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  1. Philosophies of Mathematics.Alexander George & Daniel J. Velleman - 2004 - Philosophical Quarterly 54 (214):194-196.
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  2.  8
    Morasses, diamond, and forcing.Daniel J. Velleman - 1982 - Annals of Mathematical Logic 23 (2):199.
  3.  55
    How to prove it: a structured approach.Daniel J. Velleman - 1994 - Cambridge ; New York: Cambridge University Press.
    Geared to preparing students to make the transition from solving problems to proving theorems, this text teachs them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition (...)
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  4.  48
    Constructivism liberalized.Daniel J. Velleman - 1993 - Philosophical Review 102 (1):59-84.
  5.  83
    Two conceptions of natural number.Alexander George & Daniel J. Velleman - 1998 - In Harold Garth Dales & Gianluigi Oliveri (eds.), Truth in mathematics. New York: Oxford University Press, Usa. pp. 311.
  6.  38
    The mean value theorem in second order arithmetic.Christopher S. Hardin & Daniel J. Velleman - 2001 - Journal of Symbolic Logic 66 (3):1353-1358.
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  7.  54
    Leveling the playing field between mind and machine: A reply to McCall.Alexander George & Daniel J. Velleman - 2000 - Journal of Philosophy 97 (8):456-452.
  8.  20
    Leveling the Playing Field between Mind and Machine: A Reply to McCall.Alexander George & Daniel J. Velleman - 2000 - Journal of Philosophy 97 (8):456.
  9.  10
    Zur Philosophie der Mathematik: Logizismus, Intuitionismus, Finitismus, Gödel'sche Unvollständigkeitssätze.Alexander George & Daniel J. Velleman - 2018 - Springer Berlin Heidelberg.
    Dieses Buch blickt in eine bedeutende Epoche der Philosophie der Mathematik zurück, deren Strömungen die heutige Gestalt der Mathematik prägten. In der Wende vom 19. zum 20. Jahrhundert befand sich die Mathematik in einem fundamentalen Umbruch, der die Mathematiker dieser Zeit herausforderte. Sie mussten Stellung beziehen. Die Grundsätze und Wege der philosophischen Richtungen, die dieses Buch verständlich, kritisch und anerkennend beschreibt, wurden von Mathematikern formuliert. Eine Zeit gravierender Disharmonien begann, die bis in Streit und Feindschaften mündeten und zugleich faszinierende und (...)
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    Variable declarations in natural deduction.Daniel J. Velleman - 2006 - Annals of Pure and Applied Logic 144 (1-3):133-146.
    We propose the use of variable declarations in natural deduction. A variable declaration is a line in a derivation that introduces a new variable into the derivation. Semantically, it can be regarded as declaring that the variable denotes an element of the universe of discourse. Undeclared variables, in contrast, do not denote anything, and may not occur free in any formula in the derivation. Although most natural deduction systems in use today do not have variable declarations, the idea can be (...)
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    Review of Levin's ”Putnam on reference and constructible sets' (1997). [REVIEW]Daniel J. Velleman - 1998 - MATHEMATICAL REVIEWS 98:1364.
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