On Numbers

Content:

1 What it is

2 The number 3

3 Everything is determed by numbers

4 Reality is then placed in a determined place 

5 Time is numerical

6 Proportional Numbers are there for interpretation

7 Numbers in music 

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The Mind Map

Numbers

1 What it is

Mystery of the universe to be contained in numbers (10 Timaeus Plato)

He resolved to have a moving image of eternity, and when he set in order the heaven, he made this image eternal but moving according to number, while eternity itself rests in unity;and this image we call time. Because of motion there is only “is” in time.(Plato Tameus p. 30)

 

2 The number 3

For, as the Pythagorean say, the world and all that is in it is determined by the number three, since beginning and middle and end give the number at an “all” and the number they give is triad. (Aristotle On the heavens p. 6)

3 Everything is determed by numbers

The correspondence between the central musical concords of the octave, fifth, and fourth and the whole number ratios 2 : 1, 3 : 2 and 4 : 3 is reflected in the acusmata (Iamblichus, VP 82)

4 Reality is then placed in a determined place 

At Metaphysics 986a22, after presenting his account of the philosophy of “the so-called” Pythagoreans (985b23), which has strong connections to the philosophy of Philolaus, Aristotle turns to “others of this same group” and assigns to them what is commonly known as the table of opposites (the opposites arranged according to column [kata sustoichia-n]). These Pythagoreans presented the principles of reality as consisting of ten pairs of opposites:

limit - unlimited

odd - even

unity - plurality

right - left

male - female

rest - motion

straight - crooked

light - darkness

good - bad

square - oblong

5 Time is numerical

Evidently, then, time is a number of change in respect of before and after; and because it is a number of something continuous, it is continuous. (Aristotle Physics Oxford p.108)

6 Proportional Numbers are there for interpretation

The same thing happens in understanding as in geometrical diagrams, where we draw a triangle of a certain size, even though we don’t use the particular size in our proofs. So likewise when we want to understand anything we conjure up before our eyes something of a certain size, something particular; when we want to understand a human being there comes up the image of some six-footer, for example. But the mind understands human beings as human being not as having that size. However, because what the mind may be wanting to understand is the nature of size, he goes on to say that if what is to be understood is of its nature quantitative - a line, say, or a surface of a number - but indeterminate - that is, not in its determinate particularity - we nevertheless conjure up before our eyes an imagine of determinate size; when we want to understand a line there comes up the images of a line two-foot long. For example, though the mind understands it only in its nature as a quality, not as being two-foot long. (Aquinas - Selected Philosophical Writings (Oxford) p.139)

7 Numbers in music 

The correspondence between the central musical concords of the octave, fifth, and fourth and the whole number ratios 2 : 1, 3 : 2 and 4 : 3 is reflected in the accustom (Iamblichus, VP 82)

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