•  36
    The Russellian argument against the possibility of absolutely unrestricted quantification can be answered by the partisan of that quantification in an apparently easy way, namely, arguing that the objects used in the argument do not exist because they are defined in a viciously circular fashion. We show that taking this contention along as a premise and relying on an extremely intuitive Principle of Determinacy, it is possible to devise a reductio of the possibility of absolutely unrestricted qu…Read more
  •  90
    A Philosophical Argument for the Beginning of Time
    Prolegomena 19 (2): 161-176. 2020.
    A common argument in support of a beginning of the universe used by advocates of the kalām cosmological argument (KCA) is the argument against the possibility of an actual infinite, or the “Infinity Argument”. However, it turns out that the Infinity Argument loses some of its force when compared with the achievements of set theory and it brings into question the view that God predetermined an endless future. We therefore defend a new formal argument, based on the nature of time (just as geometr…Read more
  •  59
    Proving Cleanthes wrong
    Journal of Applied Logic 8 (3): 707-736. 2021.
    Hume’s famous character Cleanthes claims that there is no difficulty in explaining the existence of causal chains with no first cause since in them each item is causally explained by its predecessor. Relying on logico-mathematical resources, we argue for two theses: (1) if the existence of Cleanthes’ chain can be explained at all, it must be explained by the fact that the causal law ruling it is in force, and (2) the fact that such a causal law is in force cannot explain the occurrence of the ev…Read more
  •  1465
    Sleeping Beauty: Exploring a Neglected Solution
    British Journal for the Philosophy of Science 71 (3): 1069-1092. 2020.
    The strong law of large numbers and considerations concerning additional information strongly suggest that Beauty upon awakening has probability 1/3 to be in a heads-awakening but should still believe the probability that the coin landed heads in the Sunday toss to be 1/2. The problem is that she is in a heads-awakening if and only if the coin landed heads. So, how can she rationally assign different probabilities or credences to propositions she knows imply each other? This is the problem I add…Read more
  •  35
    We rely on a recent puzzle by Alex Blum to offer a new argument for the old Fitch’s thesis that what we learn a posteriori in Kripkean identity statements like ‘Tully is Cicero’ is contingent and what is not contingent in such statements is analytical, hence hardly a posteriori.
  •  4
    La Insuficiencia del Discurso Racional
    Biblioteca Nueva. Colección: Razón y Sociedad. 2009.
    ¿Podría estar amenazado el futuro de nuestra civilización por un abuso secular de la razón? Cabe argumentar que la Modernidad se construyó sobre la ambición cartesiana de conocer y regular el mundo mediante el discurso racional, postergando el conocimiento sensible y descartando cualquier posibilidad de un conocimiento intelectual diferente de la razón científico-matemática. Según el autor, esta ambición ha moldeado el quehacer científico, filosófico y matemático de la Modernidad y persiste toda…Read more
  •  47
    A FailedCassatio? A Note on Valor and Martínez on Goldstein
    Proceedings of the Aristotelian Society 110 (3pt3): 383-386. 2010.
    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
  •  29
    Rescuing Poincaré from Richard’s Paradox
    History and Philosophy of Logic 38 (1): 57-71. 2017.
    Poincaré in a 1909 lecture in Göttingen proposed a solution to the apparent incompatibility of two results as viewed from a definitionist perspective: on the one hand, Richard’s proof that the definitions of real numbers form a countable set and, on the other, Cantor’s proof that the real numbers make up an uncountable class. Poincaré argues that, Richard’s result notwithstanding, there is no enumeration of all definable real numbers. We apply previous research by Luna and Taylor on Richard’s pa…Read more
  •  65
    Following an idea from Gödel and Carnap we show how we can speak with absolute generality even if we cannot quantify with absolute generality
  •  11
    In ‘The Unsatisfied Paradox’ (The Reasoner 6(12), p.184-5), Peter Eldridge-Smith has argued that no unique solution for the logical paradoxes is likely to exist in the presence of the following two kinds of paradox: 1. The Unsatisfied kind. 2. The Satisfiable kind. We argue that both kinds of paradoxes typically contain some kind of self-reference used for an attempt of self-diagonalization, and that consequently they may solvable in the same way, namely, by the acknowledgement that no intens…Read more
  •  12
    Minds vs. Machines. On Saka's Basic Blindspot Theorem
    Journal of Experimental and Theoretical Artificial Intelligence 27 (4): 483-486. 2015.
    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 general thesis that paradoxes are …Read more
  •  37
    A Note On Formal Reasoning with Extensible Domain
    The Reasoner 3 (7): 5-6. 2009.
    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
  •  68
    Taming the Indefinitely Extensible Definable Universe
    with W. Taylor
    Philosophia Mathematica 22 (2): 198-208. 2014.
    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
  •  89
    Grim’s arguments against omniscience and indefinite extensibility
    International Journal for Philosophy of Religion 72 (2): 89-101. 2012.
    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 set theoretical argument a…Read more
  •  222
    Tiny Proper Classes
    The Reasoner 10 (10): 83-83. 2016.
    We propose certain clases that seem unable to form a completed totality though they are very small, finite, in fact. We suggest that the existence of such clases lends support to an interpretation of the existence of proper clases in terms of availability, not size.
  •  465
    No successfull infinite regress
    Logic and Logical Philosophy 23 (2): 189-201. 2014.
    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.
  •  22
    Cómo hacer metafísica a partir de la lógica
    Thémata. Revista de Filosofía 45 261-274. 2012.
    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.
  •  65
    Physicalism, truth, and the Pinocchio paradox
    Mind and Matter 14 (1): 77-86. 2016.
    We develop an argument sketched by Luna (2011) based on the Pinocchio paradox, which was proposed by Eldridge-Smith and Eldridge- Smith (2010). We show that, upon plausible assumptions, the claim that mental states supervene on bodily states leads to the conclusion that some proposition is both paradoxical and not paradoxical. In order to show how the presence of paradoxes can be harnessed for philosophical argumentation, we present as well a couple of related arguments.
  •  80
    Ungrounded Causal Chains and Beginningless Time
    Logic and Logical Philosophy 18 (3-4): 297-307. 2009.
    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.
  •  38
    Intentionality and Computationalism. A Diagonal Argument.
    with Christopher Small
    Mind and Matter 7 (1): 81-90. 2009.
    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.
  •  52
    Arithmetic and Logic Incompleteness: the Link
    with Alex Blum
    The Reasoner 2 (3): 6. 2008.
    We show how second order logic incompleteness follows from incompleteness of arithmetic, as proved by Gödel
  •  7
    On non-standard models of Peano Arithmetic
    The Reasoner 2 2. 2008.
    In response to Bhupinder Singh Anand''s article CAN WE REALLY FALSIFY TRUTH BY DICTAT? in THE REASONER II, 1, January 2008,that denies the existence of nonstandard models of Peano Arithmetic, we prove from Compactness the existence of such models.
  •  749
    Cantor’s Proof in the Full Definable Universe
    with William Taylor
    Australasian Journal of Logic 9 10-25. 2010.
    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 scope of qua…Read more
  •  57
    Reasoning from paradox
    The Reasoner 5 (2): 22-23. 2011.
    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…Read more
  •  68
    Yablo’s Paradox and Beginningless Time
    Disputatio 3 (26): 89-96. 2009.
    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…Read more
  •  947
    Indefinite Extensibility in Natural Language
    The Monist 96 (2): 295-308. 2013.
    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…Read more