Search results for 'Yablo s paradox' (try it on Scholar)

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  1.  87
    Stephen Yablo (2014). Carnap’s Paradox and Easy Ontology. Journal of Philosophy 111 (9/10):470-501.
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  2.  8
    Taishi Kurahashi (2014). Rosser-Type Undecidable Sentences Based on Yablo’s Paradox. Journal of Philosophical Logic 43 (5):999-1017.
    It is widely considered that Gödel’s and Rosser’s proofs of the incompleteness theorems are related to the Liar Paradox. Yablo’s paradox, a Liar-like paradox without self-reference, can also be used to prove Gödel’s first and second incompleteness theorems. We show that the situation with the formalization of Yablo’s paradox using Rosser’s provability predicate is different from that of Rosser’s proof. Namely, by using the technique of Guaspari and Solovay, we prove that the undecidability of (...)
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  3.  35
    Ming Hsiung (2013). Equiparadoxicality of Yablo's Paradox and the Liar. Journal of Logic, Language and Information 22 (1):23-31.
    It is proved that Yablo’s paradox and the Liar paradox are equiparadoxical, in the sense that their paradoxicality is based upon exactly the same circularity condition—for any frame ${\mathcal{K}}$ , the following are equivalent: (1) Yablo’s sequence leads to a paradox in ${\mathcal{K}}$ ; (2) the Liar sentence leads to a paradox in ${\mathcal{K}}$ ; (3) ${\mathcal{K}}$ contains odd cycles. This result does not conflict with Yablo’s claim that his sequence is non-self-referential. Rather, (...)
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  4.  33
    O. Bueno & M. Colyvan (2003). Yablo's Paradox and Referring to Infinite Objects. Australasian Journal of Philosophy 81 (3):402 – 412.
    The blame for the semantic and set-theoretic paradoxes is often placed on self-reference and circularity. Some years ago, Yablo [1985; 1993] challenged this diagnosis, by producing a paradox that's liar-like but does not seem to involve circularity. But is Yablo's paradox really non-circular? In a recent paper, Beall [2001] has suggested that there are no means available to refer to Yablo's paradox without invoking descriptions, and since Priest [1997] has shown that any such description (...)
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  5.  64
    Roy A. Sorensen (1998). Yablo's Paradox and Kindred Infinite Liars. Mind 107 (425):137-155.
    This is a defense and extension of Stephen Yablo's claim that self-reference is completely inessential to the liar paradox. An infinite sequence of sentences of the form 'None of these subsequent sentences are true' generates the same instability in assigning truth values. I argue Yablo's technique of substituting infinity for self-reference applies to all so-called 'self-referential' paradoxes. A representative sample is provided which includes counterparts of the preface paradox, Pseudo-Scotus's validity paradox, the Knower, and other (...)
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  6. Otávio Bueno & Mark Colyvan, Yablo's Paradox Rides Again: A Reply to Ketland.
    Yablo’s paradox is generated by the following (infinite) list of sentences (called the Yablo list): (s1) For all k > 1, sk is not true. (s2) For all k > 2, sk is not true. (s3) For all k > 3, sk is not true. . . . . . . . .
     
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  7.  62
    Jeffrey Ketland (2005). Yablo's Paradox and Ω-Inconsistency. Synthese 145 (3):295-302.
    It is argued that Yablo’s Paradox is not strictly paradoxical, but rather ‘ω-paradoxical’. Under a natural formalization, the list of Yablo sentences may be constructed using a diagonalization argument and can be shown to be ω-inconsistent, but nonetheless consistent. The derivation of an inconsistency requires a uniform fixed-point construction. Moreover, the truth-theoretic disquotational principle required is also uniform, rather than the local disquotational T-scheme. The theory with the local disquotation T-scheme applied to individual sentences from the (...) list is also consistent. (shrink)
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  8.  84
    Jeffrey Ketland (2004). Bueno and Colyvan on Yablo's Paradox. Analysis 64 (2):165–172.
    This is a response to a paper “Paradox without satisfaction”, Analysis 63, 152-6 (2003) by Otavio Bueno and Mark Colyvan on Yablo’s paradox. I argue that this paper makes several substantial mathematical errors which vitiate the paper. (For the technical details, see [12] below.).
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  9.  24
    Claudio Bernardi (2009). A Topological Approach to Yablo's Paradox. Notre Dame Journal of Formal Logic 50 (3):331-338.
    Some years ago, Yablo gave a paradox concerning an infinite sequence of sentences: if each sentence of the sequence is 'every subsequent sentence in the sequence is false', a contradiction easily follows. In this paper we suggest a formalization of Yablo's paradox in algebraic and topological terms. Our main theorem states that, under a suitable condition, any continuous function from 2N to 2N has a fixed point. This can be translated in the original framework as follows. (...)
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  10.  21
    Lavinia María Picollo (2013). Yablo's Paradox in Second-Order Languages: Consistency and Unsatisfiability. Studia Logica 101 (3):601-617.
    Stephen Yablo [23,24] introduces a new informal paradox, constituted by an infinite list of semi-formalized sentences. It has been shown that, formalized in a first-order language, Yablo’s piece of reasoning is invalid, for it is impossible to derive falsum from the sequence, due mainly to the Compactness Theorem. This result casts doubts on the paradoxical character of the list of sentences. After identifying two usual senses in which an expression or set of expressions is said to be (...)
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  11.  32
    Eduardo Alejandro Barrio (2012). Symposium on Yablo's Paradox: Introducción. Análisis Filosófico 32 (1):5-5.
    El contenido de la presente discusión de Análisis Filosófico surge a partir de diversas actividades organizadas por mí en SADAF y en la UBA. En primer lugar, Roy Cook dictó en SADAF el seminario de investigación intensivo On Yablo's Paradox durante la última semana de julio de 2011. En el seminario, el profesor Cook presentó el manuscrito aún sin finalizar de su libro The Yablo Paradox: An Essay on Circularity, Oxford, Oxford UP, (en prensa). Extensas y (...)
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  12.  17
    Laureano Luna (2009). Yablo's Paradox and Beginningless Time. Disputatio 3 (26):89-96.
    The structure of Yablo’s paradox is analysed and generalised in order to show that beginningless step-by-step determination processes can be used to provoke antinomies, more concretely, to make our logical and our on-tological intuitions clash. The flow of time and the flow of causality are usually conceived of as intimately intertwined, so that temporal causation is the very paradigm of a step-by-step determination process. As a conse-quence, the paradoxical nature of beginningless step-by-step determina-tion processes concerns time and causality (...)
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  13. Gregory Landini (2008). Yablo’s Paradox and Russellian Propositions. Russell 28 (2).
    Is self-reference necessary for the production of Liar paradoxes? Yablo has given an argument that self-reference is not necessary. He hopes to show that the indexical apparatus of self-reference of the traditional Liar paradox can be avoided by appealing to a list, a consecutive sequence, of sentences correlated one-one with natural numbers. Yablo opens his “Paradox without Self-Reference” with the assumption that there is a sequence such that: Sn: “” Each sentence on Yablo’s list is (...)
     
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  14.  64
    Eduardo Alejandro Barrio (2010). Theories of Truth Without Standard Models and Yablo's Sequences. Studia Logica 96 (3):375-391.
    The aim of this paper is to show that it’s not a good idea to have a theory of truth that is consistent but ω -inconsistent. In order to bring out this point, it is useful to consider a particular case: Yablo’s Paradox. In theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. Firstly, I exhibit some conceptual problems that follow from so introducing it. Secondly, (...)
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  15. Graham Priest (1997). Yablo’s Paradox. Analysis 57 (4):236–242.
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  16.  4
    S. Bringsjord & B. V. Heuveln (2003). The 'Mental Eye' Defence of an Infinitized Version of Yablo's Paradox. Analysis 63 (1):61-70.
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  17.  71
    Thomas Forster (2011). Yablo's Paradox and the Omitting Types Theorem for Propositional Languages. Logique Et Analyse 54 (215):323.
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  18.  84
    J. C. Beall (2001). Is Yablo’s Paradox Non-Circular? Analysis 61 (271):176–87.
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  19. Eduardo Alejandro Barrio (2012). The Yablo Paradox and Circularity. Análisis Filosófico 32 (1):7-20.
    In this paper, I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a right representation of that paradox in first order arithmetic, there are some technical results that give rise to doubts about this possibility. Then, I present some arguments that have challenged that Yablo’s construction is non-circular. Just like that, Priest (1997) has (...)
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  20. Hannes Leitgeb (2002). What is a Self-Referential Sentence? Critical Remarks on the Alleged Mbox(Non-)Circularity of Yablo's Paradox. Logique and Analyse 177 (178):3-14.
     
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  21.  32
    James Hardy (1995). Is Yablo's Paradox Liar-Like? Analysis 55 (3):197 - 198.
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  22.  5
    G. Priest (1997). Yablo's Paradox. Analysis 57 (4):236-242.
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  23. Jeffrey Ketland (2005). Yablo’s Paradox and Ω-Inconsistency. Synthese 145 (3):295-302.
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  24.  4
    J. Beall (2001). Is Yablo's Paradox Non-Circular? Analysis 61 (3):176-187.
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  25.  4
    J. Ketland (2004). Bueno and Colyvan on Yablo's Paradox. Analysis 64 (2):165-172.
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  26.  14
    Selmer Bringsjord & Bram Van Heuveln (2003). The 'Mental Eye' Defence of an Infinitized Version of Yablo's Paradox. Analysis 63 (1):61 - 70.
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  27.  49
    Selmer Bringsjord & Bram Van Heuveln (2003). The ‘Mental Eye’ Defence of an Infinitized Version of Yablo's Paradox. Analysis 63 (277):61–70.
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  28.  47
    Cezary Cieśliński & Rafal Urbaniak (2013). Gödelizing the Yablo Sequence. Journal of Philosophical Logic 42 (5):679-695.
    We investigate what happens when ‘truth’ is replaced with ‘provability’ in Yablo’s paradox. By diagonalization, appropriate sequences of sentences can be constructed. Such sequences contain no sentence decided by the background consistent and sufficiently strong arithmetical theory. If the provability predicate satisfies the derivability conditions, each such sentence is provably equivalent to the consistency statement and to the Gödel sentence. Thus each two such sentences are provably equivalent to each other. The same holds for the arithmetization of the (...)
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  29.  33
    P. Schlenker (2007). The Elimination of Self-Reference: Generalized Yablo-Series and the Theory of Truth. [REVIEW] Journal of Philosophical Logic 36 (3):251 - 307.
    Although it was traditionally thought that self-reference is a crucial ingredient of semantic paradoxes, Yablo (1993, 2004) showed that this was not so by displaying an infinite series of sentences none of which is self-referential but which, taken together, are paradoxical. Yablo's paradox consists of a countable series of linearly ordered sentences s(0), s(1), s(2),... , where each s(i) says: For each k > i, s(k) is false (or equivalently: For no k > i is s(k) true). (...)
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  30.  61
    Federico Matías Pailos (2012). About Two Objections to Cook's Proposal. Análisis Filosófico 32 (1):37-43.
    The main thesis of this work is as follows: there are versions of Yablo’s paradox that, if Cook is right about the non-circular character of his version of it, are truly paradoxical and genuinely non-circular, and Cook’s version of Yablo’s paradox is one of them. Here I will not evaluate the"circular" or"non-circular" side to Cook’s proposal. In fact, I think that he is right about it, and that his version of Yablo’s list is non-circular. But (...)
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  31.  21
    Laureano Luna (2011). Reasoning From Paradox. The Reasoner 5 (2):22-23.
    Godel's and Tarski's theorems were inspired by paradoxes: the Richard paradox, the Liar. Godel, in the 1951 Gibbs lecture argued from his metatheoretical results for a metaphysical claim: the impossibility of reducing, both, mathematics to the knowable by the human mind and the human mind to a finite machine (e.g. the brain). So Godel reasoned indirectly from paradoxes for metaphysical theses. I present four metaphysical theses concerning mechanism, reductive physicalism and time for the only purpose of suggesting how it (...)
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  32.  21
    Declan Smithies (forthcoming). Belief and Self-Knowledge: Lessons From Moore's Paradox. Philosophical Issues 26.
    The aim of this paper is to argue that what I call the simple theory of introspection can be extended to account for our introspective knowledge of what we believe as well as what we consciously experience. In section one, I present the simple theory of introspection and motivate the extension from experience to belief. In section two, I argue that extending the simple theory provides a solution to Moore’s paradox by explaining why believing Moorean conjunctions always involves some (...)
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  33.  72
    Alessandro Giordani (2015). On a New Tentative Solution to Fitch’s Paradox. Erkenntnis.
    In a recent paper, Alexander argues that relaxing the requirement that sound knowers know their own soundness might provide a solution to Fitch’s paradox and introduces a suitable axiomatic system where the paradox is avoided. In this paper an analysis of this solution is proposed according to which the effective move for solving the paradox depends on the axiomatic treatment of the ontic modality rather than the limitations imposed on the epistemic one. It is then shown that, (...)
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  34.  83
    Cezary Cieśliński (2013). Yablo Sequences in Truth Theories. In K. Lodaya (ed.), Logic and Its Applications, Lecture Notes in Computer Science LNCS 7750. Springer 127--138.
    We investigate the properties of Yablo sentences and for- mulas in theories of truth. Questions concerning provability of Yablo sentences in various truth systems, their provable equivalence, and their equivalence to the statements of their own untruth are discussed and answered.
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  35. Andrew Bacon (2013). Curry's Paradox and Omega Inconsistency. Studia Logica 101 (1):1-9.
    In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, (...)
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  36. Jack Woods (2014). Expressivism and Moore's Paradox. Philosophers' Imprint 14 (5):1-12.
    Expressivists explain the expression relation which obtains between sincere moral assertion and the conative or affective attitude thereby expressed by appeal to the relation which obtains between sincere assertion and belief. In fact, they often explicitly take the relation between moral assertion and their favored conative or affective attitude to be exactly the same as the relation between assertion and the belief thereby expressed. If this is correct, then we can use the identity of the expression relation in the two (...)
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  37.  8
    N. Raja (2005). A Negation-Free Proof of Cantor's Theorem. Notre Dame Journal of Formal Logic 46 (2):231-233.
    We construct a novel proof of Cantor's theorem in set theory.
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  38. Clayton Littlejohn (2010). Moore's Paradox and Epistemic Norms. Australasian Journal of Philosophy 88 (1):79 – 100.
    We shall evaluate two strategies for motivating the view that knowledge is the norm of belief. The first draws on observations concerning belief's aim and the parallels between belief and assertion. The second appeals to observations concerning Moore's Paradox. Neither of these strategies gives us good reason to accept the knowledge account. The considerations offered in support of this account motivate only the weaker account on which truth is the fundamental norm of belief.
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  39.  26
    John N. Williams (2013). Moore's Paradox and the Priority of Belief Thesis. Philosophical Studies 165 (3):1117-1138.
    Moore’s paradox is the fact that assertions or beliefs such asBangkok is the capital of Thailand but I do not believe that Bangkok is the capital of Thailand or Bangkok is the capital of Thailand but I believe that Bangkok is not the capital of Thailand are ‘absurd’ yet possibly true. The current orthodoxy is that an explanation of the absurdity should first start with belief, on the assumption that once the absurdity in belief has been explained then this (...)
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  40.  15
    Prasanta S. Bandyopadhyay, Mark Greenwood, Don Dcruz & Venkata Raghavan (2015). Simpson's Paradox and Causality. American Philosophical Quarterly 52 (1):13-25.
    There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal (...)
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  41.  27
    John N. Williams (2014). Moore's Paradox in Belief and Desire. Acta Analytica 29 (1):1-23.
    Is there a Moore ’s paradox in desire? I give a normative explanation of the epistemic irrationality, and hence absurdity, of Moorean belief that builds on Green and Williams’ normative account of absurdity. This explains why Moorean beliefs are normally irrational and thus absurd, while some Moorean beliefs are absurd without being irrational. Then I defend constructing a Moorean desire as the syntactic counterpart of a Moorean belief and distinguish it from a ‘Frankfurt’ conjunction of desires. Next I discuss (...)
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  42. David Ebrey (2014). Meno's Paradox in Context. British Journal for the History of Philosophy 22 (1):4-24.
    I argue that Meno’s Paradox targets the type of knowledge that Socrates has been looking for earlier in the dialogue: knowledge grounded in explanatory definitions. Socrates places strict requirements on definitions and thinks we need these definitions to acquire knowledge. Meno’s challenge uses Socrates’ constraints to argue that we can neither propose definitions nor recognize them. To understand Socrates’ response to the challenge, we need to view Meno’s challenge and Socrates’ response as part of a larger disagreement about the (...)
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  43. Samuel Alexander (2013). An Axiomatic Version of Fitch's Paradox. Synthese 190 (12):2015-2020.
    A variation of Fitch’s paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way out (...)
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  44.  80
    Catharine Saint Croix & Richmond Thomason (2014). Chisholm's Paradox and Conditional Oughts. Lecture Notes in Computer Science 8554:192-207.
    Since it was presented in 1963, Chisholm’s paradox has attracted constant attention in the deontic logic literature, but without the emergence of any definitive solution. We claim this is due to its having no single solution. The paradox actually presents many challenges to the formalization of deontic statements, including (1) context sensitivity of unconditional oughts, (2) formalizing conditional oughts, and (3) distinguishing generic from nongeneric oughts. Using the practical interpretation of ‘ought’ as a guideline, we propose a linguistically (...)
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  45.  28
    Walter Dean (2014). Montague’s Paradox, Informal Provability, and Explicit Modal Logic. Notre Dame Journal of Formal Logic 55 (2):157-196.
    The goal of this paper is to explore the significance of Montague’s paradox—that is, any arithmetical theory $T\supseteq Q$ over a language containing a predicate $P$ satisfying $P\rightarrow \varphi $ and $T\vdash \varphi \,\therefore\,T\vdash P$ is inconsistent—as a limitative result pertaining to the notions of formal, informal, and constructive provability, in their respective historical contexts. To this end, the paradox is reconstructed in a quantified extension $\mathcal {QLP}$ of Artemov’s logic of proofs. $\mathcal {QLP}$ contains both explicit (...)
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  46.  16
    Adam Rieger (2015). Moore's Paradox, Introspection and Doxastic Logic. Thought: A Journal of Philosophy 4 (4):215-227.
    An analysis of Moore's paradox is given in doxastic logic. Logics arising from formalizations of various introspective principles are compared; one logic, K5c, emerges as privileged in the sense that it is the weakest to avoid Moorean belief. Moreover it has other attractive properties, one of which is that it can be justified solely in terms of avoiding false belief. Introspection is therefore revealed as less relevant to the Moorean problem than first appears.
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  47.  67
    Ken Binmore & Alex Voorhoeve (2003). Defending Transitivity Against Zeno’s Paradox. Philosophy and Public Affairs 31 (3):272–279.
    This article criticises one of Stuart Rachels' and Larry Temkin's arguments against the transitivity of 'better than'. This argument invokes our intuitions about our preferences of different bundles of pleasurable or painful experiences of varying intensity and duration, which, it is argued, will typically be intransitive. This article defends the transitivity of 'better than' by showing that Rachels and Temkin are mistaken to suppose that preferences satisfying their assumptions must be intransitive. It makes cler where the argument goes wrong by (...)
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  48.  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 (...)
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  49.  19
    Helge Rückert (2004). A SOLUTION TO FITCH'S PARADOX OF KNOWABILITY. In S. Rahman J. Symons (ed.), Logic, Epistemology, and the Unity of Science. Kluwer Academic Publisher 351--380.
    There is an argument (first presented by Fitch), which tries to show by formal means that the anti-realistic thesis that every truth might possibly be known, is equivalent to the unacceptable thesis that every truth is actually known (at some time in the past, present or future). First, the argument is presented and some proposals for the solution of Fitch's Paradox are briefly discussed. Then, by using Wehmeier's modal logic with subjunctive marks (S5*), it is shown how (...)
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  50.  17
    Carlo Proietti (2012). Intuitionistic Epistemic Logic, Kripke Models and Fitch's Paradox. Journal of Philosophical Logic 41 (5):877-900.
    The present work is motivated by two questions. (1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? In what follows we outline an answer to (2) and give a model-theoretic definition of the operator K. This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal logic. The interest of (...)
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