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Updated: May 10, 2025
The free act is incommensurable with the idea, and its "rationality" must be defined by this very incommensurability, which admits the discovery of as much intelligibility within it as we will. Such is the character of our own evolution; and such also, without doubt, that of the evolution of life.
The individuality and incommensurability of this psychical causality shows itself in another series of factors which make even the form of the psychical process quite distinctive, and produce phenomena which have no parallel in the material sequences of the world, indeed, conflict with all its fundamental laws.
Well then; do men deliberate about everything, and is anything soever the object of Deliberation, or are there some matters with respect to which there is none? Well: about eternal things no one deliberates; as, for instance, the universe, or the incommensurability of the diameter and side of a square.
The properties of commensurability and incommensurability in lines and surfaces, of rational and irrational lines would cease to have any meaning. In fact all that is contained in the tenth book of Euclid would lose its foundation. The atom is made complete by the accidents, without which it cannot be.
Theodorus, Plato's teacher in mathematics, extended the theory of the irrational by proving incommensurability in certain particular cases other than that of the diagonal of a square in relation to its side, which was already known.
From the oscillation of value and the irregular effects resulting therefrom the socialists and economists, each in their own way, have reasoned to opposite, but equally false, conclusions: the former have made it a text for the slander of political economy and its exclusion from social science; the latter, for the denial of all possibility of reconciliation, and the affirmation of the incommensurability of values, and consequently the inequality of fortunes, as an absolute law of commerce.
For I entreat the economists to question themselves for a moment in the silence of their hearts, far from the prejudices which disturb them, and regardless of the employments which occupy them or which they wait for, of the interests which they serve, of the votes which they covet, of the distinctions which tickle their vanity: let them tell me whether, hitherto, they have viewed the principle that all labor should leave an excess in connection with this series of premises and conclusions which we have elaborated, and whether they ever have understood these words to mean anything more than the right to speculate in values by manipulating supply and demand; whether it is not true that they affirm at once, on the one hand the progress of wealth and well-being, and consequently the measure of values, and on the other the arbitrariness of commercial transactions and the incommensurability of values, the flattest of contradictions?
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