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)

I discuss some problems related to extreme mathematical realism, focusing on a recently proposed “shut-up-and-calculate” approach to physics. I offer arguments for a moderate alternative, the essence of which lies in the acceptance that mathematics is a human construction, and discuss concrete consequences of this—at first sight purely philosophical—difference in point of view.

Arguing that our attachment to Aristotelian modes of discourse makes a revision of their conceptual foundations long overdue, the author proposes the consideration of unacknowledged factors that play a central role in argument itself. These are in particular the subjective imprint and the dynamics of argumentation. Their inclusion in a four-dimensional framework and the focus on thesis validity allow for a more realistic view of our discourse practice. Exhaustive analyses of fascinating historical and contemporary arguments are provided. These range from (...) Columbus’s advocacy of the Western Passage to India, over the trial of King Louis XVI during the French Revolution, to today’s highly charged controversies surrounding euthanasia and embryo research. Excavating foundational issues such as the purpose of argument itself and the contested role of argument as a generator of knowledge, the book culminates in a discussion of the relationship between rationality and reasonableness and criticizes the restrictions of ‘rational’ argument relying on fixed logical, economic or cultural criteria that in reality are mutable. Here, a true, open argument requires the infusion of Paul Lorenzen’s principle of ‘transsubjectivity’, which recognizes but transcends the partiality of the individual and which can be seen in the pragmatic and expanding consensus that humanity can control itself to safeguard the future of a fragile, damaged world. (shrink)

The essay revisits the puzzle of the ‘passage’ of time in relation to EPR-type measurements and asks what philosophical consequences can be drawn from them. Some argue that the lack of invariance of temporal order in the measurement of a space-like related EPR pair, under relativistic motion, casts serious doubts on the ‘reality’ of the lapse of time. Others argue thatcertain features of quantum mechanics establisha tensed theory of time – understood here as Possibilism or the growing block universe. The (...) paper analyzes the employment of frame-invariant entropic clocks in a relativistic setting and argues that tenselessness does not imply timelessness. But this conclusion does not support a tensed theory of time, which requires a preferred foliation. It is argued that the only reliable inference from the EPR example and the use of entropic clocks is an inference not just to a Leibnizian order of the succession of events but a frame-invariant order according to some selected clocks. (shrink)

This paper expands on, and provides a qualified defence of, Arthur Fine's selective interactions solution to the measurement problem. Fine's approach must be understood against the background of the insolubility proof of the quantum measurement. I first defend the proof as an appropriate formal representation of the quantum measurement problem. The nature of selective interactions, and more generally selections, is then clarified, and three arguments in their favour are offered. First, selections provide the only known solution to the measurement problem (...) that does not relinquish any of the explicit premises of the insolubility proofs. Second, unlike some no-collapse interpretations of quantum mechanics, selections suffer no difficulties with non-ideal measurements. Third, unlike most collapse interpretations, selections can be independently motivated by an appeal to quantum propensities. IntroductionThe problem of quantum measurement2.1 The ignorance interpretation of mixtures2.2 The eigenstate–eigenvalue link2.3 The quantum theory of measurementThe insolubility proof of the quantum measurement3.1 Some notation3.2 The transfer of probability condition (TPC)3.3 The occurrence of outcomes condition (OOC)A defence of the insolubility proof4.1 Stein's critique4.2 Ignorance is not required4.3 The problem of quantum measurement is an idealisationSelections5.1 Representing dispositional properties5.2 Selections solve the measurement problem5.3 Selections and ignoranceNon-ideal selections6.1 No-collapse interpretations and non-ideal measurements6.2 Exact and approximate measurements6.3 Selections for non-ideal interactions6.4 Approximate selections6.5 Implications for ignoranceSelective interactions test quantum propensities7.1 Equivalence classes as physical ‘aspects’: a critique7.2 Quantum dispositions7.3 Selections as a propensity modal interpretation7.4 A comparison with Popper's propensity interpretation. (shrink)

We re-examine Peres' statement “opposite momenta lead to opposite directions”. It will be shown that Peres' statement is only valid in the large distance or large time limit. In the short distance or short time limit an additional deviation from perfect alignment occurs due to the uncertainty of the location of the source. This error contribution plays a major role in Popper's orginal experimental proposal. Peres' statement applies rather to the phenomenon of optical imaging, which was regarded by him as (...) a verification of his statement. This is because this experiment can in a certain sense be seen as occurring in the large distance limit. We will also reconsider both experiments from the viewpoint of Bohmian mechanics. In Bohmian mechanics particles with perfectly opposite momenta will move in opposite directions. In addition it will prove particularly useful to use Bohmian mechanics because the Bohmian trajectories coincide with the conceptual trajectories drawn by Pittman et al. In this way Bohmian mechanics provides a theoretical basis for these conceptual trajectories. (shrink)

The later thought of Karl Popper—notably, his ideas about traditions and his “modified essentialism” in the philosophy of natural science— should lead to revisions in the political philosophy set out in The Open Society and Its Enemies. The structural approach allowed for by Popper's modified essentialism, and the delicate nature of traditions, buttress certain issues raised by Friedrich Hayek that pose serious problems for Popper's social‐democratic approach to politics. Fred Eidlin's review essay on my Political Thought of Karl Popper misses (...) these problems, and in general underestimates the difficulties that unintended consequences pose for any non‐utopian theory of politics. Thus, Eidlin uncritically cites Popper's abstract political recognition of unintended consequences and his idealized view of the political process, as if that puts to rest the questions my book asks. (shrink)

The prime concern of this paper is with the nature of probability. It is argued that questions concerning the nature of probability are intimately linked to questions about the nature of time. The case study here concerns the single case propensity interpretation of probability. It is argued that while this interpretation of probability has a natural place in the quantum theory, the metaphysical picture of time to be found in relativity theory is incompatible with such a treatment of probability.

To honour the memory of Sir Karl Popper, I put forward six elements of his philosophy which might be of particular interest to biologists and to philosophers of biology and which I think Popper would like them not to ignore, even if they disagree with him. They are: the primacy of problems; the criticizability of metaphysics (and thus the dubiousness of materialism); how downward causation might be real; how norms should matter to scientists; why dogmatism should be avoided; how genuine (...) science is recognizable. I preface these six things with a brief discussion of Popper's early (but later recanted) mistakes concerning biology. (shrink)

On the occasion of his ninetieth birthday, Karl Popper's lifelong pursuit of answers in several areas of scientific and philosophical thinking is briefly traced, mainly with reference to excerpts from his own writings.

The Pauli Exclusion Principle and the reduction of chemistry have been the subject of considerable philosophical debate, The present article considers the view that the lack of derivability of the Exclusion Principle represents a problem for physics and denies the reduction of chemistry to quantum mechanics. The possible connections between the Exclusion Principle and the hidden variable debate are also briefly criticised.

It is argued that a realistic interpretation of quantum mechanics is possible and useful. Current interpretations, from “Copenhagen” to “many worlds” are critically revisited. The difficulties for intuitive models of quantum physics are pointed out and possible solutions proposed. In particular the existence of discrete states, the quantum jumps, the alleged lack of objective properties, measurement theory, the probabilistic character of quantum physics, the wave–particle duality and the Bell inequalities are analyzed. The sketch of a realistic picture of the quantum (...) world is presented. It rests upon the assumption that quantum mechanics is a stochastic theory whose randomness derives from the existence of vacuum fields. They correspond to the vacuum fluctuations of quantum field theory, but taken as real rather than virtual. (shrink)

We study the correlations (and alignment as a particular case) existent between the fragments originated in a decaying process when the daughter particles interact. The interaction between the particles is modeled using the potential of coupled oscillators, which can be treated analytically. This approach can be considered as a first step towards the characterization of realistic interacting decaying systems, an archetypal process in physics. The results presented here also suggest the possibility of manipulating correlations using external fields, a technique that (...) could be useful to provide sources of entangled massive particles. (shrink)

An attempt is made to defend realism and the absence of space-like causation in quantum mechanics, by invoking indeterminism and a new necessary condition for stochastic causality, we term robustness. This condition is defended against recent critical attacks by Cartwright and Jones, and by Healey, and the violation of the robustness condition in Bell-type correlation experiments is shown to follow if an appropriate interpretation of the state vector is employed.

European intellectuals diagnosed the end of the nineteenth century as “the sickness of an age.” Schopenhauer's pessimistic books suddenly became popular; Nietzsche announced the “death of god”; and Max Nordeau's Degeneration was an international best seller. To be sure, this mood of despair was initially limited to a handful of poets and philosophers. But once the outbreak of World War I revealed what “the treacherous years were all the while making for and meaning,” the sense that the West had somehow (...) been betrayed by its own most fundamental accomplishments and beliefs was globalized. Thomas Mann's Magic Mountain captured the idea neatly by describing Europe as a tuberculosis sanatorium behind whose walls splendid accomplishment rapidly rotted toward calamity. Spengler's Decay of the West and the early volumes of Toynbee's Study of History argued that decline was inevitable. As Europeans lost faith in their ability to erect The Heavenly City Of The Eighteenth Century Philosophers [Becker, 1932], the era of “enlightenment optimism” gave way to Auden's “Age of Anxiety.” If, as T.S. Eliot put it in East Coker, “the quiet-voiced elders” bequeathed us “merely a receipt for deceit,” then, to cite again W.B. Yeats’ famous poem, it became increasingly obvious that “things fall apart, the center cannot hold.” “[F]ollowing some rough beast” that “slouches toward Bethlehem to be born,” modern civilization began a desperate search for new values that could orient society in an unexpected world. (shrink)

In modern science, the theory of probability is one of the basic tools. Scientists using probability often refer to its objective interpretation. They emphasize that their probabilistic hypotheses concern objective facts, not degrees of belief. Accordingly, the following questions arise: What is the meaning of this type of probabilistic hypothesis? Is the assumption of objectivity necessary? The paper addresses these questions by analyzing objective probability in the context of the scientific debate on determinism. Two types of arguments will be presented. (...) On the one hand, there is the assertion that objective probability can exist only in an indeterministic world. Then, on the other hand — I analyze the assertions of those who believe in the co‑existence of objective probability and determinism. As a result I show that the acceptance of deterministic and indeterministic fields as possible areas where objective probability can occur is extremely problematic. Depending on the chosen area we encounter different types of problems. Therefore, I show that a significant number of these problems are associated with the acceptance of incorrect metaphysical assumptions. And finally, I postulate that the objectivity of probability can be reduced to the epistemic variant. (shrink)

The roles of classical realism, logical positivism, and pragmatic instrumentalism in the shaping of fundamental ideas in quantum physics are examined in the light of some recent historical and sociological studies of the factors that influenced their development. It is shown that those studies indicate that the conventionalistic form of instrumentalism that has dominated all the major post-World War II developments in quantum physics is not an outgrowth of the Copenhagen school, and that despite the “schism” in twentieth century physics (...) created by the Bohr-Einstein “disagreements” on foundational issues in quantum theory, both their philosophical stands were very much opposed to those of conventionalistic instrumentalism. Quotations from the writings of Dirac, Heisenberg, Popper, Russell, and other influential thinkers, are provided, illustrating the fact that, despite the various divergencies in their opinions, they all either opposed the instrumentalist concept of “truth” in general, or its conventionalistic version in post-World War II quantum physics in particular. The basic epistemic ideas of a quantum geometry approach to quantum physics are reviewed and discussed from the point of view of a quantum realism that seeks to reconcile Bohr's “positivism” with Einstein's “realism” by emphasizing the existence of an underlying quantum reality, in which they both believed. This quantum geometry framework seeks to introduce geometro-stochastic concepts that are specifically designed for the systematic description of that underlying quantum reality, by developing the conceptual and mathematical tools that are most appropriate for such a use. (shrink)

The various physical aspects of the general relativistic principles of covariance and strong equivalence are discussed, and their mathematical formulations are analyzed. All these aspects are shown to be present in classical general relativity, although no contemporary formulation of canonical or covariant quantum gravity has succeeded to incorporate them all. This has, in part, motivated the recent introduction of a geometro-stochastic framework for quantum general relativity, in which the classical frame bundles that underlie the formulation of parallel transport in classical (...) general relativity are replaced by quantum frame bundles. It is shown that quantum frames can take over the role played by complete sets of observables in conventional quantum theory, so that they can mediate the natural transference of the general covariance and the strong equivalence principles from the classical to the quantum general relativistic regime. This results in a geometrostochastic mode of quantum propagation in general relativistic quantum bundles, which is mathematically implemented by path integration methods based on parallel transport along horizontal lifts of geodesics for the vacuum expectation values of a quantum gravitational field in a quantum spacetime supermanifold. The covariance features of this field are embedded in a quantum gravitational supergroup, which incorporates Poincaré as well as diffeomorphism invariance, and resolves the issue of time in quantum gravity. (shrink)

Since the late nineteenth century, physics has been puzzled by the time-asymmetry of thermodynamic phenomena in the light of the apparent T-symmetry of the underlying laws of mechanics. However, a compelling solution to this puzzle has proved elusive. In part, I argue, this can be attributed to a failure to distinguish two conceptions of the problem. According to one, the main focus of our attention is a time-asymmetric lawlike generalisation. According to the other, it is a particular fact about the (...) early universe. This paper aims (i) to distinguish these two different conceptions of the time-asymmetric explanandum in thermodynamics; (ii) to argue in favour of the latter; and (iii) to show that whichever we choose, our rational expectations about the thermodynamic behaviour of the future must depend on what we know about the past: contrary to the common view, statistical arguments alone do not give us good reason to expect that entropy will always continue to increase. (shrink)

Popper conceived an experiment whose analysis led to a result that he deemed absurd. Popper wrote that his reasoning was based on the Copenhagen interpretation and therefore invalidated it. Many authors who have examined Popper's analysis have found in it various technical flaws which are briefly summarized here. However, the aim of the present article is not technical. My concern is to redress logical flaws in Popper's argument: the terminology he uses is ambiguous, his analysis involves counterfactual hypotheses, and it (...) violates Bohr's complementarity principle. Therefore, the absurdity of Popper's result only confirms Bohr's approach. (shrink)

In his 1939 Lectures, the prominent Soviet physicist L. I. Mandelstam proposed an interpretation of quantum mechanics that was understood in different ways. To assess Mandelstam's interpretation, we classify contemporary interpretations of quantum mechanics and compare his interpretation with others developed in the 1930s. We conclude that Mandelstam's interpretation belongs to the family of minimal statistical interpretations and has much in common with interpretations developed by American physicists. Mandelstam's characteristic message was his theory of indirect measurement, which influenced his discussion (...) of the "reduction of the wave packet" and the Einstein, Podolsky, and Rosen argument. This article also reconstructs what lay behind Mandelstam's interpretation of quantum mechanics. This was his operationalism, by virtue of which his interpretation resembled Kemble's, in which the statistical and Copenhagen views had been combined. Like Popper and Margenau, Mandelstam followed R. von Mises's empirical conception of probability. Mandelstam, like the other proponents of the statistical approach to quantum mechanics, was affected by the culture of macroscopic experimentation with its emphasis on statistical measurement. (shrink)

Focusing on Nicholas Maxwell’s thesis that “science, properly understood, provides us the methodological key to the salvation of humanity”, the article discusses Maxwell’s aim oriented empiricism and his conception of Wisdom Inquiry as advocated in Maxwell’s (2009b, pp.1–56) essay entitled “How Can Life of Value Best Flourish in the Real World?” (in Science and the Pursuit of Wisdom: Studies in the Philosophy of Nicholas Maxwell 2009, edited by Leemon McHenry) and in Maxwell (2004 & 2009a).

One way to characterize dispositions is to take them to be reducible to categorical properties plus experimental arrangements. We argue that this view applied to Bohm 's ontological interpretation of quantum theory provides a good picture of the unremarkable nature of spin in that interpretation, and so explains how a simple realism of possessed values may be retained in the face of Kochen and Specker's theorem. With this in mind we discuss Redhead's influential analysis of Kochen and Specker's theorem which (...) does nor appear to allow for the above view. (shrink)

This essay examines some of the arguments in David Deutsch's book The Fabric of Reality , chief among them its case for the so-called many-universe interpretation of quantum mechanics (QM), presented as the only physically and logically consistent solution to the QM paradoxes of wave/particle dualism, remote simultaneous interaction, the observer-induced 'collapse of the wave-packet', etc. The hypothesis assumes that all possible outcomes are realized in every such momentary 'collapse', since the observer splits off into so many parallel, coexisting, but (...) epistemically non-interaccessible 'worlds' whose subsequent branchings constitute the lifeline-or experiential world-series- for each of those proliferating centres of consciousness. Although Deutsch concedes that his 'multiverse' theory is counter-intuitive, he none the less takes it to be borne out beyond question by the sheer observational/predictive success of QM and the conceptual dilemmas that supposedly arise with alternative (single-universe) accounts. Moreover, he claims the theory resolves a range of longstanding philosophical problems, notably those of mind/body dualism, the various traditional paradoxes of time, and the freewill/determinism issue. The essay suggests on the contrary, that Deutsch unwittingly transposes into the framework of presentday quantum debate speculative themes from the history of rationalist metaphysics, often with bizarre or philosophically dubious results, and that he rules out at least one promising rival account, namely Bohm's 'hidden variables' theory. It goes on to consider reasons for resistance to that theory among proponents of the 'orthodox' (Copenhagen) doctrine, and for the strong anti-realist, at times even irrationalist bias that has characterized much of this discussion since Bohr's debates with Einstein about quantum non-locality, observer-intervention, and the limits of precise measurement. Finally, the contrast is pointed out between Deutsch's ontologically extravagant use of the many-worlds hypothesis (akin to certain ideas advanced by speculative metaphysicians from Leibniz down) and those realist modes of counterfactual reasoning- e.g. in Kripke and the early Putnam- which deploy similar arguments to very different causal-explanatory ends. (shrink)

In this essay I examine various aspects of the nearcentury-long debate concerning the conceptualfoundations of quantum mechanics and the problems ithas posed for physicists and philosophers fromEinstein to the present. Most crucial here is theissue of realism and the question whether quantumtheory is compatible with any kind of realist orcausal-explanatory account which goes beyond theempirical-predictive data. This was Einstein's chiefconcern in the famous series of exchanges with NielsBohr when he refused to accept the truth orcompleteness of a doctrine (orthodox QM) (...) which ruledsuch questions to be strictly inadmissible. I discussthe later history of quantum-theoretical debate withparticular reference to the issue of nonlocality,i.e., the phenomenon of superluminal(faster-than-light) interaction betweenwidely-separated particles. Then I show how thestandard `Copenhagen' interpretation of QM hasinfluenced current anti-realist orontological-relativist approaches to philosophy ofscience. Indeed, there are clear signs that somephilosophers have retreated from a realist positionvery largely in response to just these problems. So itis important to ask exactly why – on what scientificor philosophical grounds – any preferred alternative(causal-realist) construal should have been ruled outas a matter of orthodox QM wisdom. Moreconstructively, my paper presents various arguments infavour of one such alternative, the `hidden-variables'theory developed since the early 1950s by David Bohmand consistently marginalised by proponents of theCopenhagen doctrine. (shrink)

In this essay, I offer a critical evaluation of Hilary Putnam's writings on epistemology and philosophy of science, in particular his engagement with interpretative problems in quantum mechanics. I trace the development of his thinking from the late 1960s when he adopted a strong causal-realist position on issues of meaning, reference, and truth, via the "internal realist" approach of his middle-period writings, to the various forms of pragmatist, naturalized, or "commonsense" epistemology proposed in his latest books. My contention is that (...) Putnam's retreat from a full-fledged realist outlook has been prompted in large part by his belief that it cannot possibly be reconciled with the implications of quantum mechanics for our understanding of processes and events in the subatomic domain. However, I suggest, this response should be seen as premature given the range of as-yet unresolved problems with quantum mechanics on the orthodox (Copenhagen) interpretation and also the existence of an alternative account - David Bohm's hidden-variables theory - which perfectly matches the established predictive-observational results while providing a credible realist ontology. I also examine Putnam's case for adopting a nonstandard (three-valued) "quantum logic" in relation to the thinking of other philosophers - Michael Dummett among them - who have espoused a more global or doctrinaire version of anti-realism. I conclude that Putnam's early (causal-realist) position is by no means untenable in light of the various arguments that he now takes as counting decisively against it. (shrink)

We introduce the concept of partial event as a pair of disjoint sets, respectively the favorable and the unfavorable cases. Partial events can be seen as a De Morgan algebra with a single fixed point for the complement. We introduce the concept of a measure of partial probability, based on a set of axioms resembling Kolmogoroff’s. Finally we define a concept of conditional probability for partial events and apply this concept to the analysis of the two-slit experiment in quantum mechanics.

We provide a formally rigorous framework for integrating singular causation, as understood by Nuel Belnap's theory of causae causantes, and objective single case probabilities. The central notion is that of a causal probability space whose sample space consists of causal alternatives. Such a probability space is generally not isomorphic to a product space. We give a causally motivated statement of the Markov condition and an analysis of the concept of screening-off. 1. Causal dependencies and probabilities1.1Background: causation in branching space-times1.2What are (...) probabilities defined for?2. Basic transitions2.1Basics of basic transitions2.2Sets of basic transitions3. Causal probability theory3.1Some simple cases3.2General causal probabilities3.3Application: probability of suprema of a chain. (shrink)

This paper offers a critique of the Bayesian interpretation of quantum mechanics with particular focus on a paper by Caves, Fuchs, and Schack containing a critique of the “objective preparations view” or OPV. It also aims to carry the discussion beyond the hardened positions of Bayesians and proponents of the OPV. Several claims made by Caves et al. are rebutted, including the claim that different pure states may legitimately be assigned to the same system at the same time, and the (...) claim that the quantum nature of a preparation device cannot legitimately be ignored. Both Bayesians and proponents of the OPV regard the time dependence of a quantum state as the continuous dependence on time of an evolving state of some kind. This leads to a false dilemma: quantum states are either objective states of nature or subjective states of belief. In reality they are neither. The present paper views the aforesaid dependence as a dependence on the time of the measurement to whose possible outcomes the quantum state serves to assign probabilities. This makes it possible to recognize the full implications of the only testable feature of the theory, viz., the probabilities it assigns to measurement outcomes. Most important among these are the objective fuzziness of all relative positions and momenta and the consequent incomplete spatiotemporal differentiation of the physical world. The latter makes it possible to draw a clear distinction between the macroscopic and the microscopic. This in turn makes it possible to understand the special status of measurements in all standard formulations of the theory. Whereas Bayesians have written contemptuously about the “folly” of conjoining “objective” to “probability,” there are various reasons why quantum-mechanical probabilities can be considered objective, not least the fact that they are needed to quantify an objective fuzziness. But this cannot be appreciated without giving thought to the makeup of the world, which Bayesians refuse to do. Doing this on the basis of how quantum mechanics assigns probabilities, one finds that what constitutes the macroworld is a single Ultimate Reality, about which we know nothing, except that it manifests the macroworld or manifests itself as the macroworld. The so-called microworld is neither a world nor a part of any world but instead is instrumental in the manifestation of the macroworld. Quantum mechanics affords us a glimpse “behind” the manifested world, at stages in the process of manifestation, but it does not allow us to describe what lies “behind” the manifested world except in terms of the finished product—the manifested world, for without the manifested world there is nothing in whose terms we could describe its manifestation. (shrink)

The propensity interpretation of probability, bred by Popper in 1957(K. R. Popper, in Observation and Interpretation in the Philosophy of Physics,S. Körner, ed. (Butterworth, London, 1957, and Dover, New York, 1962), p. 65; reprinted in Popper Selections,D. W. Miller, ed. (Princeton University Press, Princeton, 1985), p. 199) from pure frequency stock, is the only extant objectivist account that provides any proper understanding of single-case probabilities as well as of probabilities in ensembles and in the long run. In Sec. 1 of (...) this paper I recall salient points of the frequency interpretations of von Mises and of Popper himself, and in Sec. 2 I filter out from Popper's numerous expositions of the propensity interpretation its most interesting and fertile strain. I then go on to assess it. First I defend it, in Sec. 3, against recent criticisms(P. Humphreys, Philos. Rev.94,557 (1985); P. Milne, Erkenntnis25,129 (1986)) to the effect that conditional [or relative] probabilities, unlike absolute probabilities, can only rarely be made sense of as propensities. I then challenge its predominance, in Sec. 4, by outlining a rival theory: an irreproachably objectivist theory of probability, fully applicable to the single case, that interprets physical probabilities asinstantaneous frequencies. (shrink)

There is no agreement within the scientific community about the philosophy of Schrödinger. Some people think that he was a realist, while others defend him as an idealist. In this paper we study a number of Schrödinger's works and we show that the epithets of realist and idealist do not do him justice. Toward the end we conclude that it would be more adequate to place him in the trend known as the philosophy of immanence.

In this paper I put forward a new micro realistic, fundamentally probabilistic, propensiton version of quantum theory. According to this theory, the entities of the quantum domain - electrons, photons, atoms - are neither particles nor fields, but a new kind of fundamentally probabilistic entity, the propensiton - entities which interact with one another probabilistically. This version of quantum theory leaves the Schroedinger equation unchanged, but reinterprets it to specify how propensitons evolve when no probabilistic transitions occur. Probabilisitic transitions occur (...) when new "particles" are created as a result of inelastic interactions. All measurements are just special cases of this. This propensiton version of quantum theory, I argue, solves the wave/particle dilemma, is free of conceptual problems that plague orthodox quantum theory, recovers all the empirical success of orthodox quantum theory, and at the same time yields as yet untested predictions that differ from those of orthodox quantum theory. (shrink)

In this article I reply to comments made by Agustin Vicente and Giridhari Lal Pandit on Science and the Pursuit of Wisdom (McHenry 2009 ). I criticize analytic philosophy, go on to expound the argument for the need for a revolution in academic inquiry so that the basic aim becomes wisdom and not just knowledge, defend aim-oriented empiricism, outline my solution to the human world/physical universe problem, and defend the thesis that free will is compatible with physicalism.

In this paper I argue that aim-oriented empiricism (AOE), a conception of natural science that I have defended at some length elsewhere[1], is a kind of synthesis of the views of Popper, Kuhn and Lakatos, but is also an improvement over the views of all three. Whereas Popper's falsificationism protects metaphysical assumptions implicitly made by science from criticism, AOE exposes all such assumptions to sustained criticism, and furthermore focuses criticism on those assumptions most likely to need revision if science is (...) to make progress. Even though AOE is, in this way, more Popperian than Popper, it is also, in some respects, more like the views of Kuhn and Lakatos than falsificationism is. AOE is able, however, to solve problems which Kuhn's and Lakatos's views cannot solve. [Back to Top]. (shrink)

It is usually supposed that the central limit theorem explains why various quantities we find in nature are approximately normally distributed—people's heights, examination grades, snowflake sizes, and so on. This sort of explanation is found in many textbooks across the sciences, particularly in biology, economics, and sociology. Contrary to this received wisdom, I argue that in many cases we are not justified in claiming that the central limit theorem explains why a particular quantity is normally distributed, and that in some (...) cases, we are actually wrong. 1 Introduction2 Normal Distributions and the Central Limit Theorem2.1 Normal distributions2.2 The central limit theorem2.3 Terminology3 Explaining Normality3.1 Loaves of bread3.2 Varying variances and probability densities3.3 Tensile strengths and problems with summation3.4 Products of factors and log-normal distributions3.5 Transforming factors and sub-factors3.6 Transformations of quantities3.7 Quantitative genetics3.8 Inference to the best explanation4 Maximum Entropy Explanations5 Conclusion. (shrink)

Some have argued that chance and determinism are compatible in order to account for the objectivity of probabilities in theories that are compatible with determinism, like Classical Statistical Mechanics (CSM) and Evolutionary Theory (ET). Contrarily, some have argued that chance and determinism are incompatible, and so such probabilities are subjective. In this paper, I argue that both of these positions are unsatisfactory. I argue that the probabilities of theories like CSM and ET are not chances, but also that they are (...) not subjective probabilities either. Rather, they are a third type of probability, which I call counterfactual probability. The main distinguishing feature of counterfactual-probability is the role it plays in conveying important counterfactual information in explanations. This distinguishes counterfactual probability from chance as a second concept of objective probability. (shrink)

Among the most important questions in the metaphysics of science are "What are the natures of fundamental laws and chances?" and "What grounds the direction of time?" My aim in this paper is to examine some connections between these questions, discuss two approaches to answering them and argue in favor of one. Along the way I will raise and comment on a number of issues concerning the relationship between physics and metaphysics and consequences for the subject matter and methodology of (...) metaphysics. (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)

In order to solve a system of nonlinear rate equations one can try to use some soliton methods. The procedure involves three steps: find a ‘Lax representation’ where all the kinetic variables are combined into a single matrix \, all the kinetic constants are encoded in a matrix H; find a Darboux–Bäcklund dressing transformation for the Lax representation \]\), where f models a time-dependent environment; find a class of seed solutions \ that lead, via a nontrivial chain of dressings \ (...) to new solutions, difficult to find by other methods. The latter step is not a trivial one since a non-soliton method has to be employed to find an appropriate initial \. Procedures that lead to a correct \ have been discussed in the literature only for a limited class of H and f. Here, we develop a formalism that works for practically any H, and any explicitly time-dependent f. As a result, we are able to find exact solutions to a system of equations describing an arbitrary number of species interacting through catalytic feedbacks, with general time dependent parameters characterizing the nonlinearity. Explicit examples involve up to 42 interacting species. (shrink)