•  167
    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
  •  138
    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
  •  65
    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).
  •  184
    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
  •  88
    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
  • Book review (review)
    Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (4): 713-720. 2004.
  •  101
    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
  •  761
    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
  •  79
    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.
  •  470
    Withering away, weakly
    Synthese 180 (2). 2011.
    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 est…Read more
  •  25
    Cantor-Von Neumann Set-Theory
    Logique Et Analyse 54 (213). 2011.
    On the pdf
  •  65
    Essay Review of B.C. van Fraassen's *Scientific Representation: Paradoxes of Perspective* (2008).
  •  32
    The characterisation of structure: Definition versus axiomatisation
    In F. Stadler, D. Dieks, W. Gonzales, S. Hartmann, T. Uebel & M. Weber (eds.), The Present Situation in the Philosophy of Science, Springer. pp. 399--416. 2010.
  •  14
    Dikaiologische Verkenningen
    Algemeen Nederlands Tijdschrift voor Wijsbegeerte 107 (2): 185-191. 2015.
  •  109
    In this journal, Brogaard and Marlow recently argued that the relativity of simultaneity is an illusion. We claim their argument is fallacious.
  •  228
    Can a constructive empiricist adopt the concept of observability?
    Philosophy of Science 71 (1): 80-97. 2004.
    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 i…Read more
  •  41
    The Equivalence Myth of Quntum Mechanics (Addendum)
    Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 30 (4): 543-545. 1999.
  •  17
    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
  •  124
    Inconsistency in classical electrodynamics?
    Philosophy of Science 74 (2): 253-277. 2007.
    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 misleadin…Read more