PYTHAGOREANISM originated in the 6th century BC, based on the
teachings and beliefs held by
Historians from the Stanford Encyclopedia of
* 1 Two schools
* 1.1 History
* 1.2 The mathēmatikoi
* 1.2.1 Numbers
* 1.3 The akousmatikoi * 1.4 Ceremonies
* 3 Work and theories
* 3.2 Music and harmony
* 3.2.1 Composition * 3.2.2 Instruments
* 4 Views
* 4.1 Vegetarianism * 4.2 Women
* 5 Female philosophers * 6 Neopythagoreanism * 7 Influences * 8 See also * 9 References * 10 Further reading * 11 External links
According to tradition, pythagoreanism developed at some point into two separate schools of thought, the mathēmatikoi (μαθηματικοί, Greek for "Teachers") and the akousmatikoi (ἀκουσματικοί, Greek for "listeners").
John Burnet (1892) noted
Lastly, we have one admitted instance of a philosophic guild, that of
the Pythagoreans. And it will be found that the hypothesis, if it is
to be called by that name, of a regular organisation of scientific
activity will alone explain all the facts. The development of doctrine
in the hands of
There were also two forms of philosophy, for the two genera of those that pursued it: the Acusmatici and the Mathematici. The latter are acknowledged to be Pythagoreans by the rest but the Mathematici do not admit that the Acusmatici derived their instructions from Pythagoras but from Hippasus . The philosophy of the Acusmatici consisted in auditions unaccompanied with demonstrations and a reasoning process; because it merely ordered a thing to be done in a certain way and that they should endeavor to preserve such other things as were said by him, as divine dogmas. Memory was the most valued faculty. All these auditions were of three kinds; some signifying what a thing is; others what it especially is, others what ought or ought not to be done. (p. 62)
The best of all legislators came from the school of Pythagoras, Charondas , the Catanean , Zaleucus and Timaratus as well as many others, who established laws with great benevolence and political science. (p. 26)
The whole Pythagoric school produced appropriate songs, which they
called exartysis or adaptations; synarmoge or elegance of manners and
apaphe or contact, usefully conducting the dispositions of the soul to
passions contrary to those which it before possessed. By musical
sounds alone unaccompanied with words they healed the passions of the
soul and certain diseases, enchanting in reality, as they say. It is
probable that from hence this name epode, i. e., "enchantment," came
to be generally used. For his disciples,
Excerpt from a speech by the character 'Aristotle' in Protrepticus (Hutchinson and Johnson, 2015)
Thus nothing is more valuable than intelligence, which we say is a capacity of the most authoritative thing in us, to judge one disposition in comparison with another, for the cognitive part, both apart and in combination, is better than all the rest of the soul, and knowledge is its virtue. (p. 35)
Therefore its function is none of what are called 'parts of virtue', for it is better than all of them and the end produced is always better than the knowledge that produces it. Nor is every virtue of the soul in that way a function, nor is success; for if it is to be productive, different ones will produce different things, as the skill of building (which is not part of any house) produces a house. However, intelligence is a part of virtue and of success, for we say that success either comes from it or is it. (p. 36)
According to historians like
Thomas Gale (based on Archytas'
account), Thomas Taler (based on the work of Iamblichus), or Cantor,
According to the historians from the Stanford Encyclopedia of
A Echecrates is mentioned by Aristoxenus as a student of Philolaus and Eurytus. (p. 166)
The mathēmatikoi were supposed to have extended and developed the more mathematical and scientific work begun by Pythagoras. The mathēmatikoi did think that the akousmatikoi were Pythagorean, but felt that their own group was more representative of Pythagoras.
Excerpt from a speech by the character 'Aristotle' in Protrepticus (Hutchinson and Johnson, 2015 p. 32)
Many of the more recent Pythagoreans assumed that mathematics has as its subject matter only the things that are the same and in the same way, and hypothesized only these principles; so in the same way they define as different both the sciences and the demonstrations about such things. But since both in the speeches preceding this point and in the later remarks we will demonstrate that there are many and different substances that are unchangeable and exist in the same state, not only the ones in mathematics, and that those are more senior and more honorable than these, and we will also demonstrate that these mathematical principles are not the only ones, but there are also others, and these in fact are more senior and more powerful than those, and that these are not the principles of all the things that exist but only of some; so it is for these reasons that the mathematical demonstration now demands a determination of which of the qualities it can demonstrate remain the same and in the same way, and from what kinds of principles it reasons, and about what kinds of problems it produces the demonstrations.
Commentary from Sir William Smith , Dictionary of Greek and Roman Biography and Mythology (1870, p. 620).
According to Philolaus, number is the "dominant and self-produced
bond of the eternal continuance of things." But number has two forms,
the even and the odd, and a third, resulting from the mixture of the
two, the even-odd. This third species is one itself, for it is both
even and odd. One, or unity, is the essence of number, or absolute
number, and so comprises these two opposite species. As absolute
number it is the origin of all numbers, and so of all things.
(According to another passage of Aristotle, Met. xii. 6. p. 1080, b.
7. number is produced) This original unity they also termed God
(Ritter, Gesch. der FML vol. i. p. 389). These propositions, however,
would, taken alone, give but a very partial idea of the Pythagorean
system. A most important part is played in it by the ideas of limit,
and the unlimited. They are, in fact, the fundamental ideas of the
whole. One of the first declarations in the work of
According to Sir William Smith , (1870).
The Orphic worshippers of
But before this time the Orphic system had been reduced to a definite
form by Pherecydes and
Onomacritus , who stand at the head of a series
of writers, in whose works the Orphic theology was embodied; such as
Orpheus of Croton ,
Arignote , Persinus of Miletus , Timocles of Syracuse , and Zopyrus of
Heracleia or Tarentum (Mliller, p. 235). Besides these associations
there were also an obscure set of mystagogues derived from them,
called Orpheotelests ('OpipeorcAeaTal), "who used to come before the
doors of the rich, and promise to release them from their own sins and
those of their forefathers, by sacrifices and expiatory songs; and
they produced at this ceremony a heap of books of
Orpheus and Musaeus
, upon which they founded their promises" (Platon Ion, p. 536, b.;
Muller, p. 235). The nature of the Orphic theology, and the points of
difference between it and that of
The book The works of
According to Charles Peter Mason in Sir William Smith Dictionary of Greek and Roman biography and mythology (1870, see book screenshot for full quote)
It appears, in fact, from this, as well as from the extant fragments,
that the first book (from
Excerpt from a speech by the character "Aristotle" in the book Protrepticus (Hutchinson and Johnson, 2015 p. 16)
..the Pythagoreans honored the effort put into mathematics, and coordinated it with the observation of the cosmos in various ways, for example: by including number in their reasoning from the revolutions and their difference between them, by theorizing what is possible and impossible in the organization of the cosmos from what is mathematically possible and impossible, by conceiving the heavenly cycles according to commensurate numbers with a cause, and by determining measures of the heaven according to certain mathematical ratios, as well as putting together the natural science which is predictive on the basis of mathematics, and putting the mathematical objects before the other observable objects in the cosmos, as their principles.
Pythagorean thought was dominated by mathematics. In the area of
cosmology there is less agreement about what
... for they plainly say that when the one had been constructed, whether out of planes or of surface or of seed or of elements which they cannot express, immediately the nearest part of the unlimited began to be drawn in and limited by the limit.
Continuing with the Pythagoreans:
The Pythagoreans, too, held that void exists, and that it enters the heaven from the unlimited breath – it, so to speak, breathes in void. The void distinguishes the natures of things, since it is the thing that separates and distinguishes the successive terms in a series. This happens in the first case of numbers; for the void distinguishes their nature.
When the apeiron is inhaled by the peiron it causes separation, which also apparently means that it "separates and distinguishes the successive terms in a series." Instead of an undifferentiated whole we have a living whole of inter-connected parts separated by "void" between them. This inhalation of the apeiron is also what makes the world mathematical, not just possible to describe using maths, but truly mathematical since it shows numbers and reality to be upheld by the same principle. Both the continuum of numbers (that is yet a series of successive terms, separated by void) and the field of reality, the cosmos — both are a play of emptiness and form, apeiron and peiron. What really sets this apart from Anaximander's original ideas is that this play of apeiron and peiron must take place according to harmonia (harmony).
WORK AND THEORIES
After attacks on the Pythagorean meeting-places at Croton, the movement dispersed, but regrouped in Tarentum , also in Southern Italy. A collection of Pythagorean writings on ethics collected by Taylor show a creative response to the troubles.
The legacy of Pythagoras,
According to Kirk and Raven (1956), the ancient Pythagorean pentagram
was drawn with two points up and represented the doctrine of
Pentemychos . Pentemychos means "five recesses" or "five chambers,"
also known as the pentagonas — the five-angle, and was the title of
a work written by Pythagoras' teacher and friend
Pherecydes of Syros
Pythagoreans distinguished three kinds of lives: Theoretic, Practical
According to Stobaeus,
Revolving around the
Central Fire above Earth were the Moon, the Sun,
the planets, and finally—perhaps fixed and not rotating at
all—were the stars. Revolving around the
Central Fire below Earth
was another hypothetical astronomical object, the
However, it has been pointed out that
MUSIC AND HARMONY
Aristoxenus said that music was used to purify the soul just like medicine was used to purge the body. He also wrote several books about Pythagorean, a book on choruses (Περὶ χορῶν): fr. 103 Wehrli, on tragic dancing (Περὶ τραγικῆς ὀρχήσεως): fr. 104-106 Wehrli, and comparisons of dances (Συγκρίσεις): fr. 109 Wehrli, or on Listening to Music, on Tonoi, on Auloi and Instruments, as well as Elementa harmonica .
Related teachings were recorded by Philolaus' pupil
Commentary from Sir William Smith , Dictionary of Greek and Roman
Biography and Mythology (1870, p. 620). Musical principles played
almost as important a part in the Pythagorean system as mathematical
or numerical ideas. The opposite principia of the unlimited and the
limiting are, as
A musical scale presupposes an unlimited continuum of pitches, which must be limited in some way in order for a scale to arise. The crucial point is that not just any set of limiters will do. One may not simply choose pitches at random along the continuum and produce a scale that will be musically pleasing. The diatonic scale, also known as "Pythagorean," is such that the ratio of the highest to the lowest pitch is 2:1, which produces the interval of an octave. That octave is in turn divided into a fifth and a fourth, which have the ratios of 3:2 and 4:3 respectively and which, when multiplied, make an octave. If we go up a fifth from the lowest note in the octave and then up a fourth from there, we will reach the upper note of the octave. Finally the fifth can be made up by multiplication of three (largest) whole tones (each corresponding to the ratio of 9:8) and a perfecting semitone (with a ratio of 256:243). Likewise, the fourth can be made up of two whole tones and the same perfecting semitone. This is a good example of a concrete applied use of Philolaus' reasoning. In Philolaus' terms the fitting together of limiters and unlimiteds involves their combination in accordance with ratios of numbers (harmony). Similarly the cosmos and the individual things in the cosmos do not arise by a chance combination of limiters and unlimiteds; the limiters and unlimiteds must be fitted together in a "pleasing" (harmonic) way in accordance with number for an order to arise.
This idea can be seen as an influential precursor to Leibniz 's system of pre-established harmony .
Clark (1989), cited Le culte des muses chez les philosophes grecs, from Pierre Boyancé (1936) The chorus of the Muses was always one and the same, and they had charge of unison, harmony and rhythm, all that goes to make up concord.
A journal review in 1938 mentioned that Boyancé's book was about
Muses among the Greek philosophers, and mentions
Orpheus as a
musician. A thesis of the book is that
Excerpt from a speech by the character "Aristotle" in Protrepticus (Hutchinson and Johnson, 2015) Thus this is what it is to use anything: if the capacity is for a single thing, when someone is doing this very thing, and if the capacity is for a number of things, when he is doing the best of them; for example, with flutes, one uses them either only when playing the flute , or most of all then, as its other uses are presumably also for the sake of this. Thus one should say that someone who uses a thing correctly is using it more, for the natural objective and mode of use belong to someone who uses a thing in a beautiful and precise way. And now the only function of the soul, or else the greatest one of all, is thinking and reasoning. Therefore it is now simple and easy for anyone to draw the conclusion that he who thinks correctly is more alive, and he who most attains truth lives most, and this is the one who is intelligent and observing according to the most precise knowledge; and it is then and to those that living perfectly, surely, should be attributed, to those who are using their intelligence, i.e. to the intelligent. (p. 56)
Some authors mentioned a "Pythagorean diet", the abstention from eating meat, beans, or fish. Firenze debated the Pythagorean diet in 1743.
Some stories of Pythagoras' murder revolve around his aversion to beans. According to legend, enemies of the Pythagoreans set fire to Pythagoras' house, sending the elderly man running toward a bean field, where he halted, declaring that he would rather die than enter the field – whereupon his pursuers slit his throat. It has been suggested that the prohibition of beans was to avoid favism ; susceptible people may develop hemolytic anemia as a result of eating beans, or even of walking through a field where bean plants are in flower. It is more likely to have been for magico-religious reasons, perhaps because beans obviously demonstrate the potential for life, perhaps because they resemble the kidneys and genitalia. There was a belief that beans and human beings were created from the same material.
According to accounts from
Women were given equal opportunity to study as Pythagoreans, and
learned practical domestic skills in addition to philosophy. Women
were held to be different from men, sometimes in positive ways. The
priestess , philosopher and mathematician
Themistoclea is regarded as
Theano , Damo and Melissa as female disciples.
Female Pythagoreans are also some of the first female philosophers
from which we have texts. Although it is debated as to whether or not
all of the texts we have were actually written by women, we can see
Female philosophers include: Pythais (mother of Pythagoras), Theano (wife of Pythagoras), Cheilonis, Tyrsenis, Myia (Daughter of Theano and Pythagoras), Damo , Timycha , Bitale, Aspasia , Alexis, Perictione (believed to be Plato's mother), Arete , Melissa , Phintys , Ptolemais , and Arignote .
Neopythagoreanism was a revival in the 2nd century BC – 2nd century
AD period of various ideas traditionally associated with the followers
of Pythagoras, the Pythagoreans. Notable Neopythagoreans include
Nigidius Figulus ,
Apollonius of Tyana and
Moderatus of Gades . Middle
and Neo-Platonists such as Numenius and
They emphasized the distinction between the soul and the body . God
must be worshipped spiritually by prayer and the will to be good. The
soul must be freed from its material surroundings by an ascetic habit
of life. Bodily pleasures and all sensuous impulses must be abandoned
as detrimental to the spiritual purity of the soul.
In 1915, a subterranean basilica where 1st century Neo-Pythagoreans
held their meetings was discovered near
Porta Maggiore on Via
John Burnet (1892) noted The Neoplatonists were quite justified in
regarding themselves as the spiritual heirs of Pythagoras; and, in
their hands, philosophy ceased to exist as such, and became theology.
And this tendency was at work all along; hardly a single Greek
philosopher was wholly uninfluenced by it. Perhaps
* The Pythagorean idea that whole numbers and harmonic (euphonic)
sounds are intimately connected in music, must have been well known to
lute-player and maker
Vincenzo Galilei , father of
Dyad (Greek philosophy)
* ^ A B C Stanford Encyclopedia of Philosophy. "Philolaus".
Retrieved 30 May 2015.
* ^ John Burnet (1892). Early Greek Philosophy. p. 29.
* Cornelli, G.; McKirahan, R.; Macris, C. (eds.), On Pythagoreanism,
Berlin, Walter de Gruyter, 2013.
* Cerqueiro, Daniel. Evohé (
* Huffman, Carl. "Pythagoreanism". Stanford Encyclopedia of
* v * t * e