SUO: Re: Hypostatic And Prescisive Abstraction
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HAPA. Discussion Note 8
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JA = Jon Awbrey
JS = John Sowa
OS = Oliver Sacks
John,
Yes, very true, at least about the rhematic abstraction,
which is more or less the same as what Frege described
by talking of "saturated" and "unsaturated" expressions.
But still, there seems to be a difference between the
prescisive abstraction of the predicate "__ is sweet",
and the hypostatic precipitate of the abstract object
"sweetness". I am still trying to clarify the residue
of what remains a cloudy suspension, but it seems like
this has something to do with the interpretation of the
syntactic abstraction as actually denoting an object,
as a lambda abstraction denotes a real-live function,
an ens rationis.
CP 2.358 is Peirce's Baldwin Dictionary definition of "predicate".
CP 3.465 is a short summary of these poly-unsaturated "polyads".
CP 3.469 mentions the chemical analogy with "unsaturated bonds".
Jon Awbrey
JS: I would put Peirce much closer to the beginning of that
process with his writings on relations in the 1870s:
JA: Bentham's "Theory of Fictions" begat (paraphrastically)
Schönfinkel's "Bausteine" and this begat (independently)
Church's "Lambda Calculus" and this begat (in good time)
McCarthy's "Lisp" and all the rest is AI and IEEE ...
JS: Peirce constructed relational abstractions from sentences
simply by replacing any constituent with a blank. He called
the various constituents "logical subjects". For example,
start with an arbitrary sentence that states a proposition:
John gave a book to Mary.
JS: The proposition as a whole is a medad (0-adic relation).
By erasing one logical subject, you get a monad or
monadic relation:
John gave ____ to Mary.
JS: By erasing two sujects, you get a dyad or dyadic relation:
____ gave ____ to Mary.
JS: By erasing three subjects, you get a triad or triadic relation:
____ gave ____ to ____.
JS: Peirce described this process many times in many different places over
the years, but I don't happen to have any quotations handy. He does
allude to this process in his tutorial on existential graphs:
JS: http://www.jfsowa.com/peirce/ms514.htm -- Existential Graphs
JS: As another interesting example, following is an excerpt from the
book 'Seeing Voices' by Oliver Sacks. He reports the case of an
11-year-old deaf boy, who had not had the benefit of sign language
for his first 10 years:
OS: Joseph saw, distinguished, categorized, used; he had no problems with
perceptual categorization or generalization, but he could not, it seemed,
go much beyond this, hold abstract ideas in mind, reflect, play, plan.
He seemed completely literal -— unable to juggle images or hypotheses
or possibilities, unable to enter an imaginative or figurative realm ...
He seemed, like an animal, or an infant, to be stuck in the present,
to be confined to literal and immediate perception, though made
aware of this by a consciousness that no infant could have.
JS: This example highlights the importance of language in abstraction.
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