Indispensability arguments for realism about mathematical entities have come under serious attack in recent years. To my mind the most profound attack has come from Penelope Maddy, who argues that scientific/mathematical practice doesn't support the key premise of the indispensability argument, that is, that we ought to have ontological commitment to those entities that are indispensable to our best scientific theories. In this paper I defend the Quine/Putnam indispensability argument against Maddy's objections.

A century after the discovery of quantum mechanics, the meaning of quantum mechanics still remains elusive. This is largely due to the puzzling nature of the wave function, the central object in quantum mechanics. If we are realists about quantum mechanics, how should we understand the wave function? What does it represent? What is its physical meaning? Answering these questions would improve our understanding of what it means to be a realist about quantum mechanics. In this survey article, I review (...) and compare several realist interpretations of the wave function. They fall into three categories: ontological interpretations, nomological interpretations, and the sui generis interpretation. For simplicity, I will focus on non-relativistic quantum mechanics. (shrink)

In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the quantum ontology and define a unique initial condition in such a world. First, I introduce Density Matrix Realism, the thesis that the quantum universe is described by a fundamental density matrix that represents something objective. This stands in sharp contrast to Wave Function (...) Realism, the thesis that the quantum universe is described by a wave function that represents something objective. Second, I suggest that the Past Hypothesis is sufficient to determine a unique and simple density matrix. This is achieved by what I call the Initial Projection Hypothesis: the initial density matrix of the universe is the normalized projection onto the special low-dimensional Hilbert space. Third, because the initial quantum state is unique and simple, we have a strong case for the \emph{Nomological Thesis}: the initial quantum state of the universe is on a par with laws of nature. This new package of ideas has several interesting implications, including on the harmony between statistical mechanics and quantum mechanics, the dynamic unity of the universe and the subsystems, and the alleged conflict between Humean supervenience and quantum entanglement. (shrink)

Le thème d’une nature particulière des mathématiques comme connaissance a été au cœur du débat épistémologique français du XX esiècle, et ce, à partir des œuvres de Maximilien Winter, Gaston Bachelard, Albert Lautman jusqu’à Alain Connes et Gilles Châtelet. Pour le saisir au plus près, il convient d’avoir à l’esprit qu’il est le fruit d’une analyse constante et d’un approfondissement des indications données par Bernhardt Riemann sur le rapport étroit entre mathématiques et physique qui caractérisera toute la pensée physique du (...) XX e siècle. Ce qui a conduit à l’existence d’une littérature très riche mais peu étudiée qui a cherché à clarifier sur le plan épistémique le sens rationnel de l’efficacité des mathématiques dans l’exploration du réel physique, problématisée sous le titre de The Unreasonable Effectiveness of Mathematics. Cette problématique cruciale constitue l’un des apports les plus originaux de la philosophie des sciences française, sans équiva-lent dans la tradition anglo-saxonne. Prendre acte de l’existence de cette épistémologie de la physique mathématique devrait permettre de couper court à la polémique soulevée récemment en France quant à l’existence ou la non-existence d’une philosophie des sciences spécifi-quement française.During the 1900s, the theme of the particular nature of mathematics as knowledge was at the center of the French epistemological debate, starting with Maximilien Winter, Gaston Bachelard, Albert Lautman, Alain Connes and Gilles Châtelet. To be understood in its most correct dimension, it should be borne in mind that it is the result of a constant analysis and the analysis of the indications given by Bernhard Riemann about the close relationship between mathematics and physics which, as is well known, char-acterized the physical thought of on the ‘900. This has led to a large critical production that has sought to clarify on the epistemic level the rational sense of the effectiveness of mathematics in the exploration of physical reality. It has produced a whole set of articulated responses to the topic: “the unreasonable effectiveness of math”. This crucial issue is one of the most original contributions of French philosophy of sciences, problematic that even in the rich and varied tradition of Anglo-Saxon research did not find equal consideration. At the same time, acknowledge the existence of what is a true epistemology of mathematical physics, it can help to no longer fuel the controversy raised by some in France in recent years about the presence or absence of a typical French philosophy of science. Il tema della particolare natura delle matematiche come conoscenza è stato nel corso del ‘900 al centro del dibattito epistemologico francese a partire dalle opere di Maximilien Winter, Bachelard, Lautman sino à Alain Connes e Gilles Châtelet; ma per essere capito nella sua più giusta dimensione, occorre tenere presente che esso è il frutto di un’analisi costante e dell’approfondimento di indicazioni date da Bernhard Riemann circa lo stretto rapporto fra matematiche e fisica che, com’è noto ha caratterizzato l’intero pensiero fisico del ‘900. Ciò ha portato ad una ricca letteratura, poco studiata, che ha cercato di chiarire sul piano epistemico il senso razionale dell’efficacia delle matematiche nella esplorazione del reale fisico; essa ha prodotto tutta una serie di risposte articolate al tema che nella letteratura scientifica viene chiamato The Unreasonable Effectiveness of Mathematics. L’ aver posto al centro del dibattito epistemologico questa cruciale problematica costituisce uno degli apporti più originali della filosofia delle scienze francese, problematica che anche nella pur ricca e variegata tradizione di ricerca anglosassone non ha trovato una eguale considerazione. Nello stesso tempo prendere atto dell’esistenza di quella che è una vera e propria epistemologia della fisica matematica, può aiutare a non alimentare più la polemica sollevata da alcuni in Francia, in questi ultimi anni, sull’ esistenza o meno di una filosofia della scienza tipicamente francese.This article is in French. (shrink)

ArgumentIn 1895 when the Lumière brothers unveiled their cinematographic camera, many scientists were elated. Scientists hoped that the machine would fulfill a desire that had driven research for nearly half a century: that of capturing the world in its own image. But their elation was surprisingly short-lived, and many researchers quickly distanced themselves from the new medium. The cinematographic camera was soon split into two machines, one for recording and one for projecting, enabling it to further escape from the laboratory. (...) The philosopher Henri Bergson joined scientists, such as Etienne-Jules Marey, who found problems with the new cinematographic order. Those who had worked to make the dream come true found that their efforts had been subverted. This essay focuses on the desire to build a cinematographic camera, with the purpose of elucidating how dreams and reality mix in the development of science and technology. It is about desired machines and their often unexpected results. The interplay between what “is” (the technical), what “ought” (the ethical), and what “could” be (the fantastical) drives scientific research. (shrink)

It is widely believed that platonists face a formidable problem: that of providing an intelligible account of mathematical knowledge. The problem is that we seem unable, if the platonist is right, to have the causal relationships with the objects of mathematics without which knowledge of these objects seems unintelligible. The standard platonist response to this challenge is either to deny that knowledge without causation is unintelligible, or to make room for causal interactions by softening the platonism at issue. In this (...) essay I argue that the idea of causal relations with fully platonist objects is unproblematic. (shrink)

The ArgumentStarting from the thesis that a science constructs the knowledge of the part of the world allotted to it, the present paper aims at bringing together all the various aspects of physics under a unified conceptual framework — that provided by the Marxian concept “mode of production.” After an introduction providing the initial plausibility grounds for the undertaking, the concept is analyzed into its conceptual elements in Part I of the paper. The analysis presents the reconstruction initiated by Louis (...) Althusser and developed by his followers. Part II starts from a characterization of physical problems. This offers a basis for “reading” physics in the terms introduced in Part I. The rest of Part II is devoted to the identification of all the aspects of physics with the conceptual elements in question. The paper aims at three things: to uncover the connections holding among seemingly disparate aspects of physics, usually discussed in almost total independence from each other; to take full account of the social dimensions of physics without vindicating social constructivism; to show that the boundaries separating the disciplines of philosophy, history and sociology of science are more arbitrary than usually considered. (shrink)

One among many misleading quotations about the alleged mysteries of quantum theory is from Feynman (1965): Today we know that quantum theory describes many aspects of our world in a fully intelligible fashion. Pothos & Busemeyer (P&B) propose ways in which this may include psychology and cognitive science.

We analyse the way in which the principle that ‘the whole is greater than the sum of its parts’ manifests itself with phenomena of visual perception. For this investigation we use insights and techniques coming from quantum cognition, and more specifically we are inspired by the correspondence of this principle with the phenomenon of the conjunction effect in human cognition. We identify entities of meaning within artefacts of visual perception and rely on how such entities are modelled for corpuses of (...) texts such as the webpages of the World-Wide Web for our study of how they appear in phenomena of visual perception. We identify concretely the conjunction effect in visual artefacts and analyse its structure in the example of a photograph. We also analyse quantum entanglement between different aspects of meaning in artefacts of visual perception. We confirm its presence by showing that well elected experiments on images retrieved accordingly by Google Images give rise to probabilities and expectation values violating the Clauser Horne Shimony Holt version of Bell’s inequalities. We point out how this approach can lead to a mathematical description of the meaning content of a visual artefact such as a photograph. (shrink)

We model a piece of text of human language telling a story by means of the quantum structure describing a Bose gas in a state close to a Bose–Einstein condensate near absolute zero temperature. For this we introduce energy levels for the words (concepts) used in the story and we also introduce the new notion of ‘cogniton’ as the quantum of human thought. Words (concepts) are then cognitons in different energy states as it is the case for photons in different (...) energy states, or states of different radiative frequency, when the considered boson gas is that of the quanta of the electromagnetic field. We show that Bose–Einstein statistics delivers a very good model for these pieces of texts telling stories, both for short stories and for long stories of the size of novels. We analyze an unexpected connection with Zipf’s law in human language, the Zipf ranking relating to the energy levels of the words, and the Bose–Einstein graph coinciding with the Zipf graph. We investigate the issue of ‘identity and indistinguishability’ from this new perspective and conjecture that the way one can easily understand how two of ‘the same concepts’ are ‘absolutely identical and indistinguishable’ in human language is also the way in which quantum particles are absolutely identical and indistinguishable in physical reality, providing in this way new evidence for our conceptuality interpretation of quantum theory. (shrink)

Many advocates of the Everettian interpretation consider that theirs is the only approach to take quantum mechanics really seriously, and that this approach allows to deduce a fantastic scenario for our reality, one that consists of an infinite number of parallel worlds that branch out continuously. In this article, written in dialogue form, we suggest that quantum mechanics can be taken even more seriously, if the many-worlds view is replaced by a many-measurements view. This allows not only to derive the (...) Born rule, thus solving the measurement problem, but also to deduce a one-world non-spatial reality, providing an even more fantastic scenario than that of the multiverse. (shrink)

Epistemic theories of objective chance hold that chances are idealised epistemic probabilities of some sort. After giving a brief history of this approach to objective chance, I argue for a particular version of this view, that the chance of an event E is its epistemic probability, given maximal knowledge of the possible causes of E. The main argument for this view is the demonstration that it entails all of the commonly-accepted properties of chance. For example, this analysis entails that chances (...) supervene on the physical facts, that the chance function is an expert probability, that the existence of stable frequencies results from invariant chances in repeated experiments, and that chances are probably close to long-run relative frequencies in repeated experiments. Despite these virtues, epistemic approaches to chance have been neglected in recent decades, on account of their conflict with accepted views about closely related topics such as causation, laws of nature, and epistemic probability. However, existing views on these topics are also very problematic, and I believe that the epistemic view of chance is a key piece of this puzzle that, once in place, allows all the other pieces to fit together into a new and coherent way. I also respond to some criticisms of the epistemic theory that I favour. (shrink)

Einige versuchen, Wunder mit den Naturgesetzen vereinbar zu machen, indem sie „Wunder“ als etwas anderes als göttliche Eingriffe definieren. Dieser Aufsatz behauptet hin- gegen, daß Wunder die Naturgesetze nicht verletzen, obwohl sie göttliche Eingriffe sind. Wunder sind auch keine „Ausnah- men“ der Naturgesetze, noch treffen die Naturgesetze nicht auf sie zu. Naturgesetze haben nie Ausnahmen, sie werden nie verletzt oder ausgesetzt, sie sind wahrscheinlich notwen- dig und unveränderlich, und sie treffen auch auf göttliche Ein- griffe zu. Wir sollten nicht unsere (...) Vorstellung von Wundern, sondern unsere Vorstellung der Naturgesetze in Frage stel- len. Die Hauptthese dieses Aufsatzes ist, daß Naturgesetze keine Abfolgeregelmäßigkeiten implizieren und daß deshalb Wunder die Naturgesetze nicht verletzen. Wir brauchen eine neue Theorie der Naturgesetze: die Tendenztheorie. (shrink)

I begin by reviewing some recent work on the status of the geodesic principle in general relativity and the geometrized formulation of Newtonian gravitation. I then turn to the question of whether either of these theories might be said to ``explain'' inertial motion. I argue that there is a sense in which both theories may be understood to explain inertial motion, but that the sense of ``explain'' is rather different from what one might have expected. This sense of explanation is (...) connected with a view of theories---I call it the ``puzzleball view''---on which the foundations of a physical theory are best understood as a network of mutually interdependent principles and assumptions. (shrink)

The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this long-standing question. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical (...) state does it represent? In this book, I aim to make sense of the wave function in quantum mechanics and find the ontological content of the theory. The book can be divided into three parts. The first part addresses the question of the nature of the wave function. After giving a comprehensive and critical review of the competing views of the wave function, I present a new argument for the ontic view in terms of protective measurements. In addition, I also analyze the origin of the wave function by deriving the free Schroedinger equation. The second part analyzes the ontological meaning of the wave function. I propose a new ontological interpretation of the wave function in terms of random discontinuous motion of particles, and give two main arguments supporting this interpretation. The third part investigates whether the suggested quantum ontology is complete in accounting for our definite experience and whether it needs to be revised in the relativistic domain. (shrink)

Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce several notions of symmetry in mathematics and explain how they can also be used in resolving different problems in the philosophy of mathematics. We use symmetry to discuss the objectivity of mathematics, the role of mathematical objects, the unreasonable effectiveness of (...) mathematics and the relationship of mathematics to physics. (shrink)

According to Interventionism, explanations cite invariant relations which hold among multiple variables. Interventionism incorrectly implies, however, that many common scientific explanations—which cite single‐variable boundary constraints—are not actually explanatory. So I propose a different account of explanation, similar in spirit to Interventionism, which gets those cases of scientific explanation right.

It has been argued that the fundamental laws of physics do not face a ‘problem of provisos’ equivalent to that found in other scientific disciplines (Earman, Roberts and Smith 2002) and there is only the appearance of exceptions to physical laws if they are confused with differential equations of evolution type (Smith 2002). In this paper I argue that even if this is true, fundamental laws in physics still pose a major challenge to standard Humean approaches to lawhood, as they (...) are not in any obvious sense about regularities in behaviour. A Humean approach to physical laws with exceptions is possible, however, if we adopt a view of laws that takes them to be the algorithms in the algorithmic compressions of empirical data. When this is supplemented with a distinction between lossy and lossless compression, we can explain exceptions in terms of compression artefacts present in the application of the lossy laws. (shrink)

We present a derivation of the third postulate of relational quantum mechanics from the properties of conditional probabilities. The first two RQM postulates are based on the information that can be extracted from interaction of different systems, and the third postulate defines the properties of the probability function. Here we demonstrate that from a rigorous definition of the conditional probability for the possible outcomes of different measurements, the third postulate is unnecessary and the Born’s rule naturally emerges from the first (...) two postulates by applying the Gleason’s theorem. We demonstrate in addition that the probability function is uniquely defined for classical and quantum phenomena. The presence or not of interference terms is demonstrated to be related to the precise formulation of the conditional probability where distributive property on its arguments cannot be taken for granted. In the particular case of Young’s slits experiment, the two possible argument formulations correspond to the possibility or not to determine the particle passage through a particular path. (shrink)

Despite the importance of the variational principles of physics, there have been relatively few attempts to consider them for a realistic framework. In addition to the old teleological question, this paper continues the recent discussion regarding the modal involvement of the principle of least action and its relations with the Humean view of the laws of nature. The reality of possible paths in the principle of least action is examined from the perspectives of the contemporary metaphysics of modality and Leibniz's (...) concept of essences or possibles striving for existence. I elaborate a modal interpretation of the principle of least action that replaces a classical representation of a system's motion along a single history in the actual modality by simultaneous motions along an infinite set of all possible histories in the possible modality. This model is based on an intuition that deep ontological connections exist between the possible paths in the principle of least action and possible quantum histories in the Feynman path integral. I interpret the action as a physical measure of the essence of every possible history. Therefore only one actual history has the highest degree of the essence and minimal action. To address the issue of necessity, I assume that the principle of least action has a general physical necessity and lies between the laws of motion with a limited physical necessity and certain laws with a metaphysical necessity. (shrink)

On the basis of what I call physico-formalist philosophy of mathematics, I will develop an amended account of the Kantian–Reichenbachian conception of constitutive a priori. It will be shown that the features attributed to a real object are not possessed by the object as a “thing-in-itself”; they require a physical theory by means of which these features are constituted. It will be seen that the existence of such a physical theory implies that a physical object can possess a property only (...) if other contingently existing physical objects exist; therefore, the intrinsic–extrinsic distinction is flawed. (shrink)

Since its inception in the late 1920s and 30s, the main problem of quantum electrodynamics had been that any interaction or scattering event involved processes of a higher order that arose from vacuum polarization, the creation and subsequent annihilation of particle-antiparticle pairs, and the mutual interactions of all those short-lived entities.1 These processes posed two kinds of conceptual problems. First, they were not detectable individually, but had a measurable effect on the energy of the overall process. Even in simple quantum (...) systems, such as the hydrogen atom, they showed up, for instance, in the form of a further splitting up of spectral lines, most prominently the Lamb shift and measurements of... (shrink)

Discussions of the applicability of mathematics in the natural sciences have been flawed by failure to realize that there are multiple senses in which mathematics can be ‘applied’ and, correspondingly, multiple problems that stem from the applicability of mathematics. I discuss semantic, metaphysical, descriptive, and and epistemological problems of mathematical applicability, dwelling on Frege's contribution to the solution of the first two types. As for the remaining problems, I discuss the contributions of Hartry Field and Eugene Wigner. Finally, I argue (...) that there are epistemological problems concerning the applicability of mathematics that nobody in the philosophical community has yet confronted, though the problems are well known to physicists. (shrink)

Cartwright attempts to argue from an analysis of the composition of forces, and more generally the composition of laws, to the conclusion that laws must be regarded as false. A response to Cartwright is developed which contends that properly understood composition poses no threat to the truth of laws, even though agreeing with Cartwright that laws do not satisfy the "facticity" requirement. My analysis draws especially on the work of Creary, Bhaskar, Mill, and points towards a general rejection of Cartwright's (...) view that laws, especially fundamental laws, should be seen as false. (shrink)

I examine the current state of the debate on the metaphysics of science. In 1, I identify some of the main questions belonging to the MS, looking into the relationship between science and metaphysics. In 2, I expound the rise of the old wave in the MS, which endorses the belief that metaphysics is a guide to, or a heuristic for, science and outlines the stronger idea that metaphysics makes science possible. In 3, I examine the maximalist MS. This is (...) a contemporary revival of the old wave, reformulating the claim that metaphysics makes science possible. In 4, I look into the new wave in the MS, which argues that science is a guide to metaphysics and, more radically, that metaphysics is to be motivated by, and restricted to, science. In 5, I briefly introduce my own minimalist MS, which contends that science sets the epistemic, methodological and ontological criteria which should work as desiderata of the MS. I close this chapter in 6 with some concluding remarks. (shrink)

(2010). Nature's Longing for Beauty: Elegance as an Evolutionary Attractor, with Implications for Human Systems. World Futures: Vol. 66, No. 7, pp. 504-510.

Information, entropy, probability: these three terms are closely interconnected in the prevalent understanding of statistical mechanics, both when this field is taught to students at an introductory level and in advanced research into the field’s foundations. This paper examines the interconnection between these three notions in light of recent research in the foundations of statistical mechanics. It disentangles these concepts and highlights their differences, at the same time explaining why they came to be so closely linked in the literature. In (...) the literature the term ‘information’ is often linked to entropy and probability in discussions of Maxwell’s Demon and its attempted exorcism by the Landauer-Bennett thesis, and in analyses of the spin echo experiments. The direction taken in the present paper is a different one. Here we discuss the statistical mechanical underpinning of the notions of probability and entropy, and this constructive approach shows that information plays no fundamental role in these concepts, although it can be conveniently used in a sense that we shall specify. (shrink)

Statistical mechanics is the name of the ongoing attempt to explain and predict certain phenomena, above all those described by thermodynamics on the basis of the fundamental theories of physics, in particular mechanics, together with certain auxiliary assumptions. In another paper in this journal, Foundations of statistical mechanics: Mechanics by itself, I have shown that some of the thermodynamic regularities, including the probabilistic ones, can be described in terms of mechanics by itself. But in order to prove those regularities, in (...) particular the time asymmetric ones, it is necessary to add to mechanics assumptions of three kinds, all of which are under debate in contemporary literature. One kind of assumptions concerns measure and probability, and here, a major debate is around the notion of “typicality.” A second assumption concerns initial conditions, and here, the debate is about the nature and status of the so-called past hypothesis. The third kind of assumptions concerns the dynamics, and here, the possibility and significance of “Maxwell's Demon” is the main topic of discussions. This article describes these assumptions and examines the justification for introducing them, emphasizing the contemporary debates around them. (shrink)

Since causal processes can be prevented and interfered with, law-governed causation is a challenge for necessitarian theories of laws of nature. To show that there is a problematic friction between necessity and interference, I focus on David Armstrong's theory; with one proviso, his lawmaker, nomological necessity, is supposed to be instantiated as the causation of the law's second relatum whenever its first relatum is instantiated. His proviso is supposed to handle interference cases, but fails to do so. In order to (...) be able to handle interferences, any theory which utilizes a kind of necessitation as lawmaker has to downgrade what it treats as necessity to something more akin to (Newtonian) forces. (shrink)

Re-Engineering Philosophy for Limited Beings is about new approaches to many of the big topics in philosophy of science today, but with a very different take. To begin with, we are urged to reject the received Cartesian-Laplacean myths: Descartes’ certainty and Laplace’s computational omniscience. Instead, Wimsatt re-engineers a philosophy for human beings with all their cognitive limitations. His approaches find their starting point in the actual practices of scientists themselves, which he strongly identifies with engineering practices as the source of (...) researchers’ solutions for dealing with a complex world. He aims to construct an understanding of scientific methodology around the central role of reduction. But he dismisses eliminative reductionism in favor of a heuristic-based realist view. Wimsatt’s world is a complex one, and this means that science needs to do away with all the absolute and simple answers, because they do not reflect the world we are living in. A complex world requires the mindset and tinkering of an engineer to uncover its reality. The appropriate response must be heuristics all the way down as we constantly seek out reliable inferences on often shifting ground. To this end, we aim for models and theories that are robust, just as engineers aim to build robust machines. And although errors occur and approaches are fallible, they allow us to continually adapt the heuristics applied and sharpen our perceptions so as to develop more refined tools for investigating and understanding the world. (shrink)