Non‐Classical Knowledge

Philosophy and Phenomenological Research 98 (1):190-220 (2017)
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The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory validating all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker-than-classical K3 logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to--whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non-classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities.

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Ethan Jerzak
National University of Singapore

Citations of this work

KK, Knowledge, Knowability.Weng Kin San - 2023 - Mind 132 (527):605-630.
The Attitudes We Can Have.Daniel Drucker - 2020 - Philosophical Review 129 (4):591-642.
The fixed points of belief and knowledge.Daniela Schuster - forthcoming - Logic Journal of the IGPL.
Paradoxical Desires.Ethan Jerzak - 2019 - Proceedings of the Aristotelian Society 119 (3):335-355.

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References found in this work

In contradiction: a study of the transconsistent.Graham Priest - 1987 - New York: Oxford University Press.
Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
The paradox of the preface.David C. Makinson - 1965 - Analysis 25 (6):205-207.
``The Paradox of the Preface".D. C. Makinson - 1964 - Analysis 25 (6):205-207.

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