Mathematics, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the saf… - Immanuel Kant

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Mathematics, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of science. But it must not be supposed that it was as easy for mathematics as for logic, in which reason is concerned with itself alone, to find, or rather to make for itself that royal road. I believe, on the contrary, that there was a long period of tentative work (chiefly still among the Egyptians), and that the change is to be ascribed to a revolution, produced by the happy thought of a single man, whose experiments pointed unmistakably to the path that had to be followed, and opened and traced out for the most distant times the safe way of a science. The history of that intellectual revolution, which was far more important than the passage round the celebrated Cape of Good Hope, and the name of its fortunate author, have not been preserved to us. ... A new light flashed on the first man who demonstrated the properties of the isosceles triangle (whether his name was Thales or any other name), for he found that he had not to investigate what he saw hi the figure, or the mere concepts of that figure, and thus to learn its properties; but that he had to produce (by construction) what he had himself, according to concepts a priori, placed into that figure and represented in it, so that, in order to know anything with certainty a priori, he must not attribute to that figure anything beyond what necessarily follows from what he has himself placed into it, in accordance with the concept.

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About Immanuel Kant

Immanuel Kant (22 April 1724 – 12 February 1804), born Emanuel Kant, was a German philosopher.

Biography information from Wikiquote

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Alternative Names: Kant Emanuel Kant
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Additional quotes by Immanuel Kant

"Even as to himself, a man cannot pretend to know what he is in himself from the knowledge he has by internal sensation. For as he does not as it were create himself, and does not come by the conception of himself a priori but empirically, it naturally follows that he can obtain his knowledge even of himself only by the inner sense, and consequently only through the appearances of his nature and the way in which his consciousness is affected. At the same time, beyond these characteristics of his own subject, made up of mere appearances, he must necessarily suppose something else as their basis, namely, his ego, whatever its characteristics in itself may be... Now man really finds in himself a faculty by which he distinguishes himself from everything else, even from himself as affected by objects, and that is reason. This being pure spontaneity is even elevated above the understanding. For although the latter is a spontaneity and does not, like sense, merely contain intuitions that arise when we are affected by things (and are therefore passive), yet it cannot produce from its activity any other conceptions than those which merely serve to bring the intuitions of sense under rules, and thereby to unite them in one consciousness, and without this use of the sensibility it could not think at all; whereas, on the contrary, reason shows so pure a spontaneity in the case of what I call "ideas" [Ideal Conceptions] that it thereby far transcends everything that the sensibility can give it, and exhibits its most important function in distinguishing the world of sense from that of understanding, and thereby prescribing the limits of the understanding itself."

We have now completely before us one part of the solution of the grand general problem of transcendental philosophy, namely, the question — How are synthetical propositions a priori possible? That is to say, we have shown that we are in possession of pure a priori intuitions, namely, space and time, in which we find, when in a judgement a priori we pass out beyond the given conception, something which is not discoverable in that conception, but is certainly found a priori in the intuition which corresponds to the conception, and can be united synthetically with it. But the judgements which these pure intuitions enable us to make, never reach farther than to objects of the senses, and are valid only for objects of possible experience.

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