Recent Publications

Recent Publications


  • Bruno Da Ré and Lucas Rosenblatt
    Contraction, Infinitary Quantifiers, and Omega Paradoxes
    Forthcoming in Journal of Philosophical Logic

    Our main goal is to investigate whether the infinitary rules for the quantifiers endorsed by Elia Zardini in a recent paper are plausible. First, we will argue that they are problematic in several ways, especially due to their infinitary features. Secondly, we will show that even if these worries are somehow dealt with, there is another serious issue with them. They produce a truth-theoretic paradox that does not involve the structural rules of contraction.

  • Eduardo Barrio, Federico Pailos and Damian Szmuc
    A Paraconsistent Route to Semantic Closure
    Forthcoming in Logic Journal of the IGPL

    In this paper we present a non-trivial and expressively complete paraconsistent naïve theory of truth, as a step in the route towards semantic closure. We achieve this goal by expressing self-reference with a weak procedure, that uses equivalences between expressions of the language, as opposed to a strong procedure, that uses identities. Finally, we make some remarks regarding the sense in which the theory of truth discussed has a property closely related to functional completeness, and we present a sound and complete three-sided sequent calculus for this expressively rich theory.

  • Damian Szmuc
    Defining LFIs and LFUs in extensions of infectious logics
    Journal of Applied Non-Classical Logics, 26 (4): 286-314, 2016.

    The aim of this paper is to explore the peculiar case of infectious logics, a group of systems obtained generalizing the semantic behavior characteristic of the {¬, ∧, ∨}-fragment of the logics of nonsense, such as the ones due to Bochvar and Halldén, among others. Here, we extend these logics with classical negations, and we furthermore show that some of these extended systems can be properly regarded as logics of formal inconsistency (LFIs) and logics of formal undeterminedness (LFUs).

  • Eduardo Barrio, Lucas Rosenblatt and Diego Tajer
    Capturing Naive Validity in the Cut-Free Approach
    Forthcoming in Synthese

    Rejecting the Cut rule has been proposed as a strategy to avoid both the usual semantic paradoxes and the so-called v-Curry paradox. In this paper we consider if a Cut-free theory is capable of accurately representing its own notion of validity. We claim that the standard rules governing the validity predicate are too weak for this purpose and we show that although it is possible to strengthen these rules, the most obvious way of doing so brings with it a serious problem: an internalized version of Cut can be proved for a Curry-like sentence. We also evaluate a number of possible ways of escaping this difficulty.

  • Federico Pailos and Diego Tajer
    Validity in a dialetheist framework
    Forthcoming in Logique et Analyse

    In this paper, we develop two theories of validity in a dialetheist framework, both based on Meadows (2014). The first one, LPV*, has LP’s consequence relation but the validity predicate of Meadows’ construction. The second theory, DT (the one we favour), is defined in terms of its validity predicate. Therefore, in DT, the validity predicate and the consequence relation coincide. Moreover, the theory, unlike Meadows’ VAL, is reflexive.

  • Lucas Rosenblatt
    Two-valued logics for naive truth theory
    The Australasian Journal of Logic, 12 (1): 44-66, 2015.

    Adding a transparent truth predicate to a language completely governed by classical logic is not possible. The trouble, as is well-known, comes from paradoxes such as the Liar and Curry. Recently, Cobreros, Egré, Ripley and van Rooij have put forward an approach based on a non-transitive notion of consequence which is suitable to deal with semantic paradoxes while having a transparent truth predicate together with classical logic. Nevertheless, there are some interesting issues concerning the set of metainferences validated by this logic. In this paper, we show that this logic, once it is adequately understood, is weaker than classical logic. Moreover, the logic is in a way similar to the paraconsistent logic LP.

  • Eduardo Barrio and Gonzalo Rodríguez-Pereyra
    Truthmaker Maximalism defended again
    Analysis, 75 (1): 3-8, 2015.

    In this note we shall argue that Milne’s new effort does not refute Truthmaker Maximalism. According to Truthmaker Maximalism, every truth has a truthmaker. Milne (2005, Not every truth has a truthmaker. Analysis 65: 221–4; 2013, ‘Not every truth has a truthmaker II. Analysis 73: 473–81) has attempted to refute it using the following self-referential sentence M: This sentence has no truthmaker. Essential to his refutation is that M is like the Gödel sentence and unlike the Liar, and one way in which Milne supports this assimilation is through the claim that his proof is essentially object-level and not semantic. In Section 2, we shall argue that Milne is still begging the question against Truthmaker Maximalism. In Section 3, we shall argue that even assimilating M to the Liar does not force the truthmaker maximalist to maintain the ‘dull option’ that M does not express a proposition. There are other options open and, though they imply revising the logic in Milne’s reasoning, this is not one of the possible revisions he considers. In Section 4, we shall suggest that Milne’s proof requires an implicit appeal to semantic principles and notions. In Section 5, we shall point out that there are two important dissimilarities between M and the Gödel sentence. Section 6 is a brief summary and conclusion.

  • Federico Pailos and Lucas Rosenblatt
    Solving Multimodal Paradoxes
    Theoria, 81 (3): 192–210, 2015.

    Recently, it has been observed that the usual type-theoretic restrictions are not enough to block certain paradoxes involving two or more predicates. In particular, when we have a self-referential language containing modal predicates, new paradoxes might appear even if there are type restrictions for the principles governing those predicates. In this article we consider two type-theoretic solutions to multimodal paradoxes. The first one adds types for each of the modal predicates. We argue that there are a number of problems with most versions of this approach. The second one, which we favour, represents modal notions by using the truth predicate together with the corresponding modal operator. This way of doing things is not only useful because it avoids multimodal paradoxes, but also because it preserves the expressive capacity of the language. As an example of the sort of theory we have in mind, we provide a type-theoretic axiomatization that combines truth with necessity and knowledge.

  • Eduardo Barrio, Lucas Rosenblatt and Diego Tajer
    The Logics of Strict-Tolerant Logic
    Journal of Philosophical Logic, 44 (5): 551–571, 2015.

    Adding a transparent truth predicate to a language completely governed by classical logic is not possible. The trouble, as is well-known, comes from paradoxes such as the Liar and Curry. Recently, Cobreros, Egré, Ripley and van Rooij have put forward an approach based on a non-transitive notion of consequence which is suitable to deal with semantic paradoxes while having a transparent truth predicate together with classical logic. Nevertheless, there are some interesting issues concerning the set of metainferences validated by this logic. In this paper, we show that this logic, once it is adequately understood, is weaker than classical logic. Moreover, the logic is in a way similar to the paraconsistent logic LP.

  • Federico Pailos and Lucas Rosenblatt
    Non-deterministic Conditionals and Transparent Truth
    Studia Logica, 103 (3): 579-598, 2014.

    Theories where truth is a naive concept fall under the following dilemma: either the theory is subject to Curry’s Paradox, which engenders triviality, or the theory is not trivial but the resulting conditional is too weak. In this paper we explore a number of theories which arguably do not fall under this dilemma. In these theories the conditional is characterized in terms of (infinitely-valued) non-deterministic matrices. These non-deterministic theories are similar to infinitely-valued Łukasiewicz logic in that they are consistent and their conditionals are quite strong. The difference is the following: while Łukasiewicz logic is ω-inconsistent, the non-deterministic theories might turn out to be ω-consistent.

  • Lucas Rosenblatt and Damian Szmuc
    On Pathological Truths
    The Review of Symbolic Logic, 7 (4): 601–617, 2014.

    In Kripke’s classic paper on truth it is argued that by adding a new semantic category different from truth and falsity it is possible to have a language with its own truth predicate. A substantial problem with this approach is that it lacks the expressive resources to characterize those sentences which fall under the new category. The main goal of this paper is to offer a refinement of Kripke’s approach in which this difficulty does not arise. We tackle this characterization problem by letting certain sentences belong to more than one semantic category. We also consider the prospect of generalizing this framework to deal with languages containing vague predicates.

  • Lucas Rosenblatt
    The Knowability Argument and the Syntactic Type-Theoretic Approach
    THEORIA. An International Journal for Theory, History and Foundations of Science, 29 (2): 201–221, 2014.

    Some attempts have been made to block the Knowability Paradox and other modal paradoxes by adopting a type-theoretic framework in which knowledge and necessity are regarded as typed predicates. The main problem with this approach is that when these notions are simultaneously treated as predicates, a new kind of paradox appears. I claim that avoiding this paradox either by weakening the Knowability Principle or by introducing types for both predicates is rather messy and unattractive. I also consider the prospect of using the truth predicate to emulate other modal notions. It turns out that this idea works quite well.

  • Eduardo Barrio and Lavinia Picollo
    Notes on ω-inconsistent theories of truth in Second-order languages
    The Review of Symbolic Logic, 6 (4): 733–741, 2013.

    It is widely accepted that a theory of truth for arithmetic should be consistent, but ω-consistency is less frequently required. This paper argues that ω-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 ω-inconsistent truth theories for arithmetic is unsatisfiability. In order to bring out this point, well known ω-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 ω-inconsistent theories, and demonstrate some technical results that support our criticisms of such theories.

  • Lavinia Picollo
    Yablo’s paradox in second-order languages: Consistency and unsatisfiability
    Studia Logica, 101 (3): 601–617, 2012.

    Stephen Yablo 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 languages are not compact, I study the paradoxicality of Yablo’s list within these languages. While non-paradoxical in the first sense, the second-order version of the list is a paradox in our second sense. I conclude that this suffices for regarding Yablo’s original list as paradoxical and his informal argument as valid.

  • Eduardo Barrio
    Theories of truth without standard models and Yablo’s sequences
    Studia Logica, 96 (3): 375–391, 2010.

    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 that in second order theories with standard semantics the same procedure yields a theory that doesn’t have models. So, while having an ω- inconsistent theory is a bad thing, having an unsatisfiable theory of truth is actually worse. This casts doubts on whether the predicate in question is, after all, a truthpredicate for that language. Finally, I present some alternatives to prove an inconsistency adding plausible principles to certain theories of truth.