Dates: 28-29th January 2020
Venue: Seminari de Filosofia

Tuesday 28h

10-11:15 Concha Martínez Vidal, "Putnam and Contemporary Fictionalism: A Common View on Abstract Objects"

11:45-13 José Martínez, Genoveva Martí, "The representation of gappy sentences in four-valued semantics"

15-16:15 Sergi Oms, Elia Zardini, "Inclosure and Intolerance"

16:30-17:45 Eduardo Barrio, "Validities, antivalidities and ST-hierarchy"

Wednesday 29th

9-10:15 Jordi Valor, "Circularity and the meaning of Liar sentences"

10:45-12 Pilar Terrés, "Towards a consequence relation without the identity axiom"

12-13:15 Ole Hjortland, "Logical pluralism without collapse"

Abstracts

Eduardo Barrio: VALIDITIES, ANTIVALIDITIES AND ST-HiERARCHY 

The hierarchy of metainferential logics defined in [BPS 2019a and BPS2019b] recovers the classical logic, either in the sense that every classical (meta)inferential validity is valid at some point in the hierarchy, or because a logic of a transfinite level defined in terms of the hierarchy shares its validities with classical logic. Scambler (2019) presents a major challenge to this approach. He argues that this hierarchy cannot be identified with classical logic in any way because it recovers no classical antivalidities. And if it can do that, so is the case with a parallel hierarchy based on TS, that recovers every classical antivalidity, but none of its validities. I embrace Scambler challenge and develop a new hierarchy based on the previous two. This new hierarchy recovers both every classical validity and every classical antivalidity. Finally, I discuss and explore some philosophical motivations of this hierarchy of metainferential logics that capture the set of validities and antivalitidies as a part of the hierarchy of the classical logic. 

-E. Barrio, F. Pailos, and D. Szmuc. “A Hierarchy of Classical and Paraconsistent Logics”. Journal of Philosophical Logic, pages 1–28, 2019a.

DOI: https://doi.org/10.1007/s10992-019-09513-z

-E. Barrio, F. Pailos & D. Szmuc “(Meta)Inferential Levels of Entailment beyond the Tarskian Paradigm”. Synthese, 2019b

DOI: https://doi.org/10.1007/s11229-019-02411-6

-Scambler. “Classical Logic and the Strict Tolerant Hierarchy”. Journal of Philosophical Logic, page forthcoming, 2019.

DOI: https://doi.org/10.1007/s10992-019-09520-0

Ole Hjortland: LOGICAL PLURALISM WITHOUT COLLAPSE

According to logical pluralism there is more than one correct logic. After Beall & Restall's influential defence of the position, a number of pluralist theories have been defended. In response, critics such as Priest (2006), Read (2006), and Keefe (2014) have argued that pluralism isn't just unwarranted, but that the position is untenable: It collapses into logical monism. In this paper, I investigate the assumptions and targets of the collapse argument, and I argue that there are good prospects for a form of logical pluralism that avoids collapse.

Concha Martínez Vidal: PUTNAM AND COMTEMPORARY FICTIONALISM: A COMMOM VIEW ON ABSTRACT OBJETS

Traditional interpretations of Putnam’s indispensability argument endorse him with a defense of the so-called Quine-Putnam indispensability argument, 1 an argument for ontological platonism in mathematics. This interpretation has been disputed in the literature and by Putnam himself. 2 Putnam rejects that the only way of arguing for the objectivity of mathematics—the truth of mathematical statements—is by committing to ontological platonism. He contends that there is an alternative, namely, not to take mathematics at face value. The aim of the talk is to see, in the light of his acknowledged indispensability argument, where he stands in relation to certain contemporary fictionalist positions. The purpose of this talk is to show—in the light of Putnam’s preferred paraphrase of classical mathematics (Hellman’s 1989 according to Putnam 2012, 182-3, ft.5) —on one hand, that many of the arguments that Putnam (2012) waves against other authors apply to his proposal as well. On the other, we aim to maintain that, in spite of the differences in the particular strategies that Field (1980), Yablo (2005; 2013) and Putnam advocate in order to account for the applicability of mathematics, there are also enough coincidences as to contend that their views are similar and compatible with a certain conception of abstract objects. 

José Martínez/Genoveva Martí: THE REPRESENTATION OF GAPY SENTENCES IN FOUR-VALUED SEMANTICS

Three-valued logics are standardly used to formalize gappy languages. We would like to explore how to build a four-valued truth-functional semantics for a language which contains two different sources of semantic pathologies that generate two different types of gappy sentences. We will concentrate on languages that contain (i) sentences that lack classical truth value because they do not express a proposition and (ii) sentences that do express a proposition but, due to some deficiency, are neither true nor false. The semantic values will be {0,1,2,3}, with 0 (resp. 1) being assigned to sentences that express a false (resp. true) proposition, 2 to sentences that express a neither true nor false proposition and 3 to sentences that do not express a proposition at all. The search for a semantics will be conducted among the operators that are monotonic on the order 3 < 2, 2 < 0, 2 < 1. We will determine the best available options and discuss some of their properties. 

Sergi Oms/Elia Zardini: INCLOSURE AND INTOLERANCE

Graham Priest has influentially claimed that the Sorites paradox is an Inclosure paradox, concluding that his favoured dialetheic solution to the Inclosure para- doxes should be extended to the Sorites paradox. We argue that, given Priest’s dialetheic solution to the Sorites paradox, the argument for the conclusion that that paradox is an inclosure is invalid. 

Jordi Valor: CIRCULARITY AND THE MEANING OF LIAR SENTENCES

Many people think that “liar sentences” say nothing or lack meaning (in some relevant sense of the term). This verdict fits quite well some of our pretheoretic intuitions and initial reactions to the Liar paradox, but it must deal with an important problem. There are no clear syntactic features singling out “liar sentences”. The very same sentence may give rise to a paradox in some contexts and fail to do so in some others. Some story needs to be told in order to support the claim that a sentence says nothing in contexts where it gives rise to a liar like paradox. On different grounds, Grover’s prosentential theory of truth and Goldstein’s cassationist approach to the liar offer a similar diagnosis of the problem: when used in paradoxical contexts, the rules associated to the meaning of some sentences trigger some sort of vicious circularity which prevents them from acquiring truth-evaluable content in those very contexts. I wish to explore here how satisfactory this solution to the liar paradox is by examining some of its consequences.