more from this thinker | more from this text
Full Idea
Of quantities, some are discrete, others continuous. ...Discrete are number and language; continuous are lines, surfaces, bodies, and also, besides these, time and place.
Gist of Idea
Some quantities are discrete, like number, and others continuous, like lines, time and space
Source
Aristotle (Categories [c.331 BCE], 04b20)
Book Ref
Aristotle: 'Categories and De Interpretatione', ed/tr. Ackrill,J.R. [OUP 1963], p.12
A Reaction
This distinction seems to me to be extremely illuminating, when comparing natural numbers with real numbers, and it is the foundation of the Greek view of mathematics.
| 11041 | Some quantities are discrete, like number, and others continuous, like lines, time and space [Aristotle] |
| 17843 | The idea of 'one' is the foundation of number [Aristotle] |
| 17850 | Each many is just ones, and is measured by the one [Aristotle] |
| 17851 | Number is plurality measured by unity [Aristotle] |
| 1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
| 17783 | A number is not a multitude, but a unified ratio between quantities [Newton] |
| 9800 | Arithmetic is based on definitions, and Sums of equals are equal, and Differences of equals are equal [Mill] |
| 14116 | Numbers were once defined on the basis of 1, but neglected infinities and + [Russell] |
| 10205 | Mathematics originally concerned the continuous (geometry) and the discrete (arithmetic) [Shapiro] |
| 19093 | Greek mathematics is wholly sensory, where ours is wholly inferential [Macbeth] |