Now if we are to accept the common idea of continuity . . . we must either say that a continuous line contains no points or . . . that the principle … - Charles Sanders Peirce

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Now if we are to accept the common idea of continuity . . . we must either say that a continuous line contains no points or . . . that the principle of excluded middle does not hold of these points. The principle of excluded middle applies only to an individual . . . but places being mere possibilities without actual existence are not individuals.