Jon, List
I'd like to point out that sometimes I agree with one
of Jon's notes.   I believe that Peirce's three "universes of
discourse" constitute the best resolution of the debates between
Plato and Aristotle:  the universe of pure possibilities (mathematics);
the universe of actuality (everything in space and time); and the universe
of necessitants (the laws of nature, which govern the development of
actuality).  Plato said that the first and third were really real. 
Aristotle emphasized the second.  Peirce said that all three are real. 
That point is consistent with what Jon wrote below.
Unfortunately, I
must also add a "but" about the following sentence:  "They are thus real 
possibilities (1ns),
but not forms that exist in some immaterial
realm."
The universe of possibilities is an immaterial
realm, and mathematicians use existential quantifiers when writing about
the mathematical patterns (forms) in it.
John
_________________________________I agree that Peirce
was not at all a Platonist, but nevertheless uses the expression
"Platonic idea" in a peculiar way.  The passages that come to my
mind
are where he describes Platonic ideas as the constituents of the first
universe of experience.CSP: 
 Some words shall herein be capitalized when used, not as vernacular,
but as terms defined. Thus, an "idea" is the substance of an actual
unitary thought or fancy; but "Idea,"--nearer Plato's idea
of ἰδέα,--denotes
 anything whose Being consists in its mere capacity for getting fully
represented, regardless of any person's faculty or impotence to
represent it. ...Of the three Universes of Experience
familiar to us all, the first comprises all mere Ideas, those airy
nothings to which the mind of poet, pure mathematician, or another
might give
 local habitation and a name within that mind. Their very
airy-nothingness, the fact that their Being consists in mere capability
of getting thought, not in anybody's Actually thinking them, saves their
 Reality. (CP 6.452&455, EP 2:434&435,
1908)They are
thus real possibilities (1ns), but not forms that exist in
some immaterial realm.Regards,Jon Alan Schmidt

Jon, List

I'd like to point out that sometimes I completely agree with one of Jon's notes.   I believe that Peirce's three "universes of discourse" constitute the best resolution of the debates between Plato and Aristotle:  the universe of pure possibilities (mathematics); the universe of actuality (everything in time and space); and the universe of necessities (the laws of nature, which govern the development of actuality).  Plato said that the first and third were really real.  Aristotle emphasized the second.  Peirce said that all three are real.  That point is consistent with what Jon wrote below.

John

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