Themes from Kaplan

"The book contains one of David Kaplan’s most influential papers, called ‘Demonstratives’, the centre of which is his logic of demonstratives. This is a system of logic which, though a descendant of Frege’s original system, has an unusual feature. It employs terms we use in everyday life that vary their referents from speaker to speaker and use to use. Words like, ‘I’, ‘you’, ‘he’, ‘today’ and so on. What makes this interesting is that logic has always aimed, since Frege, at producing systems of proof that are mechanically checkable, so there can be no dispute about whether or not something counts as a proof. It was always thought that in order to do this you had to abstract away from natural language, and eliminate all context-sensitive words, the referents of which change from one context to another. Kaplan shows that this is not so, which is a great achievement. Other developments in logic since Frege have shown that many aspects of natural language not included in Frege’s system can be incorporated into logical systems. The effect is to give us more interesting logical languages which begin to approach languages like English in their expressive power. By applying the techniques developed for understanding the original logical languages to these richer, more English-like systems, we achieve an understanding of these systems that gives us a kind of understanding of English and other natural languages by proxy. Support Five Books Five Books interviews are expensive to produce. If you're enjoying this interview, please support us by donating a small amount . That is all to the good. On the other hand, the lesson of Kaplan’s paper is that there are limits to this. Even though he succeeds, he still has to abstract away from, and ignore, important aspects of the meanings of context-sensitive sentences in English. Thus we are left wondering whether the aims of logic construction and natural language understanding are still in some tension. I think they are, which is one reason why his paper is still a challenge to me."