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Operational Collapse: A Prior Category of Logical Failure

Kim, Seung Kyu
PhilArchive · Papers
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philosophy
The standard response to self-referential failure is substitution: replacing the problem-generating element with an innocuous proxy. Tarski and Russell index the proxy to a level; an act that dissolves its own conditions indexes it to a time. Both succeed, and both change the subject. This paper identifies when no proxy is available. Treated as a target-directed act rather than a truth-functional connective, negation requires discriminability, directionality, and operability — jointly, the applicability domain D. A negation of D that exempts its own performance targets an indexed proxy; a negation of D as such is reflexively inclusive, and operational collapse follows: performing it requires D operative in the very act whose constituted effect is D's inoperativeness. The failure precludes the act's initiation rather than spoiling its output, and marks the limit of substitution. Two consequences follow. Any system in which negation operates retains an ineliminable structural invariant. And the Liar cannot be targeted by negation at all, prior to where Kripke's construction and bilateralist treatments of denial engage it — which yields two discriminations neither account delivers: the Liar can be affirmed though it cannot be negated, and the Truth-Teller, ungrounded alongside it, can be negated.
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