Looking way back, I noticed some references to Rosens work on Hegel. If this indicates a familiarity with what you could call the circle from which Rosen came, then I want to ask about Jacob Klein. In his famous book on Mathematics, Klein suggests that the comprehensibility of symbolic logic (first developed by Frege but postulated by Descartes as the analytic art) depends on the ontological underpinnings of modern algebra. For Klein, these underpinnings include a radically different understanding of what a number is (compared to the Greeks), and, what is the condition for that, a different outlook on the relationship between the mind and the world. Specifically, Klein suggests that whereas for the ancient philosophers the mind is nothing other than the reception of the world through human speech, for the modern philosophers the mind and world are radically separated entities. This makes possible the belief that the truth of things is written in mathematical figures, not in words. It also gives rise to the notion of concepts, such that a concept is both an object of thought produced by the intellect and also that alone which can be truly known. However, the intellect cannot grasp its concepts in their purely ideal state: they remain too abstract to be operated on by thought. And so, suggests Klein, the concept of multitude in general, for example, only gets realized when it is put into a visible letter sign, like a. Thus the variable does not just represent the possibility of any number whatsoever. Rather, it is a concept in image form. And so Klein suggests that symbolic logic, which on his view is the outgrowth of modern algebra, is built on the idea that the proper expression of human thought lies not in speech but, to come full circle, in images that are inseparable from concepts, namely, symbols proper (ordinary language is not symbolic). All this being tossed out there, does anyone have any thoughts on the philosophic and historical foundation of logic as we know it today? Klein wants to argue that if we dont see the difference between Plato and Aristotle, and then ultimately between them and Descartes (where Kant is considered as furthering Descartes initial project), we will fail to understand logic (among other things) as it is known today.
Posted on: Sun, 11 Jan 2015 16:39:35 +0000
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