
433Inference to the best explanation and mathematical realismSynthese 160 (1): 1320. 2008.Arguing for mathematical realism on the basis of Field’s explanationist version of the Quine–Putnam Indispensability argument, Alan Baker has recently claimed to have found an instance of a genuine mathematical explanation of a physical phenomenon. While I agree that Baker presents a very interesting example in which mathematics plays an essential explanatory role, I show that this example, and the argument built upon it, begs the question against the mathematical nominalist

228Indispensability and ExplanationBritish Journal for the Philosophy of Science 64 (2): 255277. 2013.The question as to whether there are mathematical explanations of physical phenomena has recently received a great deal of attention in the literature. The answer is potentially relevant for the ontology of mathematics; if affirmative, it would support a new version of the indispensability argument for mathematical realism. In this article, I first review critically a few examples of such explanations and advance a general analysis of the desiderata to be satisfied by them. Second, in an attempt…Read more

202Reifying mathematics? Prediction and symmetry classificationStudies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (2): 239258. 2008.In this paper I reconstruct and critically examine the reasoning leading to the famous prediction of the ‘omega minus’ particle by M. GellMann and Y. Ne’eman (in 1962) on the basis of a symmetry classification scheme. While the peculiarity of this prediction has occasionally been noticed in the literature, a detailed treatment of the methodological problems it poses has not been offered yet. By spelling out the characteristics of this type of prediction, I aim to underscore the challenges raise…Read more

157On Bertrand's paradoxAnalysis 70 (1): 3035. 2010.The Principle of Indifference is a central element of the ‘classical’ conception of probability, but, for all its strong intuitive appeal, it is widely believed that it faces a devastating objection: the socalled (by Poincare´) ‘Bertrand paradoxes’ (in essence, cases in which the same probability question receives different answers). The puzzle has fascinated many since its discovery, and a series of clever solutions (followed promptly by equally clever rebuttals) have been proposed. However, d…Read more

145Understanding thermodynamic singularities: Phase transitions, data, and phenomenaPhilosophy of Science 76 (4): 488505. 2009.According to standard (quantum) statistical mechanics, the phenomenon of a phase transition, as described in classical thermodynamics, cannot be derived unless one assumes that the system under study is infinite. This is naturally puzzling since real systems are composed of a finite number of particles; consequently, a well‐known reaction to this problem was to urge that the thermodynamic definition of phase transitions (in terms of singularities) should not be “taken seriously.” This article ta…Read more

104Scientific explanation and understanding: unificationism reconsideredEuropean Journal for Philosophy of Science 7 (1): 103126. 2017.The articulation of an overarching account of scientific explanation has long been a central preoccupation for the philosophers of science. Although a while ago the literature was dominated by two approaches—a causal account and a unificationist account—today the consensus seems to be that the causal account has won. In this paper, I challenge this consensus and attempt to revive unificationism. More specifically, I aim to accomplish three goals. First, I add new criticisms to the standard anti…Read more

87Underdetermination and the argument from indirect confirmationRatio 19 (3). 2006.In this paper I criticize one of the most convincing recent attempts to resist the underdetermination thesis, Laudan’s argument from indirect confirmation. Laudan highlights and rejects a tacit assumption of the underdetermination theorist, namely that theories can be confirmed only by empirical evidence that follows from them. He shows that once we accept that theories can also be confirmed indirectly, by evidence not entailed by them, the skeptical conclusion does not follow. I agree that Laud…Read more

87Critical notice of C. Pincock's Mathematics and Scientific Representation (2012).

80Pythagorean heuristic in physicsPerspectives on Science 14 (4): 387416. 2006.: Some of the great physicists' belief in the existence of a connection between the aesthetical features of a theory (such as beauty and simplicity) and its truth is still one of the most intriguing issues in the aesthetics of science. In this paper I explore the philosophical credibility of a version of this thesis, focusing on the connection between the mathematical beauty and simplicity of a theory and its truth. I discuss a heuristic interpretation of this thesis, attempting to clarify where…Read more

80Steiner on the Applicability of Mathematics and NaturalismPhilosophia Mathematica 14 (1): 2643. 2006.Steiner defines naturalism in opposition to anthropocentrism, the doctrine that the human mind holds a privileged place in the universe. He assumes the anthropocentric nature of mathematics and argues that physicists' employment of mathematically guided strategies in the discovery of quantum mechanics challenges scientists' naturalism. In this paper I show that Steiner's assumption about the anthropocentric character of mathematics is questionable. I draw attention to mathematicians' rejection o…Read more

62Popper: yet again: Darrell P. Rowbottom: Popper’s critical rationalism: A philosophical investigation. New York and London: Routledge, 2010, xii+177pp, $133 HB (review)Metascience 22 (1): 165168. 2013.Popper: yet again Content Type Journal Article Category Book Review Pages 14 DOI 10.1007/s110160129669y Authors Sorin Bangu, Department of Philosophy, University of Illinois, Urbana, IL 61801, USA Journal Metascience Online ISSN 14679981 Print ISSN 08150796.

62Hard and Blind: On Wittgenstein’s Genealogical View of Logical NecessityPhilosophy and Phenomenological Research 102 (2): 439458. 2021.My main aim is to sketch a certain reading (‘genealogical’) of later Wittgenstein’s views on logical necessity. Along the way, I engage with the inferentialism currently debated in the literature on the epistemology of deductive logic.

60Wigner’s Puzzle for Mathematical NaturalismInternational Studies in the Philosophy of Science 23 (3): 245263. 2009.I argue that a recent version of the doctrine of mathematical naturalism faces difficulties arising in connection with Wigner's old puzzle about the applicability of mathematics to natural science. I discuss the strategies to solve the puzzle and I show that they may not be available to the naturalist.

55On the Role of Bridge Laws in Intertheoretic RelationsPhilosophy of Science 78 (5): 11081119. 2011.What is the role of bridge laws in intertheoretic relations? An assumption shared by many views about these relations is that bridge laws enable reductions. In this article, I acknowledge the naturalness of this assumption, but I question it by presenting a context within thermal physics (involving phase transitions) in which the bridge laws, puzzlingly, seem to contribute to blocking the reduction.

28Numerical Methods, Complexity, and Epistemic HierarchiesPhilosophy of Science 82 (5): 941955. 2015.Modern mathematical sciences are hard to imagine without appeal to efficient computational algorithms. We address several conceptual problems arising from this interaction by outlining rival but complementary perspectives on mathematical tractability. More specifically, we articulate three alternative characterizations of the complexity hierarchy of mathematical problems that are themselves based on different understandings of computational constraints. These distinctions resolve the tension bet…Read more

27Indispensability, causation and explanationTheoria : An International Journal for Theory, History and Fundations of Science 33 (2): 219232. 2018.When considering mathematical realism, some scientific realists reject it, and express sympathy for the opposite view, mathematical nominalism; moreover, many justify this option by invoking the causal inertness of mathematical objects. The main aim of this note is to show that the scientific realists’ endorsement of this causal mathematical nominalism is in tension with another position some of them also accept, the doctrine of methodological naturalism. By highlighting this conflict, I intend …Read more

27The ‘Miracle’ of Applicability? The Curious Case of the Simple Harmonic OscillatorFoundations of Physics 48 (5): 507525. 2018.The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner’s famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in…Read more

26Mathematical Explanations of Physical PhenomenaTandf: Australasian Journal of Philosophy 114. forthcoming.Can there be mathematical explanations of physical phenomena? In this paper, I suggest an affirmative answer to this question. I outline a strategy to reconstruct several typical examples of such explanations, and I show that they fit a common model. The model reveals that the role of mathematics is explicatory. Isolating this role may help to refocus the current debate on the more specific question as to whether this explicatory role is, as proposed here, also an explanatory one.

21Discontinuities and singularities, data and phenomena: for ReferentialismSynthese 196 (5): 19191937. 2019.The paper rebuts a currently popular criticism against a certain take on the referential role of discontinuities and singularities in the physics of firstorder phase transitions. It also elaborates on a proposal I made previously on how to understand this role within the framework provided by the distinction between data and phenomena.

16Later Wittgenstein's Philosophy of MathematicsIn J. Feiser & B. Dowden (eds.), Internet Encyclopedia of Philosophy, . 2012.An opinionated survey of the main topics in later Wittgenstein's philosophy of mathematics.

14Is Understanding Factive?Balkan Journal of Philosophy 9 (1): 3544. 2017.Factivism is the view that understanding why a natural phenomenon takes place must rest exclusively on truths. One of the arguments for nonfactivism—the opposite view, that falsehoods can play principal roles in producing understanding—relies on our inclination to say that past, false, now superseded but still important scientific theories do provide understanding. In this paper, my aim is to articulate what I take to be an interesting point that has yet to be discussed: the natural way in which…Read more

12Book review of Emily Grosholz's Representation and Productive Ambiguity in Mathematics and the Sciences (2007)

12Representation and Productive Ambiguity in Mathematics and the Sciences (review)Isis 100 137139. 2009.

6On The Unreasonable Effectiveness of Mathematics in the Natural SciencesIn Emiliano Ippoliti, Fabio Sterpetti & Thomas Nickles (eds.), Models and Inferences in Science, Springer. pp. 1129. 2016.I present a reconstruction of Eugene Wigner’s argument for the claim that mathematics is ‘unreasonable effective’, together with six objections to its soundness. I show that these objections are weaker than usually thought, and I sketch a new objection.

4The Applicability of Mathematics in Science: Indispensability and OntologyPalgraveMacmillan. 2012.Suppose we are asked to draw up a list of things we take to exist. Certain items seem unproblematic choices, while others (such as God) are likely to spark controversy. The book sets the grand theological theme aside and asks a less dramatic question: should mathematical objects (numbers, sets, functions, etc.) be on this list? In philosophical jargon this is the ‘ontological’ question for mathematics; it asks whether we ought to include mathematicalia in our ontology. The goal of this work is t…Read more

3SymmetryIn Batterman (ed.), The Oxford Handbook of Philosophy of Physics, Oxford Univ Press. 2013.A survey of the main themes and arguments concerning symmetry and invariance in physics and philosophy of physics.

2Later Wittgenstein on the Logicist Definition of NumberIn Sorin Costreie (ed.), Early Analytic Philosophy – New Perspectives on the Tradition, Springer Verlag. pp. 233257. 2016.The paper focuses on the lectures on the philosophy of mathematics delivered by Wittgenstein in Cambridge in 1939. Only a relatively small number of lectures are discussed, the emphasis falling on understanding Wittgenstein’s views on the most important element of the logicist legacy of Frege and Russell, the definition of number in terms of classes—and, more specifically, by employing the notion of onetoone correspondence. Since it is clear that Wittgenstein was not satisfied with this defini…Read more

2Naturalizing LogicoMathematical Knowledge: Approaches From Psychology and Cognitive Science (edited book)Routledge. 2018.This book is meant as a part of the larger contemporary philosophical project of naturalizing logicomathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logicomathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato’s dialogues, and virtually all major philosophers have expressed interest in it. The …Read more

2Later Wittgenstein On Essentialism, Family Resemblance And Philosophical MethodMetaphysica 6 (2): 5373. 2005.In this paper I have two objectives. First, I attempt to call attention to the incoherence of the widely accepted antiessentialist interpretation of Wittgenstein’s family resemblance point. Second, I claim that the family resemblance idea is not meant to reject essentialism, but to render this doctrine irrelevant, by dissipating its philosophical force. I argue that the role of the family resemblance point in later Wittgenstein’s views can be better understood in light of the provocative aim o…Read more
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