Mark Steiner
(1942 - 2020)

  •  221
    Wittgenstein as his own worst enemy: The case of gödel's theorem
    Philosophia Mathematica 9 (3): 257-279. 2001.
    Remarks on the Foundations of Mathematics, Wittgenstein, despite his official 'mathematical nonrevisionism', slips into attempting to refute Gödel's theorem. Actually, Wittgenstein could have used Gödel's theorem to good effect, to support his view that proof, and even truth, are 'family resemblance' concepts. The reason that Wittgenstein did not see all this is that Gödel's theorem had become an icon of mathematical realism, and he was blinded by his own ideology. The essay is a reply to Juliet…Read more
  •  189
    The application of mathematics to natural science
    Journal of Philosophy 86 (9): 449-480. 1989.
    The first part of the essay describes how mathematics, in particular mathematical concepts, are applicable to nature. mathematical constructs have turned out to correspond to physical reality. this correlation between the world and mathematical concepts, it is argued, is a true phenomenon. the second part of this essay argues that the applicability of mathematics to nature is mysterious, in that not only is there no known explanation for the correlation between mathematics and physical reality, …Read more
  •  145
    The applicabilities of mathematics
    Philosophia Mathematica 3 (2): 129-156. 1995.
    Discussions of the applicability of mathematics in the natural sciences have been flawed by failure to realize that there are multiple senses in which mathematics can be ‘applied’ and, correspondingly, multiple problems that stem from the applicability of mathematics. I discuss semantic, metaphysical, descriptive, and and epistemological problems of mathematical applicability, dwelling on Frege's contribution to the solution of the first two types. As for the remaining problems, I discuss the co…Read more
  •  135
    Empirical regularities in Wittgenstein's philosophy of mathematics
    Philosophia Mathematica 17 (1): 1-34. 2009.
    During the course of about ten years, Wittgenstein revised some of his most basic views in philosophy of mathematics, for example that a mathematical theorem can have only one proof. This essay argues that these changes are rooted in his growing belief that mathematical theorems are ‘internally’ connected to their canonical applications, i.e. , that mathematical theorems are ‘hardened’ empirical regularities, upon which the former are supervenient. The central role Wittgenstein increasingly assi…Read more
  •  85
    This book analyzes the different ways mathematics is applicable in the physical sciences, and presents a startling thesis--the success of mathematical physics ...
  •  70
    In lieu of an abstract, here is a brief excerpt of the content:400 KANT'S MISREPRESENTATIONS OF HUME'S PHILOSOPHY OF MATHEMATICS IN THE PROLEGOMENA In 1783, Immanuel Kant published the following reflections upon the philosophy of mathematics of David Hume, words which have colored all subsequent interpretations of the letter's work: Hume being prompted to cast his eye over the whole field of a priori cognitions in which human understanding claims such mighty possessions (a calling he felt worthy…Read more
  •  55
    Events and causality
    Journal of Philosophy 83 (5): 249-264. 1986.
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    Mathematical realism
    Noûs 17 (3): 363-385. 1983.
  •  49
    Mathematics as a science of patterns (review)
    Philosophical Review 109 (1): 115-118. 2000.
    For the past hundred years, mathematics, for its own reasons, has been shifting away from the study of “mathematical objects” and towards the study of “structures”. One would have expected philosophers to jump onto the bandwagon, as in many other cases, to proclaim that this shift is no accident, since mathematics is “essentially” about structures, not objects. In fact, structuralism has not been a very popular philosophy of mathematics, probably because of the hostility of Frege and other influ…Read more
  •  40
    320 index
    with Aw Moore, John Allen Paulos, Ad Irvine, Brian Rotman, and Neil Tennant
    Philosophical Papers 1896 (99)
  •  38
    Ontology and the Vicious Circle Principle (review)
    Journal of Philosophy 72 (7): 184-196. 1975.
  •  35
    Review of Mark Steiner: The Applicability of Mathematics as a Philosophical Problem (review)
    British Journal for the Philosophy of Science 52 (1): 181-184. 2001.
  •  19
    Penrose and platonism
    In Emily Grosholz & Herbert Breger (eds.), The growth of mathematical knowledge, Kluwer Academic Publishers. pp. 133--141. 2000.
  •  16
    Events and Causality
    Journal of Philosophy 83 (5): 249. 1986.
  •  15
    Review: Michael Detlefsen, Proof, Logic and Formalization (review)
    Journal of Symbolic Logic 58 (4): 1459-1462. 1993.
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    Author’s response
    Metascience 10 (1): 32-38. 2001.
  •  13
    Wittgenstein on the Foundations of Mathematics (review)
    Journal of Symbolic Logic 49 (4): 1415-1417. 1980.