Numbers

Philosophy Book Notes

Books used 

Plato -Timaeus

2 Notes selected

Iamblichus

2 Notes selected

Aristotle - On the soul (Oxford)

1 Notes selected

Aristotle - On the heavens 

1 Notes selected

Aristotle - The Metaphysics (Penguin)

1 Notes selected

Plato - Laws (Penguin)

1 Notes selected

Aristotle - Physics (Oxford)

1 Notes selected

Reality is then placed in a determined place 

Numbers

The Formula

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

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Identifying thought with the soul, that is, with the motion of soul-atom. His reasoning: knowledge is the same as perception because both are identical with the motion of soul-atoms (Aristotle - On the soul Oxford p. XXii)

What it is?

A selection of notes to understand Numbers. 

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

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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)

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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

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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)

Everything is determined by numbers

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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)

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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)

 Time is numerical

Proportional Numbers are there for interpretation

The number 3

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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)

Numbers in music 

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Text Version:

Soul

1 What is a soul

2 Essence

3 Mystical creation

4 It is Immortal

5 It is a source of change

6 It is the source of motion

7 The reasoning soul

8 The Soul and mind

1 What is a soul

So our conclusion is that soul is itself a thing in the sense of being able to subsist by itself, but one which does not possess a complete specific nature of its own; rather it is something which completes a human being’s specific nature by being the form of a human body. So that the soul is at once and the same time a form and itself a thing. (Aquinas - Selected Philosophical Writings (Oxford) p.189)

Soul is the dust most (pedaco de po) on air. It moves by itself even when there is no wind around. (Aristotle - On the soul p5)

Identifying thought with the soul, that is, with the motion of soul-atom. His reasoning: knowledge is the same as perception because both are identical with the motion of soul-atoms (Aristotle - On the soul Oxford p. XXii)

The gold must be a flower, the spirit must be the body and must become a soul in order to be able to live. (Kurgast - Herman Hesse)

2 Essence

Now the soul is by essence immaterial, so by essence intellectual. Intellect then is its essence, and other abilities likewise. (Aquinas - Selected Philosophical Writings (Oxford) p.124)

3 Mystical creation

In this perfect world having neither eyes nor ears, for there was nothing without him wich he could see or hear: he had no need to carry food to his mouth, nor was their air for him to breath; he did not require hands, for there were nothing of which he could take hold, nor feet. All that he did was done rationally in and by himself, and he moved in a circle turning within himself, which is the most intellectual of motions; but the other six motions were wanting to him;wherefore the universe had no feet or legs. Having intercourse with himself - the soul was made and then the body. (Plato -Timaeus p.10)

4 It is Immortal

Human soul is immortal and has been through many earthly lives and many periods of existence (A History of Greek Philosophy v4 W. K. C. Guthrie p.295) 

5 It is a source of change

This is soul, source of change and motion in all things (if the soul is older the body than is said to exist by nature. (Plato Laws p. 231)

6 It is the source of motion

Aristotle organizes his discussion thematically around the main attributes of the soul which his predecessors had identified. He begins with two - it is a source of motion and centre of awareness - and later adds a third; it is incorporeal. (Aristotle On the soul Oxford p.XXi)

7 The reasoning soul

And it is a fortiori impossible for the life-principles of things which reason, the activities of which involve abstracting the species of things not only from matter but from every material condition of particularity, so as to know them in general. And there is something further still to consider, which is peculiar to rising souls: not only do they take in species that can be understood without their matter and material condition, but, as Aristotle proves, they cannot shares that special activity of theirs with any bodily organ, in the sense of having a bodily organ for thinking as an eye is the bodily organ for seeing. (Aquinas - Selected Philosophical Writings (Oxford) p.187)

8 The Soul and mind

Thus Aristotle says that mind is sort of indecomposable substance. And Plato’s saying that soul is immortal and subsists of itself because it moves itself amounts to the same. For he is using movement broadly to mean any activity, and the mind moving itself must be interpreted to mean that it is active of itself. (Aquinas - Selected Philosophical Writings (Oxford) p.188)