Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to “speak” of indeterminism, its inability to present us a worldview in which new information is created as time passes. In such a case, scientific determinism would only be an illusion due to the timeless mathematical language scientists use. To investigate this possibility it is necessary (...) to develop an alternative mathematical language that is both powerful enough to allow scientists to compute predictions and compatible with indeterminism and the passage of time. We suggest that intuitionistic mathematics provides such a language and we illustrate it in simple terms. (shrink)

Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with quantum theory and conclude that the common real numbers are, de facto, the hidden variables of classical physics. Consequently, real numbers should not be considered as ``physically real" and classical mechanics, like quantum physics, is indeterministic.

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

The claim that the observation of a violation of a Bell inequality leads to an alleged alternative between nonlocality and non-realism is annoying because of the vagueness of the second term.

This paper is about the open future response to fatalistic arguments. I first present a typical fatalistic argument and then spell out the open future response as a response to that argument. Then I raise the question of how the open future response can be independently justified. I consider some possible ways in which the response might be defended, and I try to show that none of these is a plausible, non-question-begging defense. Next I formulate what I take to be (...) the only plausible, nonquestion-begging defense of the open future response. This defense involves both (i) the claim that the laws of nature are indeterministic and (ii) a certain version of the correspondence theory of truth. Finally, I argue that there is a very surprising consequence of justifying the open future response by making the defense in question, namely, that the past is sometimes open. Fatalism is the view that whatever will happen in the future is inevitable, due to certain considerations about truth and time. Fatalism, in turn, is normally taken to imply that there is no such thing as genuine, human free will. Suppose that I am an anti-fatalist. Suppose I believe that Joe Montana is free to choose what he will have for lunch tomorrow, and suppose I take this case to be a paradigmatic example of one involving both evitability and human free will. Now suppose that I meet a fatalist, who presents the following argument.1.. (shrink)

Propensities are presented as a generalization of classical determinism. They describe a physical reality intermediary between Laplacian determinism and pure randomness, such as in quantum mechanics. They are characterized by the fact that their values are determined by the collection of all actual properties. It is argued that they do not satisfy Kolmogorov axioms; other axioms are proposed.

The main aim of this work is to contribute tothe elucidation of the concept of informationby comparing three different views about thismatter: the view of Fred Dretske's semantictheory of information, the perspective adoptedby Peter Kosso in his interaction-informationaccount of scientific observation, and thesyntactic approach of Thomas Cover and JoyThomas. We will see that these views involvevery different concepts of information, eachone useful in its own field of application. This comparison will allow us to argue in favorof a terminological `cleansing': it (...) is necessaryto make a terminological distinction among thedifferent concepts of information, in order toavoid conceptual confusions when the word`information' is used to elucidate relatedconcepts as knowledge, observation orentropy. (shrink)

This book is an attempt to get to the bottom of an acute and perennial tension between our best scientific pictures of the fundamental physical structure of the world and our everyday empirical experience of it. The trouble is about the direction of time. The situation (very briefly) is that it is a consequence of almost every one of those fundamental scientific pictures--and that it is at the same time radically at odds with our common sense--that whatever can happen can (...) just as naturally happen backwards. Albert provides an unprecedentedly clear, lively, and systematic new account--in the context of a Newtonian-Mechanical picture of the world--of the ultimate origins of the statistical regularities we see around us, of the temporal irreversibility of the Second Law of Thermodynamics, of the asymmetries in our epistemic access to the past and the future, and of our conviction that by acting now we can affect the future but not the past. Then, in the final section of the book, he generalizes the Newtonian picture to the quantum-mechanical case and (most interestingly) suggests a very deep potential connection between the problem of the direction of time and the quantum-mechanical measurement problem. The book aims to be both an original contribution to the present scientific and philosophical understanding of these matters at the most advanced level, and something in the nature of an elementary textbook on the subject accessible to interested high-school students. Table of Contents: Preface 1. Time-Reversal Invariance 2. Thermodynamics 3. Statistical Mechanics 4. The Reversibility Objections and the Past-Hypothesis 5. The Scope of Thermodynamics 6. The Asymmetries of Knowledge and Intervention 7. Quantum Mechanics Appendix: Gedankenexperiments with Heat Engines Index Reviews of this book: The foundations of statistical mechanisms are often presented in physics textbooks in a rather obscure and confused way. By challenging common ways of thinking about this subject, Time and Chance can do quite a lot to improve this situation. --Jean Bricmont, Science Albert is perfecting a style of foundational analysis that is uniquely his own...It has a surgical precision...and it is ruthless with pretensions. The foundations of thermodynamics is a topic that has accumulated a good deal of dead wood; this is a fire that will burn and burn. --Simon W. Saunders, Oxford University As usual with Albert's work, the exposition is brisk and to the point, and exceptionally clear...The book will be an extremely valuable contribution to the literature on the subject of philosophical issues in thermodynamics and statistical mechanics, a literature which has been thin on the ground but is now growing as it deserves to. --Lawrence Sklar, University of Michigan. (shrink)

Michael Dummett; XIV—The Reality of the Past, Proceedings of the Aristotelian Society, Volume 69, Issue 1, 1 June 1969, Pages 239–258, https://doi.org/10.1093/a.

Justificationism differs from realism about how linguistic meaning is given, and hence in its associated conception of truth, and in particular in rejecting bivalence. Empirical discourse differs from mathematical primarily in that an effective decision-procedure for an empirical statement may cease to be available at a later time. The contrast is not that empirical knowledge is derived from what is mind-dependent, namely perception, whereas mathematical knowledge is not so derived. Mathematical knowledge does not accrue simply because a proof exists: the (...) proof has to be understood and recognized to be valid. Most ordinary mathematical proofs are indirect: they supply an effective means, in principle, to construct a direct or canonical proof. An indirect justification for asserting an empirical statement does not, in general, supply a means for bringing into existence a direct justification; it merely provides a ground for supposing that a direct justification would be or have been available for someone suitably placed to make the necessary observations. But it is by what constitutes direct evidence for a statement that its meaning is given; a grasp of its meaning does not rest on an ability to survey all conceivable indirect evidence. A direct justification of an empirical statement of the kind capable of being used as a report of observation must be an actual or possible observation by a suitably placed observer. A possible observation need not be explained by means of a counterfactual: it may be taken as consisting of the appropriate physical stimuli. This way of understanding it evades all three of the untenable choices Peacocke offers the justificationist. Unlike mathematical ones, empirical statements are often justifiably asserted on probabilistic grounds. When the statement admits of a conclusive justification, probabilistic evidence will not figure as a direct justification for asserting it, and hence as determining its meaning, so no circularity is involved, as Peacocke charges. There may, however, be empirical statements that can neither be reports of observation nor admit of a conclusive justification. Such statements can be asserted only on inductive or abductive grounds; this goes to characterize their meanings. Their meanings must therefore be explained by specifying such grounds as the most direct justifications of them that can be given, although they are difeasible rather than conclusive. Peacocke appears to deny that there can be statements that transcend all possible verification. To vindicate such a view from a realist standpoint is surely very difficult: it requires a demonstration that we could not grasp what it would be for such a statement to be true. It is very obscure what a realist's conception of truth is. The principle of bivalence remains a strong mark of differentiation between a justificationist and a realist conception of truth; a clear argument why the principle should be accepted would greatly help to clarify how the realist conceives of truth. I enjoyed reading Peacocke's article, but remain as perplexed as I was before just how he does conceive of truth. (shrink)