Demonstrates fixed point resolution of the liar paradox using temporal indexing mechanisms, suggesting implications for self-reference management.
This paper resolves the liar paradox through temporal indexing rather than by banning self-reference or introducing three-valued logic. A step-sequence framework is introduced in which each state carries an active tension that the present tense cannot locate. A "was" operator recruits past states as a third body outside the active tension, providing an exit from the self-referential loop. Two distinct resolution mechanisms are identified: selection, in which a specific past state is recruited directly, bypassing self-reference; and weighted vote, in which even-distance past states must dominate odd-distance states and the present flip to collapse the oscillation to a fixed point. The liar paradox is the minimal case of a period-2 cycle. The paper notes that any formalisation powerful enough to address self-referential paradox inherits the same susceptibility, the circularity is managed, not erased and that the paper's own development demonstrated this mechanism at work.
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Lee Anthony Tipping (2026) studied this question.
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