•  2
    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 one-to-one correspondence. Since it is clear that Wittgenstein was not satisfied with this defini…Read more
  •  26
    Mathematical Explanations of Physical Phenomena
    Tandf: Australasian Journal of Philosophy 1-14. 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 re-focus the current debate on the more specific question as to whether this explicatory role is, as proposed here, also an explanatory one.
  •  60
    Hard and Blind: On Wittgenstein’s Genealogical View of Logical Necessity
    Philosophy and Phenomenological Research 102 (2): 439-458. 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.
  •  27
    Indispensability, causation and explanation
    Theoria : An International Journal for Theory, History and Fundations of Science 33 (2): 219-232. 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
  •  433
    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
  •  27
    The ‘Miracle’ of Applicability? The Curious Case of the Simple Harmonic Oscillator
    with Robert H. C. Moir
    Foundations of Physics 48 (5): 507-525. 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
  •  14
    Is Understanding Factive?
    Balkan Journal of Philosophy 9 (1): 35-44. 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
  •  20
    The paper rebuts a currently popular criticism against a certain take on the referential role of discontinuities and singularities in the physics of first-order 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.
  •  2
    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
  •  80
    Pythagorean heuristic in physics
    Perspectives on Science 14 (4): 387-416. 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
  •  12
    Book review of Emily Grosholz's Representation and Productive Ambiguity in Mathematics and the Sciences (2007)
  •  1
    This paper explores the connections between K. Wynn's well-known experiments in cognitive psychology and later Wittgenstein's views on the philosophy of mathematics.
  •  103
    Scientific explanation and understanding: unificationism reconsidered
    European Journal for Philosophy of Science 7 (1): 103-126. 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
  •  2
    This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical 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
  •  3
    Symmetry
    In 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.
  •  62
    Popper: yet again Content Type Journal Article Category Book Review Pages 1-4 DOI 10.1007/s11016-012-9669-y Authors Sorin Bangu, Department of Philosophy, University of Illinois, Urbana, IL 61801, USA Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
  •  226
    Indispensability and Explanation
    British Journal for the Philosophy of Science 64 (2): 255-277. 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
  •  60
    Wigner’s Puzzle for Mathematical Naturalism
    International Studies in the Philosophy of Science 23 (3): 245-263. 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.
  •  80
    Steiner on the Applicability of Mathematics and Naturalism
    Philosophia Mathematica 14 (1): 26-43. 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
  •  157
    On Bertrand's paradox
    Analysis 70 (1): 30-35. 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 so-called (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
  •  1
    The paper discuses whether the mathematical singularities characterizing first-order phase transitions are 'fictions'.
  •  87
    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
  •  2
    In this paper I have two objectives. First, I attempt to call attention to the incoherence of the widely accepted anti-essentialist 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
  •  2
    The paper argues that the phenomenon of first-order phase transitions (e.g., freezing) has features that make it a candidate to be classified as 'emergent'. However, it cannot be described either as 'weakly emergent' or 'strongly emergent'; hence it escapes categorization in terms employed in the current literature on the metaphysics of science.
  •  28
    Numerical Methods, Complexity, and Epistemic Hierarchies
    with Nicolas Fillion
    Philosophy of Science 82 (5): 941-955. 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
  • Scientific Progress, Understanding and Unification
    In Iulian D. Toader, Gabriel Sandu & Ilie Pȃrvu (eds.), Romanian Studies in Philosophy of Science, Springer Verlag. 2015.
    The paper argues that scientific progress is best characterized as an increase in scientists' understanding of the world. It also connects this idea with the claim that scientific understanding and explanation are captured in terms of unification.
  •  54
    On the Role of Bridge Laws in Intertheoretic Relations
    Philosophy of Science 78 (5): 1108-1119. 2011.
    What is the role of bridge laws in inter-theoretic 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.