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What are groups?

Philosophical Studies 166 (2):257-272 (2013)

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  1. Four Dimensionalism: An Ontology of Persistence and Time.Theodore Sider - 2001 - Oxford University Press.
    Four- Dimensionalism defends the thesis that the material world is composed of temporal as well as spatial parts. This defense includes a novel account of persistence over time, new arguments in favour of the four-dimensional ontology, and responses to the challenges four- dimensionalism faces." "Theodore Sider pays particular attention to the philosophy of time, including a strong series of arguments against presentism, the thesis that only the present is real. Arguments offered in favour of four- dimensionalism include novel arguments based (...)
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  • Mathematics Without Numbers: Towards a Modal-Structural Interpretation.Geoffrey Hellman - 1989 - Oxford University Press.
    Develops a structuralist understanding of mathematics, as an alternative to set- or type-theoretic foundations, that respects classical mathematical truth while ...
  • Mathematics as a Science of Patterns.Michael D. Resnik - 1997 - New York ;Oxford University Press.
    This book expounds a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defense of realism about the metaphysics of mathematics--the view that mathematics (...)
  • Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford University Press.
    Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic (...)
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  • Mathematics Without Foundations.Hilary Putnam - 1967 - Journal of Philosophy 64 (1):5-22.
  • Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
  • The Metaphysics of Groups.Nikk Effingham - 2010 - Philosophical Studies 149 (2):251-267.
    If you are a realist about groups there are three main theories of what to identify groups with. I offer reasons for thinking that two of those theories fail to meet important desiderata. The third option is to identify groups with sets, which meets all of the desiderata if only we take care over which sets they are identified with. I then canvass some possible objections to that third theory, and explain how to avoid them.
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  • The Principles of Mathematics.Bertrand Russell - 1903 - Allen & Unwin.
    Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...)
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  • On Being in the Same Place at the Same Time.David Wiggins - 1968 - Philosophical Review 77 (1):90-95.
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  • A Theory of Aggregates.Tyler Burge - 1977 - Noûs 11 (2):97-117.
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  • Things and Their Parts.Kit Fine - 1999 - Midwest Studies in Philosophy 23 (1):61-74.
  • The Supreme Court and the Supreme Court Justices: A Metaphysical Puzzle.Gabriel Uzquiano - 2004 - Noûs 38 (1):135–153.
  • To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables).George Boolos - 1984 - Journal of Philosophy 81 (8):430-449.