We maximally extend the quantum‐mechanical results of Muller and Saunders ( 2008 ) establishing the ‘weak discernibility’ of an arbitrary number of similar fermions in finite‐dimensional Hilbert spaces. This confutes the currently dominant view that ( A ) the quantum‐mechanical description of similar particles conflicts with Leibniz’s Principle of the Identity of Indiscernibles (PII); and that ( B ) the only way to save PII is by adopting some heavy metaphysical notion such as Scotusian haecceitas or Adamsian primitive thisness. (...) We take sides with Muller and Saunders ( 2008 ) against this currently dominant view, which has been expounded and defended by many. *Received July 2008; revised May 2009. †To contact the authors, please write to: F. A. Muller, Faculty of Philosophy, Erasmus University Rotterdam, Burg. Oudlaan 50, H5–16, 3062 PA Rotterdam, The Netherlands; e‐mail: f.a.muller@fwb.eur.nl , and Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: f.a.muller@uu.nl . M. P. Seevinck, Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: [email protected]. (shrink)

We discuss the case against Factorism, which is the standard assumption in quantum mechanics that the labels of the $$\otimes$$ ⊗ -factor Hilbert-spaces in direct-product Hilbert-spaces of composite physical systems of similar particles refer to particles, either directly or descriptively. We distinguish different versions of Factorism and argue for their truth or falsehood. In particular, by introducing the concepts of snapshot Hilbert-space and Schrödinger-movie, we demonstrate that there are Hilbert-spaces and $$\otimes$$ ⊗ -factorisations where the labels do refer, even descriptively, (...) to similar particles, which renders them probabilistically absolutely discernible. (shrink)

One of the reasons provided for the shift away from an ontology for physical reality of material objects & properties towards one of physical structures & relations (Ontological Structural Realism: OntSR) is that the quantum-mechanical description of composite physical systems of similar elementary particles entails they are indiscernible. As material objects, they 'whither away', and when they wither away, structures emerge in their stead. We inquire into the question whether recent results establishing the weak discernibility of elementary particles pose a (...) threat for this quantum-mechanical reason for OntSR, because precisely their newly discovered discernibility prevents them from 'whithering away'. We argue there is a straightforward manner to consider the recent results as a reason in favour of OntSR rather than against it. (shrink)

By focussing on the intentional character of observation in science, we argue that Constructive Empiricism—B.C. van Fraassen’s much debated and explored view of science—is inconsistent. We then argue there are at least two ways out of our Inconsistency Argument, one of which is more easily to square with Constructive Empiricism than the other.

I begin by criticizing an elaboration of an argument in this journal due to Hawley , who argued that, where Leibniz’s Principle of the Identity of Indiscernibles faces counterexamples, invoking relations to save PII fails. I argue that insufficient attention has been paid to a particular distinction. I proceed by demonstrating that in most putative counterexamples to PII , the so-called Discerning Defence trumps the Summing Defence of PII. The general kind of objects that do the discerning in all cases (...) form a category that has received little if any attention in metaphysics. This category of objects lies between indiscernibles and individuals and is called relationals: objects that can be discerned by means of relations only and not by properties. Remarkably, relationals turn out to populate the universe. (shrink)

We inquire into the question whether the Aristotelean or classical \emph{ideal} of science has been realised by the Model Revolution, initiated at Stanford University during the 1950ies and spread all around the world of philosophy of science --- \emph{salute} P.\ Suppes. The guiding principle of the Model Revolution is: \emph{a scientific theory is a set of structures in the domain of discourse of axiomatic set-theory}, characterised by a set-theoretical predicate. We expound some critical reflections on the Model Revolution; the conclusions (...) will be that the philosophical problem of what a \emph{scientific theory} is has \emph{not} been solved yet --- \emph{pace} P.\ Suppes. While reflecting critically on the Model Revolution, we also explore a proposal of how to complete the Revolution and briefly address the intertwined subject of \emph{scientific representation}, which has come to occupy center stage in philosophy of science over the past decade. (shrink)

In a recent issue of this journal, M. Frisch claims to have proven that classical electrodynamics is an inconsistent physical theory. We argue that he has applied classical electrodynamics inconsistently. Frisch also claims that all other classical theories of electromagnetic phenomena, when consistent and in some sense an approximation of classical electrodynamics, are haunted by “serious conceptual problems” that defy resolution. We argue that this claim is based on a partisan if not misleading presentation of theoretical research in classical electrodynamics.

We inquire into the question whether the Aristotelean or classical \emph{ideal} of science has been realised by the Model Revolution, initiated at Stanford University during the 1950ies and spread all around the world of philosophy of science --- \emph{salute} P.\ Suppes. The guiding principle of the Model Revolution is: \emph{a scientific theory is a set of structures in the domain of discourse of axiomatic set-theory}, characterised by a set-theoretical predicate. We expound some critical reflections on the Model Revolution; the conclusions (...) will be that the philosophical problem of what a \emph{scientific theory} is has \emph{not} been solved yet --- \emph{pace} P.\ Suppes. While reflecting critically on the Model Revolution, we also explore a proposal of how to complete the Revolution and briefly address the intertwined subject of \emph{scientific representation}, which has come to occupy center stage in philosophy of science over the past decade. (shrink)

The author endeavours to show two things: first, that Schrödingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrödinger in 1926, is not foolproof; and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent. That they were is the Equivalence Myth. In order to make the (...) theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. -/- The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrödingers equivalence paper. Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The paper is self-contained and presupposes only basic knowledge of quantum mechanics. For reasons of length, the paper is published in two parts; Part I appeared in the previous issue of this journal. Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims; so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments. (shrink)

The author endeavours to show two things: first, that Schrödingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrödinger in 1926, is not foolproof; and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent. That they were is the Equivalence Myth. In order to make the (...) theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. -/- The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrödingers equivalence paper. Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The paper is self-contained and presupposes only basic knowledge of quantum mechanics. For reasons of length, the paper is published in two parts; Part I appeared in the previous issue of this journal. Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims; so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments. (shrink)

Alan Musgrave, Michael Friedman, Jeffrey Foss, and Richard Creath raised different objections against the Distinction between observables and unobservables when drawn within the confines of Bas C. van Fraassen's Constructive Empiricism, to the effect that the Distinction cannot be drawn there coherently. Van Fraassen has only responded to Musgrave but Musgrave claimed not to understand van Fraassen's succinct response. I argue that van Fraassen's response is not enough. What remains in the end is an unsolved problem which CE cannot afford (...) to leave unsolved, or so I argue; I then strengthen Musgrave's criticism and indicate that an extension of the epistemic policy of CE is mandatory to solve the problem. I also argue that Friedman's and Foss' objection against the Distinction in CE misses the mark on closer inspection. An objection due to Creath does hit the mark but can be taken care of without too much ado. All these objections seem alive and kicking until the present day; I try to put them all to rest. (shrink)

In his 2009 PSA Recent Ph.D. Award winning contribution to the bi-annual PSA Conference at Pittsburgh in 2008, C. Wu ̈thrich mounted an argument against struc- turalism about space-time in the context of the General Theory of Relativity, to the effect that structuralists cannot discern space-time points. An “abysmal embarrass- ment” for the structuralist, Wu ̈thrich judged. Wu ̈thrich’s characterisation of space-time structuralism is however incorrect. We demonstrate how, on the basis of a correct char- acterisation of space-time structuralism, it (...) is possible to discern space-time points in the GTR-structures under consideration. Thus Wu ̈thrich’s argument crumbles. (shrink)

In the spirit of B. C. van Fraassen's view of science called Constructive Empiricism, we propose a scientific criterion to decide whether a concrete object is observable, as well as a coextensive scientific-philosophical definition of observability, and we sketch a rigorous account of modal language occurring in science. We claim that our account of observability solves three problems to which current accounts of observability, notably van Fraassen's own accounts, give rise. We further claim that our account of modal propositions (subjunctive (...) conditionals included), which proceeds wholly within the framework of the semantic view on scientific theories, grounds his claim that such an account is possible without relying on ‘inflationary metaphysics’, notably without postulating an infinitude of different universes besides the universe we inhabit. We thus claim to solve a fourth problem: how to give a precise nominalist account of modal language in science tailor-made for Constructive Empiricism. Introduction: Rough Guides The semantic view and the wave theory of light A scientific guide and a scientific criterion A New Rough Guide and a definition The Context Problem and Psillos' Problem Musgrave's Problem Modality without inflationary metaphysics Exitum. (shrink)

The notorious ‘measurement problem’ has been roving around quantum mechanics for nearly a century since its inception, and has given rise to a variety of ‘interpretations’ of quantum mechanics, which are meant to evade it. We argue that no less than six problems need to be distinguished, and that several of them classify as different types of problems. One of them is what traditionally is called ‘the measurement problem’. Another of them has nothing to do with measurements but is a (...) profound metaphysical problem. We also analyse critically Maudlin’s (Topoi 14:7–15, 1995) well-known statement of ‘three measurements problems’, and the clash of the views of Brown (Found Phys 16:857–870, 1986) and Stein (Maximal of an impossibility theorem concerning quantum measurement. In: R. S. Cohen et al. (Eds.), Potentiality, entanglement and passion-at-a-distance, 1997) on one of the six measurement problems. Finally, we summarise a solution to one measurement problem which has been largely ignored but tacitly if not explicitly acknowledged. (shrink)

Over the past years, in books and journals (this journal included), N. Maxwell launched a ferocious attack on B. C. van Fraassen’s view of science called Constructive Empiricism (CE). This attack has been totally ignored. Must we conclude from this silence that no defence is possible and that a fortiori Maxwell has buried CE once and for all? Or is the attack too obviously flawed as not to merit exposure? A careful dissection of Maxwell’s reasoning will make it clear that (...) neither is the case. This dissection includes an analysis of Maxwell’s ‘aberrance–argument’ (omnipresent in his many writings) for the claim that science implicitly and permanently accepts a substantial, metaphysical thesis about the universe, which then paves the way for his own metaphysical-realist hierarchy-view of science. This aberrance-claim, which Maxwell directs against a widely shared and harmful ideology of science called ‘Standard Empiricism’, generally has been ignored too, for more than a quarter of a century. Our conclusions will be that (i) Maxwell’s attacks on CE can be beaten off, and (ii) his ‘aberrance–arguments’ do not establish what Maxwell believes they establish, but (iii) we can draw a number of valuable lessons from these attacks about the nature of science and of the libertarian nature of CE. (shrink)

The quest for finding the right interpretation of Quantum Mechanics is as old as QM and still has not ended, and may never end. The question what an interpretation of QM is has hardly ever been raised explicitly, let alone answered. We raise it and answer it. Then the quest for the right interpretation can continue self-consciously, for we then know exactly what we are after. We present a list of minimal requirements that something has to meet in order to (...) qualify as an interpretation of QM. We also raise, as a side issue, the question how the discourse on the interpretation of QM relates to hermeneutics in Continental Philosophy. (shrink)

This paper, accessible for a general philosophical audience having only some fleeting acquaintance with set-theory and category-theory, concerns the philosophy of mathematics, specifically the bearing of category-theory on the foundations of mathematics. We argue for six claims. (I) A founding theory for category-theory based on the primitive concept of a set or a class is worthwile to pursue. (II) The extant set-theoretical founding theories for category-theory are conceptually flawed. (III) The conceptual distinction between a set and a class can be (...) seen to be formally codified in Ackermann's axiomatisation of set-theory. (IV) A slight but significant deductive extension of Ackermann's theory of sets and classes founds Cantorian set-theory as well as category-theory, and therefore can pass as a founding theory of the whole of mathematics. (V) The extended theory does not suffer from the conceptual flaws of the extant set-theoretical founding theories. (VI) The extended theory is not only conceptually but also logically superior to the competing set-theories because its consistency can be proved on the basis of weaker assumptions than the consistency of the competition. (shrink)

Essay Review of two books of A.N. Maxwell, last of the Neo-Popperians: The Comprehensibility of the Universe (1998) and The Human World in the Physical Universe (2001).

Once Hilbert asserted that the axioms of a theory `define` theprimitive concepts of its language `implicitly''. Thus whensomeone inquires about the meaning of the set-concept, thestandard response reads that axiomatic set-theory defines itimplicitly and that is the end of it. But can we explainthis assertion in a manner that meets minimum standards ofphilosophical scrutiny? Is Jané (2001) wrong when hesays that implicit definability is ``an obscure notion''''? Doesan explanation of it presuppose any particular view on meaning?Is it not a scandal (...) of the philosophy of mathematics that no answersto these questions are around? We submit affirmative answers to allquestions. We argue that a Wittgensteinian conception of meaninglooms large beneath Hilbert''s conception of implicit definability.Within the specific framework of Horwich''s recent Wittgensteiniantheory of meaning called semantic deflationism, we explain anexplicit conception of implicit definability, and then go on toargue that, indeed, set-theory, defines the set-conceptimplicitly according to this conception. We also defend Horwich''sconception against a recent objection from the Neo-Fregeans Hale and Wright (2001). Further, we employ the philosophicalresources gathered to dissolve all traditional worries about thecoherence of the set-concept, raisedby Frege, Russell and Max Black, and whichrecently have been defended vigorously by Hallett (1984) in hismagisterial monograph Cantorian set-theory and limitationof size. Until this day, scandalously, these worries havebeen ignored too by philosophers of mathematics. (shrink)

The Special Composition Question asks under what conditions a plurality of objects form another, composite object. We propose a condition grounded in our scientific knowledge of physical reality, the essence of which is that objects form a composite object when and only when they are in a bound state – whence our Bound State Proposal. We provide a variety of reasons in favour of a mereological theory that accommodates our Proposal. We consider but reject another proposal, which is quantum-physical in (...) nature: the Entanglement Proposal. We close by responding to Teller’s ‘Suit Objection’. (shrink)

. Remarkably, despite the tremendous success of axiomatic set-theory in mathematics, logic and meta-mathematics, e.g., model-theory, two philosophical worries about axiomatic set-theory as the adequate catch of the set-concept keep haunting it. Having dealt with one worry in a previous paper in this journal, we now fulfil a promise made there, namely to deal with the second worry. The second worry is the Skolem Paradox and its ensuing Skolemite skepticism. We present a comparatively novel and simple analysis of the argument (...) of the Skolemite skeptic, which will reveal a general assumption concerning the meaning of the set-concept (we call it Connexion M). We argue that the Skolemite skeptics argument is a petitio principii and that consequently we find ourselves in a dialectical situation of stalemate.Few (if any) working set-theoreticians feel a tension – let alone see a paradox – between, on the one hand, what the Löwenheim–Skolem theorems and related results seem to be telling us about the set-concept, and, on the other hand, their uncompromising and successful use of the set-concept and their continuing enthusiasm about it, in other words: their lack of skepticism about the set-concept. Further, most (if not all) working settheoreticians have a relaxed attitude towards the ubiquitous undecidability phenomenon in set-theory, rather than a worrying one. We argue these are genuine philosophical problems about the practice of set-theory. We propound solutions, which crucially involve a renunciation of Connexion M. This breaks the dialectical situation of stalemate against the Skolemite skeptic. (shrink)

The general context of this paper is the locality problem in quantum theory. In a recent issue of this journal, Redei (1991) offered a proof of the proposition that algebraic Lorentz-covariant quantum field theory is past stochastic Einstein local. We show that Redei's proof is either spurious or circular, and that it contains two deductive fallacies. Furthermore, we prove that the mentioned theory meets the stronger condition of stochastic Haag locality.

We demonstrate that the quantum-mechanical description of composite physical systems of an arbitrary number of similar fermions in all their admissible states, mixed or pure, for all finite-dimensional Hilbert spaces, is not in conflict with Leibniz's Principle of the Identity of Indiscernibles (PII). We discern the fermions by means of physically meaningful, permutation-invariant categorical relations, i.e. relations independent of the quantum-mechanical probabilities. If, indeed, probabilistic relations are permitted as well, we argue that similar bosons can also be discerned in all (...) their admissible states; but their categorical discernibility turns out to be a state-dependent matter. In all demonstrated cases of discernibility, the fermions and the bosons are discerned (i) with only minimal assumptions on the interpretation of quantum mechanics; (ii) without appealing to metaphysical notions, such as Scotusian haecceitas, Lockean substrata, Postian transcendental individuality or Adamsian primitive thisness; and (iii) without revising the general framework of classical elementary predicate logic and standard set theory, thus without revising standard mathematics. This confutes: (a) the currently dominant view that, provided (i) and (ii), the quantum-mechanical description of such composite physical systems always conflicts with PII; and (b) that if PII can be saved at all, the only way to do it is by adopting one or other of the thick metaphysical notions mentioned above. Among the most general and influential arguments for the currently dominant view are those due to Schrodinger, Margenau, Cortes, Dalla Chiara, Di Francia, Redhead, French, Teller, Butterfield, Giuntini, Mittelstaedt, Castellani, Krause and Huggett. We review them succinctly and critically as well as related arguments by van Fraassen and Massimi. (shrink)

Essay Review of B.C. van Fraassen's *Scientific Representation: Paradoxes of Perspective* (2008).

In a recent issue of this journal, P.E. Vermaas ([2005]) claims to have demonstrated that standard quantum mechanics is technologically inadequate in that it violates the 'technical functions condition'. We argue that this claim is false because based on a 'narrow' interpretation of this technical functions condition that Vermaas can only accept on pain of contradiction. We also argue that if, in order to avoid this contradiction, the technical functions condition is interpreted 'widely' rather than 'narrowly', then Vermaas, argument for (...) his claim collapses. The conclusion is that Vermaas' claim that standard quantum mechanics is technologically inadequate evaporates. (shrink)

In this journal, Brogaard and Marlow recently argued that the relativity of simultaneity is an illusion. We claim their argument is fallacious.

In the context of discussions about the nature of ‘identical particles’ and the status of Leibniz’s Principle of the Identity of Indiscernibles in Quantum Mechanics, a novel kind of physical discernibility has recently been proposed, which we call witness-discernibility. We inquire into how witness-discernibility relates to known kinds of discernibility. Our conclusion will be that for a wide variety of cases, including the intended quantum-mechanical ones, witness-discernibility collapses extensionally to absolute discernibility, that is, to discernibility by properties.

In his influential After Finitude. An Essay on the Necessity of Contingency (2008), Quentin Meillassoux argues that *Correlationism* (an umbrella-term encompassing most varieties of Idealism) gives rise to an irresolvable paradox, called "the Paradox of the Arche-fossil", which is essentially a clash between philosophical principles and scientific findings. This irresolvable paradox of Correlationism then paves the way for the "Speculative Turn" and the ensuing rise of burgeoning "speculative realism" in Continental Philosophy: noumenal reality, as-it-is-in-and-of-itself, "the Great Outdoors", is back on (...) the Continental stage, open for speculative thought and even metaphysical knowledge. We attempt to provide a thorough and charitable analysis of the Paradox of the Arche-fossil. Our analyses lead us to conclude that Meillassoux's argument fails, due to an ambiguity with regard to the concept of being that cannot be repaired. We end by directing attention to another ominous threat to Correlationism, ignored by Meillassoux and all "speculative realists" alike, which is still breathing. (shrink)

We ponder the question whether quantum physics has had any influence on philosophy, and if not, whether it ought to have had any. Answers to these questions are provided, and they turn out to depend on which branch of the tree of philosophy we sweep, sway and swing, and even which twig of the branch we touch when we sweep, sway and swing.

A defence of constructive empiricism against an attack of N. Maxwell by means of his pet-thesis that science implicitly and permanently accepts a metaphysical thesis about the nature of the universe. We argue that Maxwell's attack can be beaten off; that his arguments do not establish what Maxwell believes they establish; and that we can draw a number of valuable lessons from these attacks about the nature of science and of the libertatian nature of constructive empiricism.

Amsterdam University Press is a leading publisher of academic books, journals and textbooks in the Humanities and Social Sciences. Our aim is to make current research available to scholars, students, innovators, and the general public. AUP stands for scholarly excellence, global presence, and engagement with the international academic community.

Amsterdam University Press is a leading publisher of academic books, journals and textbooks in the Humanities and Social Sciences. Our aim is to make current research available to scholars, students, innovators, and the general public. AUP stands for scholarly excellence, global presence, and engagement with the international academic community.

In this journal (Studia Logica), D. Rizza [2010: 176] expounded a solution of what he called “the indiscernibility problem for ante rem structuralism”, which is the problem to make sense of the presence, in structures, of objects that are indiscernible yet distinct, by only appealing to what that structure provides. We argue that Rizza’s solution is circular and expound a different solution that not only solves the problem for completely extensive structures, treated by Rizza, but for nearly (but not) all (...) mathematical structures. (shrink)

We discuss the case against Factorism, which is the standard assumption in quantum mechanics that the labels of the ⊗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\otimes$$\end{document}-factor Hilbert-spaces in direct-product Hilbert-spaces of composite physical systems of similar particles refer to particles, either directly or descriptively. We distinguish different versions of Factorism and argue for their truth or falsehood. In particular, by introducing the concepts of snapshot Hilbert-space and Schrödinger-movie, we demonstrate that there are Hilbert-spaces and ⊗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\otimes$$\end{document}-factorisations where the labels do refer, even descriptively, to similar particles, which renders them probabilistically absolutely discernible. (shrink)

Critique of set-theory as a founding theory of category-theory. Proposal of a theory of sets and classes as an adequate founding theory of mathematics and by implication of category-theory. This theory is a slight extension of Ackermann's theory of 1956.