An alternative theory of | |
---|---|
Nicomachus of Gerasa | |
Web Publication by Mountain Man Graphics, Australia | |
Nicomachus of Gerasa |
---|
The following summary of Nicomachus of Gerasa is sourced
from a Stanford University article on
pythagoreanism:
The Handbook was influential because it put forth an accessible version of Pythagorean harmonics. Nicomachus may have written a more detailed treatment of Pythagorean harmonics in a lost Introduction to Music, which was probably the basis of Books I-III of Boethius' De Institutione Musica (see Bower in Boethius 1989, xxviii). Even more influential than his work on harmonics was Nicomachus' Introduction to Arithmetic. Again Nicomachus was not an original or particularly talented mathematician, but this popularizing textbook was widely influential. There were a series of commentaries on it by Iamblichus (3rd AD), Asclepius of Tralles (6th AD), and Philoponus (6th AD) and it was translated into Latin already in the second half of the second century by Apuleius. Most importantly, Boethius (5th-6th c. AD) provides what is virtually a translation of it in his De Institutione Arithmetica, which became the standard work on arithmetic in the middle ages.
In the Introduction to Arithmetic, Nicomachus assigns to Pythagoras the Platonic division between the intelligible and sensible world, quoting the Timaeus as if it were a Pythagorean text (I 2). He also assigns Aristotelian ideas to Pythagoras, in particular a doctrine of immaterial attributes with similarities to the Aristotelian categories (I 1). Nicomachus divides reality into two forms, magnitude and multitude. Wisdom is then knowledge of these two forms, which are studied by the four sciences, which will later be known as the quadrivium: arithmetic, music, geometry and astronomy. He quotes a genuine fragment of Archytas (Fr. 1 Huffman) in support of the special position of these four sciences. Nicomachus presents arithmetic as the most important of the four, because it existed in the mind of the creating god (the demiurge) as the plan which he followed in ordering the cosmos, so that numbers thus appear to have replaced the Platonic forms as the model of creation (I 4). It is striking that, along with this Platonization of Pythagoreanism, Nicomachus does give an accurate presentation of Philolaus' basic metaphysical principles, limiters and unlimiteds, before attempting to equate them with the Platonic monad and dyad (II 18).
Another work by Nicomachus, The Theology of Arithmetic, which can be reconstructed from a summary by Photius and an anonymous work sometimes ascribed to Iamblichus and known as the Theologoumena Arithmeticae (Dillon 1977, 352-353), suggests that he largely returned to the system of principles found in Plato's unwritten doctrines and did not follow Eudorus and Moderatus in attempts to place a supreme god above the demiurge. Nicomachus apparently presents the monad as the first principle and demiurge, which then generates the dyad, but much is unclear (Dillon 1977, 353-358). The Theology of Arithmetic may have been most influential in its attempt to set up an equivalence between the pagan gods and the numbers in the decad, which was picked up later by Iamblichus and Proclus (Kahn 2001, 116). Nicomachus also wrote a Life of Pythagoras, which has not survived but which Porphyry (e.g. VP 59) and Iamblichus used.