more from this thinker | more from this text
Full Idea
What in the world can be the observed fact, or the physical fact, which is asserted in the definition of the number 777864? ...What a pity that Mill did not also illustrate the physical facts underlying the numbers 0 and 1!
Gist of Idea
What physical facts could underlie 0 or 1, or very large numbers?
Source
comment on John Stuart Mill (System of Logic [1843]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §7
Book Ref
Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.9
A Reaction
I still think patterns could be an empirical foundation for arithmetic, though you still have to grasp the abstract concept of the pattern. An innate capacity to spot resemblance gets you a long way.
| 8625 | What physical facts could underlie 0 or 1, or very large numbers? [Frege on Mill] |
| 8469 | Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein] |
| 21693 | Russell's antinomy challenged the idea that any condition can produce a set [Quine] |
| 9406 | A class is natural when everybody can spot further members of it [Quinton] |
| 9984 | We can have a series with identical members [Tait] |
| 17837 | Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M] |
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 9571 | ZFU refers to the physical world, when it talks of 'urelements' [Chihara] |
| 9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |