A Quote by Aristotle

We cannot ... prove geometrical truths by arithmetic.

Aristotle

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Arithmetic Cannot Prove Truths We Cannot

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Aristotle
Greek - Philosopher
384 BC - 322 BC

We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.

Hans Reichenbach

The higher arithmetic presents us with an inexhaustible store of interesting truths - of truths, too, which are not isolated, but stand in a close internal connection, and between which, as our knowledge increases, we are continually discovering new and sometimes wholly unexpected ties.

Carl Friedrich Gauss

There are truths, that are beyond us, transcendent truths, about beauty, truth, honor, etc. There are truths that man knows exist, but they cannot be seen - they are immaterial, but no less real, to us. It is only through the language of myth that we can speak of these truths.

J. R. R. Tolkien

Pure geometrical regularity gives a certain pleasure to men troubled by the obscurity of outside appearance. The geometrical line is something absolutely distinct from the messiness, the confusion, and the accidental details of existing things.

T. E. Hulme

In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.

Jean-Victor Poncelet

Experience alone cannot deliver to us necessary truths; truths completely demonstrated by reason. Its conclusions are particular, not universal.

John Dewey

Beauty cannot be defined by abscissas and ordinates; neither are circles and ellipses created by their geometrical formulas.

Carl von Clausewitz

...to characterize the import of pure geometry, we might use the standard form of a movie-disclaimer: No portrayal of the characteristics of geometrical figures or of the spatial properties of relationships of actual bodies is intended, and any similarities between the primitive concepts and their customary geometrical connotations are purely coincidental.

Carl Gustav Hempel

There are several kinds of truths, and it is customary to place in the first order mathematical truths, which are, however, only truths of definition. These definitions rest upon simple, but abstract, suppositions, and all truths in this category are only constructed, but abstract, consequences of these definitions ... Physical truths, to the contrary, are in no way arbitrary, and do not depend on us.

Georges-Louis Leclerc, Comte de Buffon

There are different kinds of truths for different kinds of people. There are truths appropriate for children; truths that are appropriate for students; truths that are appropriate for educated adults; and truths that are appropriate for highly educated adults, and the notion that there should be one set of truths available to everyone is a modern democratic fallacy. It doesn't work.

Irving Kristol

As a philosopher, if I were speaking to a purely philosophic audience I should say that I ought to describe myself as an Agnostic, because I do not think that there is a conclusive argument by which one can prove that there is not a God. On the other hand, if I am to convey the right impression to the ordinary man in the street I think that I ought to say that I am an Atheist, because, when I say that I cannot prove that there is not a God, I ought to add equally that I cannot prove that there are not the Homeric gods.

Bertrand Russell

You can either have software quality or you can have pointer arithmetic, but you cannot have both at the same time.

Bertrand Meyer

There are no whole truths: all truths are half-truths. It is trying to treat them as whole truths that plays to the devil.

Alfred North Whitehead

The trouble about man is twofold. He cannot learn truths which are too complicated; he forgets truths which are too simple.

Rebecca West

To parents who despair because their children are unable to master the first problems in arithmetic I can dedicate my examples. For, in arithmetic, until the seventh grade I was last or nearly last.

Jacques Hadamard

God exists because arithmetic is consistent - the Devil exists because we can't prove it!

Hermann Weyl

A Quote by Aristotle

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