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" Achilles run ten times as fast as the tortoise, yet if the tortoise has the start, Achilles will never overtake him. For suppose them to be at first separated by an interval of a thousand feet: when Achilles has run these thousand feet, the tortoise will... "
Logic: Designed as an Introduction to the Study of Reasoning - Page 108
by John Leechman - 1864 - 209 pages
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A System of Logic, Ratiocinative and Inductive: Being a Connected ..., Volume 2

John Stuart Mill - Knowledge, Theory of - 1843 - 654 pages
...interval of a thousand feet: when Achilles has run these thousand feet, the tortoise will have got on a hundred; when Achilles has run those hundred, the...any length of time that can be supposed ; but in the premisses " ever" does not mean any length of time: it means any number of subdivisions of time. It...
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A biographical history of philosophy, Volume 1

George Henry Lewes - Philosophers - 1845 - 258 pages
...tortoise will have run a hundred, and when Achilles has run those hundred the tortoise will have got on ten, and so on for ever : therefore Achilles may run...any length of time that can be supposed ; but in the premisses " ever" does not mean any length of time ; it means any number of subdivisions of time. It...
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An elementary treatise on logic, by the author of 'An antidote against ...

Portia Young - Logic - 1852 - 140 pages
...feet, the tortoise would have got 100; when Achilles has got those 100, the tortoise will have run 10, and so on for ever ; therefore, Achilles may run for ever without overtaking the tortoise. Now, " for ever," in the conclusion, means for any length of time that can be supposed ; but in the premise,...
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An Elementary Treatise on Logic: Designed Chiefly for the Use of Schools ...

1852 - 132 pages
...feet, the tortoise would have got 100 ; when Achilles has got those 100, the tortoise will have run 10, and so on for ever ; therefore, Achilles may run for ever without overtaking the tortoise. Now, " for ever," in the conclusion, means for any length of time that can be supposed ; but in the premise,...
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The Biographical History of Philosophy: From Its Origin in Greece ..., Volume 1

George Henry Lewes - Philosophers - 1857 - 396 pages
...on forever : therefore Achilles may run forever without overtaking the tortoise. Now the " forever" in the conclusion means, for any length of time that can be supposed ; but in the premises, " forever" does not mean any length of time — it means any number of subdivisions of time. It means...
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A System of Logic, Ratiocinative and Inductive

John Stuart Mill - Knowledge, Theory of - 1858 - 666 pages
...interval of a thousand feet : when Achilles has run these thousand feet, the tortoise will have got on a hundred ; when Achilles has run those hundred, the...any length of time that can be supposed ; but in the premisses " ever" does not mean any length of time : it means any number of subdivisions of time. It...
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A Treatise on Logic, Pure and Applied

Stephen Henry Emmens (writer on logic.) - Logic - 1865 - 202 pages
...interval of a thousand feet : when Achilles has run these thousand feet, the tortoise will have got on a hundred ; when Achilles has run those hundred, the tortoise, will have run ten ; therefore, Achilles may run for ever without overtaking the tortoise. " Now, the ' for ever ' in...
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The History of Philosophy: Ancient philosophy.- Vol. 2. Modern philosophy

George Henry Lewes - Philosophy - 1871 - 894 pages
...tortoise will have run a hundred, and when Achilles has run those hundred the tortoise will have got on ten, and so on for ever: therefore Achilles may run...any length of time that can be supposed ; but in the premisses ' for ever' does not mean any length of time — it means any number of subdivisions of time....
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A History of the Intellectual Development of Europe, Volume 1

John William Draper - Europe - 1875 - 464 pages
...tortoise will have run a hundred, and when Achilles has run these hundred the tortoise will have got on ten, and so on for ever; therefore Achilles may run for ever without overtaking the tortoise." Such were his arguments against the existence of motion; his proof of the existence of One, the indivisible...
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General sketch of the history of pantheism [by C.E. Plumptre].

Charles Edward Plumptre - 1878 - 422 pages
...tortoise will have run a hundred, and when Achilles has run those hundred the tortoise will have got on ten, and so on for ever ; therefore Achilles may run...any length of time that can be supposed ; but in the premisses " for ever " does not mean any length of time — it means any number of subdivisions of...
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