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Quandary and Intuitionism

I 1. The philosophical problems of vagueness are set by the sorites paradox, an instance of which is given by the following inference (SI): (1) A person with only 2¢ isn’t rich. (2) There isn’t a non-negative integer n such that a person with n¢ isn’t rich but a person with n + 1¢ is rich. (3) ∴ A person with 5,000,000,000¢—i.e. $50 million— isn’t rich. Put into symbolic abbreviation, this reads: (1) ¬R(2) (2) ¬∃n[¬R(n) & R(n + 1)] (3) ∴ ¬R(5,000,000,000) SI is a paradox because it presents four appearances that cannot all be veridical: first, it appears to be valid—after all, it’s both classically and intuitionistically valid; second, its sorites premiss, (2), seems merely to state the obvious fact that in the sorites march from 2¢ to 5,000,000,000¢ there is no precise point that marks the cutoff between not being rich and being rich; third, premiss (1), which asserts that a person with only 2¢ isn’t rich, is surely true; and fourth, the conclusion (3), which asserts that a person with 5,000,000,000¢—i.e. $50 million—isn’t rich, is surely false.