Church's Thesis After 70 Years /
Church's Thesis After 70 Years /
ed. by Adam Olszewski, Jan Wolenski, Robert Janusz.
- 1 online resource (551 p.)
- Ontos Mathematical Logic , 1 2198-2341 ; .
Frontmatter -- Contents -- Preface -- Church’s Thesis and Philosophy of Mind -- Algorithms: A Quest for Absolute Definitions -- Church’s Thesis and Bishop’s Constructivism -- On the Provability, Veracity, and AI-Relevance of the Church–Turing Thesis -- The Church–Turing Thesis. A Last Vestige of a Failed Mathematical Program -- Turing’s Thesis -- Church’s Thesis and Physical Computation -- Church’s Thesis and the Variety of Mathematical Justifications -- Did Church and Turing Have a Thesis about Machines? -- Formalizing Church’s Thesis -- Remarks on Church’s Thesis and Gödel’s Theorem -- Thesis and Variations -- On the Impossibility of Proving the “Hard-Half” of Church’s Thesis -- The Status of Church’s Thesis -- Analog Computation and Church’s Thesis -- Kreisel’s Church -- Church’s Thesis as Formulated by Church — An Interpretation -- Gödel on Turing on Computability -- Computability, Proof, and Open-Texture -- Step by Recursive Step: Church’s Analysis of Effective Calculability -- Physics and Metaphysics Look at Computation -- Church’s Thesis and Functional Programming -- Index
restricted access http://purl.org/coar/access_right/c_16ec
Church's Thesis (CT) was first published by Alonzo Church in 1935. CT is a proposition that identifies two notions: an intuitive notion of a effectively computable function defined in natural numbers with the notion of a recursive function. Despite of the many efforts of prominent scientists, Church's Thesis has never been falsified. There exists a vast literature concerning the thesis. The aim of the book is to provide one volume summary of the state of research on Church's Thesis. These include the following: different formulations of CT, CT and intuitionism, CT and intensional mathematics, CT and physics, the epistemic status of CT, CT and philosophy of mind, provability of CT and CT and functional programming.
Mode of access: Internet via World Wide Web.
In English.
9783110324945 9783110325461
10.1515/9783110325461 doi
Logic, Symbolic and mathematical.
Logik.
Mathematik.
PHILOSOPHY / Logic.
QA9 / .C58 2006
511.3
Frontmatter -- Contents -- Preface -- Church’s Thesis and Philosophy of Mind -- Algorithms: A Quest for Absolute Definitions -- Church’s Thesis and Bishop’s Constructivism -- On the Provability, Veracity, and AI-Relevance of the Church–Turing Thesis -- The Church–Turing Thesis. A Last Vestige of a Failed Mathematical Program -- Turing’s Thesis -- Church’s Thesis and Physical Computation -- Church’s Thesis and the Variety of Mathematical Justifications -- Did Church and Turing Have a Thesis about Machines? -- Formalizing Church’s Thesis -- Remarks on Church’s Thesis and Gödel’s Theorem -- Thesis and Variations -- On the Impossibility of Proving the “Hard-Half” of Church’s Thesis -- The Status of Church’s Thesis -- Analog Computation and Church’s Thesis -- Kreisel’s Church -- Church’s Thesis as Formulated by Church — An Interpretation -- Gödel on Turing on Computability -- Computability, Proof, and Open-Texture -- Step by Recursive Step: Church’s Analysis of Effective Calculability -- Physics and Metaphysics Look at Computation -- Church’s Thesis and Functional Programming -- Index
restricted access http://purl.org/coar/access_right/c_16ec
Church's Thesis (CT) was first published by Alonzo Church in 1935. CT is a proposition that identifies two notions: an intuitive notion of a effectively computable function defined in natural numbers with the notion of a recursive function. Despite of the many efforts of prominent scientists, Church's Thesis has never been falsified. There exists a vast literature concerning the thesis. The aim of the book is to provide one volume summary of the state of research on Church's Thesis. These include the following: different formulations of CT, CT and intuitionism, CT and intensional mathematics, CT and physics, the epistemic status of CT, CT and philosophy of mind, provability of CT and CT and functional programming.
Mode of access: Internet via World Wide Web.
In English.
9783110324945 9783110325461
10.1515/9783110325461 doi
Logic, Symbolic and mathematical.
Logik.
Mathematik.
PHILOSOPHY / Logic.
QA9 / .C58 2006
511.3