Deduction Quotes
I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary -- being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived.
George Boole
In every science, after having analysed the ideas, expressing the more complicated by means of the more simple, one finds a certain number that cannot be reduced among them, and that one can define no further. These are the primitive ideas of the science; it is necessary to acquire them through experience, or through induction; it is impossible to explain them by deduction.
Giuseppe Peano
You can't remember sex. You can remember the fact of it, and recall the setting, and even the details, but the sex of the sex cannot be remembered, the substantive truth of it, it is by nature self-erasing, you can remember its anatomy and be left with a judgment as to the degree of your liking of it, but whatever it is as a splurge of being, as a loss, as a charge of the conviction of love stopping your heart like your execution, there is no memory of it in the brain, only the deduction that it happened and that time passed, leaving you with a silhouette that you want to fill in again.
E. L. Doctorow
But much more vicious than these cases is the majority of foreign correspondents who never have to be placed against the wall, who are never told what to write and how to write it, but who know from contact with the great minds of the press lords or from the simple deduction that the bosses are in big business and the news must be slanted accordingly, or from the general intangible atmosphere which prevails everywhere, what they can do and what they must never do. The most stupid boast in the history of present-day journalism is that of the writer who says, "I have never been given orders; I am free to do as I like."
George Seldes
![Having red several of your books, I wonder if you [ Rudolf Steiner, the German founder of anthroposophy] could find the time to read my brochure 'Le Néo-Plasticisme', which I am closing. I believe that Neo-Plasticism is the art of the foreseeable future for all true anthroposophists and theosophists. Neo-Plasticism creates harmony through the equivalence of the two extremes: the universal and the individual. The former by 'revelation', the latter by 'deduction'... It was impossible to bring about an equilibrium of relationships other than by destroying the 'form', and replacing it by a new 'universal' expressive means. (Piet Mondrian)](https://cdn.quotesdtb.com/img/quotes_images_webp/94/piet-mondrian-anthroposophy-art-453294.webp)
In deduction the mind is under the dominion of a habit or association by virtue of which a general idea suggests in each case a corresponding reaction. This is the way the hind legs of a frog separated from the rest of the body, reason, when you pinch them. It is the lowest form of psychical manifestation.
Charles Sanders Peirce
Experience has convinced me that the proper way of teaching is to bring together that which is simple from all quarters, and, if I may use such a phrase, to draw upon the surface of the subject a proper mean between the line of closest connexion and the line of easiest deduction. This was the method followed by Euclid, who, fortunately for us, never dreamed of a geometry of triangles, as distinguished from a geometry of circles, or a separate application of the arithmetics of addition and subtraction; but made one help out the other as he best could.
Augustus De Morgan
I cannot see why it is necessary that every deduction from algebra should be bound to certain conventions incident to an earlier stage of mathematical learning, even supposing them to have been consistently used up to the point in question. I should not care if any one thought this treatise unalgebraical, but should only ask whether the premises were admissible and the conclusions logical.
Augustus De Morgan
Physical science comes nearest to that complete system of exact knowledge which all sciences have before them as an ideal. Some fall far short of it. The physicist who inveighs against the lack of coherence and the indefiniteness of theological theories, will probably speak not much less harshly of the theories of biology and psychology. They also fail to come up to his standard of methodology. On the other side of him stands an even superior being - the pure mathematician - who has no high opinion of the methods of deduction used in physics, and does not hide his disapproval of the laxity of what is accepted as proof in physical science. And yet somehow knowledge grows in all these branches. Wherever a way opens we are impelled to seek by the only methods that can be devised for that particular opening, not over-rating the security of our finding, but conscious that in this activity of mind we are obeying the light that is in our nature.
Arthur Eddington
In the original discovery of a proposition of practical utility, by deduction from general principles and from experimental data, a complex algebraical investigation is often not merely useful, but indispensable; but in expounding such a proposition as a part of practical science, and applying it to practical purposes, simplicity is of the importance:-and... the more thoroughly a scientific man has studied higher mathematics, the more fully does he become aware of this truth-and... the better qualified does he become to free the exposition and application of principles from mathematical intricacy.
William John Macquorn Rankine
7. The basis of correct knowledge is correct perception, correct deduction and correct witness (or accurate evidence).
One of the most revolutionary realizations to which the occult student has to adjust himself is the appreciation that the mind is a means whereby knowledge is to be gained...
Alice Bailey
"I exist" does not follow from "there is a thought now." The fact that a thought occurs at a given moment does not entail that any other thought has occurred at any other moment, still less that there has occurred a series of thoughts sufficient to constitute a single self. As Hume conclusively showed, no one event intrinsically points to any other. We infer the existence of events which we are not actually observing, with the help of general principle. But these principles must be obtained inductively. By mere deduction from what is immediately given we cannot advance a single step beyond. And, consequently, any attempt to base a deductive system on propositions which describe what is immediately given is bound to be a failure.
Alfred Jules Ayer
So much of modern mathematical work is obviously on the border-line of logic, so much of modern logic is symbolic and formal, that the very close relationship of logic and mathematics has become obvious to every instructed student. The proof of their identity is, of course, a matter of detail: starting with premisses which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right. If there are still those who do not admit the identity of logic and mathematics, we may challenge them to indicate at what point, in the successive definitions and deductions of Principia Mathematica, they consider that logic ends and mathematics begins. It will then be obvious that any answer must be quite arbitrary.
Bertrand Russell
