**Workshop on Philosophy of Logic (MCMP - University of Buenos Aires) **

** ****Buenos Aires, 26 y 27 de septiembre, 2013**

**SADAF - Bulnes 642 **

**Programa**

**Jueves 26 de septiembre**

Coordinador: Eduardo Barrio

15.00 hs. - Johannes Stern (MCMP) “Axiomatizing Semantic Theories of Truth?”

16.00 hs. - Ramiro Caso (CONICET - UBA) “Lessons learned from the philosophy of logic: Absolute generality and natural language semantics”

Café

Coordinador: Lucas Rosenblatt

18.00 hs. - Thomas Schindler (MCMP) "Reference Graphs, Dependency Games and Paradox"

19.00 hs. - Natalia Buacar (UBA) “Philosophical grounding of deduction”

**Viernes 27 de septiembre**

Coordinador: Federico Pailos

15.00 hs. - Catrin Campbell-Moore (MCMP) “A Kripkean fixed-point style semantics for credence”

16.00 hs. - Damian Szmuc (UBA) “On Pathological Truths”

Café

Coordinadora: Lavinia Picollo

18.00 hs. - Paula Teijeiro (UBA) “Sorites sequences and the continuum”

19.00 hs. - Eleonora Cresto (CONICET) “Group Knowledge, Evidential Probabilities and Responsibility”

Organizado por Eduardo Barrio

Este evento cuenta con el apoyo del DAAD Projekt (UBA - MCMP) 2013-2014 ID 56133156: Truth, Paradoxes and Modalities. Directores: Eduardo Barrio - Hannes Leitgeb.

**Abstracts: **

Johannes Stern (MCMP) “Axiomatizing Semantic Theories of Truth?”

We discuss the interplay between the axiomatic and the semantic approach to truth. Often, semantic constructions have guided the development of axiomatic theories and certain axiomatic theories have been claimed to capture a semantic construction. We ask under which conditions an axiomatic theory captures the semantic construction. After discussing some potential criteria, we focus on ω-categoricity as a criterion and discuss its usefulness and limits.

Ramiro Caso (Conicet - UBA) “Lessons learned from the philosophy of logic: Absolute generality and natural language semantics”

Providing a suitable semantic account of expressions of generality in natural language is not without its problems. Inquiry has focused mainly on quantifier domain restriction, taking for granted the possibility of employing usual model-theoretic methods to interpret quantifiers in natural language constructions. In this paper, I focus on the problem of absolute generality and its consequences for natural language semantics. I suggest that considerations of indefinite extensibility may make a model-theoretic understanding of quantifiers impossible, and argue that, were this so, usual model-theoretic methods could not be used to deal with the interpretation of quantified sentences in natural language. I explore possible ways of dealing with expressions of generality in natural language.

Thomas Schindler (MCMP) "Reference Graphs, Dependency Games and Paradox":

The idea that the paradoxicality of a sentence can be tied down to certain pathological patterns of reference adherent to the sentence is more or less ubiquitous throughout the literature on semantic paradoxes. However, no comprehensive account has been given so far, providing satisfactory answers to the questions (i) what patterns exactly should count as pathological and (ii) how these patterns get asssociated to the sentences of our language. We will provide a game theoretic semantics for Kripke’s theory of truth, treating various valuation schemes in a uniform manner, such that Kripke-paradoxical sentences can be characterized by properties of the game-strategies available for the player who aims to show that a sentence has a definite truth value in some Kripke fixed point. Morover, such strategies can be interpreted as (decorated) reference-graphs of the sentence in question. In this way a framework for a graph theoretic analysis of the Kripke-paradoxical sentences is provided. We will argue that, when valuation schemes stronger than Weak Kleene are considered, there are certain sentences for which no canonical reference-graph can be assigned to: the notion of a single reference-graph -applicable to Weak Kleene- must be replaced by that of a systems of reference-graphs. Nevertheless, all necessary resp. sufficient conditions we provide for a sentence' Kripke-paradoxicality - given in terms of graph-theoretic properties of its canonical reference-graph in the case of Weak Kleene - are exactly the same for all other valuation schemes, with the sole difference that now all members of the whole system of graphs have to be taken into account.

Natalia Buacar (UBA) “Philosophical grounding of deduction”

Agreement is not a widespread phenomenon among philosophers. In this sense, the confidence in deduction can be considerate atypical. To such an extent that even today many argue that deduction does not require justification. However, since the challenge posed by Lewis Carroll (1895) many philosophers of logic have taken it up. On its traditional formulation, the problem of the justification of deduction is equivalent to dealing with the circularity - apparently - inevitably involved in any attempt to justify that the deductive rules preserve truth, i.e. are valid. Answers to it point out that there is not vicious circularity involved or try to find some kind of external guarantee to break the circle. In this work I offer reasons to doubt of the correctness of the above formulation. I suggest there is a misconception on the normativity of logic underlying to it. I propose there is an interesting problem around deduction that is different from the former. I argue that that problem is of philosophical nature, as any of its answer. Finally, I outline a reply, which among other things, picks up the inferentialist program as presented in Inferential Role Semantics and discussed by Jaroslav Peregrin (*draft*). The first stress the importance of dispositions in determining which rules are meaning constitutive of expressions. The second insists also in the "normative attitudes" of speakers, the corrections they make. After commenting the notions of *rule* and* meaning constitutivity*, I highlight the importance of the so common situation of teaching deduction and its very possibility in such a determination.

Catrin Campbell-Moore (MCMP) “A Kripkean fixed-point style semantics for credence”

We provide a theory which allows us to reason about the notion of credence, in particular this allows for the formalisation of higher order credences. We argue that the best way is to conceive of credence is as a predicate, which then allows for the derivation of the diagonal lemma. We develop a semantics based on a possible-world style structure. This semantics generalises Kripke's construction from "An Outline of a Theory of Truth", and works along the lines of Halbach and Welch's "Necessities and Necessary Truths". We also give some axioms corresponding to the construction.

Damian Szmuc (UBA) “On Pathological Truths”

In Kripke’s classic paper on truth it is argued that by weakening classical logic it is possible to have a language with its own truth predicate. Usually it is claimed that a substantial problem with this approach is that it lacks the expressive resources to characterize those sentences which are pathological. The goal of this paper is to offer a refinement of Kripke’s approach in which this difficulty does not arise. We tackle the characterization problem by introducing a pathologicality operator into the language, and we propose a peculiar fixed-point semantics for the resulting theory in order to establish its consistency.

Paula Teijeiro (UBA) “Sorites sequences and the continuum”

The Sorites paradox challenges the adequacy of classical logic in dealing with vague predicates. One of the strongest alternatives is to employ fuzzy sets in order to avoid positing the existence of sharp boundaries between the extension and the anti extension of such predicates. Nevertheless, many authors, like Sainsbury, claim that no kind of set, fuzzy or otherwise, can capture the desired interpretation, and formal semantics for vague predicates has to be given up altogether. The idea is that the continuity and the imprecision cannot be captured by a mathematical model. But the relation between vagueness and continuity is not so simple: it is taken for granted by many fuzzy theorists, and it has been dismissed as trivial or inadequate by others. The aim of this project is to understand how discreteness and continuity interact to give rise to vague predicates. John Bell has been working on the topic of the continuum with regard to the role that infinitesimals have played in the history of mathematics and philosophy. According to him, the development of nonstandard and nonclassical analysis has provided a mathematically precise understanding of the “true” continuum. We will explore the possibility of framing the semantics for vague predicates in this kind of non classical setting, in a way that answers some of the objections to traditional fuzzy approaches.

Eleonora Cresto (Conicet) “Group Knowledge, Evidential Probabilities and Responsibility”

In previous work I developed a framework that allows us to attribute both knowledge and higher-order evidential probabilities to single agents. The model validates a moderate version of the so-called KK principle of epistemic logic without actually requiring that the underlying accessibility relations be transitive; I contended that moderate epistemic transparency so-conceived can be seen as a request of ideal epistemic responsibility. In this opportunity I seek to extend the previous analysis to collective agents. This involves several conceptual and technical challenges. I propose to model paradigmatic examples of group knowledge by means of the technical notions of common and distributed knowledge, as well as of various intermediate concepts; I also suggest a way to reconcile several conflicting intuitions by appealing to a dynamic framework. Among other things, ‘public announcement’ phenomena are here reinterpreted as requirements of ideal individual responsibility; an ideally responsible individual will seek to embrace the knowledge of the group and make it her own. Finally, I also explain how to deal with evidential probabilities for the group (*qua *group). First-level evidential group probabilities (in a particular world) are rendered by sets of individual measures conditional on the strongest proposition known by the group at that world. Second- and higher-level group probabilities, on the other hand, turn out to be trivial in the model, much unlike higher-order levels of individual evidential measures. I end by discussing the philosophical significance of this result.