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It is not the case that The sentence k, asserting its own unknownness, occupies a fixed point where both knowing and not-knowing it are forced by the semantic closure conditions.
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Reasons For
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Reason for
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1.
The notion of a sentence 'asserting its own unknownness' presupposes clarity about what the sentence's content actually is—which seems question-begging.
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2.
Fixed points in formal systems describe mathematical structures, not necessarily epistemic facts about what can actually be known in reality.
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3.
The claim conflates semantic properties (truth conditions) with epistemological ones (knowability), which may require separate treatment.
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Reasons Against
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Reason against
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1.
Self-referential sentences can create genuine semantic paradoxes that resist classical truth-value assignment, requiring fixed-point analysis.
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2.
A sentence asserting its own unknownness generates a constraint loop: knowing it makes it false; not knowing it makes it true.
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3.
Fixed-point theory in logic formally captures how semantic closure forces certain sentences into determinate yet paradoxical positions.
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