K. C. F. Krause: The Combinatorian as Logician

Abstract

In a time which it is not amiss to term “the Dark Ages of logic”, Karl Christian Friedrich Krause stayed not only true to logic but actually did something for its advancement. Besides making systematic use of Venn-diagrams long before Venn, Krause — once more taking his inspiration from Leibniz — propounded what appears to be the first completely symbolic systematic representation of logical forms, strongly suggestive of the powerful symbolic languages that have become the mainstay of logic since the beginning of the 20th century. However, Krause’s limits in logic are also clearly visible: Krause’s method in logic is, in the main, not axiomatic; it is combinatorial (in other words, it consists in systematically producing finite lists of logical laws, following some organizational principle). More importantly, Krause remained entirely within the confines of traditional syllogistics (his flirt with “quantification of the predicate” notwithstanding), neglecting propositional logic and, of course, first-order relational terms.