more from this thinker | more from this text
Full Idea
Ancient mathematical concepts were essentially sensory; they were not mathematical in our sense - that is, wholly constituted by their inferential potential.
Gist of Idea
Greek mathematics is wholly sensory, where ours is wholly inferential
Source
Danielle Macbeth (Pragmatism and Objective Truth [2007], p.187)
Book Ref
'New Pragmatists', ed/tr. Misak,Cheryl [OUP 2009], p.187
A Reaction
The latter view is Frege's, though I suppose it had been emerging for a couple of centuries before him. I like the Greek approach, and would love to see that reunited with the supposedly quite different modern view. (Keith Hossack is attempting it).
| 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] |