Proudhon's analysis is thoroughly confused, and made worse by very bad mathematics. As Marx describes, Proudhon's basic explanation of the existence of surplus value, or surplus product, is the role of cooperative as against individual labour. Proudhon says,
“An axiom generally admitted by economists is that all labour must leave a surplus. In my opinion this proposition is universally and absolutely true: it is the corollary of the law of proportion, which may be regarded as the summary of the whole of economic science. But, if the economists will permit me to say so, the principle that all labour must leave a surplus is meaningless according to their theory, and is not susceptible of any demonstration.” (p 85)
And,
“This principle of surplus labour,” continues M. Proudhon, “is true of individuals only because it emanates from society, which thus confers on them the benefit of its own laws." (p 85)
In other words, Proudhon divides individuals and society, and, then, makes society into a person. As Marx puts it, “he turns it into a person-society – a society which is not by any means a society of persons, since it has its law apart, which have nothing in common with the persons of which society is composed, and its “own intelligence,” which is not the intelligence of common men, but an intelligence devoid of common sense.” (p 85)
Now, it is, of course true that cooperative labour is more productive than individual labour, but Proudhon is far from being the first to have recognised that fact. It is also true, as Marx and Engels describe in many places, that the basis of all surplus-value is relative surplus value, i.e. the ability to raise productivity so that the amount of necessary labour performed by the labourer is less than the amount of labour they actually perform, and one means of achieving that is by cooperative as against individual labour.
This creation of a person-society is the same as the bourgeois-idealist notions of terms such as “nation”, “the people”, and so on, which are abstract and devoid of any concrete analysis of their division into antagonistic classes. Marx quotes Thomas Cooper.
“The moral entity – the grammatical being called a nation, has been clothed in attributes that have no real existence except in the imagination of those who metamorphose a word into a thing.... This has given rise to many difficulties and to some deplorable misunderstanding in political economy.” (p 85)
And, not only in political economy, as seen when such issues as “national self-determination” is discussed, in terms of abstract rights or struggles by “people” and “nations”, as against the rights and struggles of classes.
Proudhon seeks to prove that the surplus produced by labour is solely a consequence of society, and of cooperative labour. He even claims to have done so with mathematical rigour. But, his example is wholly confused, and the mathematics he uses absurd. He wants to show that the benefits of invention that saves labour goes to society, and not to the individual, and so the laws governing society are the opposite of those governing the activity of individuals.
He gives the example of a railway, which is four times faster than transport by road. The cost of road travel is 18 centimes per kilometre. If the railway charged this amount, it would not make 10% profit, he says, the amount made by road transport. So, although rail provides a great benefit for society, as a result of this much greater speed, and saving of its labour-time, for the individual train operator, it would not provide this benefit. Suppose, then, Proudhon says, the train operator raised prices to 25 centimes, so as to make this same profit, the result would be that they would see all of their business disappear to road transport.
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