** September 3, 4, 10, 11 2020**

SADAF – Online Conferences

via

ZOOM Meetings

If you’re interested in joining us, please request the zoom link with an e-mail to the following address: bruno.horacio.da.re [at] gmail.com

**Thursday, September 3**

10:00 to 11:00 (GMT-03) – Paul Egré: “Gibbardian Collapse and Trivalent Logics”. (joint work with Lorenzo Rossi and Jan Sprenger) (Abstract)

11:15 to 12:15 (GMT-03) – Eduardo Barrio & Federico Pailos: “ How the metainferential ST-theories contain the validities they obey” (Abstract)

**Friday, September 4**

11:00 to 12:00 (GMT-03) – Lorenzo Rossi: “Truth and Quantification” (Abstract)

12:15 to 13:15 (GMT-03) – Bruno Da Ré and Damián Szmuc: “Immune Logics” (Abstract)

**Thursday, September 10**

11:00 to 12:00 (GMT-03) – Pilar Terrés: “Minimal Content and Logical Pluralism” (Abstract)

12:15 to 13:15 (GMT-03) – Diego Tajer: “A simple solution to the collapse argument for logical pluralism” (Abstract)

**Friday, September 11**

11:00 to 12:00 (GMT-03) – Rosalie Iemhoff: “The Stability of Logical Inference” (Abstract)

12:15 to 13:15 (GMT-03) – Bruno Da Ré and Federico Pailos: “Sequent-calculi for metainferential logics” (Abstract)

This paper discusses the scope and significance of the so-called triviality result stated by Allan Gibbard for indicative conditionals, showing that if a conditional operator satisfies the Law of Import-Export, is supraclassical, and is stronger than the material conditional, then it must collapse to the material conditional. Gibbard’s result is taken to pose a dilemma for a truth-functional account of indicative conditionals: give up Import-Export, or embrace the two-valued analysis. We show that this dilemma can be averted in trivalent logics of the conditional based on Reichenbach and de Finetti’s idea that a conditional with a false antecedent is undefined. Import-Export and truth-functionality hold without triviality in such logics. We unravel some implicit assumptions in Gibbard’s proof, and discuss a recent generalization of Gibbard’s result due to Branden Fitelson.

Anti-exceptionalism about logic is the thesis that logical theories have no special epistemological status. Logical theories are continuous with scientific theories. Contemporary anti-exceptionalists include how they deal with semantic paradoxes as part of the logical evidence data. The recent development of the metainferential hierarchy of S-logics shows that there are multiple options to deal with such paradoxes. LP and ST itself are only the first steps of this hierarchy. The logics TS/ST, …, _{ω} also options to deal with semantic paradoxes. This talk explores the reasons to go beyond the first steps. We show that LP, ST, and the logics of the ST-hierarchy offer different diagnoses for the same evidence. This data is not enough to adopt one of these logics. We will thus have to discuss other elements to evaluate the revision of classical logic. How close should we be to classical logic? Which logic should be used during the revision? Should a logic be closed under its own rules? We will answer all these questions -that are often regarded as some of the main reasons against the ST-hierarchy- and will provide some philosophical interpretations of (higher-level) local metainferential validity.

**Lorenzo Rossi: “Truth and Quantification”**

Theories of self-applicable truth have been motivated in two main ways. First, if truth-conditions provide the meaning of (several kinds of) natural language expressions, then self-applicable truth is instrumental to develop the semantics of natural languages. Second, a self-applicable truth predicate is required to express generalizations that would not be expressible in natural languages without it. In order to fulfill their semantic and expressive roles, we argue, the truth predicate has to be studied in its interaction with linguistic constructs that are actually found in natural languages and extend beyond first-order logic—modals, indicative conditionals, arbitrary quantifiers, and more. Here, we focus on truth and quantification. We develop a Kripkean theory of self-applicable truth to for the language of Generalized Quantifiers Theory. More precisely, we show how to interpret a self-applicable truth predicate for the full class of type ⟨1, 1⟩ (and type ⟨1⟩) quantifiers to be found in natural languages. As a result, we can model sentences such as ‘Most of what Jane said is true’, or ‘infinitely many theorems of T are untrue’, and several others, thus expanding the scope of existing approaches to truth, both as a semantic and as an expressive device.

**Bruno Da Ré and Damián Szmuc: “Immune Logics”**

This talk is concerned with an exploration of a family of systems—called immune logics—that arise from certain dualizations of the well-known family of infectious logics. The distinctive feature of the semantic of infectious logics is the presence of a certain “infectious” semantic value which, if assigned to a formula, is so assigned to any formula in which it occurs. In a rather informal manner (to be made precise shortly) we will refer to immune logics as those systems whose underlying semantics count with a certain “immune” semantic value behaving in a way that is perfectly dual to that of the infectious values. In other words, whenever a formula is assigned this immune value, any formula in which it occurs as a proper subformula is assigned a different value—except,perhaps, if all subformulae are so assigned.

**Pilar Terrés: “Minimal Content and Logical Pluralism”**

I aim to analyse the connection between natural and formal language from a pluralist perspective, and to determine the meaning-constitutive principles for logical constants across different substructural logics.

Logical pluralism aims to resolve the apparent disagreement between rival logics. It is claimed that versions of logical pluralism which entail a variation of meaning of logical vocabulary are trivial or uninteresting, while an interesting version of logical pluralism has to keep the meaning of logical connectives fixed. Hence, pluralists have tried to find a sameness criterion across logics. One prominent proposal for determining the meaning of connectives in different proof-theoretic calculus are the right and left rules for each connective, which remain fixed across logics.

I will contrast this view with minimalism in the philosophy of language tradition, which aims to find meaning-constitutive principles for logical connectives in natural language in different contexts of use, where the same logical connective might express different things. Minimalists hold that there is a minimal content which is common in the different contexts of use.

I will argue that both proposals are in tension, and I will suggest a pragmatic solution for the clash, connecting the two traditions and aiming to illuminate the sameness thesis for logical pluralism in light of the recent debate in the philosophy of language field.

**Diego Tajer: “A simple solution to the collapse argument for logical pluralism”**

A number of philosophers (Read 2006, Priest 2006, Stei 2017, Steinberger 2019) have argued that logical pluralism is not compatible with the normativity of logic. They provided different versions of the Collapse argument: if many logics are correct and all of them are normative, then the weakest ones will be irrelevant. In other words, if a correct logic gives you entitlement to believe a sentence, then the fact that another correct logic does not give you entitlement becomes irrelevant. In this paper, I claim that the Collapse argument is based on a controversial premise: the idea that every logic should be characterized by the same bridge principle. As Macfarlane (2004) first observed, bridge principles may be expressed using different deontic modalities. I explain how to use the diversity of bridge principles in order to solve the collapse problem, maintaining both logical pluralism and the normativity of logic. I provide an example of this solution and a general recipe.

**Rosalie Iemhoff: “The Stability of Logical Inference”**

The logical principles of a theory can change when axioms are added to it, even in the case that these axioms are nonlogical. One of the most well-known examples of this phenomenon is intuitionistic set theory, which derives the law of excluded middle once the Axiom of Choice is added to it. Less well-known is the fact that also the logical inferences of a theory are not always preserved under the addition of axioms, even in case the logical principles do remain equal. In this talk I will discuss some recent results on the (un)stability of logical inference under extensions and provide many examples.

**Bruno Da Ré and Federico Pailos: “Sequent-calculi for metainferential logics”**

In recent years, some theorists have argued that the logics are not only defined by their inferences, but also by their metainferences. In this sense, logics which coincide in their inferences, but not in their metainferences were considered to be different logics. In this vein, some metainferential logics have been developed, as logics with metainferences of any level, built as hierarchies over known logics, such as ST, LP, K3 and TS. What is distinctive of these metainferential logics is that they are mixed, i.e. the standard for the premises and for the conclusion is not necessarily the same. However, so far, all of these systems have been presented following a semantical standpoint, in terms of valuations based on the Strong Kleene matrices. In this article, we provide sound and complete sequent-calculi for the valid inferences and the invalid inferences of the logics ST, LP ,K3 and TS, and introduce an algorithm that allows to obtain sound and complete sequent-calculi for the validities and the invalidities of any metainferential logic of any level.

Federico Pailós (University of Buenos Aires and IIF-SADAF-CONICET)

Paula Teijeiro (University of Buenos Aires and IIF-SADAF-CONICET)

Bruno Da Ré (University of Buenos Aires and IIF-SADAF-CONICET

Mariela Rubin (University of Buenos Aires and IIF-SADAF-CONICET)

Isis Urgell (University of Buenos Aires and IIF-SADAF-CONICET)

The series of workshops organized by BA LOGIC aims to analyze different topics in Philosophical Logic, mainly connected with semantic paradoxes, theories of truth and non-classical logics

August 27 @ SADAF: Workshop on Substructural Logics and Metainferences

We are thankful for the support provided by CONICET