The Limits of a Logical Treatment of Assertion

It is clear that the concept of assertion has played a crucial role in the construction of contemporary logic. Apart from the central notions of proposition and truth, assertion raises the issue of judgment, which constitutes the very subject of logic. The logical systems put forward by Russell between 1903 and 1925 all attribute the status of a primitive idea to assertion.1 At the same time, there is considerable variation in Russell’s interpretation of assertion. In what follows I will trace these variations. However, I will do so not for purposes of exegesis. Instead, my aim will be to offer an appreciation of the limits of the logical treatment of a complex concept; a concept which, as I will claim, can only be satisfactorily defined through a pragmatic formulation of the issues it raises. The first part of this contribution traces Russell’s thematization of assertion from the Principles of Mathematics to Principia Mathematica, while emphasizing its eminently aporetic character. I concentrate solely on the propositional calculus in order to focus the analysis on what is essential.2 The second part deals with the pragmatic treatment of assertion which began before the second edition of Principia Mathematica, with Frege’s Logische Untersuchungen (1918), and was to continue with Searle’s definition of assertive speech acts and their formalization by Daniel Vanderveken. This analysis will show that the contemporary redefinition of the field removes Russell’s aporias ; however, it will also show the surviving relevance of certain analyses presented by Russell, such as his treatment of denial.