Neo-Darwinian theory, which make substantial use of statistical reasoning and the concept of probability? Is determinism still a viable metaphysical doctrine about biological reality after the quantum revolution in (...) physics, or dowe have to abandon it in favor of an objective indeterminism? In light of such reflections, what is the relevant interpretation of probability in evolutionary theory? Do biologists use the concept of probability because they are finite cognitive agents or because the evolutionary process is fundamentally probabilistic? In this paper, I will show that we do not yet fully understand the nature of chance in evolution. (shrink)

Carl Hempel (1965) argued that probabilistic hypotheses are limited in what they can explain. He contended that a hypothesis cannot explain why E is true if the hypothesis says that E has a probability less than 0.5. Wesley Salmon (1971, 1984, 1990, 1998) and Richard Jeffrey (1969) argued to the contrary, contending that P can explain why E is true even when P says that E’s probability is very low. This debate concerned noncontrastive explananda. Here, a view of contrastive causal (...) explanation is described and defended. It provides a new limit on what probabilistic hypotheses can explain; the limitation is that P cannot explain why E is true rather than A if P assign E a probability that is less than or equal to the probability that P assigns to A. The view entails that a true deterministic theory and a true probabilistic theory that apply to the same explanandum partition are such that the deterministic theory explains all the true contrastive propositions constructable from that partition, whereas the probabilistic theory often fails to do so. (shrink)

In this short survey article, I discuss Bell’s theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2) superdeterminism. The issues they raised not only apply to a wide class of no-go theorems about quantum mechanics but are also of general philosophical interest.

This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly pick (...) out a point on a continuum, for instance using a roulette wheel or by flipping a countable infinity of fair coins, it follows, given the axioms of ZFC, that there are many different cardinalities between countable infinity and the cardinality of the continuum. (shrink)

Human freedom is in tension with nomological determinism and with statistical determinism. The goal of this paper is to answer both challenges. Four contributions are made to the free-will debate. First, we propose a classification of scientific theories based on how much freedom they allow. We take into account that indeterminism comes in different degrees and that both the laws and the auxiliary conditions can place constraints. A scientific worldview pulls towards one end of this classification, while libertarianism pulls towards (...) the other end of the spectrum. Second, inspired by Hoefer, we argue that an interval of auxiliary conditions corresponds to a region in phase space, and to a bundle of possible block universes. We thus make room for a form of non-nomological indeterminism. Third, we combine crucial elements from the works of Hoefer and List; we attempt to give a libertarian reading of this combination. On our proposal, throughout spacetime, there is a certain amount of freedom that can be interpreted as the result of agential choices. Fourth, we focus on the principle of alternative possibilities throughout and propose three ways of strengthening it. (shrink)

I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of complementary inaccuracy between spatial location and velocity is derived, and its relation to the Uncertainty Principle discussed. In addition, even if the laws of nature are deterministic, the behaviour of systems will be random to some degree. These and other (...) considerations draw classical physics closer to Quantum Mechanics. An arrow of entropy is also derived, given an arrow of time. Lastly, chaos is given an additional, objective meaning. (shrink)

Notoriously, the Einstein equations of general relativity have solutions in which closed timelike curves occur. On these curves time loops back onto itself, which has exotic consequences: for example, traveling back into one's own past becomes possible. However, in order to make time travel stories consistent constraints have to be satisfied, which prevents seemingly ordinary and plausible processes from occurring. This, and several other "unphysical" features, have motivated many authors to exclude solutions with CTCs from consideration, e.g. by conjecturing a (...) chronology protection law. In this contribution we shall investigate the nature of one particular class of exotic consequences of CTCs, namely those involving unexpected cases of indeterminism or determinism. Indeterminism arises even against the backdrop of the usual deterministic physical theories when CTCs do not cross spacelike hypersurfaces outside of a limited CTC-region|such hypersurfaces fail to be Cauchy surfaces. We shall compare this CTC-indeterminism with four other types of indeterminism that have been discussed in the philosophy of physics literature: quantum indeterminism, the indeterminism of the hole argument, non-uniqueness of solutions of differential equations and lack of predictability due to insuffcient data. By contrast, a certain kind of determinism appears to arise when an indeterministic theory is applied on a CTC: things cannot be different from what they already were. Again we shall make comparisons, this time with other cases of determination in physics. We shall argue that on further consideration both this indeterminism and determinism on CTCs turn out to possess analogues in other, familiar areas of physics. CTC- indeterminism is close to the epistemological indeterminism we know from statistical physics, while the "fixedness" typical of CTC-determinism is pervasive in physics. CTC- determinism and CTC-indeterminism therefore do not provide incontrovertible grounds for rejecting CTCs as conceptually inadmissible. (shrink)

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two (...) sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

A previously unrecognised argument against deterministic chance is introduced. The argument rests on the twin ideas that determined outcomes are settled, while chancy outcomes are unsettled, thus making cases of determined but chancy outcomes impossible. Closer attention to tacit assumptions about settledness makes available some principled lines of resistance to the argument for compatibilists about chance and determinism. Yet the costs of maintaining compatibilism may be higher with respect to this argument than with respect to existing incompatibilist arguments.

In this paper, I challenge the traditional narrative that William James’s arguments against determinism were primarily motivated by his personal struggles with depression. I argue that James presents an alternative argument against determinism that is motivated by his commitment to sound scientific practice. James argues that determinism illegitimately extrapolates from observations of past events to predictions about future events without acknowledging the distinct metaphysical difference between them. This occupation with futurity suggests that James’s true target is better understood as logical (...) determinism rather than causal determinism. This has consequences for James’s proposed alternative, which I call his probabilistic underdeterminism, a conception of the universe that is built on chance, choice, and a local teleology. All of this forms part of a broader criticism of the scientific practices of his day based on their widespread failure to acknowledge the distorting effects of observation on that which is observed. (shrink)

In a world awash in statistical patterns, should we conclude that the universe’s evolution or genesis is somehow subject to chance? I draw attention to alternatives that must be acknowledged if we are to have an adequate assessment of what chance the universe might have had.

I present an account of deterministic chance which builds upon the physico-mathematical approach to theorizing about deterministic chance known as 'the method of arbitrary functions'. This approach promisingly yields deterministic probabilities which align with what we take the chances to be---it tells us that there is approximately a 1/2 probability of a spun roulette wheel stopping on black, and approximately a 1/2 probability of a flipped coin landing heads up---but it requires some probabilistic materials to work with. I contend that (...) the right probabilistic materials are found in reasonable initial credence distributions. I note that, with some normative assumptions, the resulting account entails that deterministic chances obey a variant of Lewis's 'principal principle'. I additionally argue that deterministic chances, so understood, are capable of explaining long-run frequencies. (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)

In this book chapter written for a popular audience, I discuss classic issues surrounding luck, determinism and probability in the context of the penalty shoot-outs used in football’s World Cup. Can it ever make objective sense to blame an outcome on bad luck? I go on to discuss whether we can legitimately pin the blame on any one factor at all, such as a referee. This takes us into issues surrounding the apportioning of causal responsibility.

In this text the ancient philosophical question of determinism (“Does every event have a cause ?”) will be re-examined. In the philosophy of science and physics communities the orthodox position states that the physical world is indeterministic: quantum events would have no causes but happen by irreducible chance. Arguably the clearest theorem that leads to this conclusion is Bell’s theorem. The commonly accepted ‘solution’ to the theorem is ‘indeterminism’, in agreement with the Copenhagen interpretation. Here it is recalled that indeterminism (...) is not really a physical but rather a philosophical hypothesis, and that it has counterintuitive and far-reaching implications. At the same time another solution to Bell’s theorem exists, often termed ‘superdeterminism’ or ‘total determinism’. Superdeterminism appears to be a philosophical position that is centuries and probably millennia old: it is for instance Spinoza’s determinism. If Bell’s theorem has both indeterministic and deterministic solutions, choosing between determinism and indeterminism is a philosophical question, not a matter of physical experimentation, as is widely believed. If it is impossible to use physics for deciding between both positions, it is legitimate to ask which philosophical theories are of help. Here it is argued that probability theory – more precisely the interpretation of probability – is instrumental for advancing the debate. It appears that the hypothesis of determinism allows to answer a series of precise questions from probability theory, while indeterminism remains silent for these questions. From this point of view determinism appears to be the more reasonable assumption, after all. (shrink)

Kaum eine Äußerung Einsteins ist so bekannt wie sein Wort, dass Gott nicht würfelt. In ähnlicher Weise, wie Einstein dies unerläutert gelassen hat, ist seine gesamte Position zur Quantenmechanik, auf die es sich bezieht, von Uneindeutigkeiten nicht frei geblieben. Für seine Würfelmetapher ergibt sich ein Spielraum von gegensätzlichen Sichtweisen. Sie lässt sich zum einen mit jüngeren Forschungsresultaten verbinden und weist zum anderen auf rückschrittliche Elemente in Einsteins Denken hin. Ich wende mich zuerst diesen Elementen zu und betrachte dann eine dazu (...) entgegengerichtete Interpretationsvariante, die an den neueren Resultaten anknüpft. (shrink)

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

This chapter will review selected aspects of the terrain of discussions about probabilities in statistical mechanics (with no pretensions to exhaustiveness, though the major issues will be touched upon), and will argue for a number of claims. None of the claims to be defended is entirely original, but all deserve emphasis. The first, and least controversial, is that probabilistic notions are needed to make sense of statistical mechanics. The reason for this is the same reason that convinced Maxwell, Gibbs, and (...) Boltzmann that probabilities would be needed, namely, that the second law of thermodynamics, which in its original formulation says that certain processes are impossible, must, on the kinetic theory, be replaced by a weaker formulation according to which what the original version deems impossible is merely improbable. Second is that we ought not take the standard measures invoked in equilibrium statistical mechanics as giving, in any sense, the correct probabilities about microstates of the system. We can settle for a much weaker claim: that the probabilities for outcomes of experiments yielded by the standard distributions are effectively the same as those yielded by any distribution that we should take as a representing probabilities over microstates. Lastly, (and most controversially): in asking about the status of probabilities in statistical mechanics, the familiar dichotomy between epistemic probabilities (credences, or degrees of belief) and ontic (physical) probabilities is insufficient; the concept of probability that is best suited to the needs of statistical mechanics is one that combines epistemic and physical considerations. (shrink)

We offer a new argument for the claim that there can be non-degenerate objective chance (“true randomness”) in a deterministic world. Using a formal model of the relationship between different levels of description of a system, we show how objective chance at a higher level can coexist with its absence at a lower level. Unlike previous arguments for the level-specificity of chance, our argument shows, in a precise sense, that higher-level chance does not collapse into epistemic probability, despite higher-level properties (...) supervening on lower-level ones. We show that the distinction between objective chance and epistemic probability can be drawn, and operationalized, at every level of description. There is, therefore, not a single distinction between objective and epistemic probability, but a family of such distinctions. (shrink)

(No abstract is available for this citation).

This pair of articles provides a critical commentary on contemporary approaches to statistical mechanical probabilities. These articles focus on the two ways of understanding these probabilities that have received the most attention in the recent literature: the epistemic indifference approach, and the Lewis-style regularity approach. These articles describe these approaches, highlight the main points of contention, and make some attempts to advance the discussion. The second of these articles discusses the regularity approach to statistical mechanical probabilities, and describes some areas (...) where further research is needed. (shrink)

This pair of articles provides a critical commentary on contemporary approaches to statistical mechanical probabilities. These articles focus on the two ways of understanding these probabilities that have received the most attention in the recent literature: the epistemic indifference approach, and the Lewis-style regularity approach. These articles describe these approaches, highlight the main points of contention, and make some attempts to advance the discussion. The first of these articles provides a brief sketch of statistical mechanics, and discusses the indifference approach (...) to statistical mechanical probabilities. (shrink)

We show that determinism is false assuming a realistic interpretation of quantum mechanics and considering the sensitive dynamics of macroscopical physical systems.

I sketch a new constraint on chance, which connects chance ascriptions closely with ascriptions of ability, and more specifically with 'CAN'-claims. This connection between chance and ability has some claim to be a platitude; moreover, it exposes the debate over deterministic chance to the extensive literature on (in)compatibilism about free will. The upshot is that a prima facie case for the tenability of deterministic chance can be made. But the main thrust of the paper is to draw attention to the (...) connection between the truth conditions of sentences involving 'CAN' and 'CHANCE', and argue for the context sensitivity of each term. Awareness of this context sensitivity has consequences for the evaluation of particular philosophical arguments for (in) compatibilism when they are presented in particular contexts. (shrink)

The role of probability is one of the most contested issues in the interpretation of contemporary physics. In this paper, I’ll be reevaluating some widely held assumptions about where and how probabilities arise. Larry Sklar voices the conventional wisdom about probability in classical physics in a piece in the Stanford Online Encyclopedia of Philosophy, when he writes that “Statistical mechanics was the first foundational physical theory in which probabilistic concepts and probabilistic explanation played a fundamental role.” And the conventional wisdom (...) about quantum probabilities is that they are basic, not reducible to the types of probabilities we see in statistical mechanics. In the first section of this paper, I’ll argue that in fact classical physics was steeped in probability long before statistical mechanics came on the scene, specifically, that an objective measure over phase space is an indispensable component of any informative physical theory. In the next section, I’ll argue that this objective measure is the fundamental form of physical probability and that quantum probabilities can be defined in terms of it. In the last, I’ll raise some questions about the metaphysical status of the fundamental measure. (shrink)

I argue that there are non-trivial objective chances (that is, objective chances other than 0 and 1) even in deterministic worlds. The argument is straightforward. I observe that there are probabilistic special scientific laws even in deterministic worlds. These laws project non-trivial probabilities for the events that they concern. And these probabilities play the chance role and so should be regarded as chances as opposed, for example, to epistemic probabilities or credences. The supposition of non-trivial deterministic chances might seem to (...) land us in contradiction. The fundamental laws of deterministic worlds project trivial probabilities for the very same events that are assigned non-trivial probabilities by the special scientific laws. I argue that any appearance of tension is dissolved by recognition of the level-relativity of chances. There is therefore no obstacle to accepting non-trivial chance-role-playing deterministic probabilities as genuine chances. (shrink)

The concept of randomness has been unjustly neglected in recent philosophical literature, and when philosophers have thought about it, they have usually acquiesced in views about the concept that are fundamentally flawed. After indicating the ways in which these accounts are flawed, I propose that randomness is to be understood as a special case of the epistemic concept of the unpredictability of a process. This proposal arguably captures the intuitive desiderata for the concept of randomness; at least it should suggest (...) that the commonly accepted accounts cannot be the whole story and more philosophical attention needs to be paid. 1. Randomness in science1.1Random systems1.2Random behaviour1.3Random sampling1.4Caprice, arbitrariness and noise2. Concepts of randomness2.1Von Mises/church/martin-löf randomness2.2KCS-randomness3. Randomness is unpredictability: preliminaries3.1Process and product randomness3.2Randomness is indeterminism?4. Predictability4.1Epistemic constraints on prediction4.2Computational constraints on prediction4.3Pragmatic constraints on prediction4.4Prediction defined5. Unpredictability6. Randomness is unpredictability6.1Clarification of the definition of randomness6.2Randomness and probability6.3Subjectivity and context sensitivity of randomness7. Evaluating the analysis[R]andomness … is going to be a concept which is relative to our body of knowledge, which will somehow reflect what we know and what we don't know. Henry E. Kyburg, Jr ([1974], p. 217)Phenomena that we cannot predict must be judged random. Patrick Suppes ([1984], p. 32). (shrink)

I argue that the theory of chance proposed by David Lewis has three problems: (i) it is time asymmetric in a manner incompatible with some of the chance theories of physics, (ii) it is incompatible with statistical mechanical chances, and (iii) the content of Lewis's Principal Principle depends on how admissibility is cashed out, but there is no agreement as to what admissible evidence should be. I proposes two modifications of Lewis's theory which resolve these difficulties. I conclude by tentatively (...) proposing a third modification of Lewis's theory, one which explains many of the common features shared by the chance theories of physics. (shrink)

The four case studies on chance in evolution provide a rich source for further philosophical analysis. Among the issues raised are the following: Are there different conceptions of chance at work, or is there a common underlying conception? How can a given concept of chance be distinguished from other chance concepts and from nonchance concepts? How can the occurrence of a given chance process be distinguished empirically from nonchance processes or other chance processes? What role does chance play in evolutionary (...) theory? I argue that in order to answer these questions, a careful distinction between process and outcome must be made; however, the purpose of this essay is not to answer these questions definitively, but rather to elaborate on them and to provide a starting point for further discussion. (shrink)

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

A new philosophical analysis is provided of the notorious Sleeping Beauty Problem. It is argued that the correct solution is one-third, but not in the way previous philosophers have typically meant this. A modified version of the Problem demonstrates that neither self-locating information nor amnesia is relevant to the core Problem, which is simply to evaluate the conditional chance of heads given an undated Monday-or-Tuesday awakening. Previous commentators have failed to appreciate the significance of the information that Beauty gains upon (...) waking, and which is relevant to the conditional chance of heads: de re acquaintance with the awakening itself and the non-locating knowledge that it is an experimental awakening. David Lewis and company are committed to several unjustifiable and unacceptable probability assessments. Previous commentators have in effect confused the information that Beauty undergoes this particular experimental awakening for the information that she undergoes some experimental awakening or other. Lewis in particular thereby illegitimately tips the scales both in favor of heads and in favor of Monday. The Sleeping Beauty Problem is equivalent to a ball-in-urn word problem in elementary probability theory. (shrink)

What explains the outcomes of chance processes? We claim that their setups do. Chances, we think, mediate these explanations of outcome by setup but do not feature in them. Facts about chances do feature in explanations of a different kind: higher-order explanations, which explain how and why setups explain their outcomes. In this paper, we elucidate this 'mediator view' of chancy explanation and defend it from a series of objections. We then show how it changes the playing field in four (...) metaphysical disputes concerning chance. First, it makes it more plausible that even low chances can have explanatory power. Second, it undercuts a circularity objection against reductionist theories of chance. Third, it redirects the debate about a prominent argument against epistemic theories of chance. Finally, it sheds light on potential chancy explanations of the Universe's origin. (shrink)

This paper introduces an exact correspondence between a general class of stochastic systems and quantum theory. This correspondence provides a new framework for using Hilbert-space methods to formulate highly generic, non-Markovian types of stochastic dynamics, with potential applications throughout the sciences. This paper also uses the correspondence in the other direction to reconstruct quantum theory from physical models that consist of trajectories in configuration spaces undergoing stochastic dynamics. The correspondence thereby yields a new formulation of quantum theory, alongside the Hilbert-space, (...) path-integral, and quasiprobability formulations. In addition, this reconstruction approach opens up new ways of understanding quantum phenomena like interference, decoherence, entanglement, noncommutative observables, and wave-function collapse. (shrink)

One of our most sophisticated accounts of objective chance in quantum mechanics involves the Deutsch-Wallace theorem, which uses state-space symmetries to justify agents’ use of the Born rule when the quantum state is known. But Wallace argues that this theorem requires an Everettian approach to measurement. I find that this argument is unsound. I demonstrate a counter-example by applying the Deutsch-Wallace theorem to the de Broglie-Bohm pilot-wave theory.

Changes within observable reality at the lowest level of reality seem to occur in accordance with the probabil­ity theory in mathematics. It is quite remarkable that nature itself has chosen the probability theory to ar­range all the changes within the structure of the basic quantum fields. This rises a question about the distri­bution of properties in space and time. DOI: 10.5281/zenodo.5515861.

Neoclassical economists use expected utility theory to explain, predict, and prescribe choices under risk, that is, choices where the decision-maker knows---or at least deems suitable to act as if she knew---the relevant probabilities. Expected utility theory has been subject to both empirical and conceptual criticism. This chapter reviews expected utility theory and the main criticism it has faced. It ends with a brief discussion of subjective expected utility theory, which is the theory neoclassical economists use to explain, predict, and prescribe (...) choices under uncertainty, that is, choices where the decision-maker cannot act on the basis of objective probabilities but must instead consult her own subjective probabilities. (shrink)

The paper is concentrated on the special changes of the conception of causality from quantum mechanics to quantum information meaning as a background the revolution implemented by the former to classical physics and science after Max Born’s probabilistic reinterpretation of wave function. Those changes can be enumerated so: (1) quantum information describes the general case of the relation of two wave functions, and particularly, the causal amendment of a single one; (2) it keeps the physical description to be causal by (...) the conservation of quantum information and in accordance with Born’s interpretation; (3) it introduces inverse causality, “backwards in time”, observable “forwards in time” as the fundamentally random probability density distribution of all possible measurements of any physical quantity in quantum mechanics; (4) it involves a kind of “bidirectional causality” unifying (4.1) the classical determinism of cause and effect, (4.2) the probabilistic causality of quantum mechanics, and (4.3) the reversibility of any coherent state; (5) it identifies determinism with the function successor in Peano arithmetic, and its proper generalized causality with the information function successor in Hilbert arithmetic. (shrink)