## Program

Location: Bergsmannen, Aula Magna, Frescati Campus

09:30–11:00 Brit Brogaard, Miami: *In Defense of Hearing Meanings*

11:00–12:30 Ed Zalta, Stanford: *Convergence in the Philosophy of Mathematics*

12:30–14:00 Lunch

14:00–15:30 Denis Bonnay, Paris Ouest: *Invariance and rationality: An axiomatization of individual and social updates* (joint work with M. Cozic)

15:30–16:00 Coffee

16:00–17:30 Heinrich Wansing, Bochum: *Completeness of connexive Heyting-Brouwer logic* (joint work with Norihiro Kamide)

## Abstracts

### Brogaard

According to the inferential view of language comprehension, we hear a speaker’s utterance and infer what was said, drawing on our competence in the syntax and semantics of the language together with background information. On the alternative perceptual view, fluent speakers have a non-inferential capacity to perceive the content of speech. On this view, when we hear a speaker’s utterance, the experience confers some degree of justification on our beliefs about what was said in the absence of defeaters. So, in the absence of defeaters, we can come to know what was said merely on the basis of hearing the utterance. Several arguments have been offered against a pure perceptual view of language comprehension, among others, arguments pointing to its alleged difficulties accounting for homophones and the context-sensitivity of ordinary language. After responding to challenges to the perceptual view of language comprehension, I provide a new argument in favor of the perceptual view by looking closer at the dependence of the justificatory qualities of experience on the notion of a defeater as well as the perceptual nature of language learning and language processing.

### Zalta

The Platonist answer to the question, "What is mathematical language about?", is that it is about abstract individuals (such as zero, the null set, omega, etc.) and abstract relations (such successor, less than, set membership, group addition, etc.), though the Platonist rarely has much to say about abstract relations. I describe what appears to be a Platonist foundation for mathematics by producing a formal, axiomatic theory of abstract individuals and abstract relations, and an analysis of mathematical language that yields denotations for the terms of mathematical theories and truth conditions for mathematical claims. After quickly reviewing the theory and its application to

mathematics, I show how the formalism is subject to various interpretations. The Platonist interpretation is just one of several ways of interpreting the formalism and the analysis of mathematics. I develop fictionalist, structuralist, inferentialist, if-thenist, finitist, and logicist interpretations of the formalism. Since each interpretation offers us a clear, but different, answer to our initial question, the resulting analysis not only offers a way to make these philosophies of mathematics more precise, but also unifies them in a new and unsuspected way that explains why philosophers of mathematics often can’t even agree on the data.

### Bonnay

### Wansing

We introduce a certain bi-intuitionistic connexive logic, BCL, as a Gentzen-type sequent calculus and prove some theorems for embedding BCL into a Gentzen-type sequent calculus BL for bi-intuitionistic logic, BiInt. The completeness theorem with respect to a Kripke semantics for BCL is proved using these embedding theorems. The cut-elimination theorem and a certain duality principle are also shown for some subsystems of BCL. Moreover, we present a sound and complete triply-signed tableau calculus for BCL.