The Philosophy of Mathematics (Comte) Quotes
History of mathematics, Mathematics books, Philosophical works, Education
Top Quotes
“Mathematics”
“Auguste Comte”
“History of mathematics”
“Philosophy of mathematics”
“[T]his indirect determination of magnitudes may be indirect in very different degrees.”
“Thus... the concrete part of mathematics is composed of Geometry and Rational Mechanics.”
“The abstract part of mathematics is, then, general in its nature; the concrete part, special.”
“[T]he plural name—"The Mathematics"—would alone suffice to indicate the want of unity in the common conception of it.”
“We see, by this... comparison, how natural and profound is our fundamental division of mathematical science.”
“[I]t is only in inorganic physics, at the most, that we can justly hope ever to obtain that high degree of scientific perfection.”
“Let us... rise from this rough sketch... to a veritable definition, worthy of the importance, the extent, and the difficulty of the science.”
“Every science consists in the co-ordination of facts; if the different observations were entirely isolated, there would be no science.”
“The error of this definition consists in presenting as direct an object which is almost always, on the contrary, very indirect.”
“Their different Natures. These two parts, essentially distinct in their object... are no less so with regard to the nature of the inquiries...”
“Hence the universe, in the statical point of view, presents only geometrical phenomena; and, considered dynamically, only mechanical phenomena.”
“Hence follows the fundamental division of general mathematical science into two great sciences—Abstract Mathematics, and Concrete Mathematics.”
“[T]he final object of the calculus always is to obtain... the values of the unknown quantities by means of those which are known.”
“The abstract part of mathematics is then purely instrumental, and is only an immense and admirable extension of natural logic to a certain class of deductions.”
“According[ly]... the spirit of mathematics consists in... regarding all the quantities which any phenomenon can present, as connected and interwoven...”