A consequence relation \ is monotonic iff for premise sets \ and conclusion \, if \, \, then \; and non-monotonic if this fails in some instance. More plainly, a consequence relation is monotonic when whatever is entailed by a premise set remains entailed by any of its supersets. From the High Middle Ages through the Early Modern period, consequence in theology is assumed to be monotonic. Concomitantly, to the degree the argument formulated by Anselm at Proslogion 2–4 is taken (...) up by later commentators, it is accepted or rejected in accordance with a monotonic notion of consequence. Examining Anselm’s use of parallelism in the Proslogion, I show Anselm embeds his famous argument in Proslogion 2–4 in a non-monotonic context. The results here presented challenge some deeply ingrained ideas governing the historiography of the long twelfth century, particularly concerning how the theology of the later eleventh through the twelfth century relates to the scholasticism of the thirteenth. (shrink)

A counterpossible conditional, or counterpossible for short, is a conditional proposition whose antecedent is impossible. The filioque doctrine is a dogma of western Christian Trinitarian theology according to which the Holy Spirit proceeds from the Father and the Son. The filioque doctrine was the principal theological reason for the Great Schism, the split between Eastern Orthodoxy and western Christianity, which continues today. In the paper, I review one of the earliest medieval defenses of the doctrine in Anselm of Canterbury, and (...) I show that Anselm’s treatment of counterpossible conditionals concerning the procession of the spirit from the son in Trinitarian theology represent an early foray into default logic. Thus, the mutual estrangement of eastern and western positions on the matter may not lie fundamentally in a change in dogma, but rather in a change in logic. (shrink)

_ Source: _Volume 56, Issue 3-4, pp 201 - 221 This paper summarizes medieval definitions and divisions of consequences and explains the import of the medieval development of the theory of consequence for logic today. It then introduces the various contributions to this special issue of _Vivarium_ on consequences in medieval logic.

_ Source: _Volume 56, Issue 3-4, pp 292 - 319 With William of Ockham and John Buridan, Walter Burley is often listed as one of the most significant logicians of the medieval period. Nevertheless, Burley’s contributions to medieval logic have received notably less attention than those of either Ockham or Buridan. To help rectify this situation, the author here provides a comprehensive examination of Burley’s account of consequences, first recounting Burley’s enumeration, organization, and division of consequences, with particular attention to (...) the shift from natural and accidental to formal and material consequence, and then locating Burley’s contribution to the theory of consequences in the context of fourteenth-century work on the subject, detailing its relation to the earliest treatises on consequences, then to Ockham and Buridan. (shrink)

The resemblance of the theory of formal consequence first offered by the fourteenth-century logician John Buridan to that later offered by Alfred Tarski has long been remarked upon. But it has not yet been subjected to sustained analysis. In this paper, I provide just such an analysis. I begin by reviewing today’s classical understanding of formal consequence, then highlighting its differences from Tarski’s 1936 account. Following this, I introduce Buridan’s account, detailing its philosophical underpinnings, then its content. This then allows (...) us to separate those aspects of Tarski’s account representing genuine historical advances, unavailable to Buridan, from others merely differing from—and occasionally explicitly rejected by—Buridan’s account. (shrink)

This paper approaches the question of Levinas' relation to philosophy by situating his understanding of transcendence next to that of Leibniz. After offering some preliminary examples, I detail the structure of transcendence in the philosophies of Leibniz and Levinas, focusing on Leibniz's Principles of Nature and Grace and Levinas’ Essence and Disinterestedness. From here, I return to the question of whether Levinas’ thinking can be regarded as moving beyond philosophy as such. I conclude with some thoughts on what it would (...) take for a thinking of transcendence to genuinely move past the maneuvers so characteristic of philosophical thinking. (shrink)