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L'Unità del Pensiero |
ultimo aggiornamento: aprile 2008
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THE SCHOOL OF PYTHAGOREANS
The School of Pythagoreans, also known as “Italica”, was founded in southern Italy, precisely in the city of Croton, in the ancient Magna Grecia. Its founder was Pythagoras (est. 570-497 B.C.), a legendary character to whom demigod powers were attributed. In reality, we know very little about him, and the same Aristotle, while illustrating the principles of the school, makes reference to the Pythagoreans only in a general way, thus proving his own doubts on the person and works of Pythagoras. Our philosopher was born in the island of Samos, where it seems he lived until the age of forty. Successively, he emigrated to Croton where he founded his school, or rather, a religious society for men and women, based on very strict ascetic rules, with mysterious ceremonies (probably Orphic), and imparting an esoteric-based teaching characterised by constrained secrecy. All historians seem to agree on this point. Pythagoreanism existed for about two centuries, until it intertwined with the themes of Plato's Academy. Although the school was folded in a behaviour based on secrecy, it however was open to political activities (in favour of the Aristocrats), but when the Democrats of Croton took power following an insurrection towards the end of the 6th century, the latter burned the school, and Pythagoras was obliged to escape to Metaponto, where it seems he died in 497 B.C. His disciples were scattered: Philolaus (who is author of the first Pythagorean to write a book, and of whom a number of written fragments still survive) founded a school in Ancient Greece and another one in Thebes; Archytas went to Taranto and others, like Simmia e Cebetes, became friends of Socrates (as Plato reminds us). Pythagoras was considered by his disciples as if he was a God, and his word was never put into discussion (his disciples used to state that “ipse dixit”, or rather, “he said so”): miracles and ubiquity were also attributed to him. However we know nothing, or at least we have no certainty about any eventual works written by him, although we do have proof of his fundamental teachings at the school, which probably derived from the ancient Orphic movement: starting with metempsychosis, a belief in which the soul is immortal and is reborn in both human and animal incarnations after death, and for this reason rules were established to purify the soul, such as the prohibition against eating meat, and the compliance of practical rules such as celibacy, a daily conscience examination, etc.
First of all, for history's sake, it is of interest to ask ourselves which are the connections between the School of Pythagoreans and the previous School of Miletus. There are two ways to answer this question. The first refers to the contents, to see if the philosophers of both schools have stated the same identical or similar statements, while the second way refers to the formal sense, or rather if the conceptual structure adopted for the School of Miletus is also valid for the Pythagoreans. I would like to remind you that we have grouped the contents of the School of Miletus into much generalised concepts, in a way that, by means of this categorical structure we can distinguish the different aspects in a better way. In this way, the history of philosophy based on concepts, is born, and in this way (at least I hope) will exceed the one exposed “though narration”, and an absolute philosophy will start to be outlined. Let us return to the School of Pythagoreans, and let us consider the connections with the preceding School of Miletus from the contents' point of view: it must be stated that Pythagoras completed a one and only revolution, as we shall soon see when we expose his doctrine. In this way there is an incurable fracture between the two schools, and the Pythagoreans seem to have appeared suddenly, from thin air. If on the other hand the relation between the two philosophies is analysed from a categorical point of view, which shows the intimate logical structure, what emerges is a continuity of thought which places the Pythagoreans after the Milesians, in a natural way. In the examination and exposition of the thoughts of Thales, Anaximander and Anaximenes, the following five categories were sufficient, and thus we shall also use them for the Pythagoreans:
The category of the becoming, or rather the transformation of the being through time, is lacking, even though in some way circulation deals with this theme, though more like an end rather than an explanation. The category of the becoming will come to birth very shortly in the history of philosophy.
There is no doubt that the philosophy of the Pythagoreans finds its foundations in the mathematical sensitivity of Pythagoras who, by observing the unvarying and harmonious relations in Nature (especially of acoustics, where he discovered the musical intervals), the study of arithmetic, geometry, the movement of the stars, etc., matured a pseudo-scientific thought capable of responding to the conceptual structure of the Milesians, and not only. Actually all historians agree on the fact that in the chronology of the philosophical thought Pythagoras was the first to conceive brightly and lucidly the mathematical character of the Universe, even though the final result was a mixture of science and magic (very normal in those times). But it must also be said in his favour that he was capable of fusing together a large number of beliefs, some of which were scientific, others mystic, and others religious, into one united system. Let us now see how he responds to the categories of the Milesians, on the continuation of Naturalism. The search for the origin is confirmed, but it is not so for water, the apeiron, and air: this time the content of the category is made of the “number”, and to understand what Pythagoras wanted to state with this expression, we have to consider what Aristotle had declared: “Numbers are the origins of all things, and the elements of numbers are the elements of all things”. This definition, which is given to us by the Stagirite very briefly, must be clarified in a very careful manner; otherwise the risk is of distorting the Pythagorean thought. Therefore, how did Pythagoras come to conceive the fact that numbers are the origins of all things? Which intellectual path did he follow and logically lead him to this conclusion ? The presuppositions are two:
1) First of all, Pythagoras never conceived the meaning of “abstract rule”. The rules of Nature are not expressed by the numerical language, but in a formal manner. Only after “after” having obtained the abstract rule (or formula if you refer) can we attribute a numerical value to its variables (or rather the value of greatness), and as a result we get the number. For example, if a segment is X long, its half will measure X/2, and this is an abstract rule, and if we decide that X = 14, the half will result 14/2 =7. Pythagoras would have stated that “7 represents half the segment”, using a way of expressing himself which has also reached us, while 7 represents only a measurement. Other ways of expression of the philosopher do influence us even today, such as when we say “the squared and cubed number”. But we will get back to this topic in due time. We find numbers without formal rules when we are faced with constant relations, and this is exactly what Pythagoras found out while studying musical intervals. But constant relations in Nature are particular cases, and this was understood by Pythagoras, even though he declared that this formal rule was to be denoted as the theorem of Pythagoras. To conclude, the number-concept corresponds to a constant relation between different greatnesses (while the number is in relation between variables according to the formal rule).
2) However, we cannot simply justify Aristotle's definition. We lack a second presupposition in order to be able to reconstruct the intellectual path which had lead us to that definition. Pythagoras noticed that the number expressed a constant relation with greatness (as explained above), and thus that numbers were not influenced by the variations of this phenomena, i.e., they remained constant. Thus the quantity was imposed as matter/substance, while the quality was only apparent and changeable. And since numbers originated from the relation between things, he inverted the relation and thought that numbers were the cause of these relations. This is how numbers become the origin of all things, and every thing results as being made up of numbers. Here we have yet again an example of noumenic pantheism, and therefore metaphysics, since the origin is transferred in things in a non sensitive way. It seems to me that I have demonstrated how the Pythagorean thought originated, founded on two wrong presuppositions. In reality, (for who wants to know more) they are two typical logical errors, very common to the magical mentality of the primitives. The first consists of the confusion of the particular and the general, choosing the concrete for the abstract. The second is instead, the inversion of the relation, in our case, cause-effect. Nevertheless, the presuppositions allowed Pythagoras to respond to the first four categories of the Milesians, thus carrying on with their problematics. Let us now see how he enriched the foundations of this thought, succeeding in some way in rendering it more united.
In order to introduce immediately the doctrine, we must first deepen the important category of the “one-much motor”, or rather how one goes form the originating principle, from which all things origin, to the same things. In other words, how does the multiple determine itself with all its differences, forming what is defined as the “Being”.
(N.5, to be continued) |