I Workshop NUS – BA LOGIC

June 16, 2023

Argentinean Society of Philosophical Analysis (SADAF)

Buenos Aires, Argentina

Lavinia Picollo (NUS)

Daniel Waxman (NUS)

Ethan Jerzak (NUS)

Mariela Rubin (IIF-SADAF-CONICET & UBA)

Camila Gallovich (IIF-SADAF-CONICET & UBA)

Agustina Borzi (IIF-SADAF-CONICET & UBA)

Friday, June 16th

14:00 to 19:30 (GMT-03, Buenos Aires Local Time)

14:00 – 14:45   Daniel Waxman (NUS): “On Arithmetical Pluralism “.(joint work with Lavinia Picollo)

14:45 – 15:30   Agustina Borzi (IIF-SADAF-CONICET & UBA): “How To Model Formal Epistemic Commitments With Mixed Logics”.(joint work with Federico Pailos and Joaquín Toranzo Calderón)

15:30 – 16:00   Cofee break

16:00 – 16:45   Ethan Jerzak (NUS): “De Re Desire”.

16:45 – 17:30   Mariela Rubin (IIF-SADAF-CONICET & UBA): “Export and Gibbard´s Collapse Result”.

17:30 – 18:00   Cofee break

18:00 – 18:45   Camila Gallovich (IIF-SADAF-CONICET & UBA): “Grounded truth and non-categoricity”.

18:45 – 19:30   Lavinia Picollo (NUS): “Carnap’s categoricity problem and meta-inference validity”.

Lavinia Picollo: “Carnap’s categoricity problem and meta-inference validity”

A well-known problem, due to Carnap, concerns how the meanings of logical connectives can possibly arise from the rules governing their use. Much less discussed is an analogous problem for quantifiers. In this talk I argue that the problem for quantifiers is serious and, on plausible semantic and metasemantic assumptions, forces us into a radically revisionary view of quantifiers and the truth-conditions of quantified sentences. I go on to explore a possible response: that the issue with the quantifiers arises from a particular incorrect account of meta-inference validity, which should be replaced by an alternative notion. I argue that this alternative approach is untenable, as it clashes with our initial semantic and metasemantic assumptions. An interesting consequence is that our calculi only enable reasoning from argument-premises so long as the premises are valid.

Dan Waxman: “On Arithmetical Pluralism” (joint work with Lavinia Picollo)

Arithmetical pluralism is the view that there is no one true arithmetic but many competing arithmetical theories, each true in its own language, all equally good from an objective standpoint. Pluralist views have recently attracted much interest but have also been the subject of significant criticism, most saliently from Putnam (1979) and Koellner (2009). These critics argue that, due to the possibility of arithmetizing the syntax of arithmetical languages, one cannot coherently say that arithmetic is a matter of `taste’ whilst consistency is a matter of fact. In response, some (e.g. Warren (2015)) have forcefully argued that Putnam’s and Koellner’s argument relies on a misunderstanding. In this paper we put forward a new argument on the side of the critics: appealing to internal categoricity results for arithmetic, we argue that arithmetical pluralism cannot coherently be maintained while supposing that the consistency of mathematical theories is a matter of fact after all.

Ethan Jerzak: “De Re Desire”

Desire reports have advisory readings, on which “S wants p” can be true even if S has no idea that they want p, or even thinks that they don’t want p. In earlier work I’ve argued for a relativist theory of desire reports to account for these readings. Here I’ll consider a more conservative explanation, on which advisory reports are one side of a de re / de dicto ambiguity. I explore the relationship between de re belief reports and de re desire reports. I argue that the resulting theory suffers from two main difficulties: It has trouble accounting for negative advisory desire reports, and it has trouble systematically specifying an appropriate acquaintance property. I argue that the most plausible version of such a theory holds that everyone necessarily desires the Good— that is, that the property of being good is always available as an acquaintance property for desire reports.

Mariela Rubin: “Export and Gibbard´s Collapse Result”

The main goal of this work is to explore the least amount of assumptions needed to derive Gibbard´s collapse result regarding indicative conditionals. I will show that when translated to a sequent calculus it is possible to prove the collapse result with significantly fewer assumptions than those usually employed. In particular, the Import Law is not needed. The corollary of this result is that the collapse will take place for even stronger conditionals than the intuitionistic one. The second goal of this work is to explore which are the structural rules that are involved in the derivation and how these rules relate to the different proposals in the literature.

Agustina Borzi: “How To Model Formal Epistemic Commitments With Mixed Logics”(joint with Federico Pailos and Joaquín Toranzo Calderón)

The goal of this talk is to present two different ways in which to model every epistemic formal conditional commitment that involves (at most) three key epistemic attitudes: acceptance, rejection and neither acceptance nor rejection. The first one consists in adopting the plurality of every mixed Strong Kleene logic (along with a epistemic reading of the truth-values), and the second one involves the use of a unified system of six-sided inferences that recovers the validities of each mixed Strong Kleene logic, called 6SK. We also introduce a sequent calculus that is sound and complete with respect to both approaches. Finally, we suggest that both the plurality of Strong Kleene logics and the general framework 6SK are linked to formal epistemic norms via bridge principles.

Camila Gallovich: “Grounded truth and non-categoricity”

There are two fundamental ideas about truth that any theory seeking to provide a natural and explanatory account of this concept should be able to capture. The first idea suggests that the meaning of the truth predicate is given by the claim that the circumstances under which one may assert of a sentence that it is true (false) are exactly the same as the circumstances under which one may assert (deny) that sentence. According to the second idea, the interpretation of the sentences containing semantic predicates is determined by the interpretation of those sentences that do not contain these predicates. Whereas the first thought is silent on how to establish an appropriate extension for the concept of truth, the second thought commits one to the idea that the truth predicate has an intended interpretation. In “Kripke and the logic of Truth”, Kremer has raised an objection against Kripke’s proposal. According to this objection, the fixed-point theory fails to simultaneously capture both semantic intuitions without sacrificing a good part of its explanatory power. My first goal in this talk is to analyze this objection and to provide a response to it by making use of the fixed-point semantics. My second goal is to argue that, pace Kremer, a further problem emerges against his own inferentialist approach to truth, as the rules associated with this concept prove not to be sufficient to rule out unintended interpretations. I will also suggest that a promising strategy to address this concern emerges by making use of a bilateralist system.

Eduardo Barrio (IIF-SADAF-CONICET & UBA)

Federico Pailos (IIF-SADAF-CONICET & UBA)

Bruno Da Ré (IIF-SADAF-CONICET & UBA)

Lavinia Picollo (NUS)

We are grateful for the support provided by CONICET