Search results for 'Incompleteness' (try it on Scholar)

836 found
Order:
  1.  35
    Nicholas Harrigan & Robert W. Spekkens (2010). Einstein, Incompleteness, and the Epistemic View of Quantum States. 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 (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   6 citations  
  2.  21
    Lukas Skiba (forthcoming). Fictionalism and the Incompleteness Problem. Synthese:1-14.
    Modal fictionalists face a problem that arises due to their possible-world story being incomplete in the sense that certain relevant claims are neither true nor false according to it. It has recently been suggested that this incompleteness problem generalises to other brands of fictionalism, such as fictionalism about composite or mathematical objects. In this paper, I argue that these fictionalist positions are particularly threatened by a generalised incompleteness problem since they cannot emulate the modal fictionalists’ most attractive response. (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  3. H. Gaifman (2000). What Godel's Incompleteness Result Does and Does Not Show. Journal of Philosophy 97 (8):462-471.
    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 more forceful. Yet the (...)
    Direct download (8 more)  
     
    Export citation  
     
    My bibliography  
  4.  13
    Makoto Kikuchi, Taishi Kurahashi & Hiroshi Sakai (2012). On Proofs of the Incompleteness Theorems Based on Berry's Paradox by Vopěnka, Chaitin, and Boolos. Mathematical Logic Quarterly 58 (4‐5):307-316.
    By formalizing Berry's paradox, Vopěnka, Chaitin, Boolos and others proved the incompleteness theorems without using the diagonal argument. In this paper, we shall examine these proofs closely and show their relationships. Firstly, we shall show that we can use the diagonal argument for proofs of the incompleteness theorems based on Berry's paradox. Then, we shall show that an extension of Boolos' proof can be considered as a special case of Chaitin's proof by defining a suitable Kolmogorov complexity. We (...)
    Direct download (8 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  5.  18
    Albert Visser (2012). The Second Incompleteness Theorem and Bounded Interpretations. 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 (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  6. Christopher Gauker (2001). T-Schema Deflationism Versus Gödel’s First Incompleteness Theorem. Analysis 61 (270):129–136.
    I define T-schema deflationism as the thesis that a theory of truth for our language can simply take the form of certain instances of Tarski's schema (T). I show that any effective enumeration of these instances will yield as a dividend an effective enumeration of all truths of our language. But that contradicts Gödel's First Incompleteness Theorem. So the instances of (T) constituting the T-Schema deflationist's theory of truth are not effectively enumerable, which casts doubt on the idea that (...)
    Direct download (9 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  7.  82
    Panu Raatikainen (1998). On Interpreting Chaitin's Incompleteness Theorem. Journal of Philosophical Logic 27 (6):569-586.
    The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin's famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be good measure (...)
    Direct download (9 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  8.  16
    Makoto Kikuchi & Taishi Kurahashi (2016). Liar-Type Paradoxes and the Incompleteness Phenomena. 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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  9. Nicolás F. Lori & Alex H. Blin (2010). 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] 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 quantum to (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  10.  15
    Makoto Kikuchi (1994). A Note on Boolos' Proof of the Incompleteness Theorem. Mathematical Logic Quarterly 40 (4):528-532.
    We give a proof of Gödel's first incompleteness theorem based on Berry's paradox, and from it we also derive the second incompleteness theorem model-theoretically.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  11.  28
    Bernd Buldt (2014). The Scope of Gödel’s First Incompleteness Theorem. Logica Universalis 8 (3-4):499-552.
    Guided by questions of scope, this paper provides an overview of what is known about both the scope and, consequently, the limits of Gödel’s famous first incompleteness theorem.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  12.  15
    Paul H. Dembinski (2011). The Incompleteness of the Economy and Business: A Forceful Reminder. [REVIEW] Journal of Business Ethics 100 (S1):29-40.
    Many different but related arguments developed in the Caritas in Veritate converge on one central, yet not clearly stated, conclusion or thesis: economic and business activities are ‘incomplete’. This article will explore the above-mentioned ‘incompleteness’ thesis or argument from three different perspectives: the role, the practice and the purpose of economic and business activities in contemporary societies. In doing so, the paper will heavily draw on questions and, still not fully learned, lessons derived from the present financial and economic (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  13.  5
    Cezary Cieslinski (2002). Heterologicality and Incompleteness. Mathematical Logic Quarterly 48 (1):105-110.
    We present a semantic proof of Gödel's second incompleteness theorem, employing Grelling's antinomy of heterological expressions. For a theory T containing ZF, we define the sentence HETT which says intuitively that the predicate “heterological” is itself heterological. We show that this sentence doesn't follow from T and is equivalent to the consistency of T. Finally we show how to construct a similar incompleteness proof for Peano Arithmetic.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  14.  72
    James W. Garson (2010). Expressive Power and Incompleteness of Propositional Logics. Journal of Philosophical Logic 39 (2):159-171.
    Natural deduction systems were motivated by the desire to define the meaning of each connective by specifying how it is introduced and eliminated from inference. In one sense, this attempt fails, for it is well known that propositional logic rules underdetermine the classical truth tables. Natural deduction rules are too weak to enforce the intended readings of the connectives; they allow non-standard models. Two reactions to this phenomenon appear in the literature. One is to try to restore the standard readings, (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  15.  72
    Robert F. Hadley (2008). Consistency, Turing Computability and Gödel's First Incompleteness Theorem. 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 with (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  16.  62
    Marcelo Tsuji, Newton C. A. Costa & Francisco A. Doria (1998). The Incompleteness of Theories of Games. 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.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography  
  17.  22
    Newton C. A. Da Costa (2012). Gödel's Incompleteness Theorems and Physics. Principia 15 (3):453-459.
    This paper is a summary of a lecture in which I presented some remarks on Gödel’s incompleteness theorems and their meaning for the foundations of physics. The entire lecture will appear elsewhere. doi: http://dx.doi.org/ 10.5007 / 1808-1711.2011v15n3p453.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  18.  42
    Roman Murawski (1997). Gödel's Incompleteness Theorems and Computer Science. Foundations of Science 2 (1):123-135.
    In the paper some applications of Gödel's incompleteness theorems to discussions of problems of computer science are presented. In particular the problem of relations between the mind and machine (arguments by J.J.C. Smart and J.R. Lucas) is discussed. Next Gödel's opinion on this issue is studied. Finally some interpretations of Gödel's incompleteness theorems from the point of view of the information theory are presented.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography  
  19.  35
    Laureano Luna & Alex Blum (2008). Arithmetic and Logic Incompleteness: The Link. The Reasoner 2 (3):6.
    We show how second order logic incompleteness follows from incompleteness of arithmetic, as proved by Gödel.
    Translate
      Direct download  
     
    Export citation  
     
    My bibliography  
  20.  11
    Marcelo Tsuji, Newton C. A. Da Costa & Francisco A. Doria (1998). The Incompleteness of Theories of Games. 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.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  21.  30
    Cristian S. Calude (2002). Incompleteness, Complexity, Randomness and Beyond. Minds and Machines 12 (4):503-517.
    Gödel's Incompleteness Theorems have the same scientific status as Einstein's principle of relativity, Heisenberg's uncertainty principle, and Watson and Crick's double helix model of DNA. Our aim is to discuss some new faces of the incompleteness phenomenon unveiled by an information-theoretic approach to randomness and recent developments in quantum computing.
    Direct download (8 more)  
     
    Export citation  
     
    My bibliography  
  22.  12
    Juliana Bueno-Soler (2013). Multimodal Incompleteness Under Weak Negations. Logica Universalis 7 (1):21-31.
    This paper shows that some classes of multimodal paraconsistent logics endowed with weak forms of negation are incompletable with respect to Kripke semantics. The reach of such incompleteness is discussed, and we argue that this shortcoming, more than just a logical predicament, may be relevant for attempts to characterize quantum logics and to handle quantum information and quantum computation.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  23.  7
    L. Sacchetti (2002). Incompleteness and Fixed Points. Mathematical Logic Quarterly 48 (1):15-28.
    Our purpose is to present some connections between modal incompleteness andmodal logics related to the Gödel-Löb logic GL. One of our goals is to prove that for all m, n, k, l ∈ ℕ the logic K + equation image□i □jp ↔ p) → equation image□ip is incomplete and does not have the fixed point property. As a consequence we shall obtain that the Boolos logic KH does not have the fixed point property.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  24. Francesco Berto (2009). There's Something About Gödel: The Complete Guide to the Incompleteness Theorem. Wiley-Blackwell.
    The Gödelian symphony -- Foundations and paradoxes -- This sentence is false -- The liar and Gödel -- Language and metalanguage -- The axiomatic method or how to get the non-obvious out of the obvious -- Peano's axioms -- And the unsatisfied logicists, Frege and Russell -- Bits of set theory -- The abstraction principle -- Bytes of set theory -- Properties, relations, functions, that is, sets again -- Calculating, computing, enumerating, that is, the notion of algorithm -- Taking numbers (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  25.  7
    John-Michael Kuczynski (2016). Proof of the Incompleteness of Deductive Logic. Amazon Digital Services LLC.
    This short work proves the incompleteness of deductive logic. In other words, it proves that there is no recursive definition of K, where K is the class of all systems of logic.
    No categories
    Direct download  
     
    Export citation  
     
    My bibliography  
  26.  92
    Michael Detlefsen (1990). On an Alleged Refutation of Hilbert's Program Using Gödel's First Incompleteness Theorem. 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 (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  27.  63
    C. Chihara (1972). On Alleged Refutations of Mechanism Using Godel's Incompleteness Results. Journal of Philosophy 69 (September):507-26.
  28. Gregory J. Chaitin (1970). Computational Complexity and Godel's Incompleteness Theorem. [Rio De Janeiro,Centro Técnico Científico, Pontifícia Universidade Católica Do Rio De Janeiro.
     
    Export citation  
     
    My bibliography   2 citations  
  29.  2
    Dolph Ulrich (1992). On the Incompleteness of a Descending Chain of Extensions of Implicational S5. Mathematical Logic Quarterly 38 (1):321-323.
    C5.ω is obtained by adding, schematically, to the strict-implicational fragment C5 of S5 the axiom → ) → . This paper presents a fully general proof that neither C5.ω nor any of a descending chain of its extensions is complete with respect to any class of frames, correcting the garbled details of a version skeched in an earlier paper , 201-208).
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  30.  4
    Qiuen Yu, Consistency, Mechanicalness and Incompleteness.
    Submitted to the Faculty of Graduate Studies and Research in partial fulfilment of the requirements for the degree of Master of Arts, Department of Philosophy.
    Direct download  
     
    Export citation  
     
    My bibliography  
  31.  1
    Katsumasa Ishii (2003). A Note on the First Incompleteness Theorem. Mathematical Logic Quarterly 49 (2):214-216.
    Let T be an extension of Robinson's arithmetic Q. Then T is incomplete even if the set of the Gödel numbers of all axioms of T is ∑2.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  32. H. P. Barendregt (1976). The Incompleteness Theorems. Rijksuniversiteit Utrecht, Mathematisch Instituut.
     
    Export citation  
     
    My bibliography  
  33. Panu Raatikainen (2005). On the Philosophical Relevance of Gödel's Incompleteness Theorems. Revue Internationale de Philosophie 59 (4):513-534.
    Gödel began his 1951 Gibbs Lecture by stating: “Research in the foundations of mathematics during the past few decades has produced some results which seem to me of interest, not only in themselves, but also with regard to their implications for the traditional philosophical problems about the nature of mathematics.” (Gödel 1951) Gödel is referring here especially to his own incompleteness theorems (Gödel 1931). Gödel’s first incompleteness theorem (as improved by Rosser (1936)) says that for any consistent formalized (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  34.  26
    Susann Wagenknecht (2015). Facing the Incompleteness of Epistemic Trust: Managing Dependence in Scientific Practice. Social Epistemology 29 (2):160-184.
    Based on an empirical study of a research team in natural science, the author argues that collaborating scientists do not trust each other completely. Due to the inherent incompleteness of trust, epistemic trust among scientists is not sufficient to manage epistemic dependency in research teams. To mitigate the limitations of epistemic trust, scientists resort to specific strategies of indirect assessment such as dialoguing practices and the probing of explanatory responsiveness. Furthermore, they rely upon impersonal trust and deploy practices of (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  35. E. Sober & M. Steel (2013). Screening-Off and Causal Incompleteness: A No-Go Theorem. 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 result: (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  36. John Byron Manchak, Observational Indistinguishability and Geodesic Incompleteness.
    It has been suggested by Clark Glymour that the spatio-temporal structure of the universe might be underdetermined by all observational data that could ever, theoretically, be gathered. It is possible for two spacetimes to be observationally indistinguishable (OI) yet topologically distinct. David Malament extended the argument for the underdetermination of spacetime structure by showing that under quite general conditions (such as the absence of any closed timelike curves) a spacetime will always have an OI counterpart (at least in weak sense). (...)
    Direct download  
     
    Export citation  
     
    My bibliography  
  37.  85
    Richard Woodward (2012). Fictionalism and Incompleteness. Noûs 46 (4):781-790.
    The modal fictionalist faces a problem due to the fact that her chosen story seems to be incomplete—certain things are neither fictionally true nor fictionally false. The significance of this problem is not localized to modal fictionalism, however, since many fictionalists will face it too. By examining how the fictionalist should analyze the notion of truth according to her story, and, in particular, the role that conditionals play for the fictionalist, I develop a novel and elegant solution to the (...) problem. (shrink)
    Direct download (10 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  38. Carsten Held (2015). Einstein’s Boxes: Incompleteness of Quantum Mechanics Without a Separation Principle. Foundations of Physics 45 (9):1002-1018.
    Einstein made several attempts to argue for the incompleteness of quantum mechanics, not all of them using a separation principle. One unpublished example, the box parable, has received increased attention in the recent literature. Though the example is tailor-made for applying a separation principle and Einstein indeed applies one, he begins his discussion without it. An analysis of this first part of the parable naturally leads to an argument for incompleteness not involving a separation principle. I discuss the (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  39.  93
    Ray Buchanan & Gary Ostertag (2005). Has the Problem of Incompleteness Rested on a Mistake? Mind 114 (456):889-913.
    A common objection to Russell's theory of descriptions concerns incomplete definite descriptions: uses of (for example) ‘the book is overdue’ in contexts where there is clearly more than one book. Many contemporary Russellians hold that such utterances will invariably convey a contextually determined complete proposition, for example, that the book in your briefcase is overdue. But according to the objection this gets things wrong: typically, when a speaker utters such a sentence, no facts about the context or the speaker's communicative (...)
    Direct download (8 more)  
     
    Export citation  
     
    My bibliography   9 citations  
  40. Noson S. Yanofsky (2003). A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points. Bulletin of Symbolic Logic 9 (3):362-386.
    Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses the semantic paradoxes, and how they arise as diagonal arguments and fixed point theorems in logic, computability theory, complexity theory and formal language theory.
    Direct download (10 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  41. Harvey Friedman, Fromal Statements of Godel's Second Incompleteness Theorem.
    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.
     
    Export citation  
     
    My bibliography  
  42. Zofia Adamowicz & Teresa Bigorajska (2001). Existentially Closed Structures and Gödel's Second Incompleteness Theorem. Journal of Symbolic Logic 66 (1):349-356.
    We prove that any 1-closed (see def 1.1) model of the Π 2 consequences of PA satisfies ¬Cons PA which gives a proof of the second Godel incompleteness theorem without the use of the Godel diagonal lemma. We prove a few other theorems by the same method.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  43. Raymond M. Smullyan (1992). Gödel's Incompleteness Theorems. Oxford University Press.
    Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness (...)
    Direct download  
     
    Export citation  
     
    My bibliography   11 citations  
  44. Thomas A. C. Reydon & Markus Scholz (2014). Darwinism and Organizational Ecology A Case of Incompleteness or Incompatibility? Philosophy of the Social Sciences 44 (3):365-374.
    Recently, Dollimore criticized our claim that Organizational Ecology is not a Darwinian research program. She argued that Organizational Ecology is merely an incomplete Darwinian program and provided a suggestion as to how this incompleteness could be remedied. Here, we argue that Dollimore’s suggestion fails to remedy the principal problem that Organizational Ecology faces and that there are good reasons to think of the program as deeply incompatible with Darwinian thinking.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  45.  86
    A. O. Barut, M. Božić & Z. Marić (1988). Joint Probabilities of Noncommuting Operators and Incompleteness of Quantum Mechanics. Foundations of Physics 18 (10):999-1012.
    We use joint probabilities to analyze the EPR argument in the Bohm's example of spins.(1) The properties of distribution functions for two, three, or more noncommuting spin components are explicitly studied and their limitations are pointed out. Within the statistical ensemble interpretation of quantum theory (where only statements about repeated events can be made), the incompleteness of quantum theory does not follow, as the consistent use of joint probabilities shows. This does not exclude a completion of quantum mechanics, going (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  46.  60
    Paolo Mancosu (1999). Between Vienna and Berlin: The Immediate Reception of Godel's Incompleteness Theorems. 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.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   6 citations  
  47. Glen Hoffmann (2007). The Semantic Theory of Truth: Field's Incompleteness Objection. Philosophia 35 (2):161-170.
    According to Field’s influential incompleteness objection, Tarski’s semantic theory of truth is unsatisfactory since the definition that forms its basis is incomplete in two distinct senses: (1) it is physicalistically inadequate, and for this reason, (2) it is conceptually deficient. In this paper, I defend the semantic theory of truth against the incompleteness objection by conceding (1) but rejecting (2). After arguing that Davidson and McDowell’s reply to the incompleteness objection fails to pass muster, I argue that, (...)
    Direct download (8 more)  
     
    Export citation  
     
    My bibliography  
  48.  1
    Andreas Weiermann (2009). Phase Transitions for Gödel Incompleteness. Annals of Pure and Applied Logic 157 (2):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 Arithmetic, Bull. (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  49.  16
    Dan E. Willard (2001). Self-Verifying Axiom Systems, the Incompleteness Theorem and Related Reflection Principles. Journal of Symbolic Logic 66 (2):536-596.
    We will study several weak axiom systems that use the Subtraction and Division primitives (rather than Addition and Multiplication) to formally encode the theorems of Arithmetic. Provided such axiom systems do not recognize Multiplication as a total function, we will show that it is feasible for them to verify their Semantic Tableaux, Herbrand, and Cut-Free consistencies. If our axiom systems additionally do not recognize Addition as a total function, they will be capable of recognizing the consistency of their Hilbert-style deductive (...)
    Direct download (9 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  50. Harvey Friedman, Boolean Relation Theory and the Incompleteness Phenomena.
    ENTIRE BOOK, SINGLE FILE. BOOLEAN RELATION THEORY AND THE INCOMPLETENESS PHENOMENA. 10/30/07 version. Same as 10/01/07 version with Preface added. 568 pages without Appendix B. See above for Appendix B by Francoise Point.
     
    Export citation  
     
    My bibliography  
1 — 50 / 836