Re: SUO: Re: Hypostatic And Prescisive Abstraction
Jon,
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 ...
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.
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.
By erasing two sujects, you get a dyad or dyadic
relation:
____ gave ____ to Mary.
By erasing three subjects, you get a triad or
triadic relation:
____ gave ____ to ____.
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:
http://www.jfsowa.com/peirce/ms514.htm
Existential Graphs
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:
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.
This example highlights the importance of language
in abstraction.
John