Gottlob Frege, between philosophy and mathematics: A study of his 1879 Concept-script and its modern horizon

The dissertation seeks to gain a comprehensive understanding of Frege's watershed work of logic, the 1879 Begriffsschrift ( Concept-script). The treatise is the first since Aristotle's instauration of the discipline to have succeeded in completely recasting logic. Very generally stated, the dissertation aims at making explicit the conceptual origins of modern logic. To do that will require that each of the achievements of Concept-script be examined from one or more vantage points: either within the perspective of Frege's larger and guiding ambition, that of providing a logical justification of arithmetic; or with respect to the horizon of modernity; or in relation to later developments in logical theory and the philosophy of language, developments stimulated, albeit not exclusively, by Frege's very work. The vantage point(s) adopted in each case will depend on the nature of the topic and the extent to which it requires to be made explicit. One perspective will have preponderance, that of Frege's relationship to his early modern ancestors, a group that includes philosophers, scientists, and mathematicians. Since modernity is constituted in a nearly constant critical, if not polemical, relationship to the Ancients, they (primarily Aristotle and Greek science) will also at times be drawn into the discussion. The elucidation of Frege's breakthrough work will be guided by the following thesis: Frege's attempt to justify arithmetic logically and the fine work of clarification he produced in actualizing this project; his discovery of function-theoretic logic and his fashioning of a concept-script (a set of aphonetic signs); and his critique of natural language and the attendant semantics developed over the course of that critique constitute an unfolding and an extension of the primacy of universal method over ontology that is the signature of modern inquiry.