In his posthumous book from 1914, "New foundations of logic, arithmetic and set theory", Julius Konig develops his philosophy of mathematics. In a previous contribution, we attracted attention on the positive part (his truth and falsehood predicates being excluded) of his "pure logic": his "isology" being assimilated to mutual implication, it constitutes a genuine formalization of positive intuitionistic logic. Konig's intention was to rebuild logic in such a way that the excluded third's principle could no longer be logical. However, (...) his treatment of truth and falsehood (boiling down to negation) is purely classical. We explain here this discrepancy by the choice of the alleged more primitive notions to which the questioned notions of truth and falsehood have been reduced. Finaly, it turns out that the disjunctive and conjunctive forms of the principles of the excluded third and of contradiction have effectively been excluded, but none of their implicative forms. (shrink)
This paper dates from about 1994: I rediscovered it on my hard drive in the spring of 2002. It represents an early attempt to explore the connections between the Julius Caesar problem and Frege's attitude towards Basic Law V. Most of the issues discussed here are ones treated rather differently in my more recent papers "The Julius Caesar Objection" and "Grundgesetze der Arithmetik I 10". But the treatment here is more accessible, in many ways, providing more context and (...) a better sense of how this issue relates to broader issues in Frege's philosophy. (shrink)
This paper examines the theories of the soul proposed by Girolamo Cardano in his De immortalitate animorum (1545) and his De subtilitate (1550-4), Julius Caesar Scaliger's comprehensive critique of these views in the Exercitationes exotericae de subtilitate of 1557, and Cardano's reply to this critique in his Actio in calumniatorem of 1559. Cardano argues that the passive intellect is individuated and mortal, and that the agent intellect is immortal but subject to constant reincarnation in different human beings. His theory (...) of cognition leads him to claim that at its highest level, the intellect is converted into the object of its perception. In his refutation of the various elements of Cardano's theories, Scaliger uses his knowledge of the Greek text of Aristotle to stress the reflexive faculty of the soul, its ability to conceive of objects greater than itself, and its status as the individuating principle of the hylemorphic human being. In spite of Cardano's pretention to novelty and Scaliger's humanist credentials, both thinkers are shown to conduct their discussions in an inherited scholastic matrix of thought. (shrink)
This paper investigates the relationship between some corpuscularian and Aristotelian strands that run through the thought of the sixteenth-century philosopher and physician Julius Caesar Scaliger. Scaliger often uses the concepts of corpuscles, pores, and vacuum. At the same time, he also describes mixture as involving the fusion of particles into a continuous body. The paper explores how Scaliger’s combination of corpuscularian and non-corpuscularian views is shaped, in substantial aspects, by his response to the views on corpuscles and the vacuum (...) in the work of his contemporary, Girolamo Fracastoro. Fracastoro frequently appears in Scaliger’s work as an opponent against whom numerous objections are directed. However, if one follows up Scaliger’s references, it soon becomes clear that Scaliger also shares some of Fracastoro’s views. Like Scaliger, Fracastoro suggests corpuscularian explanations of phenomena such as water rising in lime while at the same time ascribing some non-corpuscularian properties to his natural minima. Like Scaliger, Fracastoro maintains that there is no vacuum devoid of bodies since places cannot exist independently of bodies (although their opinions diverge regarding how exactly the relevant dependency relation might be explicated). Finally, like Scaliger, Fracastoro connects a continuum view of mixture with a theory of natural minima. (shrink)
Julius König is famous for his mistaken attempt to demonstrate that the continuum hypothesis was false. It is also known that the only positive result that could have survived from his proof is the paradox which bears his name. Less famous is his 1914 book Neue Grundlagen der Logik, Arithmetik und Mengenlehre. Still, it contains original contributions to logic, like the concept of metatheory and the solution of paradoxes based on the refusal of the law of bivalence. We are (...) going to discover them by analysing the content of the book. (shrink)
1. Some twenty years ago I voiced reservations about John McDowell’s embrace of a spatial metaphor, whereby we should expand our idea of the ‘space’ occupied by the mind, locating its boundaries far outside the skin, way into the world.1 I thought at the time that the spatial metaphor was a flourish McDowell had been betrayed into, particularly by some of the terminology of his dispute with Dummett over ‘manifestation’. But over the years it began to be clear that it (...) was more than that, being one of several metaphors that figure centrally in his extensive and influential meditations on the relationship between ourselves and our world. Indeed, the best thumbnail description of his aim would be to show that the world is not ‘blankly external’ to the mind, and this description uses the metaphor. So the reservation went unheeded, and years later the metaphor and its cousins occupied large parts of Mind and World, which is the principal text which I shall consider, although they liberally sprinkle other writings as well. I shall use this opportunity to try to sensitize others to my reasons for discomfort. (shrink)
In this essay, we explore a fresh avenue into mind-body dualism by considering a seemingly distant question posed by Frege: "Why is it absurd to suppose that Julius Caesar is a number?". The essay falls into three main parts. In the first, through an exploration of Frege’s Julius Caesar problem, we attempt to expose two maxims applicable to the mind-body problem. In the second part, we draw on those maxims in arguing that “full blown dualism” is preferable to (...) more modest, property-theoretic, versions. Finally, in the third part we close by suggesting that full blown dualism need not be spooky, resurrecting a broadly Lockean, rather than Cartesian, metaphysical picture. (shrink)
This paper argues that that Caesar problem had a technical aspect, namely, that it threatened to make it impossible to prove, in the way Frege wanted, that there are infinitely many numbers. It then offers a solution to the problem, one that shows Frege did not really need the claim that "numbers are objects", not if that claim is intended in a form that forces the Caesar problem upon us.