Results for 'incompleteness'

115 found
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  1. 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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  2. On Interpreting Chaitin's Incompleteness Theorem.Panu Raatikainen - 1998 - 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 (...)
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  3. Kurt Gödel, Paper on the Incompleteness Theorems (1931).Richard Zach - 2004 - 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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  4. Incompleteness and Computability. An Open Introduction to Gödel's Theorems.Richard Zach - 2019
    Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.
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  5.  85
    Remarks on Wittgenstein, Gödel, Chaitin, Incompleteness, Impossiblity and the Psychological Basis of Science and Mathematics.Michael Richard Starks - 2019 - In Remarks on Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason in Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, da Costa, Godel, Searle, Rodych, Berto, Floyd, Moyal. Las Vegas, NV USA: Reality Press. pp. 24-38.
    It is commonly thought that such topics as Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason are disparate scientific physical or mathematical issues having little or nothing in common. I suggest that they are largely standard philosophical problems (i.e., language games) which were resolved by Wittgenstein over 80 years ago. -/- Wittgenstein also demonstrated the fatal error in regarding mathematics or language or our behavior in general as a unitary coherent logical ‘system,’ rather than (...)
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  6. Interactivity, Fictionality, and Incompleteness.Nathan Wildman & Richard Woodward - forthcoming - In Grant Tavinor & Jon Robson (eds.), The Aesthetics of Videogames. Routledge.
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  7.  61
    Eliminating Undecidability and Incompleteness in Formal Systems.Pete Olcott - manuscript
    To eliminate incompleteness, undecidability and inconsistency from formal systems we only need to convert the formal proofs to theorem consequences of symbolic logic to conform to the sound deductive inference model. -/- Within the sound deductive inference model there is a (connected sequence of valid deductions from true premises to a true conclusion) thus unlike the formal proofs of symbolic logic provability cannot diverge from truth.
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  8.  50
    Wolpert, Chaitin and Wittgenstein on Impossibility, Incompleteness, the Liar Paradox, Theism, the Limits of Computation, a Non-Quantum Mechanical Uncertainty Principle and the Universe as Computer—the Ultimate Theorem in Turing Machine Theory (Revised 2019).Michael Starks - 2019 - In Suicidal Utopian Delusions in the 21st Century -- Philosophy, Human Nature and the Collapse of Civilization -- Articles and Reviews 2006-2019 4th Edition Michael Starks. Las Vegas, NV USA: Reality Press. pp. 294-299.
    I have read many recent discussions of the limits of computation and the universe as computer, hoping to find some comments on the amazing work of polymath physicist and decision theorist David Wolpert but have not found a single citation and so I present this very brief summary. Wolpert proved some stunning impossibility or incompleteness theorems (1992 to 2008-see arxiv dot org) on the limits to inference (computation) that are so general they are independent of the device doing the (...)
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  9. David Wolpert on Impossibility, Incompleteness, the Liar Paradox, the Limits of Computation, a Non-Quantum Mechanical Uncertainty Principle and the Universe as Computer—the Ultimate Theorem in Turing Machine Theory.Michael Starks - manuscript
    I have read many recent discussions of the limits of computation and the universe as computer, hoping to find some comments on the amazing work of polymath physicist and decision theorist David Wolpert but have not found a single citation and so I present this very brief summary. Wolpert proved some stunning impossibility or incompleteness theorems (1992 to 2008-see arxiv.org) on the limits to inference (computation) that are so general they are independent of the device doing the computation, and (...)
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  10.  79
    Gödel's Incompleteness Theorems, Free Will and Mathematical Thought.Solomon Feferman - 2011 - In Richard Swinburne (ed.), Free Will and Modern Science. Oup/British Academy.
    The determinism-free will debate is perhaps as old as philosophy itself and has been engaged in from a great variety of points of view including those of scientific, theological, and logical character. This chapter focuses on two arguments from logic. First, there is an argument in support of determinism that dates back to Aristotle, if not farther. It rests on acceptance of the Law of Excluded Middle, according to which every proposition is either true or false, no matter whether the (...)
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  11. The Semantic Theory of Truth: Field’s Incompleteness Objection.Glen A. Hoffmann - 2007 - 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, (...)
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  12.  71
    Von Neumann's Methodology of Science: From Incompleteness Theorems to Later Foundational Reflections.Giambattista Formica - 2010 - Perspectives on Science 18 (4):480-499.
    In spite of the many efforts made to clarify von Neumann’s methodology of science, one crucial point seems to have been disregarded in recent literature: his closeness to Hilbert’s spirit. In this paper I shall claim that the scientific methodology adopted by von Neumann in his later foundational reflections originates in the attempt to revaluate Hilbert’s axiomatics in the light of Gödel’s incompleteness theorems. Indeed, axiomatics continues to be pursued by the Hungarian mathematician in the spirit of Hilbert’s school. (...)
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  13.  37
    The Ontic Probability Interpretation of Quantum Theory - Part I: The Meaning of Einstein's Incompleteness Claim.Felix Alba-Juez - manuscript
    Ignited by Einstein and Bohr a century ago, the philosophical struggle about Reality is yet unfinished, with no signs of a swift resolution. Despite vast technological progress fueled by the iconic EPR paper (EPR), the intricate link between ontic and epistemic aspects of Quantum Theory (QT) has greatly hindered our grip on Reality and further progress in physical theory. Fallacies concealed by tortuous logical negations made EPR comprehension much harder than it could have been had Einstein written it himself in (...)
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  14.  13
    The Ontic Probability Interpretation of Quantum Theory - Part II: Einstein's Incompleteness/Nonlocality Dilemma.Felix Alba-Juez - manuscript
    After pinpointing a conceptual confusion (TCC), a Reality preconception (TRP1), and a fallacious dichotomy (TFD), the famous EPR/EPRB argument for correlated ‘particles’ is studied in the light of the Ontic Probability Interpretation (TOPI) of Quantum Theory (QT). Another Reality preconception (TRP2) is identified, showing that EPR used and ignored QT predictions in a single paralogism. Employing TFD and TRP2, EPR unveiled a contradiction veiled in its premises. By removing nonlocality from QT’s Ontology by fiat, EPR preordained its incompleteness. The (...)
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  15. Incompleteness of a First-Order Gödel Logic and Some Temporal Logics of Programs.Matthias Baaz, Alexander Leitsch & Richard Zach - 1996 - In Hans Kleine Büning (ed.), Computer Science Logic. CSL 1995. Selected Papers. Berlin: Springer. pp. 1--15.
    It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' temporal (...)
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  16. The Incompleteness of Luck Egalitarianism.Ryan Long - 2011 - Social Philosophy Today 27:87-96.
    Luck egalitarianism makes a fundamental distinction between inequalities for which agents are responsible and inequalities stemming from luck. I give several reasons to find luck egalitarianism a compelling view of distributive justice. I then argue that it is an incomplete theory of equality. Luck egalitarianism lacks the normative resources to achieve its ends. It is unable to specify the prior conditions under which persons are situated equivalently such that their choices can bear this tremendous weight. This means that luck egalitarians (...)
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  17. Does Gödel's Incompleteness Theorem Prove That Truth Transcends Proof?Joseph Vidal-Rosset - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. pp. 51--73.
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  18. Refuting Incompleteness and Undefinability.Pete Olcott - manuscript
    Within the (Haskell Curry) notion of a formal system we complete Tarski's formal correctness: ∀x True(x) ↔ ⊢ x and use this finally formalized notion of Truth to refute his own Undefinability Theorem (based on the Liar Paradox), the Liar Paradox, and the (Panu Raatikainen) essence of the conclusion of the 1931 Incompleteness Theorem.
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  19.  98
    Wolpert, Chaitin and Wittgenstein on Impossibility, Incompleteness, the Limits of Computation, Theism and the Universe as Computer-the Ultimate Turing Theorem.Michael Starks - 2017 - Philosophy, Human Nature and the Collapse of Civilization Michael Starks 3rd Ed. (2017).
    I have read many recent discussions of the limits of computation and the universe as computer, hoping to find some comments on the amazing work of polymath physicist and decision theorist David Wolpert but have not found a single citation and so I present this very brief summary. Wolpert proved some stunning impossibility or incompleteness theorems (1992 to 2008-see arxiv.org) on the limits to inference (computation) that are so general they are independent of the device doing the computation, and (...)
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  20.  46
    Do Goedel's Incompleteness Theorems Set Absolute Limits on the Ability of the Brain to Express and Communicate Mental Concepts Verifiably?Bhupinder Singh Anand - 2004 - Neuroquantology 2:60-100.
    Classical interpretations of Goedels formal reasoning, and of his conclusions, implicitly imply that mathematical languages are essentially incomplete, in the sense that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is, both, non-algorithmic, and essentially unverifiable. However, a language of general, scientific, discourse, which intends to mathematically express, and unambiguously communicate, intuitive concepts that correspond to scientific investigations, cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth (...)
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  21. Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics.Vladimir Kanovei, Mikhail G. Katz & Thomas Mormann - 2013 - Foundations of Science 18 (2):259-296.
    We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...)
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  22. The Gödel Paradox and Wittgenstein's Reasons.Francesco Berto - 2009 - Philosophia Mathematica 17 (2):208-219.
    An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics (...)
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  23. Defending Gödel Against Floyd-Putnam's Wittgenstein.Kaave Lajevardi - manuscript
    I argue against Juliet Floyd and Hilary Putnam's (2000, 2004) reading of Wittgenstein's "notorious" paragraph on Gödel's first incompleteness theorem.
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  24.  73
    Consciousness as Computation: A Defense of Strong AI Based on Quantum-State Functionalism.R. Michael Perry - 2006 - In Charles Tandy (ed.), Death and Anti-Death, Volume 4: Twenty Years After De Beauvoir, Thirty Years After Heidegger. Palo Alto: Ria University Press.
    The viewpoint that consciousness, including feeling, could be fully expressed by a computational device is known as strong artificial intelligence or strong AI. Here I offer a defense of strong AI based on machine-state functionalism at the quantum level, or quantum-state functionalism. I consider arguments against strong AI, then summarize some counterarguments I find compelling, including Torkel Franzén’s work which challenges Roger Penrose’s claim, based on Gödel incompleteness, that mathematicians have nonalgorithmic levels of “certainty.” Some consequences of strong AI (...)
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  25. “The Animal” After Derrida: Interrogating the Bioethics of Geno-Cide.Norman Swazo - 2013 - Les Ateliers de L'Éthique 8 (1):91-123.
    Bioethics tends to be dominated by discourses concerned with the ethical dimension of medical practice, the organization of medical care, and the integrity of biomedical research involving human subjects and animal testing. Jacques Derrida has explored the fundamental question of the “limit” that identifies and differentiates the human animal from the nonhuman animal. However, to date his work has not received any reception in the field of biomedical ethics. In this paper, I examine what Derrida’s thought about this limit might (...)
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  26. Proof That Wittgenstein is Correct About Gödel.P. Olcott - manuscript
    In order to understand that Wittgenstein's refutation of Gödel's 1931 Incompleteness Theorem is correct we must fill in some details of the notion of a formal system that Wittgenstein had in mind. Expressions of language encoding analytical knowledge are only true if they have been defined to be true or valid deductions from true premises prove that they are true. When these relations are formalized as formal proofs to theorem consequences then Provable(x) cannot possibly diverge from True(x).
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  27. Review of 'The Outer Limits of Reason' by Noson Yanofsky 403p(2013).Michael Starks - 2017 - Philosophy, Human Nature and the Collapse of Civilization -- Articles and Reviews 2006-2017 3rd Ed 686p(2017).
    I give a detailed review of 'The Outer Limits of Reason' by Noson Yanofsky 403(2013) from a unified perspective of Wittgenstein and evolutionary psychology. I indicate that the difficulty with such issues as paradox in language and math, incompleteness, undecidability, computability, the brain and the universe as computers etc., all arise from the failure to look carefully at our use of language in the appropriate context and hence the failure to separate issues of scientific fact from issues of how (...)
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  28.  22
    Wolpert, Chaitin y Wittgenstein sobre la imposibilidad, la incompletitud, la paradoja mentirosa, el teísmo, los límites de la computación, un principio de incertidumbre mecánica no cuántica y el universo como computadora, el teorema definitivo en la teoría de la máquina de Turing (revisado en 2019).Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 64-70.
    It is commonly thought that Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason are disparate scientific physical or mathematical issues having little or nothing in common. I suggest that they are largely standard philosophical problems (i.e., language games) which were mostly resolved by Wittgenstein over 80years ago. -/- “What we are ‘tempted to say’ in such a case is, of course, not philosophy, but it is its raw material. Thus, for example, what a mathematician (...)
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  29. What is Mathematics: Gödel's Theorem and Around (Edition 2015).Karlis Podnieks - manuscript
    Introduction to mathematical logic, part 2.Textbook for students in mathematical logic and foundations of mathematics. Platonism, Intuition, Formalism. Axiomatic set theory. Around the Continuum Problem. Axiom of Determinacy. Large Cardinal Axioms. Ackermann's Set Theory. First order arithmetic. Hilbert's 10th problem. Incompleteness theorems. Consequences. Connected results: double incompleteness theorem, unsolvability of reasoning, theorem on the size of proofs, diophantine incompleteness, Loeb's theorem, consistent universal statements are provable, Berry's paradox, incompleteness and Chaitin's theorem. Around Ramsey's theorem.
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  30.  49
    What Do Paraconsistent, Undecidable, Random, Computable and Incomplete Mean? A Review of Godel's Way: Exploits Into an Undecidable World by Gregory Chaitin, Francisco A Doria, Newton C.A. Da Costa 160p (2012) (Review Revised 2019).Michael Starks - 2019 - In Suicidal Utopian Delusions in the 21st Century -- Philosophy, Human Nature and the Collapse of Civilization -- Articles and Reviews 2006-2019 4th Edition Michael Starks. Las Vegas, NV USA: Reality Press. pp. 278-293.
    In ‘Godel’s Way’ three eminent scientists discuss issues such as undecidability, incompleteness, randomness, computability and paraconsistency. I approach these issues from the Wittgensteinian viewpoint that there are two basic issues which have completely different solutions. There are the scientific or empirical issues, which are facts about the world that need to be investigated observationally and philosophical issues as to how language can be used intelligibly (which include certain questions in mathematics and logic), which need to be decided by looking (...)
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  31.  46
    Review of 'The Outer Limits of Reason' by Noson Yanofsky 403p (2013) (Review Revised 2019).Michael Starks - 2019 - In Suicidal Utopian Delusions in the 21st Century -- Philosophy, Human Nature and the Collapse of Civilization -- Articles and Reviews 2006-2019 4th Edition Michael Starks. Las Vegas, NV USA: Reality Press. pp. 299-316.
    I give a detailed review of 'The Outer Limits of Reason' by Noson Yanofsky from a unified perspective of Wittgenstein and evolutionary psychology. I indicate that the difficulty with such issues as paradox in language and math, incompleteness, undecidability, computability, the brain and the universe as computers etc., all arise from the failure to look carefully at our use of language in the appropriate context and hence the failure to separate issues of scientific fact from issues of how language (...)
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  32.  19
    Gödelova Věta a Relace Logického Důsledku.Jaroslav Zouhar - 2010 - Teorie Vědy / Theory of Science 32 (1):59-95.
    In his proof of the first incompleteness theorem, Kurt Gödel provided a method of showing the truth of specific arithmetical statements on the condition that all the axioms of a certain formal theory of arithmetic are true. Furthermore, the statement whose truth is shown in this way cannot be proved in the theory in question. Thus it may seem that the relation of logical consequence is wider than the relation of derivability by a pre-defined set of rules. The aim (...)
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  33.  27
    Automated Theorem Proving and Its Prospects. [REVIEW]Desmond Fearnley-Sander - 1995 - PSYCHE: An Interdisciplinary Journal of Research On Consciousness 2.
    REVIEW OF: Automated Development of Fundamental Mathematical Theories by Art Quaife. (1992: Kluwer Academic Publishers) 271pp. Using the theorem prover OTTER Art Quaife has proved four hundred theorems of von Neumann-Bernays-Gödel set theory; twelve hundred theorems and definitions of elementary number theory; dozens of Euclidean geometry theorems; and Gödel's incompleteness theorems. It is an impressive achievement. To gauge its significance and to see what prospects it offers this review looks closely at the book and the proofs it presents.
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  34. Utilitarianism with and Without Expected Utility.David McCarthy, Kalle Mikkola & Joaquin Teruji Thomas - 2016 - Journal of Mathematical Economics 87:77-113.
    We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are (...)
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  35. The Expansion View of Thick Concepts.Brent G. Kyle - forthcoming - Noûs.
    This paper proposes a new Separabilist account of thick concepts, called the Expansion View (or EV). According to EV, thick concepts are expanded contents of thin terms. An expanded content is, roughly, the semantic content of a predicate along with modifiers. Although EV is a form of Separabilism, it is distinct from the only kind of Separabilism discussed in the literature, and it has many features that Inseparabilists want from an account of thick concepts. EV can also give non-cognitivists a (...)
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  36.  50
    The Inert Vs. The Living State of Matter: Extended Criticality, Time Geometry, Anti-Entropy - An Overview.Giuseppe Longo & Maël Montévil - 2012 - Frontiers in Physiology 3:39.
    The physical singularity of life phenomena is analyzed by means of comparison with the driving concepts of theories of the inert. We outline conceptual analogies, transferals of methodologies and theoretical instruments between physics and biology, in addition to indicating significant differences and sometimes logical dualities. In order to make biological phenomenalities intelligible, we introduce theoretical extensions to certain physical theories. In this synthetic paper, we summarize and propose a unified conceptual framework for the main conclusions drawn from work spanning a (...)
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  37. Minimal Sartre: Diagonalization and Pure Reflection.John Bova - 2018 - Open Philosophy 1:360-379.
    These remarks take up the reflexive problematics of Being and Nothingness and related texts from a metalogical perspective. A mutually illuminating translation is posited between, on the one hand, Sartre’s theory of pure reflection, the linchpin of the works of Sartre’s early period and the site of their greatest difficulties, and, on the other hand, the quasi-formalism of diagonalization, the engine of the classical theorems of Cantor, Godel, Tarski, Turing, etc. Surprisingly, the dialectic of mathematical logic from its inception through (...)
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  38. The Inexpressibility of Validity.Julien Murzi - 2014 - Analysis 74 (1):65-81.
    Tarski's Undefinability of Truth Theorem comes in two versions: that no consistent theory which interprets Robinson's Arithmetic (Q) can prove all instances of the T-Scheme and hence define truth; and that no such theory, if sound, can even express truth. In this note, I prove corresponding limitative results for validity. While Peano Arithmetic already has the resources to define a predicate expressing logical validity, as Jeff Ketland has recently pointed out (2012, Validity as a primitive. Analysis 72: 421-30), no theory (...)
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  39.  61
    Representation of Strongly Independent Preorders by Sets of Scalar-Valued Functions.David McCarthy, Kalle Mikkola & Teruji Thomas - 2017 - MPRA Paper No. 79284.
    We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infi nite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfi es a condition that we call Polarization.
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  40. Continuity and Completeness of Strongly Independent Preorders.David McCarthy & Kalle Mikkola - 2018 - Mathematical Social Sciences 93:141-145.
    A strongly independent preorder on a possibly in finite dimensional convex set that satisfi es two of the following conditions must satisfy the third: (i) the Archimedean continuity condition; (ii) mixture continuity; and (iii) comparability under the preorder is an equivalence relation. In addition, if the preorder is nontrivial (has nonempty asymmetric part) and satisfi es two of the following conditions, it must satisfy the third: (i') a modest strengthening of the Archimedean condition; (ii') mixture continuity; and (iii') completeness. Applications (...)
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  41. Hayek, Gödel, and the Case for Methodological Dualism.Ludwig M. P. van den Hauwe - 2011 - Journal of Economic Methodology 18 (4):387-407.
    On a few occasions F.A. Hayek made reference to the famous Gödel theorems in mathematical logic in the context of expounding his cognitive and social theory. The exact meaning of the supposed relationship between Gödel's theorems and the essential proposition of Hayek's theory of mind remains subject to interpretation, however. The author of this article argues that the relationship between Hayek's thesis that the human brain can never fully explain itself and the essential insight provided by Gödel's theorems in mathematical (...)
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  42.  80
    The Real Problem with Uniqueness.Andrei Moldovan - 2017 - SATS 18 (2):125-139.
    Arguments against the Russellian theory of definite descriptions based on cases that involve failures of uniqueness are a recurrent theme in the relevant literature. In this paper, I discuss a number of such arguments, from Strawson (1950), Ramachandran (1993) and Szabo (2005). I argue that the Russellian has resources to account for these data by deploying a variety of mechanisms of quantifier domain restrictions. Finally, I present a case that is more problematic for the Russellian. While the previous cases all (...)
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  43. Science and Meaning.Nicholas Maxwell - 2002 - The Philosophers' Magazine (18):15-16.
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  44.  45
    A Note on Incomplete Theory.Han Geurdes - manuscript
    In the paper it is demonstrated that Bell's theorem is unproveable.
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  45.  90
    Exploring Randomness.Panu Raatikainen - 2001 - Notices of the AMS 48 (9):992-6.
    Review of "Exploring Randomness" (200) and "The Unknowable" (1999) by Gregory Chaitin.
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  46. Minimal Type Theory (MTT).Pete Olcott - manuscript
    Minimal Type Theory (MTT) is based on type theory in that it is agnostic about Predicate Logic level and expressly disallows the evaluation of incompatible types. It is called Minimal because it has the fewest possible number of fundamental types, and has all of its syntax expressed entirely as the connections in a directed acyclic graph.
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  47.  26
    ¿Qué significa paraconsistente, indescifrable, aleatorio, computable e incompleto? Una revisión de la Manera de Godel: explota en un mundo indecible (Godel’s Way: exploits into an undecidable world) por Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa 160P (2012) (revisión revisada 2019).Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 44-63.
    En ' Godel’s Way ', tres eminentes científicos discuten temas como la indecisión, la incompleta, la aleatoriedad, la computabilidad y la paraconsistencia. Me acerco a estas cuestiones desde el punto de vista de Wittgensteinian de que hay dos cuestiones básicas que tienen soluciones completamente diferentes. Existen las cuestiones científicas o empíricas, que son hechos sobre el mundo que necesitan ser investigados observacionalmente y cuestiones filosóficas en cuanto a cómo el lenguaje se puede utilizar inteligiblemente (que incluyen ciertas preguntas en matemáticas (...)
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  48.  79
    Deductively Sound Formal Proofs.P. Olcott - manuscript
    Could the intersection of [formal proofs of mathematical logic] and [sound deductive inference] specify formal systems having [deductively sound formal proofs of mathematical logic]? -/- All that we have to do to provide [deductively sound formal proofs of mathematical logic] is select the subset of conventional [formal proofs of mathematical logic] having true premises and now we have [deductively sound formal proofs of mathematical logic].
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  49.  22
    Reseña de ' Los Límites Exteriores de la Razón '(The Outer Limits of Reason) por Noson Yanofsky 403p (2013) (revision revisada 2019).Michael Richard Starks - 2019 - In Delirios Utópicos Suicidas en el Siglo 21 La filosofía, la naturaleza humana y el colapso de la civilización Artículos y reseñas 2006-2019 4a Edición. Las Vegas, NV USA: Reality Press. pp. 283-298.
    Doy una revisión detallada de ' los límites externos de la razón ' por Noson Yanofsky desde una perspectiva unificada de Wittgenstein y la psicología evolutiva. Yo indiqué que la dificultad con cuestiones como la paradoja en el lenguaje y las matemáticas, la incompletitud, la indeterminación, la computabilidad, el cerebro y el universo como ordenadores, etc., surgen de la falta de mirada cuidadosa a nuestro uso del lenguaje en el adecuado contexto y, por tanto, el Error al separar los problemas (...)
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  50.  22
    Reseña de ‘I am a Strange Loop’ (Soy un Lazo Extraño) de Douglas Hofstadter (2007) (revisión revisada 2019).Michael Richard Starks - 2019 - In Delirios Utópicos Suicidas en el Siglo 21 La filosofía, la naturaleza humana y el colapso de la civilización Artículos y reseñas 2006-2019 4a Edición. Las Vegas, NV USA: Reality Press. pp. 205-221.
    Último sermón de la iglesia del naturalismo fundamentalista por el pastor Hofstadter. Al igual que su mucho más famoso (o infame por sus incesantemente errores filosóficos) trabajo Godel, Escher, Bach, tiene una plausibilidad superficial, pero si se entiende que se trata de un científico rampante que mezcla problemas científicos reales con los filosóficos (es decir, el sólo los problemas reales son los juegos de idiomas que debemos jugar) entonces casi todo su interés desaparece. Proporciono un marco para el análisis basado (...)
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