Medieval Sophismata

Origin. 13th-14th century. Bradwardine, Heytesbury, Kilvington. Puzzle sentences. Logical analysis. Foundation of semantic puzzles.

Models. Problematic sentences analyzed. Quantifier scope. Self-reference. Semantic paradoxes. Logical distinctions.

Formalism.

Sophisma types: Grammatical: unusual constructions. Logical: quantifier/scope issues. Physical: motion, change puzzles. Self-referential: semantic paradoxes.

Example sophismata: "Omnis homo est omnis homo" (Every man is every man). Is it true? Depends on supposition. Scope ambiguity.

Insolubilia (semantic paradoxes): "What I am saying is false." Self-reference. Medieval Liar paradox. Various solutions proposed.

Solutions to Liar: Cassation: sentence says nothing. Restriction: can't refer to self. Secundum quid: true in one way, false in another. Multiple approaches.

Quantifier puzzles: "Infinitely many are finite." De dicto vs de re. Scope distinctions. Syncategorematic terms.

Heytesbury's rules: Rules for solving sophismata. Systematic method. Distinguish senses. Apply supposition theory.

Analysis method: State sophisma. Arguments pro and contra. Identify ambiguity/fallacy. Give solution. Reply to objections.

Symbols.

Term	Origin	Gloss	Role
sophisma	Latin	Puzzle sentence	The sentence posed, with arguments pro and contra
insolubile	Latin	Insoluble	A self-referential paradox, the Liar chief among them
propositio	Latin	Proposition	A token sentence, true or false as actually formed
sensus	Latin	Sense	A reading distinguished in the course of the solution
casus	Latin	Case	The scenario stipulated before the sophisma is assessed
significat	Latin	Signifies	What a proposition says to be so; Bradwardine closes it under consequence
cassatio	Latin	Cassation	The solution denying that the sentence says anything
restrictio	Latin	Restriction	The solution barring a term from suppositing for its own proposition
secundum quid	Latin	In a certain respect	Paired with simpliciter, the Aristotelian fallacy invoked in solutions
de dicto, de re	Latin	Of the saying, of the thing	The scope distinction applied to modal and epistemic sophismata

Metatheory. The insolubilia literature produced diagnoses of the Liar that can be stated and tested. Bradwardine's Insolubilia (c. 1321–24) turns on a closure principle — a proposition signifies whatever follows from what it signifies — from which he derives that a sentence signifying its own falsity thereby also signifies its own truth, so that it says two incompatible things and is false outright, with no hierarchy and no truth-value gap required. Buridan reached the same verdict by a weaker route, holding that every proposition virtually asserts its own truth. The restrictivists instead blocked the paradox by forbidding a term to supposit for the proposition containing it, and the earlier cassationists denied that the Liar says anything. Heytesbury's Regulae solvendi sophismata (1335) is the methodological monument: state the case, argue both sides, locate the ambiguity, defend the solution against objections. Read (2002) revived Bradwardine's account and argued that it survives revenge.

Applies to. Medieval logic. Paradoxes. Semantics. Philosophy of language.

Limitations. Bradwardine's closure principle carries the whole argument and is not innocuous: closing signification under consequence makes every proposition signify infinitely many things, and whether self-falsity really yields self-truth depends on which closure is assumed, the derivation having been reconstructed in several non-equivalent ways. The rival solutions fare worse. Restriction removes harmless self-reference along with the harmful, and cassation denies content to a sentence that is grammatically in order. None of the solutions came with a semantics in which it could be evaluated, so the debate had no means of settling which were consistent; that waited for the modern reconstructions. And sophismata are individual puzzles: the method distinguishes senses one case at a time, and nothing in it predicts which sentences will require distinguishing.