Medieval Consequentiae (Theory of Consequence)

Origin. 14th century. Buridan, Ockham, Burley. Inference theory. Valid consequence. Foundation of medieval proof theory.

Models. Consequentia: conditional or inference. Material vs formal. Rules of consequence. Propositional logic core. Inference analysis.

Formalism.

Consequentia structure: antecedent → consequent. "Si p, q" or "p, ergo q." Conditional or inference. Both analyzed.

Formal vs material: Formal: holds in virtue of form. Replacing categorematic terms preserves validity. Material: holds for this matter only. "A man runs, therefore an animal runs."

Formal consequence division: Simple: antecedent can't be true without consequent. As-of-now (ut nunc): true given current facts. Absolute vs temporal.

Rules (Buridan): From impossible, anything follows. Necessary follows from anything. From true, nothing false follows. To false, nothing true leads.

Propositional rules: Ex contradictoriis quodlibet. Modus ponens. Modus tollens. Hypothetical syllogism.

Distribution rules: What's distributed in consequent must be in antecedent. Descent under universal. Scope tracking.

Syncategorematic terms: omnis, nullus, aliquis (quantifiers). si, ergo (connectives). non, et, vel (operators). Logical constants.

Symbols.

Term	Latin	Meaning
consequentia	consequentia	consequence
antecedens	antecedens	antecedent
consequens	consequens	consequent
ergo	ergo	therefore

Metatheory. Inference theory. Formal validity. Distribution. Propositional logic.

Applies to. Medieval logic. Inference. History of logic. Propositional theory.

Limitations. Historical. Latin context. Manuscript variation. Interpretation debates.