During the 13th century, several logicians in the Latin medieval tradition showed a special interest in the nature of impossibility, and in the different kinds or ‘degrees’ of impossibility that could be distinguished. This discussion resulted in an analysis of the modal concept with a fineness of grain unprecedented in earlier modal accounts. Of the several divisions of the term ‘impossible’ that were offered, one became particularly relevant in connection with the debate on ars obligatoria and positio impossibilis: (...) the distinction between ‘intelligible’ and ‘unintelligible’ impossibilities. In this article, I consider some 13th-century tracts on obligations that provide an account of the relation between impossibility and intelligibility and discuss the inferential principles that are permissible when we reason from an impossible – but intelligible – premise. I also explore the way in which the 13th-century reflection on this topic survives, in a revised form, in some early 14th-century accounts of positio, namely, those of William of Ockham, Roger Swineshead and Thomas Bradwardine. (shrink)

_ Source: _Volume 56, Issue 3-4, pp 340 - 366 The history of thinking about consequences in the Middle Ages divides into three periods. During the first of these, from the eleventh to the middle of the twelfth century, and the second, from then until the beginning of the fourteenth century, the notion of natural consequence played a crucial role in logic, metaphysics, and theology. The first part of this paper traces the development of the theory of natural consequence in (...) Abaelard’s work as the conditional of a connexive logic with an equivalent connexive disjunction and the crisis precipitated by the discovery of inconsistency in this system. The second part considers the accounts of natural consequence given in the thirteenth century as a special case of the standard modal definition of consequence, one for which the principle _ex impossibili quidlibet_ does not hold, in logics in which disjunction is understood extensionally. (shrink)

_ Source: _Volume 53, Issue 2-4, pp 353 - 371 While agreeing with Professor D’Ors’ thesis that the notion of logical consequence cannot be exhaustively characterized, I depart from Professor d’Ors’ conclusion that the very notion of good consequence is primitive and can only be identified with the set of acceptable rules of inference, and from his conviction that modal notions such as necessity and impossibility are equivocal and gain such clarity as they have by their interaction with rules of (...) inference. Inspired by this picture, Professor d’Ors undertook an examination of a number of medieval attempts to analyze the notion of consequence and tried to show how certain developments in the medieval history of logic made sense in the light of debate over such analyses. This paper examines a small fragment of Professor d’Ors programme and its relation to some aspects of Jean Buridan’s account of the consequence relation. (shrink)

Buridan endorsed the principles that any impossible, and a fortiori any self-contradictory, proposition entails each proposition. These principles are usually referred to as ‘Ex impossibili quodlibet’ (EIQ) and ‘Ex contradictione quodlibet’ (ECQ). Buridan further considered the instance ECCQ according to which any proposition follows from the conjunction of two contradictory propositions. Buridan showed how ECCQ can be proven by means the usual laws of conjunction and disjunction. Furthermore, he discovered that EIQ can be derived from ECCQ by means of the (...) principle that if a conclusion q follows from two premises, one of which is necessary, then q follows from the other premise alone. Buridan thought that this principle would be provable; but his proof turned out to be circular since it presupposed EIQ. Nevertheless, EIQ is validated by the definition of a ‘bona consequentia’. Somewhat more exactly, according to Buridan one may distinguish between inferences which are formally valid, ‘materially’ valid, and valid ‘as of now’. It is shown that formally valid inferences satisfy ECQ while ‘materially’ valid inferences satisfy EIQ. Furthermore, inferences which are valid ‘as of now’ satisfy the principle ‘Ex falso quodlibet’ saying that any false proposition ‘as of now’ entails every proposition. (shrink)

In the course of his philosophy, in various contexts, Kant comes to reject three theses about existence: (i) that the thoroughgoing determination of a thing implies its existence, (ii) that existence is a real predicate or determination of a thing, and (iii) that existence is the complement of inner possibility or essence. Kant’s target here is Baumgarten, who advocates these theses as the criterion, classification, and definition of existence. In this article I seek to clarify Kant’s elusive theory of existence (...) through its opposition to Baumgarten. I will show that Kant’s refutation of (i)–(iii) does not stand alone but is grounded on his own definition of existence as (absolute) positing. Thus contrary to common practice, Kant’s negative claims about what existence is not cannot be understood in isolation but must be taken as jointly dependent on Kant’s positive claim of what existence is. I will show that the theses (i)–(iii) fail because they presuppose that existence contributes to the intension or content of a concept, whereas according to Kant existence in fact posits a (non-empty) extension to the concept. (shrink)

This paper challenges the standard a priori/a posteriori distinction by looking at statements in which comprehension requires more that merely passive awareness of objects and their properties. A proposal is made to add to the traditional categories of knowledge, the “a positio,” characterized by active, intentional, and collective involvement of language users in the existence and nature of objects of reference needed for the truth of statements about various kinds of artifacts, broadly construed. The conditions of understanding statements about (...) institutions, institutional activity and standards of measurement are considered in some detail. (shrink)

_ Source: _Volume 53, Issue 2-4, pp 372 - 390 This paper investigates a series of Oxford _Obligationes_ texts, all of which can be associated with Richard Billingham. My study is based on eleven of the surviving manuscripts and two early printed texts. I focus on one aspect of their discussion, namely the rule for granting the initial _positum_ of an obligational disputation of the type called _positio_, and the six restrictions that could be placed on that rule. I explain (...) these restrictions with reference to several sophismata that were meant to illustrate the problems that the restrictions were intended to solve, and in particular, I discuss the fifth restriction ‘not inconsistent with the _positum_’. I also shed light on the final restriction, which has not always been well understood, namely the restriction ‘wherever there is no _obligatio_ relevant to the _positum_’. (shrink)

Kretzmann and Spade were led by Richard Kilvington’s proposed revisions to the rules of obligations in his discussion of the 47th sophism in his Sophismata to claim that the purpose of obligational disputations was the same as that of counterfactual reasoning. Angel d’Ors challenged this interpretation, realising that the reason for Kilvington’s revision was precisely that he found the art of obligation unsuited to the kind of reasoning which lay at the heart of the sophismatic argument. In his criticism, Kilvington (...) focussed on a technique used by Walter Burley to force a respondent to grant an arbitrary falsehood and similar to Lewis and Langford’s famous defence of ex impossibili quodlibet. Kilvington observes that just as in obligational disputation, one may be obliged to grant a false proposition and deny a true one, so in counterfactual reasoning one may be obliged to doubt a proposition whose truth or falsity one knows, on pain of contradiction. (shrink)

One of the main controversies of the Logic Schools of the 12th century centered on the question: What follows from the impossible? In this paper arguments for two diametrically opposed positions are examined. The author of the ‘Avranches Text’ who probably belonged to the school of the Parvipontani defended the view that from an impossible proposition everything follows (‘Ex impossibili quodlibet’). In particular he developed a proof to show that by means of so-called ‘disjunctive syllogism’ any arbitrary proposition B can (...) be logically derived from a pair of contradictory propositions A and Not-A. The author of the Ars Meliduna instead argued that nothing follows from an impossible proposition (‘ex falso nihil sequitur’). This view is supported by various counterexamples which aimed to show that the admission of impossible premises would give rise to inconsistent conclusions. Upon closer analysis these inconsistencies do not, however, have the formal structure of a real contradiction like A and Not-A, but rather the structure of two rivalling conditionals like ‘If B then A’ and ‘If B then Not-A’. Hence these counterexamples rather have to be considered as refutations of the basic principles of ‘connexive logic’. (shrink)

Impossible antecedents entered the scene of medieval logic around the 1120s and soon started to dominate this scene, becoming one of the most debated issues from the second half of the twelfth century onwards. This article focuses on theories of counterpossibles from this period and aims to offer an overview of the different responses offered by twelfth-century logicians on whether everything, something, or nothing follows from an impossible statement. Rather than trying to historically reconstruct the positions of the different authors (...) – an operation that may be premature given the insufficient notions we still have of the authorship and dating of sources – I aim to provide a provisional map of the main arguments that were advanced in favour of or against the ex impossibili quodlibet principle. The article also aims to show that the strategies developed by twelfth-century logical schools in their approach to counterpossibles survive in logical discussions of the same topic during the thirteenth and the early fourteenth century, especially in the syncategoremata and sophistaria traditions. (shrink)

In the early 1980s, Paul V. Spade advanced the thesis that obligational reasoning was counterfactual reasoning, based upon his interpretation of the obligationes of Walter Burley, Richard Kilvington, and Roger Swyneshed. Eleonore Stump in a series of contemporary papers argued against Spade’s thesis with respect to Burley and Swyneshed, provisionally admitting it for Kilvington with the caveat that Kilvington’s theory is by no means clear or non-idiosyncratic. In this paper, we revisit the connection between counterfactual reasoning and obligationes, focusing on (...) one particular treatise, the anonymous early twelfth-century Obligationes Parisienses edited by L.M. de Rijk in the late 70s. We show that while positio in this treatise does not involve counterfactual reasoning, the species sit verum or rei veritas apparently does, and it is precisely this which distinguishes the two species in this treatise. (shrink)

In “Lectio 55” of his Notule libri Priorum, Robert Kilwardby discussed various objections that had been raised against Aristotle’s Theses. The first thesis, AT1, says that no proposition q is implied both by a proposition p and by its negation, ∼p. AT2 says that no proposition p is implied by its own negation. In Prior Analytics, Aristotle had shown that AT2 entails AT1, and he argued that the assumption of a proposition p such that (∼p → p) would be “absurd”. (...) The unrestricted validity of AT1, AT2, however, is at odds with other principles which were widely accepted by medieval logicians, namely the law Ex Impossibili Quodlibet, EIQ, and the rules of disjunction introduction. Since, according to EIQ, the impossible proposition (p ∧ ∼p) implies every proposition, it also implies ∼(p∧∼p), in contradiction to AT2. Furthermore, by way of disjunction introduction, the proposition (p∨∼p) is implied both by p and by ∼p, in contradiction to AT1. Kilwardby tried to defend AT1, AT2 against these objections by claiming that EIQ holds only for accidental but not for natural implications. The second argument, however, cannot be refuted in this way because Kilwardby had to admit that every disjunction (p ∨ q) is naturally implied by its disjuncts. He therefore introduced the further requirement that, in order to constitute a genuine counterexample to AT1, (p → q) and (∼p → q) have to hold “by virtue of the same thing”. In a recently published paper, Spencer Johnston accepted this futile defence of AT1 and developed a formal semantics that would fit Kilwardby’s presumably connexive implication. This procedure, however, is misguided because the remaining considerations of Lesson 55  which were entirely ignored by Johnston  show that Kilwardby eventually recognized that AT2 is bound to fail. After all he concluded: “So it should be granted that from the impossible its opposite follows, and that the necessary follows from its opposite”. (shrink)

Mitte der 80er Jahre bildete sich an der Universitat-Gesamthochschule Pader born eine Diskussionsgruppe, die unzufrieden daIiiber war, wie mit Vielfalt bzw. Alternativen in den Kulturwissenschaften umgegangen wird. Diese Unzufriedenheit bezog sieh auf die verschiedensten Gebiete. Selbst dort, wo vielfiiltige Positionen in Forschung und Lehre dargestellt werden, geschieht dies selten systematisch vergleichend. Auch werden hierbei keine Methoden entwickelt, die herausfinden lassen, ob es sieh bei den verschiedenen Positio nen urn Alternativen handelt und wie unter ihnen gegebeneofalls LOsungen als die vorerst (...) besten auszuzeichnen sind. Ohne Klarung dieses Problemkreises istnicht zu sehen, in welchem AusmaB wissenschaftliches Wissen zu verant worten ist. Angesiehts der grundlegenden technischen Herausforderungen und der Bedeu tung des wissenschaftlichen Wissens hierfiir wurde die Frage drangend, wie die angesprochene Lage zu verbessern sei. Es stellte sieh bald heraus, daB es sinnvoll sein muBte, einen neuen Typ einer wissenschaftlichen Diskussions zeitschrift zu griinden, die nieht nur Forschungen prasentiert, sondern selbst als Forschungsprojekt fur die Suche nach einem besseren Umgang mit Alternativenkonzipiertist. Ende der80erJahregriindetesieheineInitiativgruppe fur die Zeitschrift 'Ethik und Sozialwissenschaften' und konstituierte die FORSCHUNGSGRUPPE ERW AGUNGSKULTIJR, die seit 1990 diese Zeitschrift heraus gibt und Forschungsergebnisse in Arbeitspapieren veroffentlicht. Ergebnisse der Forschungen dieser Gruppe sind in diesem Band abgedruckt. (shrink)

L'articolo prende in considerazione il possibile dialogo tra i nostri modelli di razionalità e quelli di autori medievali del tardo XIII secolo circa il concetto di laicità. Non si può certo parlare di laicità nel senso contemporaneo del termine, ma un tema interessante - senza alcuna pretesa di riferirsi a impossibili precorrimenti - può essere il concetto, individuabile in alcuni autori del tardo XIII e degli inizi del XIV secolo, della possibile coesistenza di differenti tradizioni filosofiche e teologiche, con l'implicita (...) conseguenza di una sorta di pluralismo metodologico. Tali concezioni possono essere accostate alla moderna idea di libera coesistenza di posizioni diverse, e quindi all'idea di tolleranza più che a quella di laicità, e vengono contrapposte a ogni pretesa di fondare e imporre una esclusiva e univoca lettura della realtà. Da questo punto di vista viene analizzato il pensiero di un giovane magister artium della fine del XIII secolo e, nel contempo, di un giovane magister theologiae, che si identificano nella medesima persona, Giovanni Duns Scoto.This paper concerns the possible dialogue between our models of rationality and those of medieval authors of the late 13th century about the concept of secularism . It's not possible of course to speak of secularism in the contemporary sense of the term, but an interesting theme - without any claim to speak of precursory theses - can be the concept, already recognizable in some authors of the late 13th century and the beginning of the 14th century, of the possible coexistence of different philosophical and theological traditions, with the implicit consequence of a sort of methodological pluralism. These ideas may be compared to modern idea of free coexistence of different theories, and therefore to idea of tolerance more than to that of secularism, and are opposed to any claim to ground and to impose an exclusive and authoritative interpretation of reality. From this point of view is here analysed the thought of a young magister artium of the last years of the 13th century and, at the same time, of a young magister theologiae, who must be overlapped in the same man, John Duns Scotus. (shrink)

Les Méditations cartésiennes, en instaurant la métaphysique comme science de l'esprit, permettent de fonder la science physique sur elle. Ce texte montre ainsi la primauté de la science de la mens sur celle des corps : tout d'abord l'esprit, en tournant vers soi son regard , se sait cogitatio, et ensuite alors il comprend le corps comme ce qui est étendu, flexible, muable, ce qui peut être tourné diversement, bref comme son contraire. L'auto-affirmation de l'ego engage l'examen de l'hypothèse « (...) rien n'est », et demande de distinguer l'ordre de l'hypothèse, de la suppositio, de celui de la positio, de la vérité. In the Meditations of Descartes, since metaphysics is established as a science of mind, physics can be based on it. Thus, this text evinces the pre-eminence of the science of mens over that of bodies : first of all, by turning towards itself mind knows itself as cogitatio and threrefore understands the body as being flexible, mutable, having extensity, and being changeable in diverse manners ; in short, as being its opposite. The self-asserting ego implies the consideration of the « nothing exists » hypothesis and asks for a distinction between the order of hypothesis and that of truth. (shrink)