Research Seminar - 06.07.2026: Gideon Freudenthal and Israel Fischer - The Principle of No Contradiction: A Transcendental Justification

Gideon Freudenthal, Cohn Institute

Israel Fischer, Independent Scholar

The Principle of No Contradiction:

A Transcendental Justification

The paper offers a transcendental justification of Aristotle's Principle of No Contradiction (PNC) as defended in Metaphysics IV. Building on Łukasiewicz's threefold distinction between the ontological, psychological, and logical senses of the PNC, we propose a fourth: as a condition of the possibility of signification. Contradictions frustrate signification and therefore rational discourse. We argue that Aristotle's "negative proof" in Metaphysics IV, 3-4 shows that an opponent who argues against the PNC must presuppose it or remain silent. Aristotle's argument in Metaphysics IV, 3-4 hence proves to be a transcendental argument: it argues that a meaningful discourse requires that terms have a definite sense, and therefore that the meaningful discourse of the opponent proves that he, too, presupposes the validity of the PNC.

We further consider why the PNC is contested. We suggest that "change" seems to imply that contradictions are real. However, we argue that whatever the ontological status of change, our assertions about it must remain contradiction-free. We suggest that this was also Aristotle's own view.

We finally observe that Łukasiewicz and his followers ignored the transcendental argument for the validity of the PNC because they understood logic to be a theory of inference in which the principle seems to play only a minor role. Moreover, they declared that this understanding of logic was also Aristotle's own, and attempted to interpret the history of logic along these lines.

Gathering for coffee and refreshments at 16:00

Chair: Ori Belkind

The public is invited