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We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of exact science are mathematics and logic: the mathe… - Augustus De Morgan
" "We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of exact science are mathematics and logic: the mathematical sect puts out the logical eye, the logical sect puts out the mathematical eye; each believing that it can see better with one eye than with two.
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About Augustus De Morgan
Augustus De Morgan (June 27 1806 – March 18 1871) was an Indian-born British mathematician and logician; he was the first professor of mathematics at University College London. He formulated De Morgan's laws and was the first to introduce the term, and make rigorous the idea of mathematical induction. De Morgan crater on the Moon is named after him.
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Additional quotes by Augustus De Morgan
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.
The following is exactly what we mean by a <small>LIMIT</small>. ...let the several values of x... bea<sub>1</sub> a<sub>2</sub> a<sub>3</sub> a<sub>4</sub>. . . . &c.then if by passing from a<sub>1</sub> to a<sub>2</sub>, from a<sub>2</sub> to a<sub>3</sub>, &c., we continually approach to a certain quantity l [lower case L, for "limit"], so that each of the set differs from l by less than its predecessors; and if, in addition to this, the approach to l is of such a kind, that name any quantity we may, however small, namely z, we shall at last come to a series beginning, say with a<sub>n</sub>, and continuing ad infinitum,a<sub>n</sub> a<sub>n+1</sub> a<sub>n+2</sub>. . . . &c.all the terms of which severally differ from l by less than z: then l is called the limit of x with respect to the supposition in question.
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.
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