Congress of Arts And Science 1
Congress of Arts And Science 1
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But Kempe now very beautifully shows (and here lies his great and original contri- bution to our topic) — he shows, I say, that the ordinal relations of geometry, as well as of the number-system, can all be regarded as indistinguishable from mere varuxtiaria of those relations which, in pure logic, one finds to be the symmetrical relations obtaining within pairs or triads of classes or of statements. The formal identity of the geometrical relation called ''between" with a purely logical relatio...n which one can define as existing or as not existing amongst the mem- bers of a given triad of logical classes, or of logical statements, is shown by Kempe in a fashion that I cannot here attempt to expound.
But Kempe's result thus enables one, as I believe, to simplify the theory of relations far beyond the point which Russell in his brilliant book has reached. For Kempe's triadic relation in question can be stated, in what he calls its obverse form, in perfectly symmetrical terms. And he proves very exactly that the resulting logical rela- tion is precisely identical, in aU its properties, with the fundamental ordinal relation of geometry.
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You can find similar books in the "Read Also" column, or choose other free books by Münsterberg, Hugo, 1863-1916 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
But Kempe now very beautifully shows (and here lies his great and original contri- bution to our topic) — he shows, I say, that the ordinal relations of geometry, as well as of the number-system, can all be regarded as indistinguishable from mere varuxtiaria of those relations which, in pure logic, one finds to be the symmetrical relations obtaining within pairs or triads of classes or of statements. The formal identity of the geometrical relation called ''between" with a purely logical relatio...n which one can define as existing or as not existing amongst the mem- bers of a given triad of logical classes, or of logical statements, is shown by Kempe in a fashion that I cannot here attempt to expound.
But Kempe's result thus enables one, as I believe, to simplify the theory of relations far beyond the point which Russell in his brilliant book has reached. For Kempe's triadic relation in question can be stated, in what he calls its obverse form, in perfectly symmetrical terms. And he proves very exactly that the resulting logical rela- tion is precisely identical, in aU its properties, with the fundamental ordinal relation of geometry.
What to read after Congress of Arts And Science 1?
You can find similar books in the "Read Also" column, or choose other free books by Münsterberg, Hugo, 1863-1916 to read onlineMoreLess
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