Switch to: References

Add citations

You must login to add citations.
  1. Human-Effective Computability†.Marianna Antonutti Marfori & Leon Horsten - 2018 - Philosophia Mathematica 27 (1):61-87.
    We analyse Kreisel’s notion of human-effective computability. Like Kreisel, we relate this notion to a concept of informal provability, but we disagree with Kreisel about the precise way in which this is best done. The resulting two different ways of analysing human-effective computability give rise to two different variants of Church’s thesis. These are both investigated by relating them to transfinite progressions of formal theories in the sense of Feferman.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark  
  • Alan Turing and the Mathematical Objection.Gualtiero Piccinini - 2003 - Minds and Machines 13 (1):23-48.
    This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a human mathematician, for (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   21 citations  
  • Effective Computation by Humans and Machines.Shagrir Oron - 2002 - Minds and Machines 12 (2):221-240.
    There is an intensive discussion nowadays about the meaning of effective computability, with implications to the status and provability of the Church–Turing Thesis (CTT). I begin by reviewing what has become the dominant account of the way Turing and Church viewed, in 1936, effective computability. According to this account, to which I refer as the Gandy–Sieg account, Turing and Church aimed to characterize the functions that can be computed by a human computer. In addition, Turing provided a highly convincing argument (...)
    Direct download (14 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  • Sign and the Lambda-Term.Kumiko Tanaka-Ishii & Yuichiro Ishii - 2008 - Semiotica 2008 (169):197-220.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Frege’s Habilitationsschrift: Magnitude, Number and the Problems of Computability.Juan Gastaldi - unknown
    No categories
     
    Export citation  
     
    Bookmark  
  • Kurt Gödel and Computability Theory.Richard Zach - 2006 - In Arnold Beckmann, Ulrich Berger, Benedikt Löwe & John V. Tucker (eds.), Logical Approaches to Computational Barriers. Second Conference on Computability in Europe, CiE 2006, Swansea. Proceedings. Berlin: Springer. pp. 575--583.
    Although Kurt Gödel does not figure prominently in the history of computabilty theory, he exerted a significant influence on some of the founders of the field, both through his published work and through personal interaction. In particular, Gödel’s 1931 paper on incompleteness and the methods developed therein were important for the early development of recursive function theory and the lambda calculus at the hands of Church, Kleene, and Rosser. Church and his students studied Gödel 1931, and Gödel taught a seminar (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Three Dogmas of First-Order Logic and Some Evidence-Based Consequences for Constructive Mathematics of Differentiating Between Hilbertian Theism, Brouwerian Atheism and Finitary Agnosticism.Bhupinder Singh Anand - manuscript
    We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language. -/- We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'. -/- We then adopt what may (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  • Book Reviews. [REVIEW]Juliet Floyd - 2002 - Philosophia Mathematica 10 (1):67-88.
  • Mathieu Marion. Wittgenstein, Finitism, and the Foundations of Mathematics.Juliet Floyd - 2002 - Philosophia Mathematica 10 (1):67-88.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  • The Philosophy of Computer Science.Raymond Turner - 2013 - Stanford Encyclopedia of Philosophy.
  • The Prospects for Mathematical Logic in the Twenty-First Century.Samuel R. Buss, Alexander S. Kechris, Anand Pillay & Richard A. Shore - 2001 - Bulletin of Symbolic Logic 7 (2):169-196.
    The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.
    Direct download (12 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  • The Physical Church-Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
    This article defends a modest version of the Physical Church-Turing thesis (CT). Following an established recent trend, I distinguish between what I call Mathematical CT—the thesis supported by the original arguments for CT—and Physical CT. I then distinguish between bold formulations of Physical CT, according to which any physical process—anything doable by a physical system—is computable by a Turing machine, and modest formulations, according to which any function that is computable by a physical system is computable by a Turing machine. (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   17 citations  
  • Proving Church's Thesis.Robert Black - 2000 - Philosophia Mathematica 8 (3):244--58.
    Arguments to the effect that Church's thesis is intrinsically unprovable because proof cannot relate an informal, intuitive concept to a mathematically defined one are unconvincing, since other 'theses' of this kind have indeed been proved, and Church's thesis has been proved in one direction. However, though evidence for the truth of the thesis in the other direction is overwhelming, it does not yet amount to proof.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  • Turing-, Human- and Physical Computability: An Unasked Question. [REVIEW]Eli Dresner - 2008 - Minds and Machines 18 (3):349-355.
    In recent years it has been convincingly argued that the Church-Turing thesis concerns the bounds of human computability: The thesis was presented and justified as formally delineating the class of functions that can be computed by a human carrying out an algorithm. Thus the Thesis needs to be distinguished from the so-called Physical Church-Turing thesis, according to which all physically computable functions are Turing computable. The latter is often claimed to be false, or, if true, contingently so. On all accounts, (...)
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Diagonalisation and Church's Thesis: Kleene's Homework.Enrique Alonso & Maria Manzano - 2005 - History and Philosophy of Logic 26 (2):93-113.
    In this paper we will discuss the active part played by certain diagonal arguments in the genesis of computability theory. 1?In some cases it is enough to assume the enumerability of Y while in others the effective enumerability is a substantial demand. These enigmatical words by Kleene were our point of departure: When Church proposed this thesis, I sat down to disprove it by diagonalizing out of the class of the ??definable functions. But, quickly realizing that the diagonalization cannot be (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Emil Post.Alasdair Urquhart - 2009 - In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier. pp. 5--617.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  • 1999 Spring Meeting of the Association for Symbolic Logic.Charles Parsons - 1999 - Bulletin of Symbolic Logic 5 (4):479-484.