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" It remains to inquire what is the ground of our belief in axioms — what is the evidence on which they rest? I answer, they are experimental truths, generalizations from observation. The proposition, "Two straight lines cannot... "
The Collected Mathematical Papers of Arthur Cayley - Page 430
by Arthur Cayley - 1896 - 643 pages
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A System of Logic, Ratiocinative and Inductive: Being a Connected ..., Volume 1

John Stuart Mill - Knowledge, Theory of - 1846 - 624 pages
...experimental truths ; generalizations from observation. The proposition, Two straight lines cannot inclose a space — or in other words, Two straight lines which have once met, do not meet again, but continue to diverge — is an induction from the evidence of our senses. This...
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Essays on the Intellectual Powers of Man

Thomas Reid - Intellect - 1850 - 496 pages
...experimental truths ; generalizations from observation. The proposition, Two straight lines cannot inclose a space, — or, in other words, Two straight lines which have once met do not meet again, but continue to diverge, — is an induction from the evidence of our senses." According...
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Elements of the Philosophy of the Human Mind

Dugald Stewart - Psychology - 1854 - 514 pages
...experimental axioms — generalizations from observation. The proposition, ' Two straight lines cannot inclose a space' — or in other words, 'Two straight lines which have once met, do not meet again, but continue to diverge' — is an induction from the evidence of our senses." When...
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Essays on the Intellectual Powers of Man

Thomas Reid - Intellect - 1855 - 528 pages
...experimental truths ; generalizations from observation. The proposition, Two straight lines cannot inelose a space, — or, in other words, Two straight lines which have once met do not meet again, but continue to diverge, — is an induction from the evidence of our senses." According...
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Elements of the Philosophy of the Human Mind

Dugald Stewart - Psychology - 1859 - 508 pages
...axioms , — generalizations from observation. The proposition, ' Two straight lines cannot inclose a space' — or in other words, ' Two straight lines which have once met, do not meet again, but continue to diverge' — is an induction from the evidence of our senses." When...
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A Logic of Facts, Or, Every-day Reasoning

George Jacob Holyoake - Logic - 1866 - 118 pages
...truths — generalisations from observation. The proposition that Two straight lines cannot inclose a space— or, in other words, Two straight lines which have once met do not meet again, but continue to diverge — is an induction from the evidence of our senses.'^ '...
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Proceedings of the ... Annual Convocation, Issue 5

University of the State of New York - Education - 1869 - 218 pages
...experimental truths; generalizations from observation. The proposition, two straight lines cannot inclose a space, or, in other words, two straight lines which have once met do not meet again, but continue to diverge, is an induction from the evidence of our senses." In this...
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Mind, Volume 3

Electronic journals - 1878 - 608 pages
...II., cv, §§4, 5), is that these axioms are "experimental truths; generalisations from observation. The proposition, Two straight lines cannot enclose...other words, Two straight lines which have once met, do not meet again, but continue to diverge — is an induction from the evidence of our senses". With...
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The Contemporary Review, Volume 31

Great Britain - 1878 - 916 pages
...evidence on which they rest ? I answer, they are experimental truths ; generalizations from observation. The proposition, Two straight lines cannot enclose...other words, Two straight lines which have once met, do not meet again, but continue to diverge — is au induction from the evidence of our senses." This...
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Mind, Volume 3

Electronic journals - 1878 - 692 pages
...II., cv, §§4, 5), is that these axioms are "experimental truths; generalisations from observation. The proposition, Two straight lines cannot enclose...other words, Two straight lines which have once met, do not meet again, but continue to diverge — is an induction from the evidence of our senses". With...
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