Utrecht University
Department for Philosophy and Religious Studies
PhD, 1998
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##### The Influence of Quantum Physics on Philosophy Foundations of Science 1-12. forthcoming.
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.
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##### The Case Against Factorism: On the Labels of $$otimes$$ ⊗ -Factor Hilbert-Spaces of Similar Particles in Quantum Mechanics with Gijs Leegwater Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 1-16. forthcoming.
We discuss the case against Factorism, which is the standard assumption in quantum mechanics that the labels of the \-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-space…Read more
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##### On Witness-Discernibility of Elementary Particles with Oystein Linnebo Erkenntnis 78 (5): 1133-1142. 2013.
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 exten…Read more
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##### Bound states and the Special Composition Question with McKenzie Kerry In Michela Massimi, Jan-Willem Romeijn & Gerhard Schurz (eds.), EPSA15 Selected Papers: The 5th conference of the European Philosophy of Science Association in Düsseldorf, . forthcoming.
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-physic…Read more
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##### In Defence of Constructive Empiricism: Maxwell’s Master Argument and Aberrant Theories Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 39 (1): 131-156. 2008.
Over the past years, in books and journals , N. Maxwell launched a ferocious attack on B. C. van Fraassen's view of science called Constructive Empiricism . 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 a…Read more
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##### Refutability revamped: How quantum mechanics saves the phenomena Erkenntnis 58 (2). 2003.
On the basis of the Suppes–Sneed structuralview of scientific theories, we take a freshlook at the concept of refutability,which was famously proposed by K.R. Popper in 1934 as a criterion for the demarcation of scientific theories from non-scientific ones, e.g., pseudo-scientificand metaphysical theories. By way of an introduction we argue that a clash between Popper and his critics on whether scientific theories are, in fact, refutablecan be partly explained by the fact Popper and his criticsa…Read more
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##### Sets, classes, and categories (review) Bulletin of Symbolic Logic 9 (1): 43-43. 2001.
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.
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##### Is Standard Quantum Mechanics Technologically Inadequate? with M. P. Seevinck British Journal for the Philosophy of Science 58 (3): 595-604. 2007.
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 …Read more
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##### Discerning elementary particles with M. P. Seevinck Philosophy of Science 76 (2): 179-200. 2009.
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 haecceit…Read more
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##### The equivalence myth of quantum mechanics —Part I Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 28 (1): 35-61. 1997.
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 or…Read more
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No Abstract
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##### Circular Discernment in Completely Extensive Structures and How to Avoid such Circles Generally Studia Logica 100 (5): 947-952. 2012.
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 (bu…Read more
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##### The implicit definition of the set-concept Synthese 138 (3). 2004.
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…Read more
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##### Sets, classes, and categories British Journal for the Philosophy of Science 52 (3): 539-573. 2001.
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) Th…Read more
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##### Maxwell’s Lonely War Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (1): 109-119. 2004.
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).
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##### Deflating skolem Synthese 143 (3): 223-253. 2005.
.  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 s…Read more
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##### The Rise of Relationals Mind 124 (493): 201-237. 2015.
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 al…Read more
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##### The equivalence myth of quantum mechanics—part II Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 28 (2): 219-247. 1997.
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 or…Read more
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##### Reflections on the revolution at Stanford Synthese 183 (1): 87-114. 2011.
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 refl…Read more
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##### In defence of constructive empiricism: Metaphpysics versus science
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.