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Step by Recursive Step: Church's Analysis of Effective Calculability

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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universal Turing machine
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Grundlagen der Mathematik
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Collected Works I
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General recursive functions of natural numbers
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Stetigkeit und irrationale Zahlen
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universal Turing machine
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Introduction to mathematical logic
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Why Gödel didn't have church's thesis
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A. M. Turing. On computable numbers, with an application to the Entscheidungs problcm. Proceedings of the London Mathematical Society, 2 s. vol. 42 (1936–1937), pp. 230–265.
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Emil L. Post. Finite combinatory processes—formulation 1. The journal of symbolic logic, vol. 1 (1936), pp. 103–105.
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H. B. Smith. The algebra of propositions. Philosophy of science, vol. 3 (1936), pp. 551–578.
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In Memoriam: Alonzo Church 1903–1995
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A Proof of Freedom from Contradiction
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The Richard Paradox
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On the law of excluded middle
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A note on recursive functions
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Alternatives to Zermelo's Assumption
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Some properties of conversion
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Mechanical Procedures and Mathematical Experience
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Paper Machines
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Origins of Recursive Function Theory
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Highlights of the History of the Lambda-Calculus
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λ-definability and recursiveness
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A Set of Postulates for the Foundation of Logic
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The Inconsistency of Certain Formal Logics
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A Mathematical Logic Without Variables. I
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A Set of Postulates For the Foundation of Logic
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Proof by Cases in Formal Logic
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Second Thoughts about Church's Thesis and Mathematical Proofs
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Ein Verfahren der mathematischen Logik
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Finite combinatory processes—formulation
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A note on the Entscheidungsproblem
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Introduction to Mathematical Logic.
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An Unsolvable Problem of Elementary Number Theory
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A Theory of Positive Integers in Formal Logic. Part II
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Computability and Recursion
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American Logic in the 1920s
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Formal definitions in the theory of ordinal numbers
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The Law of the Excluded Middle

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Metatheory
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The Church-Turing Thesis: Consensus and Opposition
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Gödel’s Conflicting Approaches to Effective Calculability
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Kurt Gödel and Computability Theory
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Church Without Dogma: Axioms for Computability
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Theoretical Computer Science: Computability, Decidability and Logic
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What is the Church-Turing Thesis?
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Uncomputabilities, Games, Axioms, Proofs and Artificial Intelligence
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Conceptual Confluence in 1936: Post and Turing
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Why Turing’s Thesis Is Not a Thesis
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Why Post Did [Not] Have Turing’s Thesis
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Frege’s Habilitationsschrift: Magnitude, Number and the Problems of Computability
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Turing’s Theory of Computation
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Turing, the Mathematician
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Turing, Gödel and the “Bright Abyss”
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Gödel’s Reception of Turing’s Model of Computability: The “Shift of Perception” in 1934
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Mathematical and Technological Computability
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Conceptual Analysis
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Wittgenstein’s Diagonal Argument: A Variation on Cantor and Turing
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A Picaresque Approach to Set Theory Genealogy
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Toward a New Test for AI Entities: The Growth and Realization of Autonomous Wisdom (GROW-AI) Test
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Turing’s Unresolved Tension
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Turing-, Human- and Physical Computability: An Unasked Question
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Can Church’s thesis be viewed as a Carnapian explication?
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What Is Computation? And Why Turing?
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Explication as a Three-Step Procedure: the case of the Church-Turing Thesis
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On Computable Numbers, with an Application to the Entscheidungsproblem – A Correction
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ON COMPUTABILITY
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Classical Logic's Coming of Age
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What linguists are talking about when talking about…
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Emil Post
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Lambda-Calculus and Combinators in the 20th Century
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Calculations by man and machine: conceptual analysis*
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The Cambridge History of Philosophy 1870–1945
inferred← citeshttps://doi.org/10.1017/chol9780521591041.001openalex-snapshot
Frontmatter
inferred← citeshttps://doi.org/10.1017/chol9780521591041.002openalex-snapshot
Introduction
inferred← citeshttps://doi.org/10.1017/chol9780521591041.003openalex-snapshot
Positivist thought in the nineteenth century
inferred← citeshttps://doi.org/10.1017/chol9780521591041.004openalex-snapshot
Neo-Kantianism: the German idealism movement
inferred← citeshttps://doi.org/10.1017/chol9780521591041.005openalex-snapshot
Idealism in Britain and the United States
inferred← citeshttps://doi.org/10.1017/chol9780521591041.006openalex-snapshot
Idealism in Russia
inferred← citeshttps://doi.org/10.1017/chol9780521591041.007openalex-snapshot
Bergson
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Pragmatism
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Psychology: old and new
inferred← citeshttps://doi.org/10.1017/chol9780521591041.010openalex-snapshot
The unconscious mind
inferred← citeshttps://doi.org/10.1017/chol9780521591041.011openalex-snapshot
Logic: revival and reform
inferred← citeshttps://doi.org/10.1017/chol9780521591041.012openalex-snapshot
Foundations of mathematics
inferred← citeshttps://doi.org/10.1017/chol9780521591041.013openalex-snapshot
Theories of judgement
inferred← citeshttps://doi.org/10.1017/chol9780521591041.014openalex-snapshot
The logical analysis of language
inferred← citeshttps://doi.org/10.1017/chol9780521591041.015openalex-snapshot
The atomism debate
inferred← citeshttps://doi.org/10.1017/chol9780521591041.016openalex-snapshot
Theories of space-time in modern physics
inferred← citeshttps://doi.org/10.1017/chol9780521591041.017openalex-snapshot
The debate over theGeisteswissenschaftenin German philosophy
inferred← citeshttps://doi.org/10.1017/chol9780521591041.018openalex-snapshot
From political economy to positive economics
inferred← citeshttps://doi.org/10.1017/chol9780521591041.019openalex-snapshot
Sociology and the idea of social science
inferred← citeshttps://doi.org/10.1017/chol9780521591041.020openalex-snapshot
Utilitarians and idealists
inferred← citeshttps://doi.org/10.1017/chol9780521591041.021openalex-snapshot
Nietzsche
inferred← citeshttps://doi.org/10.1017/chol9780521591041.022openalex-snapshot
The new realism in ethics
inferred← citeshttps://doi.org/10.1017/chol9780521591041.023openalex-snapshot
Individualism vs. collectivism
inferred← citeshttps://doi.org/10.1017/chol9780521591041.024openalex-snapshot
Marxism and anarchism
inferred← citeshttps://doi.org/10.1017/chol9780521591041.025openalex-snapshot
Legal theory
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Sceptical challenges to faith
inferred← citeshttps://doi.org/10.1017/chol9780521591041.027openalex-snapshot
The defence of faith
inferred← citeshttps://doi.org/10.1017/chol9780521591041.028openalex-snapshot
Art and morality: aesthetics at 1870
inferred← citeshttps://doi.org/10.1017/chol9780521591041.029openalex-snapshot
Form and feeling: aesthetics at the turn of the century
inferred← citeshttps://doi.org/10.1017/chol9780521591041.030openalex-snapshot
Philosophy and the first world war
inferred← citeshttps://doi.org/10.1017/chol9780521591041.031openalex-snapshot
Logical atomism
inferred← citeshttps://doi.org/10.1017/chol9780521591041.032openalex-snapshot
The scientific world conception: logical positivism
inferred← citeshttps://doi.org/10.1017/chol9780521591041.033openalex-snapshot
The achievements of the Polish school of logic
inferred← citeshttps://doi.org/10.1017/chol9780521591041.034openalex-snapshot
Logic and philosophical analysis
inferred← citeshttps://doi.org/10.1017/chol9780521591041.035openalex-snapshot
The continuing idealist tradition
inferred← citeshttps://doi.org/10.1017/chol9780521591041.036openalex-snapshot
Transformations in speculative philosophy
inferred← citeshttps://doi.org/10.1017/chol9780521591041.037openalex-snapshot
Realism, naturalism, and pragmatism
inferred← citeshttps://doi.org/10.1017/chol9780521591041.038openalex-snapshot
French Catholic philosophy
inferred← citeshttps://doi.org/10.1017/chol9780521591041.039openalex-snapshot
Spanish philosophy
inferred← citeshttps://doi.org/10.1017/chol9780521591041.040openalex-snapshot
The phenomenological movement
inferred← citeshttps://doi.org/10.1017/chol9780521591041.041openalex-snapshot
Heidegger
inferred← citeshttps://doi.org/10.1017/chol9780521591041.042openalex-snapshot
Latin american philosophy
inferred← citeshttps://doi.org/10.1017/chol9780521591041.043openalex-snapshot
Japanese philosophy
inferred← citeshttps://doi.org/10.1017/chol9780521591041.044openalex-snapshot
Sensible appearances
inferred← citeshttps://doi.org/10.1017/chol9780521591041.045openalex-snapshot
The renaissance of epistemology
inferred← citeshttps://doi.org/10.1017/chol9780521591041.046openalex-snapshot
The solipsism debates
inferred← citeshttps://doi.org/10.1017/chol9780521591041.047openalex-snapshot
Language
inferred← citeshttps://doi.org/10.1017/chol9780521591041.048openalex-snapshot
The end of philosophy as metaphysics
inferred← citeshttps://doi.org/10.1017/chol9780521591041.049openalex-snapshot
First-order logic and its rivals
inferred← citeshttps://doi.org/10.1017/chol9780521591041.050openalex-snapshot
The golden age of mathematical logic
inferred← citeshttps://doi.org/10.1017/chol9780521591041.051openalex-snapshot
General relativity
inferred← citeshttps://doi.org/10.1017/chol9780521591041.052openalex-snapshot
Scientific explanation
inferred← citeshttps://doi.org/10.1017/chol9780521591041.053openalex-snapshot
The rise of probabilistic thinking
inferred← citeshttps://doi.org/10.1017/chol9780521591041.054openalex-snapshot
Vitalism and emergence
inferred← citeshttps://doi.org/10.1017/chol9780521591041.055openalex-snapshot
Behaviourism and psychology
inferred← citeshttps://doi.org/10.1017/chol9780521591041.056openalex-snapshot
Gestalt psychology
inferred← citeshttps://doi.org/10.1017/chol9780521591041.057openalex-snapshot
Wittgenstein’s conception of mind
inferred← citeshttps://doi.org/10.1017/chol9780521591041.058openalex-snapshot
The methodology of the social sciences
inferred← citeshttps://doi.org/10.1017/chol9780521591041.059openalex-snapshot
The rise of social anthropology
inferred← citeshttps://doi.org/10.1017/chol9780521591041.060openalex-snapshot
Western marxism and ideology critique
inferred← citeshttps://doi.org/10.1017/chol9780521591041.061openalex-snapshot
From intuitionism to emotivism
inferred← citeshttps://doi.org/10.1017/chol9780521591041.062openalex-snapshot
Philosophy of religion
inferred← citeshttps://doi.org/10.1017/chol9780521591041.063openalex-snapshot
Literature as philosophy
inferred← citeshttps://doi.org/10.1017/chol9780521591041.064openalex-snapshot
Aesthetics between the wars: art and liberation
inferred← citeshttps://doi.org/10.1017/chol9780521591041.065openalex-snapshot
Hans Kelsen and normative legal positivism
inferred← citeshttps://doi.org/10.1017/chol9780521591041.066openalex-snapshot
The liberal democratic state: defences and developments
inferred← citeshttps://doi.org/10.1017/chol9780521591041.067openalex-snapshot
The liberal democratic state: critics
inferred← citeshttps://doi.org/10.1017/chol9780521591041.068openalex-snapshot
Biobibliographical appendix
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Bibliography
inferred← citeshttps://doi.org/10.1023/a:1015659418145openalex-snapshot
Is There a Nonrecursive Decidable Equational Theory?
inferred← citeshttps://doi.org/10.1023/a:1015694932257openalex-snapshot
Effective Computation by Humans and Machines
inferred← citeshttps://doi.org/10.1023/a:1021348629167openalex-snapshot
Alan Turing and the Mathematical Objection
inferred← citeshttps://doi.org/10.1023/b:synt.0000024888.19304.0fopenalex-snapshot
Theories of Space-Time in Modern Physics
inferred← citeshttps://doi.org/10.1080/0144534042000271157openalex-snapshot
Diagonalisation and Church's Thesis: Kleene's Homework
inferred← citeshttps://doi.org/10.1090/s0002-9904-1946-08555-9openalex-snapshot
A variant of a recursively unsolvable problem
inferred← citeshttps://doi.org/10.1093/bjps/axr016openalex-snapshot
The Physical Church–Turing Thesis: Modest or Bold?
inferred← citeshttps://doi.org/10.1093/oso/9780197552384.001.0001openalex-snapshot
The Nature of Physical Computation
inferred← citeshttps://doi.org/10.1093/oso/9780197552384.002.0004openalex-snapshot
Copyright Page
inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0001openalex-snapshot
Introduction
inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0002openalex-snapshot
Desiderata of a Theory of Computation
inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0003openalex-snapshot
Turing’s Computability
inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0004openalex-snapshot
Preamble to Machine Computation
inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0005openalex-snapshot
Computation as Step-Satisfaction
inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0006openalex-snapshot
Computation as Implementation
inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0007openalex-snapshot
Computation as Mechanism
inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0008openalex-snapshot
The Semantic View of Computation
inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0009openalex-snapshot
An Argument for the Semantic View
inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0010openalex-snapshot
Computing as Modeling
inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0011openalex-snapshot
Conclusion
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Textual notes
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References
inferred← citeshttps://doi.org/10.1093/oso/9780198785156.001.0001openalex-snapshot
Recursion
inferred← citeshttps://doi.org/10.1093/oso/9780198785156.002.0004openalex-snapshot
Copyright Page
inferred← citeshttps://doi.org/10.1093/oso/9780198785156.002.0005openalex-snapshot
Dedication
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General preface
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Preface
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List of figures and tables
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List of abbreviations
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Epigraph
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Postface
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Putting up barriers
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Preliminaries
inferred← citeshttps://doi.org/10.1093/oso/9780198785156.003.0003openalex-snapshot
Recursive generation in language
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The derivations into the interfaces
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The universality and uniqueness of recursion-in-language
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On recursive parsing
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Probing recursion
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Putting it all together
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Martin Davis: An Overview of his Work in Logic, Computer Science, and Philosophy
inferred← citeshttps://doi.org/10.1093/philmat/nkag005openalex-snapshot
Is the Concept of Computation a Conceptual Fixed Point?
inferred← citeshttps://doi.org/10.1093/philmat/nkj005openalex-snapshot
Godel on computability
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Human-Effective Computability†
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ALGORITHMS: A QUEST FOR ABSOLUTE DEFINITIONS
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Sign and the lambda-term
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Concepto de computabilidad en Alan Turing
inferred← citeshttps://doi.org/10.15633/acr.4309openalex-snapshot
Johannes Paul II – neuer europäischer Seliger und Wegbereiter Europas
inferred← citeshttps://doi.org/10.15633/acr.5306openalex-snapshot
A consequence of the notional existence of an effectively calculable yet non-recursive function
inferred← citeshttps://doi.org/10.2178/bsl/1120231628openalex-snapshot
Only Two Letters: The Correspondence between Herbrand and Gödel
inferred← citeshttps://doi.org/10.22201/iifs.18704905e.2005.459openalex-snapshot
Conceptualismo realista y computabilidad
inferred← citeshttps://doi.org/10.2307/2687773openalex-snapshot
The Prospects for Mathematical Logic in the Twenty-First Century
inferred← citeshttps://doi.org/10.2307/421120openalex-snapshot
1999 Spring Meeting of the Association for Symbolic Logic
inferred← citeshttps://doi.org/10.2478/slgr-2020-0027openalex-snapshot
Implicit and Explicit Examples of the Phenomenon of Deviant Encodings
inferred← citeshttps://doi.org/10.25100/pfilosofica.v0i40.3016openalex-snapshot
Sobre el concepto de recursión y sus usos
inferred← citeshttps://doi.org/10.3389/fpsyg.2014.00382openalex-snapshot
When linguists talk mathematical logic
inferred← citeshttps://doi.org/10.48550/arxiv.0902.1064openalex-snapshot
The significance of Nathanson's 'boss' factor in legitimising Aristotle's particularisation: Why we need to revise current interpretations of Cantor's, Goedel's, Turing's and Tarski's formal reasoning
inferred← citeshttps://doi.org/10.48550/arxiv.1003.5602openalex-snapshot
Does resolving PvNP require a paradigm shift?
inferred← citeshttps://doi.org/10.48550/arxiv.1108.4597openalex-snapshot
A case for weakening the Church-Turing Thesis
inferred← citeshttps://doi.org/10.48550/arxiv.math/0607333openalex-snapshot
Why we shouldn't fault Lucas and Penrose for continuing to believe in the Goedelian argument against computationalism
inferred← citeshttps://doi.org/10.5860/choice.51-1541openalex-snapshot
An introduction to Godel's theorems
inferred← citeshttps://doi.org/10.70675/0b3f6ab0zc577z499azb8e6z4a0425f88e23openalex-snapshot
L'hyper-calcul : de la logique a la physique
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