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An Introduction To Non-aristotelian Systems And General Semantics.

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Of all men, Aristotle is the one of whom his followers have worshipped his defects as well as his excellencies: which is what he himself never did to any man living or dead; indeed, he has been accused of the contrary
fault. (354)                                                                         AUGUSTUS DE MORGAN
There is one very mportant fact on which we must be in no doubt, and that is that for any given deductive theory there is not any one system of fundamental notions nor any one system of fundamental propositions; there are generally several equally possible, i. e. from which it is equally possible to deduce correctly all the theorems. . . . This fact is very important, because it shows that there are in themselves no undefinable notions nor indemonstrable propositions; they are only so relatively to a certain adopted order, and they cease (at any rate partly) to be such if another order is adopted. This destroys the traditional conception of fundamental ideas an fundamental truths, fundamental, that is to say, absolutely and essentially. <i2o>                                                                         louis couturat
In this direction finality is not sought, for it is apparently unattainable. All that we can say is, in the words of a leading analyst, "sufficient unto the day is the rigor thereof." (23)                                                       e. t. bell
In mathematics it is new ways of looking at old things which seem to be the most prolific sources of far-reaching discoveries. (23)                E. t. bell
The first will show us how to change the language suffices to reveal generalizations not before suspected. (417) _                                   h. poincare
In sum, all the scientist creates in a fact is the language in which he enunciates it. (417)                                                                                        H. POINCARE
This long discussion brings us to the final conclusion that the concrete facts of nature are events exhibiting a certain structure in their mutual relations and certain characters of their own. The aim of science is to express the relations between their characters in terms of the mutual structural relations between the events thus characterised. (573)
We cease to seek resemblances; we devote ourselves above all to the differences, and among the differences are chosen first the most accentuated, not only because they are the most striking, but because they will be the most instructive. (417)                                                               h. poincare
The materialistic theory has all the completeness of the thought of the middle ages, which had a complete answer to everything, be it in heaven or in hell or in nature. There is trimness about it, with its instantaneous