Is There Still Logic in Bolzano ' S Key ?

1 My encounters with Bernard Bolzano I am not a Bolzano scholar, but among practising logicians, my encounters with his work seem above average. The first of these was in my student days, when reading some history of logic on my own in the great works by Bochenski, and the Kneales. I was intrigued by finding how my standard textbooks had crafted an eschatological history of the field, with latter-day saints like Tarski, relegating earlier pioneers that do not fit the story line to oblivion. Later, I read my first real sample of Bolzano as a mathematician, viz. Paradoxes of Infinity, out of an interest in pre-Cantorian science in the making. Admittedly, not an easy read – as is true for all his texts I have seen. Bolzano as a philosopher entered my life around 1980, when looking for topics for a joint course with my more continentally trained philosophical colleague Detlev Pätzold. We settled eventually on the accounts of propositions in Leibniz, Hegel, Bolzano, and Frege – and a nice course it was! And then, at last, I was ready for the heavy bulk of the Wissenschaftslehre. This was partly through an interest in interfaces between logic and methodology of science, and partly as an aspiring radical in logic, intrigued by a book which is about logic, but with a quite different agenda from the modern one. My official documented reaction to this reading is in van Benthem 1984, 1985. Our final encounter took place a few years ago in Prague, after wandering through a large cemetery with my colleague Eva Hajicova – trying to locate Bolzano's grave among overgrown paths, while talking about logical inference and intelligent search to a Dutch TV crew following us. We did reach the target. 2 The agenda of logic Why look back now? Let me start by stating my non-historian's view of the modern history of logic. Like many scientific disciplines, logic flourishes while being ill-defined. Despite textbook orthodoxy, the issue what logic should be about is a legitimate topic of discussion, and one to which answers have varied historically. One key topic is reasoning: its valid laws for competent users, and perhaps also its sins: mistakes and fallacies. But the modern core also includes independent concerns such 2 as formal languages, their semantic meaning and expressive power. Moreover, the modern research literature, much of it still in a pre-textbook stage, reveals …