Results for 'Gödel’s incompleteness result'

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  1. On Alleged Refutations of Mechanism Using Godel's Incompleteness Results.Charles S. Chihara - 1972 - Journal of Philosophy 69 (September):507-26.
  2.  27
    Goedel's Way: Exploits Into an Undecidable World.Gregory J. Chaitin - 2011 - Crc Press.
    This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no ...
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  3. What Godel's Incompleteness Result Does and Does Not Show.Haim Gaifman - 2000 - Journal of Philosophy 97 (8):462.
    In a recent paper S. McCall adds another link to a chain of attempts to enlist Gödel’s incompleteness result as an argument for the thesis that human reasoning cannot be construed as being carried out by a computer.1 McCall’s paper is undermined by a technical oversight. My concern however is not with the technical point. The argument from Gödel’s result to the no-computer thesis can be made without following McCall’s route; it is then straighter and (...)
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  4. Gödel's Incompleteness Results.Haim Gaifman - unknown
    This short sketch of Gödel’s incompleteness proof shows how it arises naturally from Cantor’s diagonalization method [1891]. It renders Gödel’s proof and its relation to the semantic paradoxes transparent. Some historical details, which are often ignored, are pointed out. We also make some observations on circularity and draw brief comparisons with natural language. The sketch does not include the messy details of the arithmetization of the language, but the motives for it are made obvious. We suggest this (...)
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  5.  42
    Mathematical Incompleteness Results in First-Order Peano Arithmetic: A Revisionist View of the Early History.Saul A. Kripke - 2021 - History and Philosophy of Logic 43 (2):175-182.
    In the Handbook of Mathematical Logic, the Paris-Harrington variant of Ramsey's theorem is celebrated as the first result of a long ‘search’ for a purely mathematical incompleteness result in first-order Peano arithmetic. This paper questions the existence of any such search and the status of the Paris-Harrington result as the first mathematical incompleteness result. In fact, I argue that Gentzen gave the first such result, and that it was restated by Goodstein in a (...)
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  6.  2
    Hierarchical Incompleteness Results for Arithmetically Definable Extensions of Fragments of Arithmetic.Rasmus Blanck - 2021 - Review of Symbolic Logic 14 (3):624-644.
    There has been a recent interest in hierarchical generalizations of classic incompleteness results. This paper provides evidence that such generalizations are readily obtainable from suitably formulated hierarchical versions of the principles used in the original proofs. By collecting such principles, we prove hierarchical versions of Mostowski’s theorem on independent formulae, Kripke’s theorem on flexible formulae, Woodin’s theorem on the universal algorithm, and a few related results. As a corollary, we obtain the expected result that the formula expressing “ (...)
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  7. Gödel's Incompleteness Theorems.Panu Raatikainen - 2013 - The Stanford Encyclopedia of Philosophy (Winter 2013 Edition), Edward N. Zalta (Ed.).
    Gödel's two incompleteness theorems are among the most important results in modern logic, and have deep implications for various issues. They concern the limits of provability in formal axiomatic theories. The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried out, there are statements of the language of F which can neither be proved nor disproved in F. According to the second incompleteness theorem, such a (...)
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  8.  6
    Goedel's Property Abstraction and Possibilism.Randoph Rubens Goldman - 2014 - Australasian Journal of Logic 11 (2).
    Gödel’s Ontological argument is distinctive because it is the most sophisticated and formal of ontological arguments and relies heavily on the notion of positive property. Gödel uses a third-order modal logic with a property abstraction operator and property quantification into modal contexts. Gödel describes positive property as "independent of the accidental structure of the world"; "pure attribution," as opposed to privation; "positive in the 'moral aesthetic sense.'" Pure attribution seems likely to be related to the Leibnizian concept of perfection.By (...)
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  9.  1
    Goedel's Property Abstraction and Possibilism.Randoph Rubens Goldman - 2014 - Australasian Journal of Logic 14 (3).
    Gödel’s Ontological argument is distinctive because it is the most sophisticated and formal of ontological arguments and relies heavily on the notion of _positive property_. Gödel uses a third-order modal logic with a property abstraction operator and property quantification into modal contexts. Gödel describes _positive property_ as "independent of the accidental structure of the world"; "pure attribution," as opposed to privation; "positive in the 'moral aesthetic sense.'" _Pure attribution_ seems likely to be related to the Leibnizian concept of perfection. (...)
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  10.  10
    Generalizations of Gödel’s Incompleteness Theorems for ∑N-Definable Theories of Arithmetic.Makoto Kikuchi & Taishi Kurahashi - 2017 - Review of Symbolic Logic 10 (4):603-616.
    It is well known that Gödel’s incompleteness theorems hold for ∑1-definable theories containing Peano arithmetic. We generalize Gödel’s incompleteness theorems for arithmetically definable theories. First, we prove that every ∑n+1-definable ∑n-sound theory is incomplete. Secondly, we generalize and improve Jeroslow and Hájek’s results. That is, we prove that every consistent theory having ∏n+1set of theorems has a true but unprovable ∏nsentence. Lastly, we prove that no ∑n+1-definable ∑n-sound theory can prove its own ∑n-soundness. These three results (...)
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  11. On the Philosophical Relevance of Gödel's Incompleteness Theorems.Panu Raatikainen - 2005 - Revue Internationale de Philosophie 59 (4):513-534.
    A survey of more philosophical applications of Gödel's incompleteness results.
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  12.  50
    Husserl and Gödel’s Incompleteness Theorems.Mirja Hartimo - 2017 - Review of Symbolic Logic 10 (4):638-650.
    The paper examines Husserl’s interactions with logicians in the 1930s in order to assess Husserl’s awareness of Gödel’s incompleteness theorems. While there is no mention about the results in Husserl’s known exchanges with Hilbert, Weyl, or Zermelo, the most likely source about them for Husserl is Felix Kaufmann (1895–1949). Husserl’s interactions with Kaufmann show that Husserl may have learned about the results from him, but not necessarily so. Ultimately Husserl’s reading marks on Friedrich Waismann’s Einführung in das mathematische (...)
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  13.  74
    Between Vienna and Berlin: The Immediate Reception of Godel's Incompleteness Theorems.Paolo Mancosu - 1999 - History and Philosophy of Logic 20 (1):33-45.
    What were the earliest reactions to Gödel's incompleteness theorems? After a brief summary of previous work in this area I analyse, by means of unpublished archival material, the first reactions in Vienna and Berlin to Gödel's groundbreaking results. In particular, I look at how Carnap, Hempel, von Neumann, Kaufmann, and Chwistek, among others, dealt with the new results.
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  14. Application of Quantum Darwinism to Cosmic Inflation: An Example of the Limits Imposed in Aristotelian Logic by Information-Based Approach to Gödel’s Incompleteness[REVIEW]Nicolás F. Lori & Alex H. Blin - 2010 - Foundations of Science 15 (2):199-211.
    Gödel’s incompleteness applies to any system with recursively enumerable axioms and rules of inference. Chaitin’s approach to Gödel’s incompleteness relates the incompleteness to the amount of information contained in the axioms. Zurek’s quantum Darwinism attempts the physical description of the universe using information as one of its major components. The capacity of quantum Darwinism to describe quantum measurement in great detail without requiring ad-hoc non-unitary evolution makes it a good candidate for describing the transition from (...)
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  15.  79
    The Nature and Significance of Gödel's Incompleteness Theorems.Solomon Feferman - manuscript
    What Gödel accomplished in the decade of the 1930s before joining the Institute changed the face of mathematical logic and continues to influence its development. As you gather from my title, I’ll be talking about the most famous of his results in that period, but first I want to indulge in some personal reminiscences. In many ways this is a sentimental journey for me. I was a member of the Institute in 1959-60, a couple of years after receiving my PhD (...)
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  16. Incompleteness and Incomparability in Preference Aggregation: Complexity Results.M. S. Pini, F. Rossi, K. B. Venable & T. Walsh - 2011 - Artificial Intelligence 175 (7-8):1272-1289.
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  17.  28
    Mathematical Logic.Heinz-Dieter Ebbinghaus - 1996 - Springer.
    This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most (...)
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  18.  47
    Inconsistent Models for Relevant Arithmetics.Robert Meyer & Chris Mortensen - 1984 - Journal of Symbolic Logic 49 (3):917-929.
    This paper develops in certain directions the work of Meyer in [3], [4], [5] and [6]. In those works, Peano’s axioms for arithmetic were formulated with a logical base of the relevant logic R, and it was proved finitistically that the resulting arithmetic, called R♯, was absolutely consistent. It was pointed out that such a result escapes incau- tious formulations of Goedel’s second incompleteness theorem, and provides a basis for a revived Hilbert programme. The absolute consistency result (...)
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  19.  46
    Malebranche's Doctrine of Freedom / Consent and the Incompleteness of God's Volitions.Andrew Pessin - 2000 - British Journal for the History of Philosophy 8 (1):21 – 53.
    'God needs no instruments to act', Malebranche writes in Search 6.2.3; 'it suffices that He wills in order that a thing be, because it is a contradiction that He should will and that what He wills should not happen. Therefore, His power is His will' (450). After nearly identical language in Treatise 1.12, Malebranche writes that '[God's] wills are necessarily efficacious ... [H]is power differs not at all from [H]is will' (116). God's causal power, here, clearly traces only to His (...)
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  20.  14
    What's so Special About Kruskal's Theorem and the Ordinal Γo? A Survey of Some Results in Proof Theory.Jean H. Gallier - 1991 - Annals of Pure and Applied Logic 53 (3):199-260.
    This paper consists primarily of a survey of results of Harvey Friedman about some proof-theoretic aspects of various forms of Kruskal's tree theorem, and in particular the connection with the ordinal Γ0. We also include a fairly extensive treatment of normal functions on the countable ordinals, and we give a glimpse of Verlen hierarchies, some subsystems of second-order logic, slow-growing and fast-growing hierarchies including Girard's result, and Goodstein sequences. The central theme of this paper is a powerful theorem due (...)
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  21. Einstein, Incompleteness, and the Epistemic View of Quantum States.Nicholas Harrigan & Robert W. Spekkens - 2010 - Foundations of Physics 40 (2):125-157.
    Does the quantum state represent reality or our knowledge of reality? In making this distinction precise, we are led to a novel classification of hidden variable models of quantum theory. We show that representatives of each class can be found among existing constructions for two-dimensional Hilbert spaces. Our approach also provides a fruitful new perspective on arguments for the nonlocality and incompleteness of quantum theory. Specifically, we show that for models wherein the quantum state has the status of something (...)
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  22. On an Alleged Refutation of Hilbert's Program Using Gödel's First Incompleteness Theorem.Michael Detlefsen - 1990 - Journal of Philosophical Logic 19 (4):343 - 377.
    It is argued that an instrumentalist notion of proof such as that represented in Hilbert's viewpoint is not obligated to satisfy the conservation condition that is generally regarded as a constraint on Hilbert's Program. A more reasonable soundness condition is then considered and shown not to be counter-exemplified by Godel's First Theorem. Finally, attention is given to the question of what a theory is; whether it should be seen as a "list" or corpus of beliefs, or as a method for (...)
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  23. Consistency, Turing Computability and Gödel’s First Incompleteness Theorem.Robert F. Hadley - 2008 - Minds and Machines 18 (1):1-15.
    It is well understood and appreciated that Gödel’s Incompleteness Theorems apply to sufficiently strong, formal deductive systems. In particular, the theorems apply to systems which are adequate for conventional number theory. Less well known is that there exist algorithms which can be applied to such a system to generate a gödel-sentence for that system. Although the generation of a sentence is not equivalent to proving its truth, the present paper argues that the existence of these algorithms, when conjoined (...)
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  24.  40
    Gödel's Third Incompleteness Theorem.Timothy McCarthy - 2016 - Dialectica 70 (1):87-112.
    In a note appended to the translation of “On consistency and completeness” (), Gödel reexamined the problem of the unprovability of consistency. Gödel here focuses on an alternative means of expressing the consistency of a formal system, in terms of what would now be called a ‘reflection principle’, roughly, the assertion that a formula of a certain class is provable in the system only if it is true. Gödel suggests that it is this alternative means of expressing consistency that we (...)
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  25. Incompleteness and Jump Hierarchies.James Walsh & Patrick Lutz - 2020 - Proceedings of the American Mathematical Society 148 (11):4997--5006.
    This paper is an investigation of the relationship between G\"odel's second incompleteness theorem and the well-foundedness of jump hierarchies. It follows from a classic theorem of Spector's that the relation $\{(A,B) \in \mathbb{R}^2 : \mathcal{O}^A \leq_H B\}$ is well-founded. We provide an alternative proof of this fact that uses G\"odel's second incompleteness theorem instead of the theory of admissible ordinals. We then derive a semantic version of the second incompleteness theorem, originally due to Mummert and Simpson, from (...)
     
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  26.  52
    The Incomplete Universe: Totality, Knowledge, and Truth.Patrick Grim - 1991 - Cambridge: Mass.: Mit Press.
    This is an exploration of a cluster of related logical results. Taken together these seem to have something philosophically important to teach us: something about knowledge and truth and something about the logical impossibility of totalities of knowledge and truth. The book includes explorations of new forms of the ancient and venerable paradox of the :Liar, applications and extensions of Kaplan and Montague's paradox of the Knower, generalizations of Godel's work on incompleteness, and new uses of Cantorian diagonalization. Throughout, (...)
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  27. Fromal Statements of Godel's Second Incompleteness Theorem.Harvey Friedman - manuscript
    Informal statements of Gödel's Second Incompleteness Theorem, referred to here as Informal Second Incompleteness, are simple and dramatic. However, current versions of Formal Second Incompleteness are complicated and awkward. We present new versions of Formal Second Incompleteness that are simple, and informally imply Informal Second Incompleteness. These results rest on the isolation of simple formal properties shared by consistency statements. Here we do not address any issues concerning proofs of Second Incompleteness.
     
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  28.  18
    A Note on Murakami’s Theorems and Incomplete Social Choice Without the Pareto Principle.Wesley H. Holliday & Mikayla Kelley - 2020 - Social Choice and Welfare 55:243-253.
    In Arrovian social choice theory assuming the independence of irrelevant alternatives, Murakami (1968) proved two theorems about complete and transitive collective choice rules that satisfy strict non-imposition (citizens’ sovereignty), one being a dichotomy theorem about Paretian or anti-Paretian rules and the other a dictator-or-inverse-dictator impossibility theorem without the Pareto principle. It has been claimed in the later literature that a theorem of Malawski and Zhou (1994) is a generalization of Murakami’s dichotomy theorem and that Wilson’s (1972) impossibility theorem is stronger (...)
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  29.  35
    Incompleteness Via Paradox and Completeness.Walter Dean - 2020 - Review of Symbolic Logic 13 (3):541-592.
    This paper explores the relationship borne by the traditional paradoxes of set theory and semantics to formal incompleteness phenomena. A central tool is the application of the Arithmetized Completeness Theorem to systems of second-order arithmetic and set theory in which various “paradoxical notions” for first-order languages can be formalized. I will first discuss the setting in which this result was originally presented by Hilbert & Bernays and also how it was later adapted by Kreisel and Wang in order (...)
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  30.  28
    Incompleteness of Intuitionistic Propositional Logic with Respect to Proof-Theoretic Semantics.Thomas Piecha & Peter Schroeder-Heister - 2019 - Studia Logica 107 (1):233-246.
    Prawitz proposed certain notions of proof-theoretic validity and conjectured that intuitionistic logic is complete for them [11, 12]. Considering propositional logic, we present a general framework of five abstract conditions which any proof-theoretic semantics should obey. Then we formulate several more specific conditions under which the intuitionistic propositional calculus turns out to be semantically incomplete. Here a crucial role is played by the generalized disjunction principle. Turning to concrete semantics, we show that prominent proposals, including Prawitz’s, satisfy at least one (...)
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  31.  24
    On Essential Incompleteness of Hertz’s Experiments on Propagation of Electromagnetic Interactions.R. Smirnov-Rueda - 2005 - Foundations of Physics 35 (1):1-31.
    The historical background of the 19th century electromagnetic theory is revisited from the standpoint of the opposition between alternative approaches in respect to the problem of interactions. The 19th century electrodynamics became the battle-field of a paramount importance to test existing conceptions of interactions. Hertz’s experiments were designed to bring a solid experimental evidence in favor of one of them. The modern scientific method applied to analyze Hertz’s experimental approach as well as the analysis of his laboratory notes, dairy and (...)
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  32. The Emperor's Real Mind -- Review of Roger Penrose's The Emperor's New Mind: Concerning Computers Minds and the Laws of Physics.Aaron Sloman - 1992 - Artificial Intelligence 56 (2-3):355-396.
    "The Emperor's New Mind" by Roger Penrose has received a great deal of both praise and criticism. This review discusses philosophical aspects of the book that form an attack on the "strong" AI thesis. Eight different versions of this thesis are distinguished, and sources of ambiguity diagnosed, including different requirements for relationships between program and behaviour. Excessively strong versions attacked by Penrose (and Searle) are not worth defending or attacking, whereas weaker versions remain problematic. Penrose (like Searle) regards the notion (...)
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  33.  27
    How to Extend the Semantic Tableaux and Cut-Free Versions of the Second Incompleteness Theorem Almost to Robinson's Arithmetic Q.Dan E. Willard - 2002 - Journal of Symbolic Logic 67 (1):465-496.
    Let us recall that Raphael Robinson's Arithmetic Q is an axiom system that differs from Peano Arithmetic essentially by containing no Induction axioms [13], [18]. We will generalize the semantic-tableaux version of the Second Incompleteness Theorem almost to the level of System Q. We will prove that there exists a single rather long Π 1 sentence, valid in the standard model of the Natural Numbers and denoted as V, such that if α is any finite consistent extension of Q (...)
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  34.  6
    Phase Transitions for Gödel Incompleteness.Andreas Weiermann - 2009 - Annals of Pure and Applied Logic 157 (2-3):281-296.
    Gödel’s first incompleteness result from 1931 states that there are true assertions about the natural numbers which do not follow from the Peano axioms. Since 1931 many researchers have been looking for natural examples of such assertions and breakthroughs were obtained in the seventies by Jeff Paris [Some independence results for Peano arithmetic. J. Symbolic Logic 43 725–731] , Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977] and Laurie Kirby [L. Kirby, Jeff Paris, Accessible independence results for Peano (...)
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  35. Kurt Gödel, Paper on the Incompleteness Theorems (1931).Richard Zach - 2005 - In Ivor Grattan-Guinness (ed.), Landmark Writings in Mathematics. Amsterdam: North-Holland. pp. 917-925.
    This chapter describes Kurt Gödel's paper on the incompleteness theorems. Gödel's incompleteness results are two of the most fundamental and important contributions to logic and the foundations of mathematics. It had been assumed that first-order number theory is complete in the sense that any sentence in the language of number theory would be either provable from the axioms or refutable. Gödel's first incompleteness theorem showed that this assumption was false: it states that there are sentences of number (...)
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  36.  94
    Reflections on Concrete Incompleteness.G. Longo - 2011 - Philosophia Mathematica 19 (3):255-280.
    How do we prove true but unprovable propositions? Gödel produced a statement whose undecidability derives from its ad hoc construction. Concrete or mathematical incompleteness results are interesting unprovable statements of formal arithmetic. We point out where exactly the unprovability lies in the ordinary ‘mathematical’ proofs of two interesting formally unprovable propositions, the Kruskal-Friedman theorem on trees and Girard's normalization theorem in type theory. Their validity is based on robust cognitive performances, which ground mathematics in our relation to space and (...)
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  37.  51
    The Second Incompleteness Theorem and Bounded Interpretations.Albert Visser - 2012 - Studia Logica 100 (1-2):399-418.
    In this paper we formulate a version of Second Incompleteness Theorem. The idea is that a sequential sentence has ‘consistency power’ over a theory if it enables us to construct a bounded interpretation of that theory. An interpretation of V in U is bounded if, for some n , all translations of V -sentences are U -provably equivalent to sentences of complexity less than n . We call a sequential sentence with consistency power over T a pro-consistency statement for (...)
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  38.  77
    The Incompleteness of Theories of Games.Marcelo Tsuji, Newton C. A. Costa & Francisco A. Doria - 1998 - Journal of Philosophical Logic 27 (6):553-568.
    We first state a few previously obtained results that lead to general undecidability and incompleteness theorems in axiomatized theories that range from the theory of finite sets to classical elementary analysis. Out of those results we prove several incompleteness theorems for axiomatic versions of the theory of noncooperative games with Nash equilibria; in particular, we show the existence of finite games whose equilibria cannot be proven to be computable.
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  39.  28
    Complete Additivity and Modal Incompleteness.Wesley H. Holliday & Tadeusz Litak - 2019 - Review of Symbolic Logic 12 (3):487-535.
    In this article, we tell a story about incompleteness in modal logic. The story weaves together an article of van Benthem, “Syntactic aspects of modal incompleteness theorems,” and a longstanding open question: whether every normal modal logic can be characterized by a class of completely additive modal algebras, or as we call them, ${\cal V}$-baos. Using a first-order reformulation of the property of complete additivity, we prove that the modal logic that starred in van Benthem’s article resolves the (...)
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  40.  73
    The Incompleteness of Ideal Theory.Jörg Schaub - 2014 - Res Publica 20 (4):413-439.
    Can one give an account of a perfectly just society without invoking principles governing our responses to injustice? My claim is that addressing this question puts us in a position to reveal ambiguities and problems with the way in which Rawls draws the ideal/nonideal theory distinction that have so far gone unnoticed. In the first part of my paper, I demonstrate that Rawls’s original definition of the ideal/nonideal theory distinction is ambiguous as it is composed of two different conceptual distinctions, (...)
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  41.  44
    Liar-Type Paradoxes and the Incompleteness Phenomena.Makoto Kikuchi & Taishi Kurahashi - 2016 - Journal of Philosophical Logic 45 (4):381-398.
    We define a liar-type paradox as a consistent proposition in propositional modal logic which is obtained by attaching boxes to several subformulas of an inconsistent proposition in classical propositional logic, and show several famous paradoxes are liar-type. Then we show that we can generate a liar-type paradox from any inconsistent proposition in classical propositional logic and that undecidable sentences in arithmetic can be obtained from the existence of a liar-type paradox. We extend these results to predicate logic and discuss Yablo’s (...)
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  42.  45
    The Incompleteness of Theories of Games.Marcelo Tsuji, Newton C. A. Da Costa & Francisco A. Doria - 1998 - Journal of Philosophical Logic 27 (6):553 - 568.
    We first state a few previously obtained results that lead to general undecidability and incompleteness theorems in axiomatized theories that range from the theory of finite sets to classical elementary analysis. Out of those results we prove several incompleteness theorems for axiomatic versions of the theory of noncooperative games with Nash equilibria; in particular, we show the existence of finite games whose equilibria cannot be proven to be computable.
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  43.  49
    Godel's Theorem and Mechanism.David Coder - 1969 - Philosophy 44 (September):234-7.
    In “Minds, Machines, and Gödel”, J. R. Lucas claims that Goedel's incompleteness theorem constitutes a proof “that Mechanism is false, that is, that minds cannot be explained as machines”. He claims further that “if the proof of the falsity of mechanism is valid, it is of the greatest consequence for the whole of philosophy”. It seems to me that both of these claims are exaggerated. It is true that no minds can be explained as machines. But it is not (...)
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  44.  57
    Completeness and Incompleteness for Intuitionistic Logic.Charles McCarty - 2008 - Journal of Symbolic Logic 73 (4):1315-1327.
    We call a logic regular for a semantics when the satisfaction predicate for at least one of its nontheorems is closed under double negation. Such intuitionistic theories as second-order Heyting arithmetic HAS and the intuitionistic set theory IZF prove completeness for no regular logics, no matter how simple or complicated. Any extensions of those theories proving completeness for regular logics are classical, i.e., they derive the tertium non datur. When an intuitionistic metatheory features anticlassical principles or recognizes that a logic (...)
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  45.  52
    The Impact of the Incompleteness Theorems on Mathematics.Solomon Feferman - manuscript
    In addition to this being the centenary of Kurt Gödel’s birth, January marked 75 years since the publication (1931) of his stunning incompleteness theorems. Though widely known in one form or another by practicing mathematicians, and generally thought to say something fundamental about the limits and potentialities of mathematical knowledge, the actual importance of these results for mathematics is little understood. Nor is this an isolated example among famous results. For example, not long ago, Philip Davis wrote me (...)
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  46. Incompleteness – the Very Idea.Peter Smith - unknown
    Why these notes? After all, I’ve written An Introduction to Gödel’s Theorems. Surely that’s more than enough to be going on with? Ah, but there’s the snag. It is more than enough. In the writing, as is the way with these things, the book grew far beyond the scope of the lecture notes from which it started. And while I hope the result is still pretty accessible to someone prepared to put in the time and effort, there’s a (...)
     
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  47. Screening-Off and Causal Incompleteness: A No-Go Theorem.Elliott Sober & Mike Steel - 2013 - British Journal for the Philosophy of Science 64 (3):513-550.
    We begin by considering two principles, each having the form causal completeness ergo screening-off. The first concerns a common cause of two or more effects; the second describes an intermediate link in a causal chain. They are logically independent of each other, each is independent of Reichenbach's principle of the common cause, and each is a consequence of the causal Markov condition. Simple examples show that causal incompleteness means that screening-off may fail to obtain. We derive a stronger (...): in a rather general setting, if the composite cause C1 & C2 & … & Cn screens-off one event from another, then each of the n component causes C1, C2, …, Cn must fail to screen-off. The idea that a cause may be ordinally invariant in its impact on different effects is defined; it plays an important role in establishing this no-go theorem. Along the way, we describe how composite and component causes can all screen-off when ordinal invariance fails. We argue that this theorem is relevant to assessing the plausibility of the two screening-off principles. The discovery of incomplete causes that screen-off is not evidence that causal completeness must engender screening-off. Formal and epistemic analogies between screening-off and determinism are discussed. (shrink)
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  48.  16
    Primitive Recursion and Isaacson’s Thesis.Oliver Tatton-Brown - 2019 - Thought: A Journal of Philosophy 8 (1):4-15.
    Although Peano arithmetic is necessarily incomplete, Isaacson argued that it is in a sense conceptually complete: proving a statement of the language of PA that is independent of PA will require conceptual resources beyond those needed to understand PA. This paper gives a test of Isaacon’s thesis. Understanding PA requires understanding the functions of addition and multiplication. It is argued that grasping these primitive recursive functions involves grasping the double ancestral, a generalized version of the ancestral operator. Thus, we can (...)
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  49.  34
    Undecidability and Intuitionistic Incompleteness.D. C. McCarty - 1996 - Journal of Philosophical Logic 25 (5):559 - 565.
    Let S be a deductive system such that S-derivability (⊦s) is arithmetic and sound with respect to structures of class K. From simple conditions on K and ⊦s, it follows constructively that the K-completeness of ⊦s implies MP(S), a form of Markov's Principle. If ⊦s is undecidable then MP(S) is independent of first-order Heyting arithmetic. Also, if ⊦s is undecidable and the S proof relation is decidable, then MP(S) is independent of second-order Heyting arithmetic, HAS. Lastly, when ⊦s is many-one (...)
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  50.  43
    Physicians' Intent to Comply with the American Medical Association's Guidelines on Gifts From the Pharmaceutical Industry.S. L. Pinto, E. Lipowski, R. Segal, C. Kimberlin & J. Algina - 2007 - Journal of Medical Ethics 33 (6):313-319.
    Objective: To identify factors that predict physicians’ intent to comply with the American Medical Association’s ethical guidelines on gifts from the pharmaceutical industry.Methods: A survey was designed and mailed in June 2004 to a random sample of 850 physicians in Florida, USA, excluding physicians with inactive licences, incomplete addresses, addresses in other states and pretest participants. Factor analysis extracted six factors: attitude towards following the guidelines, subjective norms , facilitating conditions , profession-specific precedents , individual-specific precedents and intent. Multivariate regression (...)
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