On Judgements and Propositions

Dear Hans-Jörg! In the seventies and early eighties we have been colleagues in the ‘Automatentheorie und Formale Sprachen’ group at TU Berlin and shared many interests. Later we departed into different fields of research and followed different directions of thought. It is thirty years now that we have completed our PhD at TU Berlin, and this year is your sixtieth birthday. Since the times at ATFS we have not met often but have never lost the feeling of friendship and trust. What we have lost is to know much about each other. I therefore think that it is natural to ask, “What are you doing?” With the publication of this birthday volume I have the opportunity to briefly give you an answer and to honour you with a paper on a question which is presently twisting my mind: What is the fundament of logic that admits the different views on it? It may come as a surprise that after all these years of teaching and research in logic I am unable to answer this question right away, but I must admit that exercising logic formally attracts the attention to the formal aspects of logic as a language and of logic as a calculus rather than to the fundamental question of its origins. It turned out that I could not avoid to answering this question: I teach a mandatory course to the first semester students, called ‘Informatik Propädeutikum,’ and I thought it would not suffice to start explaining logic with the words “assume you have a family of countably infinite sets of variables and a ...” But I thought it would be more appropriate to explain logic in this ‘Propädeutikum’ by the fundamental conceptions underlying its formalisation. My hypothetical answer to the above question is that logic is rooted on conceptions of judgement and proposition. Both have been a matter of dispute since the beginning of Greek philosophy and are still today under debate. It was therefore only natural to look at some of their prominent conceptualisations and to try to gain a better understanding of what is meant by these and what is their relation. It turned out, however, that this is not easy at all as the notions of judgement and proposition are deeply involved. They touch on and relate fundamental questions of language, ontology, psychology, philosophy and mathematics, and their meaning is far from being common sense. By some authors the notion of proposition is even objected to be meaningful at all [vOQ80, pp. 331–401], and the word judgement is taken to express things of the most different kind, from the most elementary relation between the human mind and the world [Kan90], up to what is realised by natural deduction proofs in intuition-