Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond

Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory. Robinson's hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, Robinson regards Berkeley's criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley's criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz's infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz's defense of infinitesimals is more firmly grounded than Berkeley's criticism thereof. We show, moreover, that Leibniz's system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz's strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity.Comment: 69 pages, 3 figure

Are Counterpossibles Epistemic?

It has been suggested that intuitions supporting the nonvacuity of counterpossibles can be explained by distinguishing an epistemic and a metaphysical reading of counterfactuals. Such an explanation must answer why we tend to neglect the distinction of the two readings. By way of an answer, I offer a generalized pattern for explaining nonvacuity intuitions by a stand-and-fall relationship to certain indicative conditionals. Then, I present reasons for doubting the proposal: nonvacuists can use the epistemic reading to turn the table against vacuists, telling apart significant from spurious intuitions. Moreover, our intuitions tend to survive even if we clear-headedly intend a metaphysical reading

G. W. Leibniz, Interrelations between Mathematics and Philosophy

Drawing on the extensive number of letters and papers published in recent years, the volume investigates the interconnections between mathematics and philosophy in Leibniz's thought

G. W. Leibniz, Interrelations between Mathematics and Philosophy

Drawing on the extensive number of letters and papers published in recent years, the volume investigates the interconnections between mathematics and philosophy in Leibniz's thought

On the mechanism for plasma hydrogenation of graphene

This article discusses the mechanism for plasma hydrogenation of graphene

Gastrin Antibodies: Induction, Demonstration, and Specificity

Antibodies to the antral hormone gastrin have been induced in the rabbit and detected by passive hemagglutination. Specificity of the antibody, as determined by three methods, is directed to gastrins I and II, gastrin pentapeptide, and gastrin tetrapeptide, as well as to the stage-1 gastrin used for immunization