A Quote by Immanuel Kant
I assert that, in any particular natural science, one encounters genuine scientific substance only to the extent that mathematics is present.
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A number of aspects of mathematics are not much talked about in contemporary histories of mathematics. We have in mind business and commerce, war, number mysticism, astrology, and religion. In some instances, writers, hoping to assert for mathematics a noble parentage and a pure scientific experience, have turned away their eyes. Histories have been eager to put the case for science, but the Handmaiden of the Sciences has lived a far more raffish and interesting life than her historians allow.
It is one thing to say that science is only equipped to test for natural causes and cannot speak to any others. It is quite another to insist that science proves that no other causes could possibly exist. . . . There would be no experimental model for testing the statement: 'No supernatural cause for any natural phenomenon is possible.' It is therefore a philosophical presupposition and not a scientific finding.
An important tradition within westren philosophy believes in the primacy of natural science as a guide to truth. This is sometimes met with the charge that such an allegiance amounts to scientism - the view that the only things that really exist are those recognized by fundamental physical theory, and that the only forms of genuine knowledge are scientific ones.
If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.
Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.
The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. . . . Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.
The confidence in the unlimited power of science is only too often based on a false belief that the scientific method consists in the application of a ready-made technique, or in imitating the form rather than the substance of scientific procedure, as if one needed only to follow some cooking recipes to solve all social problems. It sometimes almost seems as if the techniques of science were more easily learnt than the thinking that shows us what the problems are and how to approach them.
Communication of science as subject-matter has so far outrun in education the construction of a scientific habit of mind that to some extent the natural common sense of mankind has been interfered with to its detriment.
Particular facts are never scientific; only generalization can establish science.
Mathematics never reveals man to the degree, never expresses him in the way, that any other field of human endeavour does: the extent of the negation of man's corporeal self that mathematics achieves cannot be compared with anything. Whoever is interested in this subject I refer to my articles. Here I will say only that the world injected its patterns into human language at the very inception of that language; mathematics sleeps in every utterance, and can only be discovered, never invented.
Statistics is, or should be, about scientific investigation and how to do it better, but many statisticians believe it is a branch of mathematics. Now I agree that the physicist, the chemist, the engineer, and the statistician can never know too much mathematics, but their objectives should be better physics, better chemistry, better engineering, and in the case of statistics, better scientific investigation. Whether in any given study this implies more or less mathematics is incidental.
Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and mathematics that a more apt definition became fully evident: mathematics is the science of patterns.
In fact, the answer to the question "What is mathematics?" has changed several times during the course of history... It was only in the last twenty years or so that a definition of mathematics emerged on which most mathematicians agree: mathematics is the science of patterns.
All the sciences have a relation, greater or less, to human nature; and...however wide any of them may seem to run from it, they still return back by one passage or another. Even Mathematics, Natural Philosophy, and Natural Religion, are in some measure dependent on the science of MAN; since they lie under the cognizance of men, and are judged of by their powers and faculties.
The significance of the vast Islamic scientific tradition for Muslims and especially for young Muslims today is not only that it gives them a sense of pride in their own civilization because of the prestige that science fhas in the present day world. It is furthermore a testament to the way Islam was able to cultivate various sciences extensively without becoming alienated from the Islamic world view and without creating a science whose application would destroy the world of nature and the harmony that must exist between man and the natural environment.
The 'medical examination' to which abductees are said to be subjected, often accompanied by sadistic sexual manipulation, is reminiscient of the medieval tales of encounters with demons. It makes no sense in a sophisticated or technical framework: any intelligent being equipped with the scientific marvels that UFOs possess would be in a position to achieve any of these alleged scientific objectives in a shorter time and with fewer risks.
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