The Conception of the Infinite And the Solution of the Mathematical Antinomies
The Conception of the Infinite And the Solution of the Mathematical Antinomies
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We THE ANTINOMIES OF HAMILTON. 43 cannot conceive the infinite regress of time; for such a notion could only be realized by the infinite addition in thought of finite times, and such an addition would itself require an eternity for its accomplishment. If we dream of effect- ing this, we only deceive ourselves by substi- tuting the indefinite for the infinite, than which no two notions can be more opposed. " The negation of a commencement of time involves, likewise, the affirmation that an infin...ite time has, at every moment, already run ; that is, it implies the contradiction that an infinite has been completed. For the same reasons we are unable to conceive an infinite progress of time; while the infinite regress and the infinite prog- ress, taken together, involve the triple contra- diction of an infinite concluded, of an infinite commencing, and of two infinities not exclusive of each other. " * The statement that past time cannot be re- garded as infinite because limited by the present * " Metaphysics, " New York, 1880, p.
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To quickly assess the difficulty of the text, read a short excerpt:
We THE ANTINOMIES OF HAMILTON. 43 cannot conceive the infinite regress of time; for such a notion could only be realized by the infinite addition in thought of finite times, and such an addition would itself require an eternity for its accomplishment. If we dream of effect- ing this, we only deceive ourselves by substi- tuting the indefinite for the infinite, than which no two notions can be more opposed. " The negation of a commencement of time involves, likewise, the affirmation that an infin...ite time has, at every moment, already run ; that is, it implies the contradiction that an infinite has been completed. For the same reasons we are unable to conceive an infinite progress of time; while the infinite regress and the infinite prog- ress, taken together, involve the triple contra- diction of an infinite concluded, of an infinite commencing, and of two infinities not exclusive of each other. " * The statement that past time cannot be re- garded as infinite because limited by the present * " Metaphysics, " New York, 1880, p.
What to read after The Conception of the Infinite And the Solution of the Mathematical Antinomies?
You can find similar books in the "Read Also" column, or choose other free books by Fullerton George Stuart to read onlineMoreLess
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