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Lavinia Picollo [12]Lavinia María Picollo [1]
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Lavinia Maria Picollo
University College London
  1.  76
    Disquotation and Infinite Conjunctions.Lavinia Picollo & Thomas Schindler - 2017 - Erkenntnis (5):1-30.
    One of the main logical functions of the truth predicate is to enable us to express so-called ‘infinite conjunctions’. Several authors claim that the truth predicate can serve this function only if it is fully disquotational, which leads to triviality in classical logic. As a consequence, many have concluded that classical logic should be rejected. The purpose of this paper is threefold. First, we consider two accounts available in the literature of what it means to express infinite conjunctions with a (...)
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  2.  58
    Reference in Arithmetic.Lavinia Picollo - 2018 - Review of Symbolic Logic 11 (3):573-603.
    Self-reference has played a prominent role in the development of metamathematics in the past century, starting with Gödel’s first incompleteness theorem. Given the nature of this and other results in the area, the informal understanding of self-reference in arithmetic has sufficed so far. Recently, however, it has been argued that for other related issues in metamathematics and philosophical logic a precise notion of self-reference and, more generally, reference is actually required. These notions have been so far elusive and are surrounded (...)
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  3.  6
    Disquotation and Infinite Conjunctions.Thomas Schindler & Lavinia Picollo - 2018 - Erkenntnis 83 (5):899-928.
    One of the main logical functions of the truth predicate is to enable us to express so-called ‘infinite conjunctions’. Several authors claim that the truth predicate can serve this function only if it is fully disquotational, which leads to triviality in classical logic. As a consequence, many have concluded that classical logic should be rejected. The purpose of this paper is threefold. First, we consider two accounts available in the literature of what it means to express infinite conjunctions with a (...)
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  4.  68
    Deflationism and the Function of Truth.Lavinia Picollo & Thomas Schindler - 2018 - Philosophical Perspectives 32 (1):326-351.
    Deflationists claim that the truth predicate was introduced into our language merely to full a certain logico-linguistic function. Oddly enough, the question what this function exactly consists in has received little attention. We argue that the best way of understanding the function of the truth predicate is as enabling us to mimic higher-order quantification in a first-order framework. Indeed, one can show that the full simple theory of types is reducible to disquotational principles of truth. Our analysis has important consequences (...)
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  5.  52
    Yablo’s Paradox in Second-Order Languages: Consistency and Unsatisfiability.Lavinia María Picollo - 2013 - 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 paradoxical, since second-order (...)
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  6.  10
    Truth in a Logic of Formal Inconsistency: How Classical Can It Get?Lavinia Picollo - 2020 - Logic Journal of the IGPL 28 (5):771-806.
    Weakening classical logic is one of the most popular ways of dealing with semantic paradoxes. Their advocates often claim that such weakening does not affect non-semantic reasoning. Recently, however, Halbach and Horsten have shown that this is actually not the case for Kripke’s fixed-point theory based on the Strong Kleene evaluation scheme. Feferman’s axiomatization $\textsf{KF}$ in classical logic is much stronger than its paracomplete counterpart $\textsf{PKF}$, not only in terms of semantic but also in arithmetical content. This paper compares the (...)
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  7.  48
    Notes on Ω-Inconsistent Theories of Truth in Second-Order Languages.Eduardo Barrio & Lavinia Picollo - 2013 - Review of Symbolic Logic 6 (4):733-741.
    It is widely accepted that a theory of truth for arithmetic should be consistent, but -consistency is a highly desirable feature for such theories. The point has already been made for first-order languages, though the evidence is not entirely conclusive. We show that in the second-order case the consequence of adopting -inconsistent theories of truth are considered: the revision theory of nearly stable truth T # and the classical theory of symmetric truth FS. Briefly, we present some conceptual problems with (...)
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  8.  53
    The Old-Fashioned Yablo Paradox.Lavinia Picollo - 2012 - Análisis Filosófico 32 (1):21-29.
    The Yablo Paradox’ main interest lies on its prima facie non-circular character, which many have doubted, specially when formulated in an extension of the language of firstorder arithmetic. Particularly, Priest (1997) and Cook (2006, forthcoming) provided contentious arguments in favor of circularity. My aims in this note are (i) to show that the notion of circularity involved in the debate so far is defective, (ii) to provide a new sound and useful partial notion of circularity and (iii) to show there (...)
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  9.  24
    Alethic Reference.Lavinia Picollo - 2020 - Journal of Philosophical Logic 49 (3):417-438.
    I put forward precise and appealing notions of reference, self-reference, and well-foundedness for sentences of the language of first-order Peano arithmetic extended with a truth predicate. These notions are intended to play a central role in the study of the reference patterns that underlie expressions leading to semantic paradox and, thus, in the construction of philosophically well-motivated semantic theories of truth.
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  10.  7
    Corrigendum for "Truth in a Logic of Formal Inconsistency: How Classical Can It Get?".Lavinia Picollo - forthcoming - Logic Journal of the IGPL.
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  11.  14
    La inocencia del deflacionismo.Lavinia Picollo - 2010 - Manuscrito 33 (2):425-443.
    De acuerdo con Shapiro , el deflacionismo debe buscar la conservatividad de sus teorías de la verdad sobre cualquier teoría base. De lo contrario, la noción de verdad que ellas presentan daría lugar a más afirmaciones acerca de la ontología de la teoría base que ésta misma. Así, la verdad tendría poder explicativo y, por tanto, sería en algún sentido una noción metafísicamente sustantiva. El objetivo del artículo es rechazar esta tesis para algunas teorías de la verdad cuyos axiomas son (...)
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  12.  30
    Proof and Falsity: A Logical Investigation.Lavinia Picollo - forthcoming - Analysis.
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  13.  14
    Reference and Truth.Lavinia Picollo - 2020 - Journal of Philosophical Logic 49 (3):439-474.
    I apply the notions of alethic reference introduced in previous work in the construction of several classical semantic truth theories. Furthermore, I provide proof-theoretic versions of those notions and use them to formulate axiomatic disquotational truth systems over classical logic. Some of these systems are shown to be sound, proof-theoretically strong, and compare well to the most renowned systems in the literature.
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