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  • PhD, Universidad Nacional de Educación a Distancia, 1994.

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  1. Laureano Luna (forthcoming). Minds Vs. Machines. On Saka's Basic Blindspot Theorem. Journal of Experimental and Theoretical Artificial Intelligence.
    Under the name of ‘Basic Blindspot Theorem’, Paul Saka has proposed in the special issue on mind and paradox of this journal a Gödelian argument to the effect that no cognitive system can be complete and correct. We show that while the argument is successful as regards mechanical and formal systems, it may fail with respect to minds, so contributing to draw a boundary between the former and the latter. The existence of such a boundary may lend support to Saka’s (...)
     
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  2. Laureano Luna (2014). No Successfull Infinite Regress. Logic and Logical Philosophy 23 (2).
    We model infinite regress structures -not arguments- by means of ungrounded recursively defined functions in order to show that no such structure can perform the task of providing determination to the items composing it, that is, that no determination process containing an infinite regress structure is successful.
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  3. Laureano Luna & William Taylor (2014). Taming the Indefinitely Extensible Definable Universe. Philosophia Mathematica 22 (2):198-208.
    In previous work in 2010 we have dealt with the problems arising from Cantor's theorem and the Richard paradox in a definable universe. We proposed indefinite extensibility as a solution. Now we address another definability paradox, the Berry paradox, and explore how Hartogs's cardinality theorem would behave in an indefinitely extensible definable universe where all sets are countable.
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  4. Laureano Luna (2013). Indefinite Extensibility in Natural Language. The Monist 96 (2):295-308.
    The Monist’s call for papers for this issue ended: “if formalism is true, then it must be possible in principle to mechanize meaning in a conscious thinking and language-using machine; if intentionalism is true, no such project is intelligible”. We use the Grelling-Nelson paradox to show that natural language is indefinitely extensible, which has two important consequences: it cannot be formalized and model theoretic semantics, standard for formal languages, is not suitable for it. We also point out that object-object mapping (...)
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  5. Laureano Luna (2013). Satisfiable and Unsatisfied Paradoxes. How Closely Related? The Reasoner 7 (5):56-7.
  6. Laureano Luna (2012). Cómo Hacer Metafísica a Partir de la Lógica. Thémata. Revista de Filosofía 45:261-274.
    We offer a number of arguments for or against particular metaphysical theses. All of them are based in phenomena or results in mathematical logic, broadly conceived, and are offered as exemplification of the possibility of arguing in metaphysics from such results.
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  7. Laureano Luna (2012). Grim's Arguments Against Omniscience and Indefinite Extensibility. International Journal for Philosophy of Religion 72 (2):89-101.
    Patrick Grim has put forward a set theoretical argument purporting to prove that omniscience is an inconsistent concept and a model theoretical argument for the claim that we cannot even consistently define omniscience. The former relies on the fact that the class of all truths seems to be an inconsistent multiplicity (or a proper class, a class that is not a set); the latter is based on the difficulty of quantifying over classes that are not sets. We first address the (...)
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  8. 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 could (...)
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  9. Laureano Luna (2010). A FailedCassatio? A Note on Valor and Martínez 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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  10. 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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  11. 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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  12. Laureano Luna (2009). A Note On Formal Reasoning with Extensible Domain. The Reasoner 3 (7):5-6.
    Assuming the indefinite extensibility of any domain of quantification leads to reasoning with extensible domain semantics. It is showed that some theorems (e.g. Thomson's) in conventional semantics logic are not theorems in a logic provided with this new semantics.
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  13. 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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  14. 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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  15. Laureano Luna (2008). Can We Consistently Say That We Cannot Speak About Everything? The Reasoner 2 (9):5-7.
    Following an idea from Gödel and Carnap we show how we can speak with absolute generality even if we cannot quantify with absolute generality.
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  16. Laureano Luna (2008). On Non-Standard Models of Peano Arithmetic. The Reasoner 2:2.
     
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  17. 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.
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