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The issue is much more general than it appears in the above mathematical examples. The issue is: ‘Is there any sense in saying that a proposition is either true or false when there is no way of deciding the alternative?' or, to put the matter in a different form, ‘Should “true" be identified with “verifiable"?' I do not think we can make such an identification unless we commit ourselves to gross and gratuitous paradoxes. Take such a proposition as the following: 'It snowed on Manhattan Island on the 1st January in the year 1 A. D.'. There is no conceivable method by which we can discover whether this proposition is true or false, but it seems preposterous to maintain that it is neither.
Source: My Philosophical Development, 1959, by Bertrand Russell
More info.: https://russell-j.com/beginner/BR_MPD_10-030.HTM