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From Wikipedia article on Critique of Pure Reason:
1. Synthetic judgments add something to a concept, (e.g. an observation, like all objects are heavy) whereas analytic judgments only explain what is already contained in the concept (e.g. all objects are experienced by a subject.)
2. For Kant, mathematics is a priori synthetic judgment. For example, Kant uses the classical example of 7 + 5 = 12.
The science of all the principles of sensibility a priori, I call transcendental aesthetic.* There must, then, be such a science forming the first part of the transcendental doctrine of elements, in contradistinction to that part which contains the principles of pure thought, and which is called transcendental logic.
From the Wikipedia article on Critique of Pure Reason: Transcendental Aesthetic and the Transcendental Logic, (reflect) his basic distinction between sensibility and the understanding.
that is, regards the object as a mere phenomenon. In reference to this subject, see the remark in Section I (SS 4)
At page 53 of "Basic Writings of Kant" in F. Max Muller translation in "Basic Writings of Kant" edited by Allen Wood. The upcoming text was skipped in the Muller translation through the highlighting on page 50 in this translation.
Against this theory, which grants empirical reality to time, but denies to it absolute and transcendental reality, I have heard from intelligent men an objection so unanimously urged that I conclude that it must naturally present itself to every reader to whom these considerations are novel. It runs thus: "Changes are real" (this the continual change in our own representations demonstrates, even though the existence of all external phenomena, together with their changes, is denied). Now, changes are only possible in time, and therefore time must be something real. But there is no difficulty in
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Highlighting from here down through the highlighting pn page 50 means the text is skipped in the F. Max Muller translation in "Basic Writings of Kant" edited by Allen Wood.
BOOK I. SS 2. Analytic of Conceptions. By the term Analytic of Conceptions, I do not understand the analysis of these, or the usual process in philosophical investigations of dissecting the conceptions which present themselves, according to their content, and so making them clear; but I mean the hitherto little attempted dissection of the faculty of understanding itself, in order to investigate the possibility of conceptions a priori, by looking for them in the understanding alone, as their birthplace, and analysing the pure use of this faculty. For this is the proper duty of a transcendental
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A remark which will be explained in the sequel.]
relates to
BOOK II.
The three modi of time are permanence, succession, and coexistence.