David William Sullivan

Frege's advances in the development of quantification have rarely been subjected to historical interpretation. While the characterization of existence as a second-order concept awaited the invention of the Begriffsschrift, important philosophical innovations had taken place since Kant's critique of the ontological argument. In particular, Herbart had re-conceptualized the nature of existential judgement and this was recognized and adopted by Brentano. In this light, thepossible influence of Herbart and Brentano (or their schools) upon Frege's work is elaborated and critically considered.

Frege's historical milieu is investigated under the rubric of the "neo-Kantian paradigm." This term is used loosely to describe those philosophers in the fourth generation after Kant who went back to Kant in protest to the vulgar or scientific materialism which had prevailed in the previous decades. This paradigm is characterized in a linguistic or conceptual fashion, after the historical precedent of the so-called "Cambridge school" . ;Frege's relation to the neo-Kantians of his own day, to Lotze, and to Herbart and the Brentano school are examined. Correlations are traced between the motivations and the impetus for the development of the "new logic" in light of the increasing emphasis upon logic and its relation to thought by such figures as Lotze, Cohen, Natorp, and Husserl. Frege's own developments are then outlined by illustrating how the functional innovations of his Begriffsschrift made possible new accounts of negation, numerical and existential quantification, and the notion of the object, but are accomplished nonetheless against the backdrop of the work of such thinkers as Herbart, Lotze, Stumpf, and Marty. Finally, this historical interpretation is brought to bear on a much-debated topic in the recent literature: Frege's two stipulations of the logical form of the statement of number