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date: 15 May 2021

Abstract and Keywords

The first part of this article shows some main points of Brouwer's mathematics and the philosophical doctrines that anchor it. It points out that Brouwer's special conception of human consciousness spawns his positive ontological and epistemic doctrines as well as his negative program. The second part focuses on intuitionistic logic: once again a brief picture of the technical field will precede the philosophical analyses—this time those of Heyting and Dummett—of formal intuitionistic logic and its role in intuitionism. The third part, however, aims to show that matters aren't (or needn't be) so bleak. It suggests, in particular, that putting all this in historical perspective will show intuitionism as technically less quixotic and philosophically more unified than it had initially seemed.

Keywords: Brouwer's mathematics, human consciousness, epistemic doctrines, ontology, intuitionistic logic, philosophical doctrines

Carl Posy

Carl Posy is Professor of Philosophy at the Hebrew University of Jerusalem. His work covers philosophical logic, the philosophy of mathematics, and the history of philosophy. He is editor of Kant's Philosophy of Mathematics: Modern Essays (1992). A recent publication on logic and the philosophy of mathematics is “Epistemology, Ontology and the Continuum” (in Mathematics and the Growth of Knowledge, E. Grossholz, ed., 2001). A recent paper on the history of philosophy is “Between Leibniz and Mill: Kant's Logic and the Rhetoric of Psychologism” (in Philosophy, Psychology, and Psychologism: Critical and Historical Readings on the Psychological Turn in Philosophy, D. Jacquette, ed., 2003).

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