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Inverse View
It is not the case that Definition (D3) is equivalent to definition (D1).
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Reasons For
2 perspectives
Reason for 1 of 2
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1.
An agent can know p without knowing that they know p, as Williamson's anti-luminosity argument demonstrates for fallible knowers.
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2.
If KKp does not follow from Kp, then the infinite regress in D3 imposes strictly stronger conditions than D1's simple knowledge requirement.
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Reason for 2 of 2
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1.
Believing the denial of a known proposition is psychologically impossible only for beings whose belief states are perfectly transparent to themselves.
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2.
A being could satisfy D1 by knowing all truths while lacking the higher-order metacognitive access D3 requires, making D3 non-equivalent to D1.
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Reasons Against
1 perspective
Reason against
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It is impossible to believe the denial of a proposition one knows to be true, knows that one knows to be true, knows is the denial of a proposition one knows, etc.
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