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INTUITIONISTIC EPISTEMIC LOGIC

Published online by Cambridge University Press:  21 March 2016

SERGEI ARTEMOV  and
TUDOR PROTOPOPESCU
SERGEI ARTEMOV*
Affiliation:
The Graduate Center, The City University of New York
TUDOR PROTOPOPESCU*
Affiliation:
The Graduate Center, The City University of New York
*
*PROGRAMS IN COMPUTER SCIENCE, MATHEMATICS AND PHILOSOPHY THE GRADUATE CENTER, THE CITY UNIVERSITY OF NEW YORK 365 FIFTH AVENUE, RM. 4329 NEW YORK CITY, NY, 10016, NY, USA E-mail: [email protected]
†PROGRAM IN PHILOSOPHY THE GRADUATE CENTER, THE CITY UNIVERSITY OF NEW YORK 365 FIFTH AVENUE NEW YORK CITY, NY, 10016, NY, USA E-mail: [email protected]
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Abstract

We outline an intuitionistic view of knowledge which maintains the original Brouwer–Heyting–Kolmogorov semantics for intuitionism and is consistent with the well-known approach that intuitionistic knowledge be regarded as the result of verification. We argue that on this view coreflection A → KA is valid and the factivity of knowledge holds in the form KA → ¬¬A ‘known propositions cannot be false’.

We show that the traditional form of factivity KA → A is a distinctly classical principle which, like tertium non datur A ∨ ¬A, does not hold intuitionistically, but, along with the whole of classical epistemic logic, is intuitionistically valid in its double negation form ¬¬(KA ¬ A).

Within the intuitionistic epistemic framework the knowability paradox is resolved in a constructive manner. We argue that this paradox is the result of an unwarranted classical reading of constructive principles and as such does not have the consequences for constructive foundations traditionally attributed it.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 2 , June 2016 , pp. 266 - 298
Copyright
Copyright © Association for Symbolic Logic 2016 

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References

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