# Why is this a Proof?

## Festschrift for Luiz Carlos Pereira

This volume includes fifteen research papers to celebrate Luiz Carlos Pereira's 60th birthday. Among the authors contributing to the volume we find colleagues, friends - including his PhD advisor - and admirers. Similar to Luiz Carlos Pereira's intellectual interests and work, the contributions range from Philosophy to Mathematics, from Mathematics to Logic, and from Logic to Philosophy, passing through Computer Science. They are the result of current research by well-known scholars in these fields. Proof Theory is, maybe, the Ariadne's thread that unites the different subjects treated. Questions around the nature of proofs are often present in Luiz Carlos' formal and informal talks and publications. Of course, he was not the first to dedicate himself to these questions, but he always raises and deals with them enthusiastically. This enthusiasm, together with his intellectual perspicacity, has allowed us to enjoy a wonderful journey into the world of proofs. Although not all contributions focus directly on proof theory, we can feel its echos in all of them.

Edward Hermann Haeusler, Wagner de Campos Sanz and Bruno Lopes, eds.

ISBN 978-1-84890-172-8

Published by College Publications

## Table of contents

On some functions of symbols in Hilbert’s formalism (Abel Lassalle Casanave)

Classical versus intuitionistic logic (Dag Prawiz)

Experiments with negation (Frank Tommas Sautter)

In a wittgensteinian light (Gisele Dalva Secco)

Wittgenstein on diagonalization (Guido Imaguire)

Some remarks on proof-theoretic semantics and the universalist perspective of language (Javier Legris)

On the ordered Dedekind real numbers in toposes (Marcelo E. Coniglio and Luís A. Sbardellini)

The True, the False, and the slingshot arguments (Oswaldo Chateaubriand)

On being naturally general (Paulo A. S. Veloso, Sheila R. M. Veloso and Leonardo B. Vana)

Proof-theoretic validity based on elimination rules (Peter Schroeder-Heister)

Expanding intuitionistic logic with a constant (Rodolfo Ertola)

Bounded dialectica interpretation: categorically (Valeria de Paiva)

Contradictions, inconsistencies and other oxymora (Walter Carnielli and Abilio Rodrigues)

On the definition of the classical connectives and quantifiers (Gilles Dowek)