166:'s work on the Liar paradox and constructs a similar hierarchy of knowledge predicates. Another approach upholds a single knowledge predicate but takes the paradox to call into doubt either the unrestricted validity of (PK) or at least knowledge of (KF). The second kind of strategy also subdivides in several alternatives. One approach rejects the
142:, we can conclude that (K) is not known. Now, this conclusion, which is the sentence (K) itself, depends on no undischarged assumptions, and so has just been proved. Therefore, by (PK), we can further conclude that (K) is known. Putting the two conclusions together, we have the contradiction that (K) is both not known and known.
106:(where we use single quotes to refer to the linguistic expression inside the quotes and where 'is known' is short for 'is known by someone at some time'). It also seems to be governed by the principle that
154:, every sufficiently strong theory will have to accept something like (K), absurdity can only be avoided either by rejecting one of the two principles of knowledge (KF) and (PK) or by rejecting
158:(which validates the reasoning from (KF) and (PK) to absurdity). The first kind of strategy subdivides in several alternatives. One approach takes its inspiration from the hierarchy of
55:. In the wake of the modern discussion of the paradoxes of self-reference, the paradox has been rediscovered (and dubbed with its current name) by the US logicians and philosophers
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saying of itself that it is not known, and apparently deriving the contradiction that such sentence is both not known and known.
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Morgenstern, L. (1986), 'A First Order Theory of
Planning, Knowledge and Action', in Halpern, J. (ed.),
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and thus accepts the conclusion that (K) is both not known and known, thereby rejecting the
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Theoretical
Aspects of Reasoning about Knowledge: Proceedings of the 1986 Conference
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Cross, C. (2001), 'The
Paradox of the Knower without Epistemic Closure',
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202:, Latin text and English translation by Stephen Read, Peeters, Leuven.
231:, 3rd edition, Cambridge University Press, Cambridge, pp. 115–120.
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Maitzen, S. (1998), 'The Knower
Paradox and Epistemic Closure',
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that (K) is known. Then, by (KF), (K) is not known, and so, by
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Kaplan, D. and
Montague, R. (1960), 'A Paradox Regained',
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seems to be governed by the principle that knowledge is
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A version of the paradox occurs already in chapter 9 of
240:Anderson, A. (1983), 'The Paradox of the Knower',
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301:Priest, G. (1991), 'Intensional Paradoxes',
35:). Informally, it consists in considering a
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168:law of excluded middle
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