ONT Re: New List & Classification of Signs
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BU = Ben Udell
BU: Are not the combinatory functors so many "this"s, "look here"s,
"voila"s, "ecce"s in the statement? The very arrangement of
symbols in a statement/thought has combinatory significance in
terms of combinatory rules/habits of statement/thought-formation.
The "this!" that refers to a physical object outside the statement
could be taken as an extrovert combinatory functor.
Ben,
Your note is too long, my eyes are too blurry,
so I think I'll just ramble the evening away.
I am pretty sure that I first looked into Murphey's Peirce
during the second half of my Justin Morrill years (1972-76).
I had already spent two or three years immersed in CP 3-4.
And wouldn't it be hilarious if someone were raking over
our reminiscences the way we are post-mortifying Peirce's?
Ah, Blessed Nepenthe! Anyway, I could not have seen the
'Chronological Edition' yet, so the revelations of Peirce's
Harvard and Lowell lectures, in their inelastically intact
impact on my brain, were still a decade in the future, and
I can remember that I mostly accepted the story of Peirce's
Protean conversions pretty much as it was told here and there.
Except that I had spent quite a bit of time worrying over the
whole tangled tale of "existential import", or the lack thereof,
in the tortoise's transit from classical to modern logic, which
caused me to work through the "Description of a Notation" (1870)
and its sequels with particular care. The upshot of the story
is that I can distinctly remember how I first interpreted these
problematic passages. It did not seem that Peirce was talking
about anything so hot off the presses, since what he mentioned
was only "nominally" novel in comparison to what I had read in
his 1870's papers, but mostly that he was paying a compliment
to own long-held and previously published ideas in the guise
of his protege Mitchell.
That is about what I remember, and I can see nothing yet that
contradicts that impression, indeed, in retrospect, very much
more that confirms it, from the incidental to the substantial.
Are you referring to Quine's combinatory functors?
If so, it would help to let me know which version
you have in mind. I am a little more conversant
with the standard Schoenfinkel brands: S, K, I.
The whole intent of combinators was to eliminate
the variable (the formal index or pronoun) as a
primitive theoretical construct. I have always
wondered what this would mean philosophically.
It might just mean that the entire indicative
aspect has been relegated to the tabula rasa,
the uncarved block, the unmarked medium that
bears the inscription, or the lack thereof.
Just a thought ...
Jon
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