Tuesday, April 4, 2023

Revisiting the Platonic Form Unit covering up noncommutative Pythagorean time-frequency truth nonlocality Apeiron

 "Magnitudes have all the characteristics Plato attributes to Apeiron."

p. 394

Socratic, Platonic and Aristotelian Studies: Essays in Honor of Gerasimos Santas 2011

It was when the Attic alphabet arose that Number aligned with a Form as the phonic symbol enabled Number to no longer be inherently Cardinal [a number that says how many of something there are], but instead be just a "heap" of "substance" , as both integers and geometric units combined. see John J. Cleary, "Aristotle's Criticism of Plato's Theory of Form Numbers," in Platon und Aristoteles, sub ratione veritatis: Festschrift für Wolfgang Wieland zum 70. Geburtstag
The Platonic Form of Twoness is Two.
page 14:
"Aristotle argues....if the units in the first Two come into being simultaneously, then they can not be ordered as prior and posterior, as the hypothesis of non-comparability [of Platonic Forms] implies."
p. 15... "he [Aristotle] argues it is impossible that two be some nature separated from two units....Here he is raising the difficulty of how Platonic Form numbers can exist separately (actually) apart from the units that constitute them...How can a number like 2 be a unity?...a collection is not an entity over and above its members."

 The metric system is for physical quantities and measurable distances, not time: "points in time are not units."

 

 Noncommutative origin of the Pythagorean Comma.

https://en.wikipedia.org/wiki/Pythagorean_comma

 Apotome and limma are the two kinds of semitones defined in Pythagorean tuning. Namely, the apotome (e.g. from C to C) is the chromatic semitone, or augmented unison (A1), while the limma (e.g. from C to D) is the diatonic semitone, or minor second (m2).

 

 

 Plato’s insistence on picking up a certain pair (τινε) which “is correctly
called ‘both’” 29 (ὀρθῶς ἔχει καλεῖσθαι ἀμφοτέρω) before saying that they
are two shows us that he didn’t consider obtaining δύο as a simple and
univocal procedure (ex. 1+1). The procedure of obtaining two is the
following: we take a τινε (a pair of two eyes, two legs etc.) that we divide
into each member (e.g. ἑκάτερος, which will be the opposite of ἀμφότερος),
and thus we have independent members from which we can have two.
Thus the pair relation comes first, and after that their numerosity, namely
that there are two things. The twoness of the one and being is an instance
of ἀμφοτέρω (duality), and not of the cardinality of δύο (number two), in the
sense that the duality refers to pairs, while two itself refers to only any two
things. 30 Ross is right in saying that: “Aristotle is not quite fair in assuming
that the indefinite dyad is an ordinary member of the class of 2’s”. 31 The
cardinality of the dyad is only an Aristotelian reading, and a sophism. 32

 https://philpapers.org/archive/CALOTT-3.pdf

 

 

 

 

 

 

 

 

 

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