Hmm. You seem to be defining 'thinking' as only an act of abstract
intellectual analysis.
But Peircean 'thinking' includes non-analytic feeling [Firstness] as
well as direct physical experience [Secondness] and also, that
abstract analytic process [Thirdness].
Edwina
On Sat 30/01/21 2:20 PM , "Brooks, William F" w-bro...@illinois.edu
sent:
Hello, everyone,
There seems to be a lot of crossfire here. Perhaps I can create a
diversionary skirmish . . .
"A mathematician or a musician thinks only in terms of the
patterns, the operations on those patterns, and their relationship to
whatever notation is used to represent them.”
Okay, well, first-person accounts are suspect, one can’t
generalise, etc., etc.
But.
I have been a musician for seventy years, and I was a serious
mathematician until age twenty. (I graduated with a double degree.) I
can assure you that I don’t think “only in terms of the patterns .
. .” In fact, in my most treasured musical experiences—and I’d
venture to say the same for mathematics—I barely “think” at
all. It’s an embodied understanding: I “feel” what I
apprehend—and only after the fact, with a great sense of loss, do I
“think” about it. And when I do “think” I mostly struggle to
find some faint simulacrum of my experience. Sometimes that might
involve patterns; sometimes I might draw pictures or notes or words;
sometimes I simply get up from the desk and pace, wave my arms, sing
a little. (Except for the singing, the same definitely goes for
mathematics.)
Now, I don’t know nearly enough about Peirce. But what little I
do know suggests that he was a very physical person, with appetites,
passions, and bodily understandings. How did he apprehend
mathematics, or logic, or—for that matter—music? In what ways
can we, should we, be informed by our conclusions about the nature of
his apprehension?
And what has any of this to do with silence? Or the absence of
logic?
Bill
William Brooks
w-bro...@illinois.edu [1]
Emeritus Professor of Music
University of Illinois
Urbana, IL 61801
United States
(+1-217-417-4165)
William Brooks
w.f.bro...@york.ac.uk
Professor of Music
University of York
Heslington, York YO10 5DD
United Kingdom
(+44-1904-324449)
William Brooks
Senior Research Fellow and Series Editor
Orpheus Institute, Ghent, Belgium
william.bro...@orpheusinstituut.be
Take care of things. And people.
On Jan 29, 2021, at 21:38, John F. Sowa wrote:
Gary R,
My remarks were ad rem, not ad hominem. Mathematics is like music.
A mathematician or a musician thinks only in terms of the patterns,
the operations on those patterns, and their relationship to whatever
notation is used to represent them.
The words used to describe those patterns are useful for
communication among teachers, students, and critics. But those words
are absent from the minds of the artists (musical or mathematical) who
are imagining and creating novel patterns.
Peirce was a great mathematical/logical artist. In June 1911, he
had a new insight into the melodies of logic. Any logician can
"hear" an exciting new melody in R670 and L231 that was not present
in R669 or the Monist article of 1906. Peirce didn't have to write
a "note to self" about the change. He just did it. And any logician
can "hear" it.
But I realize that many people can't feel or hear the difference. I
plan to post the 1906 version and the 1911 version on my web site, and
I'll point out exactly where the differences occur and their
implications.
I'll post that in the next two days. And I won't refer to any other
person's comments or opinions on the subject.
Meanwhile, I recommend the following slides and their quotations of
mathematicians, logicians, and linguists about their subject:
http://jfsowa.com/talks/ppe.pdf__;!!DZ3fjg!o-XxG2rDqisSRvTETFntihZBRphzzSQPlUzHO-wbSLZObJwfIVahs0glXGwhSAbt84V_$
[3]" target="_blank"> http://jfsowa.com/talks/ppe.pdf [4] . The
application of Peirce's EGs to Euclidean diagrams is easy with the
1911 EGs, but not with the earlier versions. That application is one
of the strongest arguments in support of Peirce's claim that EGs
represent "the action of the mind in thought."
John _ _ _ _ _ _ _ _ _ _
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