It is now a quarter of a century ago that Wolfgang Stegmfiller wrote his monograph 'Das Wahrheitsproblem und die Idee der Semantik' (1957) which dealt with Tarski's and Carnap's foundational work in the field of semantics. While this book is about the definition of the basic semantical concepts in artificial formal languages there is an article written a year earlier (1956) in which Stegmfiller addresses himself specifically to the relation between logic and natural language. Here he gives a logical analysis (...) of the standard structural expressions in language that are still of primary concern for current semantics: quantifiers, pronouns, articles, etc. The motives for such an analysis at that time were mainly philosophical: the aim was to expose the misconceptions and pitfalls of traditional philosophy arising from the disregard of various systematic semantic ambiguities in everyday language. Or as Stegmfiller puts it: Ober sie [i.e. einige nicht triviale F~ille von Vagheit in der A11tagssprache] Klarheit zu gewinnen, ist schon deshalb yon auBerordentlicher Bedeutung, weil Unkenntnis fiber sie zu schwersten philosophischen Verirrungen ffihren kann, namlich entweder der Unterlassung von berechtigten Fragestellungen, oder, was weit h~ufiger vorgekommen ist, der Formulierung yon falsch gestellten Fragen, denen gegenfiber man dann nur die Wahl hat, entweder fiberhaupt keine oder nur sinnlose Antworten zu geben. So logic was to regiment language. Sentences involving the copula and the above-mentioned structure words are assigned one or more unambiguous formal representations in an already interpreted formal language, usually the first order predicate calculus. The natural language expressions thereby receive a precise meaning, since the semantics of the formal language has been specified in advance, as is always assumed. This procedure has, of course, always been common practice, witness the typical syntactical argot of the mathematicians. It carries, however, an obvious methodological presupposition: it is the idea that the logic of our choice to which the formal representations belong is in some sense an adequate framework to express our thoughts. (shrink)
Reductivist programs in logicand philosophy, especially inthe philosophy of mathematics,are reviewed. The paper argues fora ``methodological realism'' towardsnumbers and sets, but still givesreductionism an important place,albeit in methodology/epistemologyrather than in ontology proper.