Johan van Benthem
University Professor of
Logic and Professor of Philosophy
My book The Logic of Time (1983) used formal methods to analyze temporal arguments from the philosophical literature. But it also used them to construct several new ontologies for time, especially interval-based ones outside of the standard mathematical canon, increasing the range of temporal pictures that we can use in imagining and presenting things. Since time is so pervasive in all our activities, any logical insight into its structure and representation immediately percolates across a lot of disciplines. The book is still selling, even though it is not an easy read. From continuing private reactions by readers, sometimes from quite surprising places, it seems to me that it still manages to attract congenial spirits who think like me.
My work on logical syntax and semantics of natural language (Essays in Logical Semantics 1986, Language in Action 1991) had a similar flavor. I was deeply impressed by the work of Barwise and others around 1980 of stepping away from sterile antagonistic conceptions of 'logical versus linguistic form', and it seemed that every month, beautiful new structures were falling into my lap in quantification, and the general combinatorics of natural language. Moreover, this work led to a new view of the 'natural logic' inside natural language, with elegant calculi of monotonicity reasoning, as opposed to just the predicate-logical canon: including a reappraisal of traditional pre-Fregean logic. But again, one should never be a slave to reality. One strand in that work was my use of semantic automata as evaluation procedures for quantifiers, which led to an upward hierarchy of complexity that certainly transcends the usual repertoire of natural languages. I notice with interest that some of my work from this phase is being taken up to-day by neuro-scientists in experimental settings.
Finally, my current work is on dynamic-epistemic logics of information-carrying actions, and more general design of logics for interaction (Exploring Logical Dynamics 1996, Logic in Games 1999). This, too, shows all the above features. I am surprised by seeing logical structures in information flow, communication, and games. I see beauty and regularity in conversations, discussions, and even the wildest argumentative outbursts at department meetings, and other venues where we meet to disagree. Moreover, the dynamic stance making action and interactive processes a core topic for explicit theorizing beyond static propositions and 'meanings' has an interesting synchronicity in philosophy, logic, artificial intelligence, and computer science - and I am sure it will spread still further. My current focus is on the interface between logic and game theory, since games seem the interactive model par excellence, and in their restricted compass, they put familiar notions from mathematical and philosophical logic in a clear new light.
Also, in doing this sort of research putting actions at centre stage, I am very much taken with the idea of not only analyzing, but also designing new 'social software', in the recently emerging sense. We can enrich our social repertoire of behavior, and in that way, also become more free as human agents.
One final aspect of formal structure that intrigues me here is its recurrence across disciplines, and hence the potential for hybrids. For instance, when Montague stated his famous Thesis that there is no difference in principle between natural and formal languages, he merely made an analytical observation. But once you see the analogy, one can also cross-breed the two kinds of language to form hybrids, and we do, both in science, law, an other practices. Moreover, the same formal structures also occur in a third realm: programming languages and other media in computer science. In a non-analytical but rather activist mode, insights like these drive the current interaction of humans and machines.