John, Jerry, list,
I think, at this point we should take quantums- an relativity theories in regard, which of course Peirce didn´t know. According to them, I think, that discrete points do form a continuum, because they are blurred. Or something like that. Anyway, space and matter are functions of each other, and time and space can transform ino each other (Lorenz-transformation). Or, again, something like that. How ever it correctly is, it does not refute Peirce, but, on the contrary, allows speculations like that maybe time and signs are functions of, or conditions for each other. But we may refute Zenon´s paradoxon, I guess, by saying: Moments are blurred (Heisenberg-uncertainty).
Best, Helmut
19. April 2018 um 16:39 Uhr
"John F Sowa" <[email protected]>
wrote:
wrote:
Jerry,
I promised that I would stop.
> JLRC: The emotions that different compositions raise in me
> are not expressed in first order logic.
>
> JFS: I certainly agree with that point...
> I'll quit on this point of agreement.
But this morning I woke up with the realization that music
notation is based on the Peirce-Aristotle ontology of time.
Zeno's paradox about Apollo and the tortoise is based on the
assumption that points are the ultimate parts of a line or time
interval. But Aristotle resolved that paradox by claiming that
the parts of a line or time interval are smaller parts and
points are just markers on a line.
Cantor followed Zeno. Peirce admired Cantor's hierarchies of
infinity, but he followed Aristotle. Peirce claimed that no
discrete set of points could ever form a true continuum. For
discussion, see the intro to RLT by Ketner and Putnam.
With the Peirce-Aristotle ontology of time, there is only one
temporal system in music: a continuous line subdivided in
intervals. The beats per measure are markers on that interval.
And by the way, Euclid also followed Aristotle. He used letters
to mark significant points on his figures, but those points are
are markers, not parts. Ketner and Putnam discuss this "point".
John
-----------------------------
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I promised that I would stop.
> JLRC: The emotions that different compositions raise in me
> are not expressed in first order logic.
>
> JFS: I certainly agree with that point...
> I'll quit on this point of agreement.
But this morning I woke up with the realization that music
notation is based on the Peirce-Aristotle ontology of time.
Zeno's paradox about Apollo and the tortoise is based on the
assumption that points are the ultimate parts of a line or time
interval. But Aristotle resolved that paradox by claiming that
the parts of a line or time interval are smaller parts and
points are just markers on a line.
Cantor followed Zeno. Peirce admired Cantor's hierarchies of
infinity, but he followed Aristotle. Peirce claimed that no
discrete set of points could ever form a true continuum. For
discussion, see the intro to RLT by Ketner and Putnam.
With the Peirce-Aristotle ontology of time, there is only one
temporal system in music: a continuous line subdivided in
intervals. The beats per measure are markers on that interval.
And by the way, Euclid also followed Aristotle. He used letters
to mark significant points on his figures, but those points are
are markers, not parts. Ketner and Putnam discuss this "point".
John
-----------------------------
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----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
