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<mailto:w-bro...@illinois.edu> 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 <s...@bestweb.net<mailto:s...@bestweb.net>> 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<https://urldefense.com/v3/__http://jfsowa.com/talks/ppe.pdf__;!!DZ3fjg!o-XxG2rDqisSRvTETFntihZBRphzzSQPlUzHO-wbSLZObJwfIVahs0glXGwhSAbt84V_$> . The application of Peirce's EGs to Euclidean diagrams is easy with the 1911 EGs, but not with the earlier versions. That application is one of the strongest arguments in support of Peirce's claim that EGs represent "the action of the mind in thought." John _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu<mailto:peirce-L@list.iupui.edu> . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu<mailto:l...@list.iupui.edu> with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at https://urldefense.com/v3/__http://www.cspeirce.com/peirce-l/peirce-l.htm__;!!DZ3fjg!o-XxG2rDqisSRvTETFntihZBRphzzSQPlUzHO-wbSLZObJwfIVahs0glXGwhSHheI-8y$ . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
_ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
