69 found
Order:
  1. Dedekind’s Analysis of Number: Systems and Axioms.Wilfried Sieg & Dirk Schlimm - 2005 - Synthese 147 (1):121-170.
    Wilfred Sieg and Dirk Schlimm. Dedekind's Analysis of Number: Systems and Axioms.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   20 citations  
  2. Hilbert's Programs: 1917–1922.Wilfried Sieg - 1999 - Bulletin of Symbolic Logic 5 (1):1-44.
    Hilbert's finitist program was not created at the beginning of the twenties solely to counteract Brouwer's intuitionism, but rather emerged out of broad philosophical reflections on the foundations of mathematics and out of detailed logical work; that is evident from notes of lecture courses that were given by Hilbert and prepared in collaboration with Bernays during the period from 1917 to 1922. These notes reveal a dialectic progression from a critical logicism through a radical constructivism toward finitism; the progression has (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   25 citations  
  3.  9
    Natural Formalization: Deriving the Cantor-Bernstein Theorem in Zf.Wilfried Sieg & Patrick Walsh - forthcoming - Review of Symbolic Logic:1-44.
    Natural Formalization proposes a concrete way of expanding proof theory from the meta-mathematical investigation of formal theories to an examination of “the concept of the specifically mathematical proof.” Formal proofs play a role for this examination in as much as they reflect the essential structure and systematic construction of mathematical proofs. We emphasize three crucial features of our formal inference mechanism: (1) the underlying logical calculus is built for reasoning with gaps and for providing strategic directions, (2) the mathematical frame (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  4.  34
    Fragments of Arithmetic.Wilfried Sieg - 1983 - Annals of Pure and Applied Logic 28 (1):33-71.
    We establish by elementary proof-theoretic means the conservativeness of two subsystems of analysis over primitive recursive arithmetic. The one subsystem was introduced by Friedman [6], the other is a strengthened version of a theory of Minc [14]; each has been shown to be of considerable interest for both mathematical practice and metamathematical investigations. The foundational significance of such conservation results is clear: they provide a direct finitist justification of the part of mathematical practice formalizable in these subsystems. The results are (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   46 citations  
  5.  70
    Mechanical Procedures and Mathematical Experience.Wilfried Sieg - 1994 - In Alexander George (ed.), Mathematics and Mind. Oxford University Press. pp. 71--117.
    Wilfred Sieg. Mechanical Procedures and Mathematical Experience.
    No categories
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   30 citations  
  6.  38
    Church Without Dogma: Axioms for Computability.Wilfried Sieg - unknown
    Church's and Turing's theses dogmatically assert that an informal notion of effective calculability is adequately captured by a particular mathematical concept of computability. I present an analysis of calculability that is embedded in a rich historical and philosophical context, leads to precise concepts, but dispenses with theses. To investigate effective calculability is to analyze symbolic processes that can in principle be carried out by calculators. This is a philosophical lesson we owe to Turing. Drawing on that lesson and recasting work (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  7.  47
    Step by Recursive Step: Church's Analysis of Effective Calculability.Wilfried Sieg - 1997 - Bulletin of Symbolic Logic 3 (2):154-180.
    Alonzo Church's mathematical work on computability and undecidability is well-known indeed, and we seem to have an excellent understanding of the context in which it arose. The approach Church took to the underlying conceptual issues, by contrast, is less well understood. Why, for example, was "Church's Thesis" put forward publicly only in April 1935, when it had been formulated already in February/March 1934? Why did Church choose to formulate it then in terms of Gödel's general recursiveness, not his own λ (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   18 citations  
  8.  39
    The Ways of Hilbert's Axiomatics: Structural and Formal.Wilfried Sieg - 2014 - Perspectives on Science 22 (1):133-157.
    Hilbert gave lectures on the foundations of mathematics throughout his career. Notes for many of them have been preserved and are treasures of information; they allow us to reconstruct the path from Hilbert's logicist position, deeply influenced by Dedekind and presented in lectures starting around 1890, to the program of finitist proof theory in the early 1920s. The development toward proof theory begins, in some sense, in 1917 when Hilbert gave his talk Axiomatisches Denken in Zürich. This talk is rooted (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  9. An Abstract Model For Parallel Computations: Gandy’s Thesis.Wilfried Sieg & John Byrnes - 1999 - The Monist 82 (1):150-164.
    Wilfried Sieg and John Byrnes. AnModel for Parallel Computation: Gandy's Thesis.
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  10. Only Two Letters: The Correspondence Between Herbrand and Gödel.Wilfried Sieg - 2005 - Bulletin of Symbolic Logic 11 (2):172-184.
    Two young logicians, whose work had a dramatic impact on the direction of logic, exchanged two letters in early 1931. Jacques Herbrand initiated the correspondence on 7 April and Kurt Gödel responded on 25 July, just two days before Herbrand died in a mountaineering accident at La Bérarde (Isère). Herbrand's letter played a significant role in the development of computability theory. Gödel asserted in his 1934 Princeton Lectures and on later occasions that it suggested to him a crucial part of (...)
    Direct download (14 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  11.  26
    Hilbert's Programs and Beyond.Wilfried Sieg - 2013 - Oup Usa.
    David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations.
    Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  12.  21
    Calculations by Man and Machine: Conceptual Analysis.Wilfried Sieg - unknown
    Wilfried Sieg. Calculations by Man and Machine: Conceptual Analysis.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  13.  20
    Herbrand Analyses.Wilfried Sieg - 1991 - Archive for Mathematical Logic 30 (5-6):409-441.
    Herbrand's Theorem, in the form of $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\exists } $$ -inversion lemmata for finitary and infinitary sequent calculi, is the crucial tool for the determination of the provably total function(al)s of a variety of theories. The theories are (second order extensions of) fragments of classical arithmetic; the classes of provably total functions include the elements of the Polynomial Hierarchy, the Grzegorczyk Hierarchy, and the extended Grzegorczyk Hierarchy $\mathfrak{E}^\alpha $ , α < ε0. A subsidiary aim of the paper is to show (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   17 citations  
  14.  58
    Dedekind's Abstract Concepts: Models and Mappings.Wilfried Sieg & Dirk Schlimm - 2014 - Philosophia Mathematica:nku021.
    Dedekind's mathematical work is integral to the transformation of mathematics in the nineteenth century and crucial for the emergence of structuralist mathematics in the twentieth century. We investigate the essential components of what Emmy Noether called, his ‘axiomatic standpoint’: abstract concepts, models, and mappings.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  15. Relative Consistency and Accessible Domains.Wilfried Sieg - 1990 - Synthese 84 (2):259 - 297.
    Wilfred Sieg. Relative Consistency and Accesible Domains.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  16.  65
    Hilbert's Program Sixty Years Later.Wilfried Sieg - 1988 - Journal of Symbolic Logic 53 (2):338-348.
  17.  33
    Searching for Proofs.Wilfried Sieg & Richard Scheines - unknown
    The Carnegie Mellon Proof Tutor project was motivated by pedagogical concerns: we wanted to use a "mechanical" (i.e. computerized) tutor for teaching students..
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  18.  7
    The AProS Project: Strategic Thinking & Computational Logic.Wilfried Sieg - 2007 - Logic Journal of the IGPL 15 (4):359-368.
    The paper discusses tools for teaching logic used in Logic & Proofs, a web-based introduction to modern logic that has been taken by more than 1,300 students since the fall of 2003. The tools include a wide array of interactive learning environments or cognitive mini-tutors; most important among them is the Carnegie Proof Lab. The Proof Lab is a sophisticated interface for constructing natural deduction proofs and is central, as strategically guided discovery of proofs is the distinctive focus of the (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  19.  46
    K-Graph Machines: Generalizing Turing's Machines and Arguments.Wilfried Sieg & John Byrnes - unknown
    Wilfred Sieg and John Byrnes. K-Graph Machines: Generalizing Turing's Machines and Arguments.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  20.  67
    Normal Natural Deduction Proofs (in Classical Logic).Wilfried Sieg & John Byrnes - 1998 - Studia Logica 60 (1):67-106.
    Natural deduction (for short: nd-) calculi have not been used systematically as a basis for automated theorem proving in classical logic. To remove objective obstacles to their use we describe (1) a method that allows to give semantic proofs of normal form theorems for nd-calculi and (2) a framework that allows to search directly for normal nd-proofs. Thus, one can try to answer the question: How do we bridge the gap between claims and assumptions in heuristically motivated ways? This informal (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  21.  10
    Natural Logic.Wilfried Sieg - 1983 - Journal of Symbolic Logic 48 (1):215-217.
    Direct download  
     
    Export citation  
     
    Bookmark   9 citations  
  22.  23
    Rick L. Smith. The Consistency Strengths of Some Finite Forms of the Higman and Kruskal Theorems. Harvey Friedman's Research on the Foundations of Mathematics, Edited by L. A. Harrington, M. D. Morley, A. S̆c̆edrov, and S. G. Simpson, Studies in Logic and the Foundations of Mathematics, Vol. 117, North-Holland, Amsterdam, New York, and Oxford, 1985, Pp. 119–136. [REVIEW]Wilfried Sieg - 1990 - Journal of Symbolic Logic 55 (2):869-870.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  23.  30
    Note by the Guest Editors.Wilfried Sieg & Frank Pfenning - 1998 - Studia Logica 60 (1):1-1.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  24.  20
    Tennant Neil. Natural Logic. Edinburgh University Press, Edinburgh 1978, Ix + 196 Pp. [REVIEW]Wilfried Sieg - 1983 - Journal of Symbolic Logic 48 (1):215-217.
  25.  57
    Foundations for Analysis and Proof Theory.Wilfried Sieg - 1984 - Synthese 60 (2):159 - 200.
  26.  11
    Fragments of Arithmetic.Wilfried Sieg - 1987 - Journal of Symbolic Logic 52 (4):1054-1055.
    Direct download  
     
    Export citation  
     
    Bookmark   6 citations  
  27.  17
    Calculations by Man and Machine: Mathematical Presentation.Wilfried Sieg - unknown
    Wilfried Sieg. Calculations by Man and Machine: Mathematical Presentation.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  28.  18
    Stephen G. Simpson. Friedman's Research on Subsystems of Second Order Arithmetic. Harvey Friedman's Research on the Foundations of Mathematics, Edited by L. A. Harrington, M. D. Morley, A. S̆c̆edrov, and S. G. Simpson, Studies in Logic and the Foundations of Mathematics, Vol. 117, North-Holland, Amsterdam, New York, and Oxford, 1985, Pp. 137–159. [REVIEW]Wilfried Sieg - 1990 - Journal of Symbolic Logic 55 (2):870-874.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  29.  38
    Unification For Quantified Formulae.Wilfried Sieg - unknown
    — via appropriate substitutions — syntactically identical. The method can be applied directly to quantifierfree formulae and, in this paper, will b e extended in a natural and strai ghlforward way to quantified formulae.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  30.  35
    Proof Theory.Wilfried Sieg - unknown
  31. Kurt Gödel Collected Works IV-V: Correspondence.Solomon Feferman, John W. Dawson, Warren Goldfarb, Charles Parsons & Wilfried Sieg - 2004 - Bulletin of Symbolic Logic 10 (4):558-563.
  32.  36
    Review: Stephen G. Simpson, Friedman's Research on Subsystems of Second Order Arithmetic. [REVIEW]Wilfried Sieg - 1990 - Journal of Symbolic Logic 55 (2):870-874.
  33.  22
    Dedekind’s Structuralism: Creating Concepts and Deriving Theorems.Wilfried Sieg & Rebecca Morris - 2018 - In Erich Reck (ed.), Logic, Philosophy of Mathematics, and their History: Essays in Honor W.W. Tait. College Publications.
    Dedekind’s structuralism is a crucial source for the structuralism of mathematical practice—with its focus on abstract concepts like groups and fields. It plays an equally central role for the structuralism of philosophical analysis—with its focus on particular mathematical objects like natural and real numbers. Tensions between these structuralisms are palpable in Dedekind’s work, but are resolved in his essay Was sind und was sollen die Zahlen? In a radical shift, Dedekind extends his mathematical approach to “the” natural numbers. He creates (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  34.  20
    In Memoriam: Solomon Feferman.Charles Parsons & Wilfried Sieg - 2017 - Bulletin of Symbolic Logic 23 (3):337-344.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  35.  15
    Normal Natural Deduction Proof (In Non-Classical Logics).Wilfried Sieg & Saverio Cittadini - unknown
    Wilfred Sieg and Saverio Cittadini. Normal Natural Deduction Proof (In Non-Classical Logics.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  36. Trees in Metamathematics.Wilfried Sieg - 1977 - Dissertation, Stanford University
    No categories
     
    Export citation  
     
    Bookmark   2 citations  
  37.  55
    David Hilbert and Paul Bernays, Grundlagen der Mathematik I and II: A Landmark.Wilfried Sieg & Mark Ravaglia - unknown
    Wilfred Sieg and Mark Ravaglia. David Hilbert and Paul Bernays, Grundlagen der Mathematik I and II: A Landmark.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  38.  22
    Program Transformation and Proof Transformation.Wilfried Sieg & Stanley S. Wainer - unknown
    Wilfred Sieg and Stanley S. Wainer. Program Transformation and Proof Transformation.
    No categories
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  39.  22
    Computability Theory.Daniele Mundici & Wilfried Sieg - unknown
    Daniele Mundici and Wilfred Sieg. Computability Theory.
    Direct download  
    Translate
     
     
    Export citation  
     
    Bookmark   1 citation  
  40.  18
    Generalizing Turing's Machine and Arguments.Wilfried Sieg & John Byrnes - unknown
    Wilfred Sieg and John Byrnes. Generalizing Turing's Machine and Arguments.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  41.  8
    Mechanisms and Search: Aspects of Proof Theory.Wilfried Sieg - unknown
    Wilfred Sieg. Mechanisms and Search: Aspects of Proof Theory.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  42. Computing Machines.Wilfried Sieg & Rossella Lupacchini - unknown
    Any thorough discussion of computing machines requires the examination of rigorous concepts of computation and is facilitated by the distinction between mathematical, symbolic and physical computations. The delicate connection between the three kinds of computations and the underlying questions, "What are machines?" and "When are they computing?", motivate an extensive theoretical and historical discussion. The relevant outcome of this..
    Translate
     
     
    Export citation  
     
    Bookmark  
  43.  6
    Reductions of Theories for Analysis.Wilfried Sieg, Georg Dorn & P. Weingartner - 1990 - Journal of Symbolic Logic 55 (1):354-354.
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  44.  34
    Toward Finitist Proof Theory.Wilfried Sieg - unknown
    This is a summary of developments analysed in my (1997A). A first version of that paper was presented at the workshop Modern Mathematical Thought in Pittsburgh (September 21-24, 1995).
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  45.  34
    A Symposium on Hilbert's Program.Wilfrid Hodges & Wilfried Sieg - 1988 - Journal of Symbolic Logic 53 (2):337.
  46.  23
    Review: Neil Tennant, Natural Logic. [REVIEW]Wilfried Sieg - 1983 - Journal of Symbolic Logic 48 (1):215-217.
  47.  33
    Formal Systems, Church Turing Thesis, and Gödel's Theorems: Three Contributions to The MIT Encyclopedias of Cognitive Science.Wilfried Sieg - unknown
    Wilfried Sieg. Formal Systems, Church Turing Thesis, and Gödel's Theorems: Three Contributions to The MIT Encyclopedias of Cognitive Science.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  48.  29
    Mathematics Studies Machines.Daniele Mundici & Wilfried Sieg - unknown
    Machines were introduced as calculating devices to simulate operations carried out by human computors following fixed algorithms: this is true for the early mechanical calculators devised by Pascal and Leibniz, for the analytical engine built by Babbage, and the theoretical machines introduced by Turing. The distinguishing feature of the latter is their universality: They are claimed to be able to capture any algorithm whatsoever and, conversely, any procedure they can carry out is evidently algorithmic. The study of such "paper machines" (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  49.  17
    Of the Association for Symbolic Logic.Sergei Artemov, Peter Koellner, Michael Rabin, Jeremy Avigad, Wilfried Sieg, William Tait & Haim Gaifman - 2006 - Bulletin of Symbolic Logic 12 (3-4):503.
  50.  23
    Computer Environments for Proof Construction.Richard Scheines & Wilfried Sieg - unknown
    Richard Scheines and Wilfred Sieg. Computer Environments for Proof Construction.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
1 — 50 / 69