Non‐Classical Knowledge


Authors
Ethan Jerzak
University of California, Berkeley
Abstract
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.
Keywords epistemic logic  semantic paradox  epistemology  philosophical logic
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DOI 10.1111/phpr.12448
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References found in this work BETA

Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Shadows of the Mind.Roger Penrose - 1994 - Oxford University Press.
The Paradox of the Preface.David C. Makinson - 1965 - Analysis 25 (6):205.
Belief and Indeterminacy.Michael Caie - 2012 - Philosophical Review 121 (1):1-54.

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Citations of this work BETA

Paradoxical Desires.Ethan Jerzak - forthcoming - Proceedings of the Aristotelian Society.

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