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Updated: May 6, 2025
As far as the question of the right to interpret nature teleologically is concerned, it would be entirely indifferent whether what Korschinsky calls “the tendency to progress,” and the system of laws in obedience to which evolution brings forth its forms, can be interpreted “mechanically” or not; that is to say, whether or not evolution depends on conditions and potentialities of living matter, which can be demonstrated and made mechanically commensurable or not.
As we have seen, the discovery of the incommensurable rendered inadequate the Pythagorean theory of proportion, which applied to commensurable magnitudes only. It would no doubt be possible, in most cases, to replace proofs depending on proportions by others; but this involved great inconvenience, and a slur was cast on geometry generally.
The next words, “And he gave him to be the head over all things to the church,” do furnish another argument against him. Christ’s headship, and his government as Mediator, are commensurable, and of an equal extent. Christ is a head to none but to his church; therefore no government is given to him as Mediator but the government of his church.
The next step is to classify pains and pleasures, which though commensurable as psychological forces, have obviously very different qualities. Bentham gives the result of his classification without the analysis upon which it depends. J. S. Mill remarks that this table should be studied by any one who would understand Bentham's philosophy. Such a study would suggest some unfavourable conclusions.
First of all the great legal maxim was proclaimed, that freedom is not a possession commensurable with property, but an eternal right of man, of which the state is entitled judicially to deprive the criminal alone, not the debtor.
Many a nebulous mass of hieroglyphically inscribed meanings did he this Champollion, defying all human enigmas, this Herschel, or Lord Rosse, forever peering into the obscure chasms and yawning abysses of human astronomy resolve into orderly constellations, that, once and for all, through his telescopic interpretation and enlargement, were rendered distinct and commensurable amongst men.
If a unified and “natural” explanation is really possible, the beginning and end of all this “reducing to simpler terms” must be to bridge over the gulf between these; but this, in the sense of naturalism, necessarily means that the mental sciences must in some way be reduced to terms of natural science, and that the phenomena, processes, sequences, and laws of consciousness must likewise be made “commensurable” with and be linked on to the apparently simpler and clearer knowledge of “Nature,” and, if possible, be subordinated to its phenomena and laws, if not indeed derived from them.
The telegraph completes the mastery over space in the conveyance of thought that the railway attains in that of persons and property. Its facilities here are commensurable with its duty of placing thousands of all countries in instantaneous communication with their homes.
Aristotle mentions an ancient proof of the incommensurability of the diagonal with the side by a reductio ad absurdum showing that, if the diagonal were commensurable with the side, it would follow that one and the same number is both odd and even. This proof was doubtless Pythagorean. A word should be added about the Pythagorean astronomy.
This is not a singular eccentric idea of mine; it is one for which ample support is to be found in the writings of absolutely respectable contemporaries, who are quite untainted by association with fiction. It is now understood that conceivably only in the subjective world, and in theory and the imagination, do we deal with identically similar units, and with absolutely commensurable quantities.
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