Frege's Begriffsschrift notation: Design principles and trade-offs

Dirk Schlimm (McGill University)

Pořádá Oddělení logiky FLÚ AV ČR

Well over a century after its introduction, Frege's two-dimensional Begriffsschrift notation is still considered mainly a curiosity that stands out for its clumsiness rather than anything else. It stands out by its two-dimensional layout with symbols for logical relations (implication and negation) on the left and the propositional content on the right. In this paper the propositional fragment of the notation is looked at in detail. In the first part, several idiosyncrasies of the notation, which allow an easy conversion of logically equivalent formulas, are discussed and by showing its close connection to syntax trees I argue for the perspicuity and readability of the notation. In the second part, the aims that Frege pursued with his system together with some justifications for the design principles underlying the Begriffsschrift are discussed.