Revistas
Revista:
SYNTHESE
ISSN:
0039-7857
Año:
2021
N°:
198
Págs.:
8251 - 8265
Substructural approaches to paradoxes have attracted much attention from the philosophical community in the last decade. In this paper we focus on two substructural logics, named ST and TS, along with two structural cousins, LP and K3. It is well known that LP and K3 are duals in the sense that an inference is valid in one logic just in case the contrapositive is valid in the other logic. As a consequence of this duality, theories based on either logic are tightly connected since many of the arguments for and objections against one theory reappear in the other theory in dual form. The target of the paper is making explicit in exactly what way, if any, ST and TS are dual to one another. The connection will allow us to gain a more fine-grained understanding of these logics and of the theories based on them. In particular, we will obtain new insights on two questions concerning ST which are being intensively discussed in the current literature: whether ST preserves classical logic and whether it is LP in sheep's clothing. Explaining in what way ST and TS are duals requires comparing these logics at a metainferential level. We provide to this end a uniform proof theory to decide on valid metainferences for each of the four logics. This proof procedure allows us to show in a very simple way how different properties of inferences (unsatisfiability, supersatisfiability and antivalidity) that behave in very different ways for each logic can be captured in terms of the validity of a metainference.
Autores:
Cobreros, Pablo; La Rosa, E.; Tranchini, L. (Autor de correspondencia)
Revista:
JOURNAL OF PHILOSOPHICAL LOGIC
ISSN:
0022-3611
Building on early work by Girard (1987) and using closely related techniques from the proof theory of many-valued logics, we propose a sequent calculus capturing a hierarchy of notions of satisfaction based on the Strong Kleene matrices introduced by Barrio et al. (Journal of Philosophical Logic 49:93-120, 2020) and others. The calculus allows one to establish and generalize in a very natural manner several recent results, such as the coincidence of some of these notions with their classical counterparts, and the possibility of expressing some notions of satisfaction for higher-level inferences using notions of satisfaction for inferences of lower level. We also show that at each level all notions of satisfaction considered are pairwise distinct and we address some remarks on the possible significance of this (huge) number of notions of consequence.
Revista:
SYNTHESE
ISSN:
0039-7857
Año:
2021
Vol.:
199
N°:
Supl. 3
Págs.:
681 - 705
The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approaches and examine three specific consequence relations in relation to those, which we call: strict-to-tolerant entailment, pragmatic-to-tolerant entailment, and pragmatic-to-pragmatic entailment. The first two are nontransitive, whereas the latter two are nonmonotonic.
Revista:
JOURNAL OF PHILOSOPHICAL LOGIC
ISSN:
0022-3611
Año:
2020
Vol.:
49
Págs.:
1057 - 1077
In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between metainferences holding in the strict-tolerant logic of transparent truthST(+)and inferences holding in the logic of paradoxLP(+). They argue thatLP(+)isST(+)'s external logic and they question whetherST(+)'s solution to the semantic paradoxes is fundamentally different fromLP(+)'s. Here we establish that by parity of reasoning,ST(+)can be related toLP(+)'s dual logicK3(+). We clarify the distinction between internal and external logic and argue that whileST(+)'s nonclassicality can be granted, its self-dual character does not tie it toLP(+)more closely than toK3(+).
Revista:
LOGIQUE ET ANALYSE
ISSN:
0024-5836
Año:
2017
Vol.:
60
N°:
239
Págs.:
355 - 373
Revista:
SCIENTIA ET FIDES
ISSN:
2300-7648
Año:
2016
Vol.:
4
N°:
1
Págs.:
61 - 75
If God knew I were going to write this paper, was I able to refrain from writing it this morning? One possible response to this question is that God's knowledge does not take place in time and therefore He does not properly fore-know. According to this response, God knows absolutely everything, it's just that He knows everything outside of time. The so-called timeless solution was one of the influential responses to the foreknowledge problem in classical Christian Theology. This solution, however, seemed to lose support in the recent debate. For example, Pike claims that "the doctrine of God's timelessness entered Christian Theology (only) because Platonic thought was stylish at the time" (Pike, 1970, 190) and Hasker (2001) catalogues this as one of the minor solutions to the problem. One possible source for this general attitude towards timelessness is the thought that the very idea of timelessness is incoherent. In this paper I argue that that the timeless solution to the foreknowledge problem is congenial with the supervaluationist theory of branching time and that this formal framework provides, in fact, a precise characterization of the timeless solution to the foreknowledge problem. The views presented in this paper are in line with those of Kretzmann and Stump (1981), Leftow (1991) and De Florio and Frigerio (2015).
Revista:
JOURNAL OF PHILOSOPHICAL LOGIC
ISSN:
0022-3611
Revista:
JOURNAL OF APPLIED NON-CLASSICAL LOGICS
ISSN:
1166-3081
Año:
2014
Vol.:
24
N°:
1-2
Págs.:
1 - 11
Revista:
THOUGHT: A JOURNAL OF PHILOSOPHY
ISSN:
2161-2234
Año:
2014
Vol.:
3
N°:
2
Págs.:
136 -144
This article deals with supervaluationism and the failure of truth-functionality. It draws some distinctions that may contribute to a better understanding of this semantic framework.
Revista:
METAPHYSICA. INTERNATIONAL JOURNAL FOR ONTOLOGY AND METAPHYSICS
ISSN:
1437-2053
Año:
2013
Vol.:
14
N°:
2
Págs.:
253 - 264
Arguments based on Leibniz's Law seem to show that there is no room for either indefinite or contingent identity. The arguments seem to prove too much, but their conclusion is hard to resist if we want to keep Leibniz's Law. We present a novel approach to this issue, based on an appropriate modification of the notion of logical consequence.
Revista:
MIND
ISSN:
0026-4423
Año:
2013
Vol.:
122
N°:
488
Págs.:
841 - 866
This paper presents and defends a way to add a transparent truth predicate to classical logic, such that T<A> and A are everywhere intersubstitutable, where all T-biconditionals hold, and where truth can be made compositional. A key feature of our framework, called STTT (for Strict-Tolerant Transparent Truth), is that it supports a non-transitive relation of consequence. At the same time, it can be seen that the only failures of transitivity STTT allows for arise in paradoxical cases.
Revista:
PHILOSOPHY COMPASS
ISSN:
1747-9991
Año:
2013
Vol.:
8
N°:
5
Págs.:
472 - 485
Supervaluationism is a well known theory of vagueness. Subvaluationism is a less well known theory of vagueness. But these theories cannot be taken apart, for they are in a relation of duality that can be made precise. This paper provides an introduction to the subvaluationist theory of vagueness in connection to its dual, supervaluationism. A survey on the supervaluationist theory can be found in the Compass paper of Keefe (2008); our presentation of the theory in this paper will be short to get rapidly into the logical issues. This paper is relatively self-contained. A modest background on propositional modal logic is, though not strictly necessary, advisable. The reader might find useful the Compass papers Kracht (2011) and Negri (2011) (though these papers cover issues of more complexity than what is demanded to follow this paper).
Revista:
STUDIA LOGICA
ISSN:
0039-3215
Año:
2012
Vol.:
100
N°:
4
Págs.:
855 - 877
In a previous paper (see `Tolerant, Classical, Strict¿, henceforth TCS) we investigated a semantic framework to deal with the idea that vague predicates are tolerant, namely that small changes do not affect the applicability of a vague predicate even if large changes do. Our approach there rests on two main ideas. First, given a classical extension of a predicate, we can define a strict and a tolerant extension depending on an indifference relation associated to that predicate. Second, we can use these notions of satisfaction to define mixed consequence relations that capture non-transitive tolerant reasoning. Although we gave some empirical motivation for the use of strict and tolerant extensions, making use of them commits us to the view that sentences of the form ` p¿¬p ¿ and ` p¿¬p ¿ are not automatically valid or unsatisfiable, respectively. Some philosophers might take this commitment as a negative outcome of our previous proposal. We think, however, that the general ideas underlying our previous approach to vagueness can be implemented in a variety of ways. This paper explores the possibility of defining mixed notions of consequence in the more classical super/sub-valuationist setting and examines to what extent any of these notions captures non-transitive tolerant reasoning.
Revista:
JOURNAL OF PHILOSOPHICAL LOGIC
ISSN:
0022-3611
Año:
2012
Vol.:
41
N°:
2
Págs.:
347 - 385
In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases.
Revista:
SYNTHESE
ISSN:
0039-7857
Año:
2011
Vol.:
183
N°:
2
Págs.:
211 - 227
Paraconsistent approaches have received little attention in the literature on vagueness (at least compared to other proposals). The reason seems to be that many philosophers have found the idea that a contradiction might be true (or that a sentence and its negation might both be true) hard to swallow. Even advocates of paraconsistency on vagueness do not look very convinced when they consider this fact; since they seem to have spent more time arguing that paraconsistent theories are at least as good as their paracomplete counterparts, than giving positive reasons to believe on a particular paraconsistent proposal. But it sometimes happens that the weakness of a theory turns out to be its mayor ally, and this is what (I claim) happens in a particular paraconsistent proposal known as subvaluationism. In order to make room for truth-value gluts subvaluationism needs to endorse a notion of logical consequence that is, in some sense, weaker than standard notions of consequence. But this weakness allows the subvaluationist theory to accommodate higher-order vagueness in a way that it is not available to other theories of vagueness (such as, for example, its paracomplete counterpart, supervaluationism).
Revista:
MIND
ISSN:
0026-4423
Año:
2011
Vol.:
120
N°:
479
Págs.:
833 - 843
Though it is standardly assumed that supervaluationism applied to vagueness is committed to global validity, Achille Varzi (2007) argues that the supervaluationist should take seriously the idea of adopting local validity instead. Varzi¿s motivation for the adoption of local validity is largely based on two objections against the global notion: that it brings some counterexamples to classically valid rules of inference and that it is inconsistent with unrestricted higher-order vagueness. In this discussion I review these objections and point out ways to address them not considered in Varzi¿s paper.
Capítulos de libros
Libro:
The Sorites Paradox
Lugar de Edición:
Cambridge
Editorial:
Cambridge University Press
Año:
2019
Págs.:
38 - 62
One way in which we might approach the challenge posed by the Sorites Paradox is considering that Sorites-susceptible predicates have several candidate extensions, or several ways in which these expressions can be made precise. For example, a candidate extension for the predicate `is a baby¿ is the set of humans of less than two years, but also the set of those less than two years and one second, and of those less than two years and two seconds. In this chapter we present and discuss two theories for vague predicates based on this idea: super-valuationism and subvaluationism. The chapter is structured in three parts. The first presents the super- and subvaluationist theories: their similarities and differences in the semantics, the resulting logics with their most characteristic features. The second reviews the super- and subvaluationist solutions to the Sorites Paradox and provides discussion on several controversies surrounding these theories. The third part introduces proof procedures for s¿valuationist logics.
Libro:
Solutions to the Sorites Paradox
Editorial:
Cambridge University Press
Año:
2019
Págs.:
38-62
Libro:
Unifying the philosophy of truth
Lugar de Edición:
Dordrecht-Heidelberg-New York-London
Editorial:
Ed. Springer
Año:
2015
Págs.:
409 - 430
We say that a sentence A is a permissive consequence of a set of
premises Gamma whenever, if all the premises of Gamma hold up to some standard, then A
holds to some weaker standard. In this paper, we focus on a three-valued version
of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness
toward a unified treatment of the paradoxes of vagueness and self-referential
truth. For vagueness, st-consequence supports the principle of tolerance; for truth,
it supports the requisit of transparency. Permissive consequence is non-transitive,
however, but this feature is argued to be an essential component to the understanding
of paradoxical reasoning in cases involving vagueness or self-reference
Libro:
Recent trends in philosophical logic
Lugar de Edición:
Cham
Editorial:
Springer
Año:
2014
Págs.:
75 - 83
In his chapter `Non-transitive identity¿ [8], Graham Priest develops a notion of non-transitive identity based on a second-order version of LP. Though we are sympathetic to Priest¿s general approach to identity we think that the account can be refined in different ways. Here we present two such ways and discuss their appropriateness for a metaphysical reading of indefiniteness in connection to Evans¿ argument.
Libro:
Vagueness and language use
Lugar de Edición:
Houndmills
Editorial:
Palgrave MacMillan
Año:
2011
Págs.:
207 - 221
Libro:
Vagueness in communication
Lugar de Edición:
Bordeaux
Editorial:
Springer Berlin/Heidelberg
Año:
2011
Págs.:
51 - 63
The supervaluationist theory of vagueness provides a notion of logical consequence that is akin to classical consequence. In the absence of a definitely operator, supervaluationist consequence coincides with classical consequence. In the presence of `definitely¿, however, supervaluationist logic gives raise to counterexamples to classically valid patterns of inference. Foes of supervaluationism emphasize the last result to argue against the supervaluationist theory. This paper shows a way in which we might obtain systems of deduction adequate for supervaluationist consequence based on systems of deduction adequate for classical consequence. Deductions on the systems obtained this way adopt a completely classical form with the exception of a single step. The paper reviews (at least part of) the discussion on the non-classicality of supervaluationist logic under the light of this result.
