Notes on the Assertoric and Modal Propositional Logic of the Pseudo-Scotus

Abstract

Notes on the Assertoric and Modal Propositional Logic of the Pseudo-Scotus A. CHARLENE SENAPE McDERMOTT I. INTRODUCTION THIS STUDY ATTEMPTSto view the Pseudo-Scotus's propositional logical rules from the perspective of a contemporary logical system.1 Pseudo-Scotus's assertoric propositional logic is similar to that of the Stoics in many respects, while his modal propositional logic distinguishes 2 between, then encompasses and develops both the Aristotelian and the Theophrastian theories of modality.3 The texts upon which my investigation centers comprise pp. 1-347 of volume II of the twenty-six volume edition of the collected works of John Duns Scotus, Viv6s edition (Paris, 1891-1895), reprinted from the 1639 edition of Luke Wadding. (R. P. E. Longpre's examination of the material in question led him to the now generally accepted conclusion (ca. 1936) that Wadding had erred in ascribing these pages to Duns Scotus; so another 4 "Pseudo-Scotus" was born, this one perhaps John of Cornwall.) Special attention has been given to the Pseudo-Scotus's commentaries on Aristotle's Prior Analytics (Books I and II)5--this, in spite of J. M. Bochenski's 1 Twentieth century formal or mathematical logic has proved to be an expository device unsurpassed in its ability to explicate the logical structures found in Scholastic treatises. The temptation to baldly identify the scholastic theory being analyzed with any contemporary system, of course, must be resisted. 2 Pseudo-Scotus's writings evince the first clear grasp of the difference between the modal logics of Aristotle and Theophrastus. a Aristotle most often employs modalities in the so-called divisive sense in his syllogistic, whereas Theophrastus's are modal in the composite sense. (See p. 282 of this paper. For an interesting recent development along these lines see P. Weingartner, "Modal Logics With Two Kinds of Necessity and Possibility," Notre Dame Journal of Formal Logic, IX, 2, [April 1968],97-159.) A further major difference is that Aristotle seems to treat chiefly contingent (neither necessary nor impossible) premisses under the rubric of problematic modalities, whereas Theophrastus restricts his attention to premisses possible in the sense of being not impossible alone. An account of Pseudo-Scotus's distinctionbetween these is given on p. 300. 4 Wadding assigned many questionable texts to Duns Scotus. Some have since been set to the credit of various authors: e.g., Thomas d'Erfurt, Antonius Andreas. Others are still listed as anonymous . See E. Gilson, Jean Duns Scot (Paris, 1952), pp. 670-675 for a detailed list of genuine and spurious writings. 5 pp. 81-197, Vives edition. [2731 274 HISTORY OF PHILOSOPHY qualms about assigning both these glosses to the same author. 6 1 have not been able to discover any inconsistency between the two texts (although there are surely redundancies ); on the contrary, they seem to corroborate one another quite neatly. More tentatively, I have made use of some relevant passages in which Pseudo-Scotus expands on Aristotle's Posterior Analytics (Books I and II) and on his Sophistic Elenchus. 7 I say "tentatively" because of certain minor stylistic differences between the commentary on the Prior Analytics and the discussion of the Posterior Analytics. Throughout, my emphasis is on propositional logic. In order to confine this paper to reasonable limits, I have not included a detailed treatment of PseudoScotus 's predicate logic as such, nor even of his syllogistic,s Reference to predicate logic is restricted to examples which bear directly on problems in propositional logic. One further restriction propter brevitatem. Mode, as discussed by the PseudoScotus has a much broader compass than we are generally accustomed to give it. For him (and for his compeers), any operator determinative of the whole proposition can be designated as a mode. g The following list of "modes" has been culled from PS An Pr I 143a: necessarium, possibile, impossibile, contingens, verum, 1~ falsum, per se, scitum, dubium, opinatur, apparens, noturn, volitum, and dilectum. The present analysis will cover only the first four of these, the so-called "alethic" modalities, in some detail. Now, in addition to the above modal qualifications, Pseudo-Scotus's logic is able to deal with four sorts of superposed tense changes: It should...

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