"Temporalis" in Medieval Logic

Abstract

"TEMPORALIS" IN MEDIEVAL LOGIC Medieval logicians generally accepted the distinction between atomic and molecular propositions. The molecular propositions, which are also known as hypotheticals, are in fact formed from the atomic (or simple) propositions by means of propositional connectives. In the Middle Ages, however, there was very little agreement as to which connectives should be taken into consideration within the logical theories. Even the number of propositional connectives was not fixed in general. William of Ockham claimed: Est itaque propositio hypothetica omnis proposito, in qua coniunguntur plures propositiones categoricae mediante aliquo adverbio vel coniunctione. Et ponuntur communiter quinqué, quae magis sunt famosae et magis communes inter omnes; et est conditionalis , copulativa, disiunctiva, temporalis, causalis.1 Ockham is thus suggesting that the number of hypotheticals is five. In his opinion, however, the hypotheticals which he has Usted are the most interesting and important ones. But he does not claim that they are the only ones possible or that they are mutuaUy independent in a strong logical sense. In his De Puritate Artis Logicae, Tractatus Longior, Walter Burleigh writes the foUowing: Intelligendum est, quod communiter assignantur quinqué species propositionis hypotheticae, scilicet conditionalis, causalis, temporalis , copulativa, disiunctiva.2 Burleigh points out that other hypotheticals might be defined, but 1 Ockham, Elementarium Logicae, ed. Eligius Buytaert, O.F.M., Franciscan Studies, 25 (1965), 198. 2 Walter Burleigh, De Puritate Artis Logicae Tractatus, ed. Philotheus Boehner, O.F.M., (St. Bonaventure, N.Y., 1955), p. 107. "Temporalis" in Medieval Logic167 that it wiU turn out that these new hypotheticals can be reduced to the five fundamental ones which he has mentioned. Ockham and Burleigh thus agree on which hypotheticals to be regarded as important or basic. Writing a few decades later John Buridan lists six hypotheticals: Sex sunt propositionis hypotheticae species scilicet conditionalis, copulativa, disiunctiva, causalis, temporalis et localis.3 Buridan accepts the five hypotheticals of Ockham and Burleigh, and in addition he takes localis into consideration. Writing a few decades after Buridan, Richard Lavenham lists seven important hypotheticals. In his treatise De Propositionibus Hypotheticis he states the following: Species hypotheticae sunt vii, videlicet: conditionalis, copulativa, disiunctiva, causalis, temporalis, et localis et rationalis.4 The difference between this group of hypotheticals and that of Buridan is that Richard mentions the "rational" connective "igitur" or "ergo" as a basic connective. Ockham as well as Buridan would probably assume that rationalis is nothing but another version of conditionalis. The medieval discussion regarding the number of basic hypotheticals has been summed up by Paul of Venice in his Lógica Magna: Some posit five kinds of hypotheticals, some six, others seven, others ten, others fourteen etc. But leaving all those aside, I say that there are three and no more kinds of hypotheticals that do not coincide in significance..."5 According to Paul himself there are only three species of hypotheticals : conditionalis, copulativa and distiunctiva. He does not admit "dum," "ubi," "quia" etc. as primitive or irreducible propositionforming functors. It appears that Paul's view has remained the usual 8 I quote from MS. Krakow BJ 662 f. 7r. 4 P. V. Spade, "The Treatises on Modal Propositions and on Hypothetical Propositions by Richard Lavenham," Mediaeval Studies, 35 (1973), 57. 5 I. M. Bochenski, A History of Formal Logic, trans. Ivo Thomas (University of Notre Dame Press, 1961), p. 198 1 68PETER 0HRSTR0M one in logical theories since the Reinaissance. In this paper I will concentrate on the medieval use of temporalis. This type of hypothetical proposition which is accepted within several medieval theories will be investigated with respect to truth-conditions and logical theses. I am also going to deal with the use of temporalis in connection with tensed and modal propositions. FinaUy I intend to examine why temporalis came to be rejected as a proper species of proposition. i. The Definition of Temporalis What is the temporalis} According to medieval logic a temporal proposition is composed of two or more atomic propositions joined by some adverb of time. Ockham's definition is the following: Temporalis est quae componitur ex pluribus catégoriels mediante aliquo adverbio temporis.8 Burleigh uses almost the same formulation: Et est hypothetica temporalis ilia, quae componitur ex pluribus categoricis mediante adverbio temporis...