Augustus De Morgan: Quotes about knowledge

“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

Introductory p.2
A Budget of Paradoxes (1872)

Mathematics , Knowledge

“My specific… object has been to contain, within the prescribed limits, the whole of the student's course, from the confines of elementary algebra and trigonometry, to the entrance of the highest works on mathematical physics. A learner who has a good knowledge of the subjects just named, and who can master the present treatise, taking up elementary works on conic sections, application of algebra to geometry, and the theory of equations, as he wants them, will, I am perfectly sure, find himself able to conquer the difficulties of anything he may meet with; and need not close any book of Laplace, Lagrange, Legendre, Poisson, Fourier, Cauchy, Gauss, Abel, Hindenburgh and his followers. or of any one of our English mathematicians, under the idea that it is too hard for him.”

Augustus De Morgan

Preface, p. iii
The Differential and Integral Calculus (1836)

Books , Mathematics , Idea , Knowledge

“I… subjoin references to those parts of the work for which I have not been indebted to my knowledge of what has been written before me: much of what is cited is probably not new, indeed it is dangerous for any one at the present day to claim anything as belonging to himself; several things which I once thought to have entered in this list have been since found (either by myself, or by a friend to whom I referred it) in preceding writers.”

Augustus De Morgan

Preface, p. v
The Differential and Integral Calculus (1836)

Knowledge , Parting

“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 acquantance 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

A Budget of Paradoxes (1872)

Men , Knowledge , Learning , Science

“In order to see the difference which exists between… studies,—for instance, history and geometry, it will be useful to ask how we come by knowledge in each. Suppose, for example, we feel certain of a fact related in history… if we apply the notions of evidence which every-day experience justifies us in entertaining, we feel that the improbability of the contrary compels us to take refuge in the belief of the fact; and, if we allow that there is still a possibility of its falsehood, it is because this supposition does not involve absolute absurdity, but only extreme improbability.
In mathematics the case is wholly different… and the difference consists in this—that, instead of showing the contrary of the proposition asserted to be only improbable, it proves it at once to be absurd and impossible. This is done by showing that the contrary of the proposition which is asserted is in direct contradiction to some extremely evident fact, of the truth of which our eyes and hands convince us. In geometry, of the principles alluded to, those which are most commonly used are—
I. If a magnitude is divided into parts, the whole is greater than either of those parts.
II. Two straight lines cannot inclose a space.
III. Through one point only one straight line can be drawn, which never meets another straight line, or which is parallel to it.
It is on such principles as these that the whole of geometry is founded, and the demonstration of every proposition consists in proving the contrary of it to be inconsistent with one of these.”

Augustus De Morgan

Source: On the Study and Difficulties of Mathematics (1831), Ch. I.

Truth , Feeling , History , Mathematics

“There is a mistake into which several have fallen, and have deceived others, and perhaps themselves, by clothing some false reasoning in what they called a mathematical dress, imagining that by the application of mathematical symbols to their subject, they secured mathematical argument. This could not have happened if they had possessed a knowledge of the bounds within which the empire of mathematics is contained. That empire is sufficiently wide, and might have been better known, had the time which has been wasted in aggressions upon the domains of others, been spent in exploring the immense tracts which are yet untrodden.”

Augustus De Morgan

Source: On the Study and Difficulties of Mathematics (1831), Ch. I.

Imagination , Mathematics , Knowledge , Time

“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

Introductory p.4
A Budget of Paradoxes (1872)

Knowledge , Sense , Dependency

“All existing things upon this earth, which have knowledge of their own existence, possess, some in one degree and some in another, the power of thought, accompanied by perception, which is the awakening of thought by the effects of external objects upon the senses.”

Augustus De Morgan

Formal Logic (1847)

Knowledge , Sense

“The absolute requisites for the study of this work… are a knowledge of algebra to the binomial at least, plane and solid geometry, plane trigonometry, and the most simple part of the usual applications of algebra to geometry.
…A. De Morgan. London July 1, 1836”

Augustus De Morgan

The Differential and Integral Calculus (1836)

Knowledge , Study , Parting

“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

Introductory p.5
A Budget of Paradoxes (1872)

Knowledge , Chance