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  1. Wayne Aitken & Jeffrey A. Barrett (2008). Abstraction in Algorithmic Logic. Journal of Philosophical Logic 37 (1):23 - 43.
    We develop a functional abstraction principle for the type-free algorithmic logic introduced in our earlier work. Our approach is based on the standard combinators but is supplemented by the novel use of evaluation trees. Then we show that the abstraction principle leads to a Curry fixed point, a statement C that asserts C ⇒ A where A is any given statement. When A is false, such a C yields a paradoxical situation. As discussed in our earlier work, this situation leaves (...)
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  2. Wayne Aitken & Jeffrey A. Barrett (2007). Stability and Paradox in Algorithmic Logic. Journal of Philosophical Logic 36 (1):61 - 95.
    There is significant interest in type-free systems that allow flexible self-application. Such systems are of interest in property theory, natural language semantics, the theory of truth, theoretical computer science, the theory of classes, and category theory. While there are a variety of proposed type-free systems, there is a particularly natural type-free system that we believe is prototypical: the logic of recursive algorithms. Algorithmic logic is the study of basic statements concerning algorithms and the algorithmic rules of inference between such statements. (...)
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  3. Wayne Aitken & Jeffrey A. Barrett (2004). Computer Implication and the Curry Paradox. Journal of Philosophical Logic 33 (6):631-637.
    There are theoretical limitations to what can be implemented by a computer program. In this paper we are concerned with a limitation on the strength of computer implemented deduction. We use a version of the Curry paradox to arrive at this limitation.
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  4. Seiki Akama (1996). Curry's Paradox in Contractionless Constructive Logic. Journal of Philosophical Logic 25 (2):135 - 150.
    We propose contractionless constructive logic which is obtained from Nelson's constructive logic by deleting contractions. We discuss the consistency of a naive set theory based on the proposed logic in relation to Curry's paradox. The philosophical significance of contractionless constructive logic is also argued in comparison with Fitch's and Prawitz's systems.
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  5. C. Anthony Anderson (1987). Semantical Antinomies in the Logic of Sense and Denotation. Notre Dame Journal of Formal Logic 28 (1):99-114.
  6. Bradley Armour-Garb & James A. Woodbridge (2010). Truthmakers, Paradox and Plausibility. Analysis 70 (1):11-23.
    In a series of articles, Dan Lopez De Sa and Elia Zardini argue that several theorists have recently employed instances of paradoxical reasoning, while failing to see its problematic nature because it does not immediately (or obviously) yield inconsistency. In contrast, Lopez De Sa and Zardini claim that resultant inconsistency is not a necessary condition for paradoxicality. It is our contention that, even given their broader understanding of paradox, their arguments fail to undermine the instances of reasoning they attack, either (...)
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  7. F. G. Asenjo (1966). A Calculus for Antinomies. Notre Dame Journal of Formal Logic 16 (1):103-105.
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  8. F. G. Asenjo & J. Tamburino (1975). Logic of Antinomies. Notre Dame Journal of Formal Logic 16 (1):17-44.
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  9. E. J. Ashworth (1972). The Treatment of Semantic Paradoxes From 1400 to 1700. Notre Dame Journal of Formal Logic 13 (1):34-52.
  10. Andrew Bacon (2011). A Paradox for Supertask Decision Makers. Philosophical Studies 153 (2):307.
    I consider two puzzles in which an agent undergoes a sequence of decision problems. In both cases it is possible to respond rationally to any given problem yet it is impossible to respond rationally to every problem in the sequence, even though the choices are independent. In particular, although it might be a requirement of rationality that one must respond in a certain way at each point in the sequence, it seems it cannot be a requirement to respond as such (...)
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  11. Francesca Rivetti Barbò (1968). A Philosophical Remark on Gödel's Unprovability of Consistency Proof. Notre Dame Journal of Formal Logic 9 (1):67-74.
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  12. Jeffrey Barrett (2007). Stability and Paradox in Algorithmic Logic. Journal of Philosophical Logic 36 (1):61 - 95.
    There is significant interest in type-free systems that allow flexible self-application. Such systems are of interest in property theory, natural language semantics, the theory of truth, theoretical computer science, the theory of classes, and category theory. While there are a variety of proposed type-free systems, there is a particularly natural type-free system that we believe is prototypical: the logic of recursive algorithms. Algorithmic logic is the study of basic statements concerning algorithms and the algorithmic rules of inference between such statements. (...)
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  13. 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, I show (...)
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  14. Timothy Bays, Reflections on Skolem's Paradox.
    The Lowenheim-Skolem theorems say that if a first-order theory has infinite models, then it has models which are only countably infinite. Cantor's theorem says that some sets are uncountable. Together, these two theorems induce a puzzle known as Skolem's Paradox: the very axioms of (first-order) set theory which prove the existence of uncountable sets can themselves be satisfied by a merely countable model.
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  15. Timothy Bays (2009). Skolem's Paradox. In Edward N. Zalta (ed.), Stanford Encyclopedia of Philosophy.
    Skolem's Paradox involves a seeming conflict between two theorems from classical logic. The Löwenheim Skolem theorem says that if a first order theory has infinite models, then it has models whose domains are only countable. Cantor's theorem says that some sets are uncountable. Skolem's Paradox arises when we notice that the basic principles of Cantorian set theory—i.e., the very principles used to prove Cantor's theorem on the existence of uncountable sets—can themselves be formulated as a collection of first order sentences. (...)
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  16. Timothy Bays (2006). The Mathematics of Skolem's Paradox. In Dale Jacquette (ed.), Philosophy of Logic. North Holland. 615--648.
    Over the years, Skolem’s Paradox has generated a fairly steady stream of philosophical discussion; nonetheless, the overwhelming consensus among philosophers and logicians is that the paradox doesn’t constitute a mathematical problem (i.e., it doesn’t constitute a real contradiction). Further, there’s general agreement as to why the paradox doesn’t constitute a mathematical problem. By looking at the way firstorder structures interpret quantifiers—and, in particular, by looking at how this interpretation changes as we move from structure to structure—we can give a technically (...)
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  17. Francesco Berto (2007). How to Sell a Contradiction. College Publications.
    There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth – viz. that the same thing cannot at one and the same time be and not be": with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not (...)
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  18. Francesco Berto (2006). Meaning, Metaphysics, and Contradiction. American Philosophical Quarterly 43 (4):283-297.
  19. Andrew Boucher, A Comprehensive Solution to the Paradoxes.
    A solution to the paradoxes has two sides: the philosophical and the technical. The paradoxes are, first and foremost, a philosophical problem. A philosophical solution must pinpoint the exact step where the reasoning that leads to contradiction is fallacious, and then explain why it is so.
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  20. OtáVio Bueno & Mark Colyvan (2003). Paradox Without Satisfaction. Analysis 63 (2):152–156.
    Consider the following denumerably infinite sequence of sentences: (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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  21. Roy T. Cook (2009). Curry, Yablo and Duality. Analysis 69 (4):612-620.
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  22. Gregor Damschen (2008). This is Nonsense. The Reasoner 2 (10):6-8.
    In his Paradoxes (1995: Cambridge University Press: 149) Mark Sainsbury presents the following pair of sentences: Line 1: The sentence written on Line 1 is nonsense. Line 2: The sentence written on Line 1 is nonsense. Sainsbury (1995: 149, 154) here makes three assertions: (1) The sentence in Line 1 is so viciously self-referential that it falls into the truth-value gap. The sentence is really nonsense. (2) The sentence in Line 2 is by contrast true. For it states precisely that (...)
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  23. Hartry Field (forthcoming). Disarming a Paradox of Validity. Notre Dame Journal of Formal Logic.
    Abstract. Any theory of truth must find a way around Curry’s paradox, and there are well-known ways to do so. This paper concerns an apparently analogous paradox, about validity rather than truth, which JC Beall and Julien Murzi (“Two Flavor's of Curry's Paradox”) call the v-Curry. They argue that there are reasons to want a common solution to it and the standard Curry paradox, and that this rules out the solutions to the latter offered by most “naive truth theorists”. To (...)
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  24. Pierdaniele Giaretta (2009). The Paradox of Knowability From a Russellian Perspective. Prolegomena 8 (2):141-158.
    The paradox of knowability and the debate about it are shortly presented. Some assumptions which appear more or less tacitly involved in its discussion are made explicit. They are embedded and integrated in a Russellian framework, where a formal paradox, very similar to the Russell-Myhill paradox, is derived. Its solution is provided within a Russellian formal logic introduced by A. Church. It follows that knowledge should be typed. Some relevant aspects of the typing of knowledge are pointed out.
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  25. Patrick Girard & Luca Moretti (2014). Antirealism and the Conditional Fallacy: The Semantic Approach. Journal of Philosophical Logic 43 (4):761-783.
    The expression conditional fallacy identifies a family of arguments deemed to entail odd and false consequences for notions defined in terms of counterfactuals. The antirealist notion of truth is typically defined in terms of what a rational enquirer or a community of rational enquirers would believe if they were suitably informed. This notion is deemed to entail, via the conditional fallacy, odd and false propositions, for example that there necessarily exists a rational enquirer. If these consequences do indeed follow from (...)
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  26. Patrick Greenough (2011). Truthmaker Gaps and the No-No Paradox. Philosophy and Phenomenological Research 82 (3):547 - 563.
    Consider the following sentences: The neighbouring sentence is not true. The neighbouring sentence is not true. Call these the no-no sentences. Symmetry considerations dictate that the no-no sentences must both possess the same truth-value. Suppose they are both true. Given Tarski’s truth-schema—if a sentence S says that p then S is true iff p—and given what they say, they are both not true. Contradiction! Conclude: they are not both true. Suppose they are both false. Given Tarski’s falsity-schema—if a sentence S (...)
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  27. Patrick Greenough (2001). Free Assumptions and the Liar Paradox. American Philosophical Quarterly 38 (2):115 - 135.
    A new solution to the liar paradox is developed using the insight that it is illegitimate to even suppose (let alone assert) that a liar sentence has a truth-status (true or not) on the grounds that supposing this sentence to be true/not-true essentially defeats the telos of supposition in a readily identifiable way. On that basis, the paradox is blocked by restricting the Rule of Assumptions in Gentzen-style presentations of the sequent-calculus. The lesson of the liar is that not all (...)
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  28. Michael Hand & Jonathan L. Kvanvig (1999). ``Tennant on Knowability&Quot. Australasian Journal of Philosophy 77:422-428.
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  29. Claire Ortiz Hill (2004). Reference and Paradox. Synthese 138 (2):207 - 232.
    Evidence is drawn together to connect sources of inconsistency that Frege discerned in his foundations for arithmetic with the origins of the paradox derived by Russell in Basic Laws I and then with antinomies, paradoxes, contradictions, riddles associated with modal and intensional logics. Examined are: Frege's efforts to grasp logical objects; the philosophical arguments that compelled Russell to adopt a description theory of names and a eliminative theory of descriptions; the resurfacing of issues surrounding reference, descriptions, identity, substitutivity, paradox in (...)
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  30. Jonathan L. Kvanvig (2009). ``Restriction Strategies for Knowability: Lessons in False Hope&Quot. In Joseph Salerno (ed.), New Essays on Knowability. Oxford: Oxford University Press. 205-222.
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  31. Laureano (2010). A Failed Cassatio? A Note on Valor and Martinez on Goldstein. Proceedings of the Aristotelian Society 110 (3pt3):383-386.
    I address the claim by Valor and Martínez that Goldstein's cassationist approach to Liar-like paradoxes generates paradoxes it cannot solve. I argue that these authors miss an essential point in Goldstein's cassationist approach, namely the thesis that paradoxical sentences are not able to make the statement they seem to make.
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  32. Ken Levy (2009). The Solution to the Surprise Exam Paradox. Southern Journal of Philosophy 47 (2):131-158.
    The Surprise Exam Paradox continues to perplex and torment despite the many solutions that have been offered. This paper proposes to end the intrigue once and for all by refuting one of the central pillars of the Surprise Exam Paradox, the 'No Friday Argument,' which concludes that an exam given on the last day of the testing period cannot be a surprise. This refutation consists of three arguments, all of which are borrowed from the literature: the 'Unprojectible Announcement Argument,' the (...)
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  33. Laureano Luna (2010). Ungrounded Causal Chains and Beginningless Time. Logic and Logical Philosophy 18 (3-4):297-307.
    We use two logical resources, namely, the notion of recursively defined function and the Benardete-Yablo paradox, together with some inherent features of causality and time, as usually conceived, to derive two results: that no ungrounded causal chain exists and that time has a beginning.
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  34. 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 as usually (...)
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  35. Laureano Luna & Christopher Small (2009). Intentionality and Computationalism. A Diagonal Argument. Mind and Matter 7 (1):81-90.
    Computationalism is the claim that all possible thoughts are computations, i.e. executions of algorithms. The aim of the paper is to show that if intentionality is semantically clear, in a way defined in the paper, then computationalism must be false. Using a convenient version of the phenomenological relation of intentionality and a diagonalization device inspired by Thomson's theorem of 1962, we show there exists a thought that canno be a computation.
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  36. Laureano Luna & William Taylor (2010). Cantor's Proof in the Full Definable Universe. Australasian Journal of Logic 9:11-25.
    Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable on another. We argue that the claim that definitional contexts impose restrictions on the (...)
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  37. Christopher Menzel (1984). Cantor and the Burali-Forti Paradox. The Monist 67 (1):92-107.
    In studying the early history of mathematical logic and set theory one typically reads that Georg Cantor discovered the so-called Burali-Forti (BF) paradox sometime in 1895, and that he offered his solution to it in his famous 1899 letter to Dedekind. This account, however, leaves it something of a mystery why Cantor never discussed the paradox in his writings. Far from regarding the foundations of set theory to be shaken, he showed no apparent concern over the paradox and its implications (...)
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  38. Thomas Mormann (2014). Set Theory, Topology, and the Possibility of Junky Worlds. Notre Dame Journal of Formal Logic 55 (1): 79 - 90.
    A possible world is a junky world if and only if each thing in it is a proper part. The possibility of junky worlds contradicts the principle of general fusion. Bohn (2009) argues for the possibility of junky worlds, Watson (2010) suggests that Bohn‘s arguments are flawed. This paper shows that the arguments of both authors leave much to be desired. First, relying on the classical results of Cantor, Zermelo, Fraenkel, and von Neumann, this paper proves the possibility of junky (...)
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  39. Daniel Nolan & Alexander Sandgren (2014). Creationism and Cardinality. Analysis 74 (4):615-622.
    Creationism about fictional entities requires a principle connecting what fictions say exist with which fictional entities really exist. The most natural way of spelling out such a principle yields inconsistent verdicts about how many fictional entities are generated by certain inconsistent fictions. Avoiding inconsistency without compromising the attractions of creationism will not be easy.
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  40. Paloma Pérez-Ilzarbe (2009). Late Medieval Trinitarian Syllogistics: From the Theological Debates to a Logical Textbook. In A. Schuman (ed.), Logic in Religious Discourse. Ontos Verlag.
    Jerónimo Pardo's analysis of the problems raised by some popular trinitarian paralogisms is studied in this paper. The purpose is to show how the notions employed by the theologians in order to solve theological problems were introduced into a textbook on logic to deal with some genuinely logical problems. First, the problem, common to all logical approaches, of achieving a fine-grained analysis of the logical form of syllogistical inferences. Second, the problem, typical of the terminist approach to logic, of guaranteeing (...)
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  41. Diego L. Rapoport (2009). Surmounting the Cartesian Cut with Philosophy, Physics, Cybernetics and Geometry; Self.Reference, Torsion, the Klein Bottle, Multivalued Logics and Quantum Mechanics. Foundations of Physics 39 (9).
    In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology -after Merleau-Ponty, Heidegger and Rosen- and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further (...)
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  42. Stephen Read (2010). Field's Paradox and Its Medieval Solution. History and Philosophy of Logic 31 (2):161-176.
    Hartry Field's revised logic for the theory of truth in his new book, Saving Truth from Paradox , seeking to preserve Tarski's T-scheme, does not admit a full theory of negation. In response, Crispin Wright proposed that the negation of a proposition is the proposition saying that some proposition inconsistent with the first is true. For this to work, we have to show that this proposition is entailed by any proposition incompatible with the first, that is, that it is the (...)
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  43. Stephen Read (2006). Symmetry and Paradox. History and Philosophy of Logic 27 (4):307-318.
    The ?no???no? paradox (so-called by Sorensen) consists of a pair of propositions each of which says of the other that it is false. It is not immediately paradoxical, since it has a solution in which one proposition is true, the other false. However, that is itself paradoxical, since there is no clear ground for determining which is which. The two propositions should have the same truth-value. The paper shows how a proposal by the medieval thinker Thomas Bradwardine solves not only (...)
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  44. Charles Sayward (2002). Convention T and Basic Law V. Analysis 62 (4):289–292.
    It is argued that Convention T and Basic Law V of Frege’s Grungesetze share three striking similarities. First, they are universal generalizations that are intuitively plausible because they have so many obvious instances. Second, both are false because they yield contradictions. Third, neither gives rise to a paradox.
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  45. Lionel Shapiro (2013). Validity Curry Strengthened. Thought: A Journal of Philosophy 2 (1):100-107.
    Several authors have argued that a version of Curry's paradox involving validity motivates rejecting the structural rule of contraction. This paper criticizes two recently suggested alternative responses to “validity Curry.” There are three salient stages in a validity Curry derivation. Rejecting contraction blocks the first, while the alternative responses focus on the second and third. I show that a distinguishing feature of validity Curry, as contrasted with more familiar forms of Curry's paradox, is that paradox arises already at the first (...)
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  46. Theodore Sider (1997). On the Paradox of the Question. Analysis 57 (2):97–101.
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  47. Nicholas J. J. Smith (2000). The Principle of Uniform Solution (of the Paradoxes of Self-Reference). Mind 109 (433):117-122.
    Graham Priest (1994) has argued that the following paradoxes all have the same structure: Russell’s Paradox, Burali-Forti’s Paradox, Mirimanoff’s Paradox, König’s Paradox, Berry’s Paradox, Richard’s Paradox, the Liar and Liar Chain Paradoxes, the Knower and Knower Chain Paradoxes, and the Heterological Paradox. Their common structure is given by Russell’s Schema: there is a property φ and function δ such that..
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  48. Gabriel Uzquiano (2004). The Paradox of the Knower Without Epistemic Closure? Mind 113 (449):95-107.
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  49. Zach Weber (2010). Explanation And Solution In The Inclosure Argument. Australasian Journal of Philosophy 88 (2):353-357.
    In a recent article, Emil Badici contends that the inclosure schema substantially fails as an analysis of the paradoxes of self-reference because it is question-begging. The main purpose of this note is to show that Badici's critique highlights a necessity condition for the success of dialectic about paradoxes. The inclosure argument respects this condition and remains solvent.
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  50. G. White (1993). Are We Finite? Notre Dame Journal of Formal Logic 34 (3):311--333.
    We argue that the unexpected examination paradox can be regarded as showing that the logic of temporally indexed epistemic states, although it is intuitively appealing, cannot be recursively axiomatised.
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