Non-normal Propositions in Buridan’s Logic

Abstract

John Buridan’s introduction of the notion of non-normal propositions (propositiones de modo loquendi inconsueto) in his theory of the syllogism is a marked example of the influence of vernacular languages on the use of Latin in medieval logic and the regimentation of the language used. Classical Latin is an SOV language, in which the word order of the simplest sentence form is subject-object-verb, in contrast to the SVO order of the vernacular languages of the later Middle Ages. Buridan’s so-called non-normal propositions arise from deeming the normal order to be the SVO of the vernacular, and so taking SOV, where the object-term precedes the verb, to be non-normal. In particular, introducing O-propositions of non-normal form permits conversion of normal O-propositions, meaning that all four propositions of the traditional square of opposition can be converted, thereby adding further possibilities to the theory of the assertoric syllogism. 1 Dante and the Accusative In Prue Shaw’s 1995 edition of Dante’s Monarchia, we read: “Et nota quod argumentum sumptum a destructione consequentis, licet de sua forma per aliquem locum teneat, tamen vim suam per secundam figuram ostendit, si reducatur sicut argumentum a positione consequentis per primam. Reducitur enim sic: omne iniustum persuadetur iniuste: Cristus non persuasit iniuste: ergo non persuasit iniustum. A positione consequentis sic: omne iniustum persuadetur iniuste: Cristus persuasit quoddam iniustum: ergo persuasit iniuste.”1 ∗This work was supported by Research Grant AH/F018398/1 (Foundations of Logical Consequence) from the Arts and Humanities Research Council, UK. Presented at the 19 European Symposium of Medieval Logic and Semantics (Geneva, June 12-16, 2012): Formal Approaches and Natural Language in Medieval Logic. Shaw (1995a, pp. 94-95): “And note that our argument, which is based on denying the consequent, although valid in its form by virtue of a common-place, yet reveals its full