This talk concerns the connection between speech act theory, especially the theory of assertion, and deduction, especially Natural Deduction.

From a very abstract point of view, an assertion of a content p can be described as the ascription of the property of being p to the actual index, or point of evaluation. This is the abstract characterization of assertoric force. Let’s assume that the actual index is a possible world, namely the actual world. Thus, the conclusion of a closed argument, as an act, is an assertion, and thereby characterized as the ascription of the conclusion content as a property to the actual world.

The question that will concern us in this talk is how this idea extends to the status of other acts in the practice of Natural Deduction. In these terms, what is the force of an inference that depends on one or more open assumptions? What is the force of the assumption itself? What is the force of an assertion that uses an entire derivation as a premise? Do we need to ascribe a force to the derivation as a whole? Is there a coherent complete theory of act forces of Natural Deduction along these lines? What role will be played in such a theory by the concept of validity of an argument?

Here are the slides.

It is a fact that for more than two millennia a single logic prevailed, the Aristotelian logic, the logic that obeyed some fundamental principles, such as the principles of non-contradictions (the supreme principle of all principles), the principle of the excluded middle and the principles of identity. Even with the Fregian revolution at the end of the 19th century, this situation does not change: only one logic, classical logic. It is also a fact that this situations has changed drastically in the last hundred years: several logics presented themselves as extensions or rivals of classical logic. For example, adding several operators of a modal nature to the so-called classical logic produced modal logics of various types (alethic modal logics, epistemic logics, temporal logics, computational logics). Such logics can be considered as extensions of classical logic in the sense that only the scope of the logical-conceptual analysis is expanded. On the other hand, the questioning of the unrestricted validity of certain fundamental principles produced a set of logics that presented themselves as real alternatives to classical logic, as rivals to classical logic. For example, intuitionist logic emerged, questioning the unrestricted validity of the principle of the excluded-middle, and several paraconsistent logics, questioned the unrestricted validity of the principle of non-contradiction. But how is it possible to question principles as fundamental as the principle of the excluded-middle and the principle of non-contradiction? How is it possible that such deep disagreements arise in the realm of logic? In 2015, Dag Prawitz proposed a codification in which rival logics could "live in peace": The Ecumenical System for classical and intuitionistic logic! The aim of this tutorial is to give a general introduction to the ecumenical perspective.

Outline of the tutorial:

• Motivation

• Some Proof Theory

• Ecumenism

• Ecumenic natural deduction

• Ecumenic sequent calculus

• Modalities

• The challenge of constructive modal logic

• Ecumenic modal logic

• Purity!

• To wrap up