Obligations, Sophisms and Insolubles

The focus of the paper is a sophism based on the proposition ‘This is Socrates’ found in a short treatise on obligational casus attributed to William Heytesbury. First, the background to the puzzle in Walter Burley’s traditional account of obligations (the responsio antiqua), and the objections and revisions made by Richard Kilvington and Roger Swyneshed, are presented. All six types of obligations described by Burley are outlined, including sit verum, the type used in the sophism. Kilvington and Swyneshed disliked the dynamic nature of the responsio antiqua, and Kilvington proposed a revision to the rules for irrelevant propositions. This allowed him to use a form of reasoning, the “disputational meta-argument”, which is incompatible with Burley’s rules. Heytesbury explicitly rejected Kilvington’s revision and the associated meta-argument. Swyneshed also revised Burley’s account of obligations, formulating the so-called responsio nova, characterised by the apparently surprising thesis that a conjunction can be denied both of whose conjuncts are granted. On closer inspection, however, his account is found to be less radical than first appears

‘Everything true will be false’: Paul of Venice’s two solutions to the insolubles

In his Quadratura, Paul of Venice considers a sophism involving time and tense which appears to show that there is a valid inference which is also invalid. His argument runs as follows: consider this inference concerning some proposition A: A will signify only that everything true will be false, so A will be false. Call this inference B. Then B is valid because the opposite of its conclusion is incompatible with its premise. In accordance with the standard doctrine of ampliation, Paul takes A to be equivalent to 'Everything that is or will be true will be false'. But he proceeds to argue that it is possible that B's premise ('A will signify only that everything true will be false') could be true and its conclusion false, so B is not only valid but also invalid. Thus A and B are the basis of an insoluble. In his Logica Parva, a self-confessedly elementary text aimed at students and not necessarily representing his own view, and in the Quadratura, Paul follows the solution found in the Logica Oxoniensis, which posits an implicit assertion of its own truth in insolubles like B. However, in the treatise on insolubles in his Logica Magna, Paul develops and endorses Swyneshed's solution, which stood out against this ''multiple-meanings'' approach in offering a solution that took insolubles at face value, meaning no more than is explicit in what they say. On this account, insolubles imply their own falsity, and that is why, in so falsifying themselves, they are false. We consider how both types of solution apply to B and how they complement each other. On both, B is valid. But on one (following Swyneshed), B has true premises and false conclusion, and contradictories can be false together; on the other (following the Logica Oxoniensis), the counterexample is rejected

The philosophy of logic

Postprin

Introducción al problema de la libertad en la obra de Thomas Bradwardine.

Sin resume

La estructura formal del «De causa Dei» de Thomas Bradwardine.

Sin resume

Robert Halifax, un calculador de sombras de Oxford

In his commentary on Lombardʼs Sentences, question 1, Robert Halifax OFM presents a remarkably original and inventive optical argument. It compares two pairs of luminous and opaque bodies with two shadow cones until the luminous bodies reach the zenith. In placing two moving human beings into the shadow cones whose moral evolution parallels the size of the shadows, Halifax creates an unprecedented shadow theater equipped with mathematics and theorems of motion from Thomas Bradwardineʼs Treatise on Proportions. This paper is a first attempt at analyzing this imaginary experiment and the mathematics of the infinite it implies. It also shows that optics had new aims through its connexion with the theorems of motion of the Oxford Calculators.En su Comentario a las Sentencias de Pedro Lombardo, cuestión 1, Robert Halifax OFM presenta un argumento óptico notablemente original e inventivo. Compara dos pares de cuerpos luminosos y opacos con dos conos de sombra hasta que los cuerpos luminosos alcanzan el cenit. Al situar en los conos de sombra a dos seres humanos en movimiento cuya evolución moral es paralela al tamaño de las sombras, Halifax crea un teatro de sombras sin precedentes, dotado con la matemática y los teoremas del movimiento derivados del Tratado de las Proporciones de Thomas Bradwardine. Este artículo es un primer intento de analizar este experimento imaginario y las matemáticas del infinito por él implicadas. Muestra además que la óptica ha tenido nuevos objetivos a través de su conexión con los teoremas del movimiento de los Calculadores de Oxford

Foreknowledge, Free Will, and the Divine Power Distinction in Thomas Bradwardine\u27s De futuris contingentibus

Thomas Bradwardine (d. 1349) was an English philosopher, logician, and theologian of some note; but though recent scholarship has revived an interest in much of his work, little attention has been paid to an early treatise he wrote on the topic of future contingents, entitled De futuris contingentibus. In this thesis I aim to address this deficit, arguing in particular that the treatise makes original use of the divine power distinction to resolve the apparent conflict between God’s foreknowledge on the one hand, and human free will on the other. Bradwardine argues that God’s foreknowledge operates in accord with God’s ordained power, and so relative to God’s ordained power, our actions are indeed compelled; however, because of Bradwardine’s appeal to the distinction in power, he is able to maintain that our actions remain free relative to God’s absolute power, and are thus free, absolutely speaking. This solution is, I argue, unique to Bradwardine, although it seems to be abandoned in his later writing. Bradwardine’s approach to the problem is heavily influenced by three figures in particular — Boethius, Anselm of Canterbury, and John Duns Scotus — each of whose solutions I discuss in some detail. Furthermore, Bradwardine explicitly places his own solution in opposition to that of William Ockham, and so I give substantial attention to examining Ockham’s position. But while I agree with Bradwardine’s assessment that Ockham’s position undermines God’s foreknowledge in ways that should be untenable to someone of 14th-century Christian commitments, I argue that Bradwardine’s solution amounts to an equally untenable determinism. An appendix contains excerpts from my own English translation of the De futuris contingentibus (the first into any modern language), in parallel with the original Latin