"[W]hile we put number into objects, on the other hand we derive our idea of number only from the presence of the world external to the mind. We see a group of people, and we begin by making an abstraction ("people"), and we say, "Here are ten people"—thus calling them all by the one abstract name, even though the individuals be very different. "A careful observation shows us, however, that there are no objects exactly alike; but by a mental operation of which we are quite unconscious, although it holds within itself the entire secret of mathematical abstraction, we take in objects which seem to be alike, rejecting for the time being their differences. Here is to be found the source of calculation." So the idea of number is generated in the mind by the sense perception of a group of things supposed to be alike."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
David Eugene Smith, The Teaching of Elementary Mathematics (1904) p. 100, and quoting , La mathématique: Philosophie-Enseignement (1898) p. 15.
https://en.wikiquote.org/wiki/Abstraction_(mathematics)
Revision History
No revisions have been submitted for this quote.
Categories
Abstraction (mathematics)
12 quotes on TrueQuotesView all quotes by Abstraction (mathematics) →
Related Quotes
"[M]ental Abstraction... is not [only the] Property of Mathematics, but is common to all Sciences. For every Science c…"
"They who are acquainted with the present state of the theory of Symbolical Algebra, are aware that the validity of th…"
"The chemist, in describing some mineral, may present all its attributes, color mass, density, volume, molecular const…"
"Change of state involves what is meant by the word "time," which, like space, is a necessary condition for thought, o…"
"Geometry can in no way be viewed... as a branch of mathematics, instead, geometry relates to something already given …"
"Abstraction is the immediate ulterior result of analysis. We may speak of the analysis of the mathematical whole, and…"
"The word element is a term which frequently occurs in philosophy. It signifies any of those parts of an object into w…"
"It was only in the nineteenth century that the winds of change started to blow. First, the introduction of abstract g…"
"Berkeley Bishop of Cloyne was a man of first-rate talents, distinguished as a metaphysician, a philosopher, and a div…"
"Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life ar…"