SUO: Re: Foundations For Ontology
Jon Awbrey wrote:
> JA: As I understand them, 1st-ness, 2nd-ness, 3rd-ness are abstractions
> from solid realities, a matter of the aspects to which we attend
> and the depth of perspective that we apply to what we observe,
> nothing more.
Peirce understood them to be something to be found in phenomena, real or
unreal, one implication of that being that logic does not depend upon
metaphysics. I understand that to mean that, for example, Russell's theory
of definite descriptions loses its motivation, at least as Russell conceived
it. (Quine's view is similarly affected, I take it.) In general, the
treatment of fictional objects will be different depending upon whether or
not there is supposed to be any need to resort to paraphrase in order to
account for reference to unreal or non-existent objects. My impression is
that, in recent years, formal logicians no longer take Russell's
metaphysically-driven view for granted, as they once did.
In response to John Sowa's comment:
> JS: I am traveling right now, so I don't have access to all my
> books and notes, so I can't quote the appropriate references.
> However, if someone would be so kind as to look up CSP's
> classification of the various fields of science (including
> both the physical and the psychical), there is something in
> his later philosophy where he puts mathematics at the top,
> and everything else under it. In that same classification,
> he subdivides the field of "critical logic" into "deduction,
> induction, and abduction" in that order.
The sense in which all other sciences are "under" math is that they all
presuppose it, whereas it presupposes nothing (thus math is not regarded as
presupposing logic: Peirce was a foe of logicism, a view with which he was
acquainted from Peano, before Russell heard of it). The manuscript L75 (the
"Carnegie Application") available at the website ARISBE provides one good
textual reference for these considerations: