Frege against the Booleans (Q1096601)

The paper discusses the controversy between Frege and certain Booleans, notably Schroeder. Each claimed that they had provided a conceptual language for mathematics whilst the other had provided a mere ``calculating device''. The author locates the key disagreement as one concerning the nature of concepts. Schroeder endorsed a ``bottom up'' approach: concepts are derived from a few simple concepts using a few basic operations. Frege endorsed a ``top down'' approach: concepts are to be arrived at by analyzing whole judgements, which are therefore primary. Crucially, Frege's methodology allowed him to conceptualize the quantifier, something that went beyond the Boolean apparatus.