History of Western Philosophy - Bertrand Russell [25]
But what has all this to do with mathematics? It is connected by means of an ethic which praised the contemplative life. Burnet sums up this ethic as follows:
We are strangers in this world, and the body is the tomb of the soul, and yet we must not seek to escape by self-murder; for we are the chattels of God who is our herdsman, and without His command we have no right to make our escape. In this life, there are three kinds of men, just as there are three sorts of people who come to the Olympic Games. The lowest class is made up of those who come to buy and sell, the next above them are those who compete. Best of all, however, are those who come simply to look on. The greatest purification of all is, therefore, disinterested science, and it is the man who devotes himself to that, the true philosopher, who has most effectually released himself from the 'wheel of birth.'6
The changes in the meanings of words are often very instructive. I spoke above about the word 'orgy'; now I want to speak about the word 'theory'. This was originally an Orphic word, which Cornford interprets as 'passionate sympathetic contemplation'. In this state, he says, 'The spectator is identified
with the suffering God, dies in his death, and rises again in his new birth.' For Pythagoras, the 'passionate sympathetic contemplation' was intellectual, and issued in mathematical knowledge. In this way, through Pythagoreanism, 'theory' gradually acquired its modern meaning; but for all who were inspired by Pythagoras it retained an element of ecstatic revelation. To those who have reluctantly learnt a little mathematics in school this may seem strange; but to those who have experienced the intoxicating delight of sudden understanding that mathematics gives, from time to time, to those who love it, the Pythagorean view will seem completely natural even if untrue. It might seem that the empirical philosopher is the slave of his material, but that the pure mathematician, like the musician, is a free creator of his world of ordered beauty.
It is interesting to observe, in Burnet's account of the Pythagorean ethic, the opposition to modern values. In connection with a football match, modern-minded men think the players grander than the mere spectators. Similarly as regards the State: they admire more the politicians who are the contestants in the game than those who are only onlookers. This change of values is connected with a change in the social system—the warrior, the gentleman, the plutocrat, and the dictator, each has his own standard of the good and the true. The gentleman has had a long innings in philosophical theory, because he is associated with the Greek genius, because the virtue of contemplation acquired theological endorsement, and because the ideal of disinterested truth dignified the academic life. The gentleman is to be defined as one of a society of equals who live on slave labour, or at any rate upon the labour of men whose inferiority is unquestioned. It should be observed that this definition includes the saint and the sage, insofar as these men's lives are contemplative rather than active
Modern definitions of truth, such as those of pragmatism and instrumentalism, which are practical rather than contemplative, are inspired by industrialism as opposed to aristocracy.
Whatever may be thought of a social system which tolerates slavery, it is to gentlemen in the above sense that we owe pure mathematics. The contemplative ideal, since it led to the creation of pure mathematics, was the source of a useful activity; this increased its prestige, and gave it a success in theology, in ethics, and in philosophy, which it might not otherwise have enjoyed.
So much by way of explanation of the two aspects of Pythagoras: as religious prophet and as pure mathematician. In both respects he was immeasurably influential, and the two were not so separate as they seem to a modern mind.
Most sciences, at their inception, have been connected with some form of false belief, which gave them a fictitious value. Astronomy was connected