I show how classical and quantum physics approach the problem of randomness and probability. Contrary to popular opinions, neither we can prove that classical mechanics is a deterministic theory, nor that quantum mechanics is a nondeterministic one. In other words it is not possible to show that randomness in classical mechanics has a purely epistemic character and that of quantum mechanics an ontic one. Nevertheless, recent developments of quantum theory and increasing experimental possibilities to check its predictions call for returning (...) to the problem of comparing possibilities given by classical and quantum physics to accommodate and prove the existence of a `genuine randomness'. Recent results concerning `amplification of randomness' show that, in certain sense, quantum physics is in fact ‘more random’ that classical and outperforms it in producing a `truly random process'. (shrink)

How should we characterise the observable aspects of quantum theory? This paper argues that philosophers and physicists should jettison a standard dogma: that observables must be represented by self-adjoint or Hermitian operators. Four classes of non-standard observables are identified: normal operators, symmetric operators, real-spectrum operators, and none of these. The philosophical and physical implications of each are explored.

There are many ontologies of the world or of specific phenomena such as time, matter, space, and quantum mechanics1. However, ontologies of information are rather rare. One of the reasons behind this is that information is most frequently associated with communication and computing, and not with ‘the furniture of the world’. But what would be the nature of an ontology of information? For it to be of significant import it should be amenable to formalization in a logico-grammatical formalism. A candidate (...) ontology satisfying such a requirement can be found in some of the ideas of K. Turek, presented in this paper. Turek outlines the ontology of information conceived of as a part of nature, and provides the ‘missing link’ to the Z axiomatic set theory, offering a proposal for developing a formal ontology of information both in its philosophical and logicogrammatical representations. (shrink)

John Bell proposed an ontology for the GRW modification of quantum mechanics in terms of flashes occurring at space- time points. This article spells out the motivation for this ontology, inquires into the status of the wave function in it, critically examines the claim of its being Lorentz invariant, and considers whether it is a parsimonious but nevertheless physically adequate ontology.

This chapter outlines a metaphysics of science in the sense of a naturalized metaphysics. It considers in the first place the interplay of physics and metaphysics in Newtonian mechanics, then goes into the issues for the metaphysics of time that relativity physics raises, shows that what one considers as the referent of quantum theory depends on metaphysical considerations and finally explains how the stance that one takes with respect to objective modality and laws of nature shapes the options that are (...) available for an ontology of quantum physics. In that way, this chapter seeks to make a case for a natural philosophy that treats physics and metaphysics as inseparable in the enquiry into the constitution of the world, there being neither a neo-positivist way of deducing metaphysics from the formalisms of physical theories, nor a neo-rationalist realm of investigation for metaphysics that is independent of physics. (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.

This article focuses on three recent discussions on determinism in the philosophy of science. First, determinism and predictability will be discussed. Then, second, the paper turns to the topic of determinism, indeterminism, observational equivalence and randomness. Finally, third, there will be a discussion about deterministic probabilities. The paper will end with a conclusion.

The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR experiment. That assumption is one of the premises of Bell’s theorem. I first argue that only a premise to the effect that what determines the choice of the measurement settings is independent of what determines the past state of the measured system is needed for the (...) derivation of Bell’s theorem. Determinism as such does not undermine that independence . Only entanglement could do so. However, generic entanglement without collapse on the level of the universal wave-function can go together with effective wave-functions for subsystems of the universe, as in Bohmian mechanics. The paper argues that such effective wave-functions are sufficient for the mentioned independence premise to hold. (shrink)

The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of properties that dynamical systems can possess. Its five levels are egrodicity, weak mixing, strong mixing, Kolomogorov, and Bernoulli. Although EH is a mathematical theory, its concepts have been widely used in the foundations of statistical physics, accounts of randomness, and discussions about the nature of chaos. We introduce EH and discuss how its applications in these fields.

We investigate the fate of determinism in general relativity, comparing the philosopher’s account with the physicist’s well-posed initial value formulations. The fate of determinism is interwoven with the question of what it is for a spacetime to be ‘physically reasonable’. A central concern is the status of global hyperbolicity, a putatively necessary condition for determinism in GR. While global hyperbolicity may fail to be true of all physically reasonable models, we analyze whether global hyperbolicity should be imposed by fiat; established (...) from weaker assumptions, as in cosmic censorship theorems; or justified by beyond-GR physics. (shrink)

These preprints were automatically compiled into a PDF from the collection of papers deposited in PhilSci-Archive in conjunction with the PSA 2018.

The aim of this paper is to establish that free agency, which is a capacity of many animals including human beings, is compatible with indeterminism: an indeterministic world allows for the existence of free agency. The question of the compatibility of free agency and indeterminism is less discussed than its mirror image, the question of the compatibility of free agency and determinism. It is, however, of great importance for our self-conception as free agents in our (arguably) indeterministic world. We begin (...) by explicating the notions of indeterminism and free agency and by clarifying the interrelation of free agency and the human-specific notion of free will. We then situate our claim of the compatibility of free agency and indeterminism precisely in the landscape of the current debate on freedom and determinism, exposing an unhappy asymmetry in that debate. Then we proceed to make our case by describing the mathematically precise, physically motivated model of projective simulation, which employs indeterminism as a central resource for agency modeling. We argue that an indeterministic process of deliberation modeled by the dynamics of projective simulation can exemplify free agency under indeterminism, thereby establishing our compatibility claim: Free agency can develop and thrive in an indeterministic world. (shrink)

Hilary Putnam has argued that from a realist perspective, quantum mechanics stands in need of an interpretation. Ironically, this hypothesis may appear vulnerable against arguments drawing on Putnam's own work. Nancy Cartwright has urged that his 1962 essay on the meaning of theoretical terms suggests that quantum mechanics needs no interpretation and thus stands in tension with his claim of three years later. She furthermore contends that this conflict should be resolved in favour of the earlier work, as quantum mechanics, (...) like all successful theories, does not need an interpretation. The first part of this essay deflates both of these objections. The second part addresses and evaluates Putnam's own assessments of the main interpretative options available in 1965 and 2005. Although we may disagree on some aspects, his pessimistic conclusion will come out largely unscathed, and, in fact, enhanced. I will close by briefly stating the historical relevance of this work. (shrink)

In this paper I address the question of whether the probabilities that appear in models of stochastic gene expression are objective or subjective. I argue that while our best models of the phenomena in question are stochastic models, this fact should not lead us to automatically assume that the processes are inherently stochastic. After distinguishing between models and reality, I give a brief introduction to the philosophical problem of the interpretation of probability statements. I argue that the objective vs. subjective (...) distinction is a false dichotomy and is an unhelpful distinction in this case. Instead, the probabilities in our models of gene expression exhibit standard features of both objectivity and subjectivity. (shrink)

The Free Will Theorem of Conway \& Kochen on the one hand follows from uncontroversial parts of modern physics and elementary mathematical and logical reasoning, but on the other hand seems predicated on an undefined notion of free will. Although Conway and Kochen informally claim that their theorem supports indeterminism and, in its wake, a libertarian agenda for free will, inferring the former from the Free Will Theorem is a \emph{petitio principii}. Of course, this also considerably weakens the case for (...) the latter. A recent reformulation of the Free Will Theorem due to Cator and the author uses a mathematically precise formulation of the idea that experimentalists freely choose their settings even in a deterministic world, and thence construes the theorem as providing constraints on determinism. In the present paper we argue that the concept of free will used in this version of the theorem is essentially the one proposed by Lewis, also known as `local miracle compatibilism'. To do so, we give a mathematical reformulation of this idea, which we believe to be well within its spirit and which may be of independent interest. On this double reformulation the Free Will Theorem shows that local miracle compatibilism contradicts the parts of modern physics used in its assumptions. Therefore, although the intention of Conway and Kochen was to support free will through their theorem, what they actually achieved is the opposite: a well-known, philosophically viable version of free will now turns out to be incompatible with physics! (shrink)

This essay provides an analysis of two important theorems that arise in the context of quantum mechanics: the Kochen-Specker theorem, which challenges the existence of hidden variable theories; and the Conway-Kochen theorem, which can be seen as an improvement over the Kochen-Specker theorem, but instead focuses on challenging determinism.