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.