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Single Idea 9406

[filed under theme 4. Formal Logic / F. Set Theory ST / 7. Natural Sets ]

Full Idea

To say that a class is natural is to say that when some of its members are shown to people they pick out others without hesitation and in agreement.

Gist of Idea

A class is natural when everybody can spot further members of it

Source

Anthony Quinton (The Nature of Things [1973], 9 'Nat')

Book Ref

Quinton,Anthony: 'The Nature of Things' [RKP 1973], p.264


A Reaction

He concedes a number of problems with his view, but I admire his attempt to at least begin to distinguish the natural (real!) classes from the ersatz ones. A mention of causal powers would greatly improve his story.


The 10 ideas with the same theme [which sets are natural, rather than conventional]:

What physical facts could underlie 0 or 1, or very large numbers? [Frege on Mill]
Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein]
Russell's antinomy challenged the idea that any condition can produce a set [Quine]
A class is natural when everybody can spot further members of it [Quinton]
We can have a series with identical members [Tait]
Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]
Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
The master science is physical objects divided into sets [Maddy]
ZFU refers to the physical world, when it talks of 'urelements' [Chihara]
A flock of birds is not a set, because a set cannot go anywhere [Brown,JR]