The Paradox Docket: A Computable Classification of the Classical Paradoxes

Abstract

For twenty-three centuries the word "paradox" has been handed out without an audit: it is worn by genuine logical dead ends, by harmless puzzles, and by plainly ill-posed questions. We conducted the audit. The classical collection — the liar and its family, Russell, Curry, Yablo, the crocodile, the Ship of Theseus and others — was run through a single executable instrument that, for every self-referential sentence, counts the number of consistent classical solutions and issues a passport: zero solutions — a genuine paradox (refusal forever); exactly one — the verdict is forced; two or more — not a paradox but a choice awaiting a decree. The result is a court docket: 21 case files and nine short verdicts, each reproducible with a single command. Few of the celebrities keep the title "paradox" once the papers are checked; most had been wearing it without documents. The taxonomy descends from Kripke and from Gupta–Belnap and is credited to them explicitly; what is new is executability: disputes that are decades or centuries old — is circularity vicious; is a loop hidden inside Yablo; is Curry just the liar; is the Ship of Theseus a paradox at all — receive measured rather than argued answers. In this version the same count is turned on Agrippa's trilemma, and his third horn does not survive it intact: a stopping point with two admissible settings is a choice that was really made, while one with exactly one is a terminus nobody chose, and the difference is arithmetic rather than temperament. New in v1.1. A ninth verdict: Agrippa's dogmatic horn splits under this paper's own count. A self-supporting foundation is UNDERDETERMINED with two admissible settings, so the stop was a real choice with a coherent rival — the fifth postulate, the axiom of choice, propositional extensionality — and Agrippa's complaint lands in full. A self-forcing one is INTRINSIC with exactly one setting: nothing was chosen, and "you could have gone otherwise" has no referent. A nullary ground — an operation with no arguments — is a terminus of the second kind, and Agrippa's argument, being about the justification of statements, does not reach it; that is a weaker result than a refutation and is stated as such. No priority is claimed for the philosophical move, which is Wittgenstein's bedrock, the pragmatists' answer, and nearest of all Brouwer, for whom the primordial intuition is explicitly not an axiom; what is claimed is the exhibit — a foundation whose axiom cost is zero and machine-confirmed. Both honest limits are measured rather than conceded: nullarity is declared and unverifiable, so the ledger promises disclosure rather than detection, and the horn carries a price range rather than a price, since a five-storey regress warrants nothing at any storey while the identical chain with one document beneath it earns all five and that one document carries the whole structure. Four jurisdiction edges declared in v1.0 are now crossed rather than merely named — the sorites, the surprise exam, the lottery and Berry — plus Moore's paradox, which never appeared on the list, and which the passport office correctly cannot judge while the judge can. A second genre of defect is added: the empty description and the status E, where an expression names nothing at all and there is nothing to count. The docket table is re-measured row by row against the machine on every regression run, so a published cell cannot drift from the code without failing the build. Two corrections are recorded in the text rather than silently applied: the count of crossed edges, and a claim about where robustness comes from, which the Agrippa case refuted — support in this register was conjunctive, so a second ground read as a second liability, and once the ledger could express alternative grounds the same structure took no damage at all. A classification that can be corrected by its own cases is the only kind worth publishing. Version 1.1 supersedes version 1.0 (DOI 10.5281/zenodo.21864082). No verdict published in v1.0 is withdrawn and the docket table is unchanged.