This demonstration does far more than establish priorities (which would have been of the least imaginable interest to Klein himself ). It is, in its penetrating meticulousness, an invaluable introduction to Husserl’s definingworks. Moreover, the very closeness of Hopkins’s critical treatment serves to bring out Husserl’s empires i allies hack v 2.1 human probity and philosophical depth, the fundamental well-directedness of his search for the nature of the modern scientific achievement, and the cognitive crisis it has brought in its train.

Certainly in 1966 I had no clear notion of the explanatory force residing in the kind of history sketched out by one man and actually pursued by the other, an enterprise totally different from the crude historicism then quite prevalent in the academy, according to which all the works of thought were simply attributed to the spirit of the times.

I will not preempt Hopkins’s careful delineations of Husserl’s “intentional history,” except to say empires i allies hack v 2.1 that it enjoins on the historian one chief task, that of “desedimentation” and, as Hopkins says, “reactivation.” These terms refer to the scraping away of the accumulated strata of tradition and the reanimating ecollection of the thinking that had been skewed, superseded, and “ruptured” at crucial moments, but had remained embalmed—one might say, semi-consciously preserved—within those modern concepts that are so effective precisely because the burden of their origin is ignored.

It seems to me now a major finding that the revolution in the conceptuality of “number” both marked and characterized the inception of modernity.

I say ‘conceptuality’—as opposed to ‘concept’—advisedly. Such abstract “second-intentional” terminology (see below) was deeply, even passionately repugnant to Klein; it was the personal consequence of his studies. Yet the revolution in question was not about this or that individual notion, but about the mode of concept-formation itself, which is properly called ‘conceptuality’.

The much abused word ‘revolution’ is also in order: Although long in preparation, the new number concept came abruptly upon the world, its prime agent being Vieta (§ 101), its clarifier Descartes (§ 111), and its finalizer Wallis (§ 117). Moreover, number was not only an emblem of the new order of the age, meaning that the way of conceiving that produced it showed up in non-mathematical theorizing, but also perhaps the moderns’ most powerful tool. For it was algebra, the first, powerful fruit of the new conceptualizing, that made analytic natural science possible.

The desedimentation of our concept of empires i allies hack v 2.1 number, while a work of philosophical inquiry, required large scholarly means: the ability to deal directly with sources in ancient and modern languages, because translations tend to the heedless use of merely apparent modern equivalents; some competence in ancient and early modern mathematics, which, though elemenxxiv Preface tary, uses notation that is at once obsolete and significant; and a willingness to let the sources speak for themselves.