more from this thinker | more from this text
Full Idea
Maddy dispenses with pure sets, by sketching a strong set theory in which everything is either a physical object or a set of sets of ...physical objects. Eventually a physiological story of perception will extend to sets of physical objects.
Gist of Idea
Maddy replaces pure sets with just objects and perceived sets of objects
Source
report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3
Book Ref
Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.223
A Reaction
This doesn't seem to find many supporters, but if we accept the perception of resemblances as innate (as in Hume and Quine), it is isn't adding much to see that we intrinsically see things in groups.
| 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] |