Jean Buridan Research Articles

Christian theology and the principle of inertia in physics

The article discusses the dependence of the formulation of law of inertia in classical mechanics on theological concepts of its time. It is shown that in medieval science, all attempts to solve the problem of motion of a thrown body were made within the framework of the Aristotelian understanding of motion as the actualization of the possible. Nevertheless, within the framework of the theory of impetus (John Philopon), medieval natural philosophers came close to the principle of preserving the amount of movement (Jean Buridan). Galileo, who himself began his work on the theory of motion with an attempt to mathematize the concept of impetus, in his mature works proceeded to a principled criticism of the Aristotelian understanding of motion. However, despite all the Socratic power of the Maevtic method, he failed to prove the law of inertia. Galileo’s virtuoso dialectic only allowed him to destroy all objections to the movement by inertia. Descartes gives a positive proof of the law of inertia, and the basis of his deduction is the theological thesis about the immutability of God. The law of inertia in the classical mechanics of Descartes and Newton was closely related to the thesis of the passivity of matter. The article shows that this thesis echoes the Protestant understanding (Luther’s) of the Christian way as the cultivation of passive righteousness, where all the activity of salvation is conditioned only by the action of God.

Time and Indexicality in Buridan’s Concept of Logical Consequence

Jean Buridan developed his theory of consequence within a semantical framework compatible with what we now call token-based semantics. In his Treatise on Consequences and Sophismata, Buridan showed that the notion of consequence accepted by the logicians of his time (that the antecedent cannot be true without the consequent being true) fails when we consider inferences such as: (1) ‘No proposition is negative, therefore, no ass is running’; and (2) ‘Every proposition is affirmative, therefore, no proposition is negative’. Our analysis of Buridan’s semantic and logical theory shows that: (a) for Buridan, time was a fundamental needed concept to adequately define the notion of consequence; (b) sentences like ‘No proposition is negative’ — appearing in (1) and (2) — are temporal indexicals; (c) these indexicals appealed to Buridan because they suggest a new type of validity, that has been called contextual validity by Blackburn and Jørgensen, and which was originally discussed by Kamp and Kaplan in the twentieth century. Finally, we offer a reconstruction of Buridan’s theory of consequence in terms of a contextual hybrid logic, a logical-symbolic apparatus that allows us to assess Buridan’s logical and philosophical contributions in contemporary terms and contribute to the current discussion on the topic.

Pierre Duhem and the Continuous Development of Science

When attempting to assess what history of science, doubtless an important element of our culture, owes to the French philosopher and scientist Pierre Duhem, one has to emphasise the critical role he played in rethinking the world outlook inherited from the preceding times and in developing a new one more apt to contemporary science. This analysis draws on such key Duhem’s writings as «The World System» («Le système du monde») and «Studies on Leonardo da Vinci» («Études sur Léonard de Vinci»). Two Duhem’s theses deserve particular attention. One is his assertion that Christianity (and the Catholic Church for that) did not impede, but rather contributed to the development of science having dispensed with cosmological assumptions of Greek Paganism incompatible with contemporary science. Secondly, Duhem argues that intuitions to pave way to the scientific revolution were first advocated by such Sorbonne Scholastics as Jean Buridan and Nicholas Oresme. It is noteworthy that the French scientist clearly underestimates the contribution of non-French thinkers to the emerging set of cultural axioms. Duhem’s new ontology of cognition is closely related to the ideas of new epistemology. Viewing evolution of science as a gradual continuous process, he endorsed the holist idea that isolated scientific propositions could neither be verified nor falsified. The truth of any proposition is inseparable from the truth of the system of hypotheses as a whole. Hence science progresses not by rejecting old theories, but by modifying them: in due course old concepts give way to new ones. This topical assumption that progress of science is to be viewed and understood in its specific socio-cultural context delineates the principle on which the answer to the no less topical question of the philosophy of culture, viz. why modern science has emerged in Europe rather than elsewhere, is to be based on.

Vicent Ferrer i la lògica del segle XIV

[ca] Mentre exercia de lector logicae a l’studium sollemne que els dominicans tenien a Lleida, Vicent Ferrer redactà dos textos de lògica: la questió De unitate universalis, probablement el sumari de collationes mantingudes amb els seus alumnes, i el tractat De suppositionibus, una exposició àmplia i rigorosa d’un tema complex de fi losofi a del llenguatge, molt debatut a mitjan segle XIV. No són pas textos redactats per un magister artium experimentat, són el fruit de la seva dedicació juvenil (acabava de fer 22 anys) i esporàdica perquè no escriví cap altra obra escolàstica. Cal considerar- los, doncs, l’obra d’un ensenyant precoç, coneixedor tant dels escrits dels pensadors de la seva època –Gualter Burley, Guillem d’Ockham, Joan Buridan– com del pensament d’Aristòtil i de Tomàs d’Aquino.

Psychophysiological approach to the Liar paradox: Jean Buridan’s virtual entailment principle put to the test

This article presents an empirical examination of the consequences of the virtual entailment principle proposed by Jean Buridan to resolve the Liar paradox. This principle states that every sentence in natural language implicitly asserts its own truth. Adopting this principle means that the Liar sentence is not paradoxical but false, because its content is contradictory to what is virtually implied. As a result, humans should perceive the Liar sentence the same way as any other false sentence. This solution to the Liar paradox received criticism for making ad hoc claims about the natural language. However, thanks to modern advancements in psychophysiology, it became possible to empirically investigate if the human brain really perceives the Liar sentence like a false sentence. We designed and conducted an experiment to examine brain activity in response to true sentences, false sentences and self-referential sentences (including the Liar and the Truthteller). Our results provide support for the Buridan’s hypothesis and show that the Liar sentence is processed by the human brain identically to false sentences, while the Truthteller sentence is perceived identically to true sentences. This agrees with predictions derived from the virtual entailment principle and supports the idea that humans think with the logic of truth—a logic for which the truth is a designated value of its adequate semantics.

The significance of the idea of impetus for the development of natural science

In the discourse around theories explaining scientific progress, natural philosophy of the Late Medieval Period is seen as playing the role of apologetics. For philosophers of science, with their repudiation of metaphysics, the task of providing a rational reconstruction of how scientific progress has occurred is nigh on impossible. Even explanations such as the Popperian and the Kuhnian strain under great difficulty and provide only partly satisfactory results. In his “Logik der Forschung” (1934) Karl Raimund Popper argues that metaphysics plays an accidental part in the emergence of new scientific ideas. Correspondingly, in “Structure of Scientific Revolutions” (1962), by carrying out theoretical interpretations and classification of empirical facts without their metaphysical premises, Thomas Kuhn comes to the conclusion that natural science was formed under the influence of erroneous interpretations of Aristotelian natural philosophy presented by medieval natural philosophers. These are some of the reasons why medievalists are still made to defend late medieval natural philosophy from shallow convictions that at medieval universities nothing of any significance to contemporary science and philosophy took place at all. Seeking to render a fragment of a coherent reconstruction of the development of natural philosophy, I will investigate one idea of late medieval philosophy – the explanation of motion (impetus). The main statement of the paper holds that the ideas of late medieval natural philosophy have a decisive significance for the development of modern natural science instead of accidental or negative one. In the paper, following Aristotelian philosophical approach, premises of Jean Buridan’s theory of impetus will be exposed. Then, debates over the explanation of projectile motion are going to be presented, and finally, the necessary significance of this metaphysical idea on the modifications of natural philosophy is going to be ascertained.

RUNNING DETAILS ON THE TWO MOVEMENTS IN THE INTELLECTUAL HISTORY OF SCIENCE AND IDEAS

A long tradition concerning the causes of the planetary movements existed as to the movements on the earth: the so called problem de motu locali. Starting from late middle Ages many criticisms were carried out against the Aristotelian doctrine of natural and violent motions. A well accredited and historically coherent theory to explain the movement and the change of movement was the medieval theory of impetus substantially developed by Jean Buridan (ca. 1300–ca. 1360) and by Nicolas d’Oresme (1320? 1325?–1382) on the basis of ideas that came back to John Philoponus (490–570).

Book Review: Jean Buridan, Treatise on Consequences

Book Review: Jean Buridan, Treatise on Consequences

Ex impossibili quodlibet sequitur (Angel d’Ors)

While agreeing with Professor D’Ors’ thesis that the notion of logical consequence cannot be exhaustively characterized (though not with his grounds for it), I depart from Professor d’Ors’ conclusion that the very notion of good consequence is primitive and can only be identified with the (incompletable) 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.

Induction and Natural Necessity in the Middle Ages

Drawing the complex terrain of the theories of induction and of the various ways to ground inductive knowledge in the middle ages is the aim of this paper. There have already been two excellent attempts to draw this terrain. The first is by Julius R. Weinberg (1965) and the second by E. P. Bos (1993). My attempt differs from theirs in two major respects. The first is that it is more detailed in the examination of the various theories and their relations. The second is that I focus on the role of natural necessities in induction. In particular, I try to place the various conceptions of induction within a network of issues that relate to the problem of universals, natural necessities and a power-based approach to activity in nature. Here is the road map. Section 2 explains Aristotle’s views of induction, as this were mainly developed in Posterior Analytics Book II.19 and states what I take it to be the main dilemma of induction, as this was described by Sextus Empiricus: induction is either perfect and impossible or imperfect and unjustified. In section 3, I move to Thomas Aquinas and his own attempt to justify induction and the actuality of general and necessary principles based on experience by an appeal to the natural light of reason. In section 4 I discuss John Duns Scotus’s reliance on a self-evident maxim to bridge the gap between imperfect and perfect induction. Section 5 moves to William of Ockham’s peculiar attempt to justify single-instance inductions. Then, section 6 offers a detailed account of Jean Buridan’s ground-breaking re-conceptualisation of induction and the role of intellect in it. Section 7 discusses the critique of induction by Nicolaus of Autrecourt. Finally, section 8 offers a brief account of Pseudo-Scotus’s move from knowledge to opinion.

Buridan's Solution to the Liar Paradox

Jean Buridan has offered a solution to the Liar Paradox, i.e. to the problem of assigning a truth-value to the sentence ‘What I am saying is false’. It has been argued that either (1) this solution is ad hoc since it would only apply to self-referencing sentences [Read, S. 2002. ‘The Liar Paradox from John Buridan back to Thomas Bradwardine’, Vivarium, 40 (2), 189–218] or else (2) it weakens his theory of truth, making his ‘a logic without truth’ [Klima, G. 2008. ‘Logic without truth: Buridan on the Liar’, in S. Rahman, T. Tulenheimo and E. Genot, Unity, Truth and the Liar: The Modern Relevance of Medieval Solutions to the Liar Paradox, Berlin: Springer, 87–112 (Chapter 5); Dutilh Novaes, C. 2011. ‘Lessons on truth from mediaeval solutions to the Liar Paradox’, The Philosophical Quarterly, 61 (242), 58–78]. Against (1), I will argue that Buridan's solution by means of truth by supposition does not involve new principles. Self-referential sentences force us to handle supposition more carefully, which does not warrant the accusation of adhoccery. I will also argue, against (2), that it is exaggerated to assert that this solution leads to a ‘weakened’ theory of truth, since it is consistent with other passages of the Sophismata, which only gives necessary conditions for the truth of affirmative propositions, but sufficient conditions for falsity.

Truths ancient and modern

The paper presents a comparison of the theories of truth, and the solutions of the liar paradox, proposed by Thomas Bradwardine (c. 1290-1349), Jean Buridan (c. 1295-1358), and Alfred Tarski (1901-1983).

Prior on an insolubilium of Jean Buridan

We present Prior’s discussion of a puzzle about valditity found in the writings of the fourteenth-century French logician Jean Buridan and show how Prior’s study of this puzzle may have provided the conceptual inspiration for his development of hybrid logic.

El octagon medieval de oposición y equivalencia: tres aplicaciones / The Medieval Octagon of Opposition and Equivalence: Three Applications

I describe an octagon of opposition and equivalence developed by fourteenth-century logicians, in particular by Jean Buridan in his Summulae de dialectica. This «square» of opposition displays complex logical relations, one of which is not found in the traditional square of opposition. The octagon allows expression of three kinds of sentences: quantified modal sentences, oblique sentences, and sentences with quantified predicates. The octagon shows that medieval logicians were working with a logic of relations, an identity logic, and a modal logic not unlike the logic of our own day.

Validity Now and Then

It is often said that an argument is valid if and only if it is impossible for its premises to be jointly true and its conclusion false. Usually there is little harm in saying this but it places the concept of truth at the very heart of logic and, given how complex and obscure that concept is, one might wonder if trouble arises from this.It does - in at least two contexts. One of these was explored in the first half of the fourteenth century by Jean Buridan and by the mysterious figure known as the Pseudo-Scotus of the Questions on the Prior Analytics printed in the edition of Scotus's works edited by Luke Wadding. Buridan thought that the bearers of truth were particular sentence-tokens; he thought of ttuth as a property of those tokens and he thought that nothing had properties unless it existed.

Philosophers and Physicians on the Scientific Validity of Latin Physiognomy, 1200-1500

The article surveys and contextualizes the main arguments among philosophers and academic physicians surrounding the status of physiognomy as a valid science from the thirteenth to the early sixteenth centuries. It suggests that despite constant doubts, learned Latin physiognomy in the later Middle Ages was recognized by natural philosophers (William of Spain, Jean Buridan, William of Mirica) and academic physicians (Rolandus Scriptor, Michele Savonarola, Bartolomeo della Rocca [Cocles]) as a body of knowledge rooted in a sound theoretical basis. Physiognomy was characterized by stability and certainty. As a demonstrative science it was expected to provide rational explanation for every bodily sign. In this respect, learned physiognomy in the Middle Ages was dramatically different from its classical sources, from Islamic and possibly from early-modern physiognomy as well.

Francis of Marchia's Virtus derelicta and the Context of Its Development

AbstractThis article offers the first critical edition of the most important version of Francis of Marchia's famous question 1 of his commentary on Book IV of the Sentences, in which the Franciscan theologian puts forth his virtus derelicta theory of projectile motion. The introduction attempts to place Marchia's theory in its proper context. The theory might seem to us an obvious improvement on Aristotle, but rather than an immediate and complete break with tradition that all scholastics quickly adopted, Marchia's virtus derelicta was more a stage in a gradual process that had begun many decades before and did not find universal acceptance among his first successors. Moreover, Marchia himself did not take the theory to what might seem the obvious conclusion that Jean Buridan would draw, because Marchia employed the virtus derelicta to explain more phenomena than just projectile motion.

Juan Luis Vives' Conception of Freedom of the Will and Its Scholastic Background

AbstractThe aim of the present paper is to approach Juan Luis Vives' conception of freedom of the will in light of scholastic discussions on will and free choice, and point to some interesting similarities with the analysis of free choice contained in Jean Buridan's Quaestiones super decem libros Ethicorum Aristotelis ad Nicomachum.

Tomismo y nominalismo en la lógica novohispana

I present some ideas from medieval thinkers concerning sentences which subject term has no reference and as kif those sentences can admit truth values. I present the ideas of William of Ockham, Jean Buridan and Albert of Saxony, from the nominalist side, and Vicente Ferrer exposing the moderate realism. Then we present two New Spain thinkers, Alonso de la Veracruz and Tomas de Mercado.

The University of Paris at the Time of Jean Buridan and Nicole Oresme

The University of Paris at the Time of Jean Buridan and Nicole Oresme