Multiple generality has long been known to cause confusion. For example, “Everyone has a donkey that is running” has two readings: either (i) there is a donkey, owned by everyone, and it is running; or (ii) everyone owns some donkey or other, and all such donkeys run. Medieval logicians were acutely aware of such ambiguities, and the logical problems they pose, and sought to sort them out. One of the most ambitious undertakings in this regard is a pair of massive (...) diagrams (magnae figurae) which map out the logical interrelations of two sets of doubly-general forms. These appear in a fourteenth-century MS of John Buridan’s Summulae de Propositionibus. In this paper, I present these diagrams, and determine the truth conditions of their different forms. To that end, I have developed a bespoke system of diagrams to display their truth conditions. As we will see, such forms present significant difficulties for an all-encompassing account of the role form plays in logic. Accordingly, they can tell us important things about the role logical form plays in Buridan’s account of logical foundations. (shrink)

The Oxford Calculator Roger Swyneshed put forward three provocative claims in his treatise on insolubles, written in the early 1330s, of which the second states that there is a formally valid inference with true premises and false conclusion. His example deployed the Liar paradox as the conclusion of the inference: ‘The conclusion of this inference is false, so this conclusion is false’. His account of insolubles supported his claim that the conclusion is false, and so the premise, referring to the (...) conclusion, would seem to be true. But what is his account of validity that can allow true premises to lead to a false conclusion? This article considers Roger’s own account, as well as that of Paul of Venice, writing some sixty years later, whose account of the truth and falsehood of insolubles followed Roger’s closely. Paul endorsed Roger’s three claims. But their accounts of validity were different. The question is whether these accounts are coherent and support Paul’s claim in his Logica Magna that he endorsed all the normal rules of inference. (shrink)

In False Wisdom, Gary H. Merrill develops criteria for distinguishing genuine from pseudo-philosophy, and then applies his criteria to several case studies, including Ayn Rand, all of whom he finds to be pseudo-philosophers. While offering a mostly helpful overview of better and worse ways of doing philosophy, Merrill fails to motivate adequately his way of distinguishing pseudo-philosophy from mere philosophical vices, errors, or failings. He is inconsistent in his characterization of the criteria for pseudo-philosophy and his application of those criteria, (...) harbors a narrow conception of what counts as philosophy, and displays a lack of interpretive charity toward several thinkers. (shrink)

_ Source: _Volume 56, Issue 3-4, pp 222 - 240 In medieval theories of consequence, we encounter several criteria of validity. One of these is known as the containment criterion: a consequence is valid when the consequent is contained or understood in the antecedent. The containment criterion was formulated most frequently in the thirteenth and fourteenth centuries, but it can be found in earlier writings as well. In _The Tradition of the Topics in the Middle Ages_, N.J. Green-Pedersen claimed that (...) this criterion originated with Boethius. In this article, the author shows that a notion of containment is indeed present in Boethius, but is not used to define or describe the relation between antecedent and consequent, i.e., the relation of consequence, as Green-Pedersen asserted. The author then offers two interpretations of the notion of containment that are present in Boethius – a metaphysical and a semantic interpretation – and shows how these relate to the containment criterion. (shrink)

_ Source: _Volume 55, Issue 4, pp 273 - 306 Jan Dullaert was a direct student of John Mair and a teacher of Gaspar Lax, Juan de Celaya, and Juan Luis Vives. His commentary on Aristotle’s _Peri Hermeneias_ addresses the foundations of propositional logic, including a detailed analysis of conditionals and the semantics of logical connectives. Dullaert’s propositional logic is limited to the immediate implications of the semantics of these connectives, i.e., their introduction and elimination rules. In the same context, (...) he discusses several alternative treatments of semantic paradoxes, paying most attention to the approaches derived from Martin Le Maistre and John Mair. (shrink)