14248
|
We could accept the integers as primitive, then use sets to construct the rest [Cohen]
|
|
Full Idea:
A very reasonable position would be to accept the integers as primitive entities and then use sets to form higher entities.
|
|
From:
Paul J. Cohen (Set Theory and the Continuum Hypothesis [1966], 5.4), quoted by Oliver,A/Smiley,T - What are Sets and What are they For?
|
|
A reaction:
I find this very appealing, and the authority of this major mathematician adds support. I would say, though, that the integers are not 'primitive', but pick out (in abstraction) consistent features of the natural world.
|
7634
|
Icons resemble their subject, an index is a natural sign, and symbols are conventional [Peirce, by Maund]
|
|
Full Idea:
For Peirce there are three different kinds of sign, which are different kinds of representation, built on different relationships: an 'icon' represents what it resembles, an 'index' is a natural sign, and a 'symbol' is a conventional sign.
|
|
From:
report of Charles Sanders Peirce (Logic as Semiotic: Theory of Signs [1897]) by Barry Maund - Perception Ch.4
|
|
A reaction:
Maund makes use of natural signs (like footprints) to explain representative perception. Peirce's distinctions seem useful in philosophy of mind generally, if the brain somehow represents what it experiences. How subjective are signs?
|