Augustus De Morgan - A Budget of Paradoxes

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Wrong hypotheses, rightly worked from, have produced more useful results than unguided observations.

Augustus De Morgan
I had expressed my wish to have a thermometer of probability, with impossibility at one end, as 2 plus 2 makes 5, and necessity at the other as 2 plus 2 make 4.

Augustus De Morgan
There are no limits in mathematics, and those that assert there are, are infinite ruffians, ignorant, lying blackguards. There is no differential calculus, no Taylor's theorem, no calculus of variations, &c... in mathematics. There is no quackery whatever in mathematics.

Augustus De Morgan
Madmen reason rightly upon wrong premises: Mr. Smith [a circle squarer] reasons wrongly upon no premises at all.

Augustus De Morgan
Would Mathematicals — forsooth — If true, have failed to prove truth? Would not they — if they could — submit Some overwhelming proofs of it?

Augustus De Morgan
Let him also say what this mysterious 3.14159...really is, which comes in at every door and window, and down every chimney, calling itself the circumference to a unit of diameter.

Augustus De Morgan
My opinion of mankind is founded upon the mournful fact that, so far as I can see, they find within themselves the means of believing in a thousand times as much as there is to believe in.

Augustus De Morgan
Proof requires a person who can give and a person who can receive.

Augustus De Morgan
Great discoveries are always laughed at: but it is very often not the laugh of incredulity; it is a mode of distorting the sense of inferiority into a sense of superiority, or a mimicry of superiority interposed between the laughter and his feeling of inferiority.

Augustus De Morgan
A person of small knowledge is in danger of trying to make his little do the work of more; but a person without any is in more danger of making his no knowledge do the work of some.

Augustus De Morgan
The pseudomath is a person who handles mathematics as the monkey handled the razor.

Augustus De Morgan
Astronomers! What can avail Those who calumniate us; Experiment can never fail With such an apparatus.

Augustus De Morgan
I will not, from henceforward, talk to any squarer of the circle, trisector of the angle, duplicator of the cube, constructor of perpetual motion, subverter of gravitation, stagnator of the earth, builder of the universe, etc.

Augustus De Morgan
The history of the intellectual world is the history of the worship of one idol after another.

Augustus De Morgan
Mysterious 3.14159...comes in at every door and window, and down every chimney.

Augustus De Morgan
Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn have, greater fleas to go on;
While these again have greater still, and greater still, and so on.

Augustus De Morgan
During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical.

Augustus De Morgan
The gambling reasoner is incorrigible; if he would but take to the squaring of the circle, what a load of misery would be saved.

Augustus De Morgan
The manner in which a paradoxer will show himself, as to sense or nonsense, will not depend upon what he maintains, but upon whether he has or has not made a sufficient knowledge of what has been done by others, especially as to the mode of doing it, a preliminary to inventing knowledge for himself.

Augustus De Morgan
Aspiring to lead others, they have never given themselves the fair chance of being first led by other others into something better than they can start for themselves; and that they should first do this is what both those classes of others have a fair right to expect. New knowledge... must come by contemplation of old knowledge... mechanical contrivance sometimes, not very often, escapes this rule.

Augustus De Morgan
All the men who are now called discoverers, in every matter ruled by thought, have been men versed in the minds of their predecessors, and learned in what had been before them. There is not one exception. I do not say that every man has made direct acquaintance with the whole of his mental ancestry... But... it is remarkable how many of the greatest names in all departments of knowledge have been real antiquaries in their several subjects.
I may cite among those... in science, Aristotle, Plato, Ptolemy, Euclid, Archimedes, Roger Bacon, Copernicus, Francis Bacon, Ramus, Tycho Brahe, Galileo, Napier, Descartes, Leibnitz, Newton, Locke.

Augustus De Morgan
Spinoza's Philosophia Scripturæ Interpres, Exercitatio Paradoxa, printed anonymously... is properly paradox, though also heterodox. It supposes, contrary to all opinion, orthodox and heterodox, that philosophy can... explain the Athanasian doctrine so as to be at least compatible with orthodoxy. The author would stand almost alone, if not quite; and this is what he meant.

Augustus De Morgan
In every age of the world there has been an established system, which has been opposed from time to time by isolated and dissentient reformers. The established system has sometimes fallen, slowly and gradually: it has either been upset by the rising influence of some one man, or it has been sapped by gradual change of opinion in the many.

Augustus De Morgan