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My work starts from a simple but demanding idea: vagueness is not a mere defect of language but the embodied boundary where inquiry meets the world. When our concepts strain against experience, the right response is often not to force a sharp verdict but to hold a statement open—to let the question live—while we continue to investigate.
The two following papers on negation are the technical head of this programme: they show, in detail, how the absence of a privileged resolution and the presence of schematic plurality force us to rethink what it is for negation and consequence to be “fixed,” and how truth can depend on the very indeterminacy that inquiry reveals.
On this picture:
- There is no final “master logic” or completed, gapless continuum that captures all motion, concept‑use, or meaning once and for all.
- Questions, potential, and indeterminacy are structural features of our engagement with the world, not noise to be eliminated.
- Poetry and pedagogy are not merely illustrative; they are among the primary places where vagueness and pluralism are lived and can be studied with the same seriousness as formal systems.
Taken together, these claims support a picture in which logic, mathematics, and language are continuous with lived inquiry and poetry, not insulated from them. The same phenomena that appear in stories, metaphors, and classroom experiments—borderline cases, unresolved questions, plural paths—reappear in the formal study of negation, consequence, and completeness.
This paper argues that some cases of semantic individuation cannot be cleanly classified as either ambiguous or vague. The central claim is conditional: if no resolution of a term’s candidate readings is privileged, and if refinement of those readings never terminates, then the classication of the term as ambiguous rather than vague never completes, and no verdict is
stable. Applied to negation, the consequence is that a stock of negations that remains sharp at every resolution but keeps refining without terminating is not well captured by the received ambiguity/vagueness taxonomy. The paper defends this claim by combining a philosophical argument from resolution-dependence with a formal model of endlessly refinable readings.
The load-bearing premise is metaphysical: the absence of a privileged resolution is the absence of a fact, not merely of a reason, and the paper identifies the principal deniers of that premise the semantic epistemicist, who posits an unknowable fact of individuation, and the logical monist, for whom abduction or joint-carving selects a uniquely correct framework. The paper also answers the reflexive worry that its own assertions fall to its own thesis: because every admissible negation is classical on the classical values, the paper’s metalinguistic claims are fixed points of the variation the thesis describes.
“Preprint version, not peer‑reviewed. I am continuing background reading on related work in philosophy of logic, and the arguments may be revised in light of further research.”
This paper defends two connected claims. First, in a schematic theory with two negation indices and no index-specific semantic or metasemantic fixing facts, there is no fact of the matter as to which index denotes which negation. The relata are determinate; the pairing is not. Second, for a suitable witness sentence with middle value, the truth-status of a mixed formula built from those negations depends on that pairing-indeterminacy rather than standing independently of it. The order of explanation matters: individuation comes first, truth-indeterminacy second.
The paper also clarifies a potential misdescription of the result. The view defended is not that no disambiguation is possible in every setting whatsoever. It is the conditional thesis that, within a genuinely schematic theory that excludes index-specific semantic stipulation and metasemantic use-facts, no privileged pairing is fixed. Under those conditions, the standard permutation argument goes through. This conditional result is philosophically substantive because logical vocabulary is often thought to have its meaning fixed by role alone. The schematic condition (S) is not an artificial vacuum: it formalizes the situation that logical pluralists explicitly assert and that inferentialists implicitly presuppose, so the conditional result binds both camps. A further dichotomy sharpens the antecedent: constraints that treat the indices alike can narrow the stock of admissible negations, but they cannot select within a symmetric orbit, so every index-neutral resource either leaves the indeterminacy in place or dissolves the plurality on which it feeds. Even the dissolving cases are frame-relative: the excluded-middle rule that collapses the stock under one designation and disjunction preserves plurality under neighboring settings, so which horn of the dichotomy a constraint occupies is itself a resolution-dependent matter.