Chance and Objective Probability

Suppose your evil sibling travels back in time, intending to lethally poison your grandfather during his infancy. Determined to save grandpa, you grab two antidotes and follow your sibling through the wormhole. Under normal circumstances, each antidote has a 50% chance of curing a poisoning. Upon finding young grandpa, poisoned, you administer the first antidote. Alas, it has no effect. The second antidote is your last hope. You administer it---and success: the paleness vanishes from grandpa's face, he is healed. As (...) you administered the first antidote, what was the chance that it would be effective? -/- This essay offers a systematic account of this case, and others like it. The central question is this: Given a certain time travel structure, what are the chances? In particular, I'll develop a theory about the connection between these chances and the chances in ordinary, time-travel-free contexts. Central to the account is a Markov condition involving the boundaries of spacetime regions. (shrink)

The philosophy of superdeterminism is based on a single scientific fact about the universe, namely that cause and effect in physics are not real. In 2020, accomplished Swedish theoretical physicist, Dr. Johan Hansson published a physics proof using Albert Einstein’s Theory of Special Relativity that our universe is superdeterministic meaning a predetermined static block universe without cause and effect in physics. The unity of our universe originates from its creation from the same nothingness under the zero energy universe theory. However, (...) nothingness cannot actually cause a universe to exist on its own under superdeterminism due to the absence of cause and effect in physics. Moreover, nothingness is the absence of anything real and cannot logically be the reality underlying our universe. Consequently, our universe must exist from the reality of the logic or Logos underlying our physical reality resulting from the origination of our universe from the same nothingness or common creation. (shrink)

In this work, we derive the standard formalism of quantum theory by analyzing the behavior of single-variable systems under measurements. These systems, with minimal information capacity, exhibit indeterministic behavior in independent measurements while yielding probabilistically predictable outcomes in dependent measurements. Enforcing probability conservation in the probability transformations leads to the derivation of the Born rule, which subsequently gives rise to the Hilbert space structure and the Schrödinger equation. Additionally, we show that preparing physical systems in coherent states —crucial for observing (...) quantum phenomena— effectively reduces the number of independent variables to one. This first-principles derivation of quantum theory from probability conservation in single-variable systems offers new insights into the physical meaning of quantum theory and clarifies its domain of applicability. (shrink)

According to libertarianism about free will, at least some of the choices we make are free and undetermined. Many libertarians also accept the thesis that, before we make an undetermined choice, there is a nontrivial objective probability that we will make that choice. In the literature on free will, the ascription of objective probabilities is sometimes justified via an “Argument from Motivation,” which adverts to the fact that typically, in situations of choice, we are more motivated to choose some options (...) over others. In this paper, I will examine this argument and I will argue that it is unsound, as one of its premises is at odds with a widely accepted principle governing the evolution of objective probabilities over time. (shrink)

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 (...) by introducing the concept of Type I error rates and distinguishing between statistical errors and 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)

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

The propensity nature of evolutionary fitness has long been appreciated and is nowadays amply discussed. The discussion has, however, on occasion followed long standing conflations in the philosophy of probability literature between propensities, probabilities, and frequencies. In this paper, I apply a more recent conception of propensities in modelling practice to some of the key issues, regarding the mathematical representation of fitness and how it may be regarded as explanatory. The ensuing complex nexus of fitness emphasises the distinction between biological (...) propensities and the probability distributions over offspring numbers that they give rise to; and how critical it is to distinguish the possession conditions of the underlying dispositional properties from those of their probabilistic manifestations. (shrink)

A popular conception of probability for many years now has been the relative frequency interpretation, made famous by the work of Reichenbach and von Mises, and more recently by Salmon and others. The frequency view has played important roles of various sorts in virtually every area in epistemology and the philosophy of science, including explanation, causation, the justification of induction, the nature of laws and lawlike statements, and so on. A major attraction of the frequency conception has been its claim (...) to be a strictly empirical view. In this paper we argue that on prima facie grounds the frequency view violates some of our deepest intuitions regarding the notions of probability and possibility. (shrink)

The term probability can be used in two main senses. In the frequency interpretation it is a limiting ratio in a sequence of repeatable events. In the Bayesian view, probability is a mental construct representing uncertainty. This 2002 book is about these two types of probability and investigates how, despite being adopted by scientists and statisticians in the eighteenth and nineteenth centuries, Bayesianism was discredited as a theory of scientific inference during the 1920s and 1930s. Through the examination of a (...) dispute between two British scientists, the author argues that a choice between the two interpretations is not forced by pure logic or the mathematics of the situation, but depends on the experiences and aims of the individuals involved. The book should be of interest to students and scientists interested in statistics and probability theories and to general readers with an interest in the history, sociology and philosophy of science. (shrink)

In this work, five different interpretations of "probability" are analyzed: the classical, logical, subjective, relative frequency, and propensity interpretations. The objective is to determine which of these interpretations is most suitable for probability applications in the physical and biological sciences. The first state of this analysis involves evaluating the different interpretations with respect to the probability calculus. The objective at this point is not to reject any interpretations outright, but rather to keep in mind any difficulties in adherence to the (...) calculus when evaluating these interpretations in later chapters. The second stage involves defending the need for an "objectivity criterion" and evaluating the various interpretations of "probability" with respect to this criterion. This "objectivity criterion" states that an adequate analysis of "probability" should result in probability statements that are true or false in virtue of the way the world is, independently of anyone's state of knowledge or beliefs about the probabilities in question. Based on this criterion, the classical, logical, and subjective interpretations are rejected. The third stage involves evaluating the relative frequency interpretation in greater detail. Both the actual relative frequency interpretation and the hypothetical relative frequency interpretation are evaluated. The actual relative frequency interpretation is found to be a promising candidate for providing an adequate analysis of "probability" for the physical and biological sciences. The fourth stage involves a detailed evaluation of the propensity interpretation. The propensity interpretation is shown to be in a weaker epistemological position than the relative frequency interpretation and to stem largely from misguided motivations concerning the importance of the single case in scientific applications and the nature of scientific explanation. Ultimately, it is concluded that the traditional actual relative frequency interpretation provides the best analysis of "probability" for applications in the physical and biological sciences. (shrink)

Chapter 1 of this thesis concerns counterfactual conditionals. David Lewis has offered a natural and influential analysis of counterfactuals. But the analysis fails to take into account the asymmetry of entropy, and comes to grief precisely because of that failure. The cause of the grief is that processes involving the increase of entropy are exceedingly sensitive to small changes in their final conditions. ;Chapter 2 concerns robust dispositions. Drop an ordinary rock into hydrofluoric acid, and---almost no matter what is going (...) on far away---it will dissolve. In other words, the rock displays a disposition to dissolve that is robust with respect to small variations in its environment. Why is it that so many objects display robust dispositions to melt, cool down, explode, hatch, and so on? Because entropy increases over time. ;Chapter 3 concerns conscious experience. Take any world with fundamental dynamical laws rather like ours, but in which entropy doesn't increase. Take any system in that world that changes state by changing thermodynamically. That system has no experiences whatsoever. That's because , in order to have an experience it is necessary to display certain robust dispositions. And such systems fail to display the requisite dispositions. (shrink)

A pragmatic account of scientific understanding is used both to examine and to unify fundamental questions concerning the propensity interpretation of probability and theories of chance, causation, and explanation. One of the most important problems to be addressed is the problem of defining homogeneous reference classes in theories of chance, causation, and explanation. The consistency of the propensity interpretation is defended against traditional criticisms such as "Humphreys's paradox." It is demonstrated that the application of this interpretation to theories of chance (...) and probabilistic causation provides insights into problems common to both theories. Various approaches to causation are examined, including those based on identifying sufficient causal factors, necessary causal factors, and contrastive causes. These insights are applied to quantum mechanics and are presented in terms of a set of controlled experiments. The study of quantum mechanics focuses on the paradox of the two slit experiment and quantum logical and quantum probabilistic attempts to resolve this paradox. Finally, the analysis of chance and causation provides the basis for a version of the contrastive theory of explanation. This theory of explanation provides a unique understanding of the nature of explanation, and lessens the impact of the problems of homogeneity and of explanatory ambiguity. (shrink)

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The Empire of Chance tells how quantitative ideas of chance transformed the natural and social sciences, as well as daily life over the last three centuries. A continuous narrative connects the earliest application of probability and statistics in gambling and insurance to the most recent forays into law, medicine, polling and baseball. Separate chapters explore the theoretical and methodological impact in biology, physics and psychology. Themes recur - determinism, inference, causality, free will, evidence, the shifting meaning of probability - but (...) in dramatically different disciplinary and historical contexts. In contrast to the literature on the mathematical development of probability and statistics, this book centres on how these technical innovations remade our conceptions of nature, mind and society. Written by an interdisciplinary team of historians and philosophers, this readable, lucid account keeps technical material to an absolute minimum. It is aimed not only at specialists in the history and philosophy of science, but also at the general reader and scholars in other disciplines. (shrink)