Our Knowledge of the External World

Cover Our Knowledge of the External World
Our Knowledge of the External World
Russell Bertrand
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The above illustration of Kant's antinomies has only been introduced in order to show the relevance of the problem of infinity to the problem of the reality of objects of sense.
In the remainder of the present lecture, I wish to state and explain the problem of infinity, to show how it arose, and to show the irrelevance of all the solutions proposed by philosophers. In the following lecture, I shall try to explain the true solution, which has been discovered by the mathematicians, but neverthel
...ess belongs essentially Digitized by Google i6o SCIENTIFIC METHOD IN PHILOSOPHY to philosophy. The solution is definitive, in the sense that it entirely satisfies and convinces all who study it carefully. For over two thousand years the human intellect was baffled by the problem ; its many failures and its ultimate success make this problem peculiarly apt for the illustration of method.
The problem appears to have first arisen in some such way as the following.^ Pythagoras and his followers, who were interested, like Descartes, in the application of number to geometry, adopted in that science more arithmetical methods than those with which Euclid has made us familiar.


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