Zitate von Nikomachos von Gerasa

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Nikomachos von Gerasa

Geburtstag: 60 n.Chr.
Todesdatum: 120

Nikomachos von Gerasa war ein antiker Philosoph, Mathematiker und Musiktheoretiker. Er lebte in der römischen Kaiserzeit; seine Geburt fällt frühestens ins 1. Jahrhundert, sein Tod spätestens ins späte 2. Jahrhundert. Nikomachos war Pythagoreer und Platoniker. Als Pythagoreer gehört er zur neupythagoreischen Richtung, als Platoniker zählt er zu den Vertretern des Mittelplatonismus. Wikipedia

Zitate Nikomachos von Gerasa

„If geometry exists, arithmetic must also needs be implied“

—  Nicomachus

Kontext: If geometry exists, arithmetic must also needs be implied... But on the contrary 3, 4, and the rest might be 5 without the figures existing to which they give names. Hence arithmetic abolishes geometry along with itself, but is not abolished by it, and while it is implied by geometry, it does not itself imply geometry.<!--Book I, Chapter IV

„Since, however, all multitude and magnitude are by their own nature of necessity infinite“

—  Nicomachus

Kontext: Things... are some of them continuous... which are properly and peculiarly called 'magnitudes'; others are discontinuous, in a side-by-side arrangement, and, as it were, in heaps, which are called 'multitudes,' a flock, for instance, a people, a heap, a chorus, and the like.
Wisdom, then, must be considered to be the knowledge of these two forms. Since, however, all multitude and magnitude are by their own nature of necessity infinite—for multitude starts from a definite root and never ceases increasing; and magnitude, when division beginning with a limited whole is carried on, cannot bring the dividing process to an end... and since sciences are always sciences of limited things, and never of infinites, it is accordingly evident that a science dealing with magnitude... or with multitude... could never be formulated.... A science, however, would arise to deal with something separated from each of them, with quantity, set off from multitude, and size, set off from magnitude.<!--pp.183-184

„Things… are some of them continuous“

—  Nicomachus

Kontext: Things... are some of them continuous... which are properly and peculiarly called 'magnitudes'; others are discontinuous, in a side-by-side arrangement, and, as it were, in heaps, which are called 'multitudes,' a flock, for instance, a people, a heap, a chorus, and the like.
Wisdom, then, must be considered to be the knowledge of these two forms. Since, however, all multitude and magnitude are by their own nature of necessity infinite—for multitude starts from a definite root and never ceases increasing; and magnitude, when division beginning with a limited whole is carried on, cannot bring the dividing process to an end... and since sciences are always sciences of limited things, and never of infinites, it is accordingly evident that a science dealing with magnitude... or with multitude... could never be formulated.... A science, however, would arise to deal with something separated from each of them, with quantity, set off from multitude, and size, set off from magnitude.<!--pp.183-184

„Now it is with such things that 'wisdom' is particularly concerned, but accidentally also with“

—  Nicomachus

Kontext: Bodily, material things are... continuously involved in continuous flow and change—in imitation of the nature and peculiar quality of that eternal matter and substance which has been from the beginning... The bodiless things, however, of which we conceive in connection with or together with matter, such as qualities, quantities, configurations, largeness, smallness, equality, relations, actualities, dispositions, places, times, all those things... whereby the qualities in each body are comprehended—all these are of themselves immovable and unchangeable, but accidentally they share in and partake of the affections of the body to which they belong. Now it is with such things that 'wisdom' is particularly concerned, but accidentally also with... bodies.<!--p.181

„All that has by nature, with systematic method, been arranged in the universe, seems“

—  Nicomachus

Kontext: All that has by nature, with systematic method, been arranged in the universe, seems both in part and as a whole to have been determined and ordered in accordance with number, by the forethought and the mind of him that created all things; for the pattern was fixed, like a preliminary sketch, by the domination of number preëxistent in the mind of the world-creating God, number conceptual only and immaterial in every way, but at the same time the true and the eternal essence, so that with reference to it, as to an artistic plan, should be created all these things: time, motion, the heavens, the stars, all sorts of revolutions.<!--Book I, Chapter VI

„This 'wisdom' he defined as the knowledge, or science, of the truth in real things, conceiving 'science' to be a steadfast and firm apprehension of the underlying substance. and 'real things' to be those which continue uniformly and the same in the universe and never depart even briefly from their existence; these real things would be things immaterial“

—  Nicomachus

Commentary (p.92): Nichomacus is an idealist. He states his position in a way that recalls Plato's distinction between "that which ever exists, having no becoming" and "that which is ever becoming, never existent,"... On the one hand there are "the real things... which exist forever changeless and in the same way in the cosmos, never departing from their existence even for a brief moment," and on the other "the original eternal matter and substance" which was entirely "subject to deviation and change."
Kontext: The ancients, who under the leadership of Pythagoras first made science systematic, defined philosophy as the love of wisdom... [Οἱ παλαιοὶ καὶ πρώτοι μεθοδεύσαντες ἐπιστήμην κατάρξαντος Πυθαγόρου ὡρίζοντο φιλοσοφίαν εἶναι φιλίαν σοφίας... ] This 'wisdom' he defined as the knowledge, or science, of the truth in real things, conceiving 'science' to be a steadfast and firm apprehension of the underlying substance. and 'real things' to be those which continue uniformly and the same in the universe and never depart even briefly from their existence; these real things would be things immaterial...<!--p.181

„A science, however, would arise to deal with something separated from each of them“

—  Nicomachus

Kontext: Things... are some of them continuous... which are properly and peculiarly called 'magnitudes'; others are discontinuous, in a side-by-side arrangement, and, as it were, in heaps, which are called 'multitudes,' a flock, for instance, a people, a heap, a chorus, and the like.
Wisdom, then, must be considered to be the knowledge of these two forms. Since, however, all multitude and magnitude are by their own nature of necessity infinite—for multitude starts from a definite root and never ceases increasing; and magnitude, when division beginning with a limited whole is carried on, cannot bring the dividing process to an end... and since sciences are always sciences of limited things, and never of infinites, it is accordingly evident that a science dealing with magnitude... or with multitude... could never be formulated.... A science, however, would arise to deal with something separated from each of them, with quantity, set off from multitude, and size, set off from magnitude.<!--pp.183-184

„Bodily, material things are… continuously involved in continuous flow and change“

—  Nicomachus

Kontext: Bodily, material things are... continuously involved in continuous flow and change—in imitation of the nature and peculiar quality of that eternal matter and substance which has been from the beginning... The bodiless things, however, of which we conceive in connection with or together with matter, such as qualities, quantities, configurations, largeness, smallness, equality, relations, actualities, dispositions, places, times, all those things... whereby the qualities in each body are comprehended—all these are of themselves immovable and unchangeable, but accidentally they share in and partake of the affections of the body to which they belong. Now it is with such things that 'wisdom' is particularly concerned, but accidentally also with... bodies.<!--p.181

„And once more is this true in the case of music“

—  Nicomachus

Kontext: And once more is this true in the case of music; not only because the absolute is prior to the relative, as 'great' to 'greater' and 'rich' to 'richer' and 'man' to 'father,' but also because the musical harmonies, diatessaron, diapente, and diapason, are named for numbers; similarly all of their harmonic ratios are arithmetical ones, for the diatessaron [], is the quadruple ratio [4 : 1].<!--Book I, Chapter V

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„Since of quantity, one kind is viewed by itself, having no relation to anything else“

—  Nicomachus

Kontext: Since of quantity, one kind is viewed by itself, having no relation to anything else, as 'even,' 'odd,' 'perfect,' and the like, and the other is relative to something else, and is conceived of together with its relationship to another thing, like' double,', greater,' 'smaller,' 'half,' 'one and one-half times,' 'one and one-third times,' and so forth, it is clear that two scientific methods will lay hold of and deal with the whole investigation of quantity: arithmetic, [with] absolute quantity; and music, [with] relative quantity.<!--Book I, Chapter III, p.184

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