Categories and Modalities of Uncertainty - trivent.hu

Paradox of Small Number
Let N = {1, 2, ……, 100} be a universe of discourse.
Consider the following assertions in binary valued logic:
(i) 1 is a small number.
(ii) A small number added by 1 is also a small number.
Then, we conclude that any number, e.g., 100 is small.
This is not acceptable.
Therefore, there is something wrong about the assertions.
Since (i) is correct, (ii) must be wrong. That is, there may
exist a certain number n * such that n is small if n n *
,
and otherwise, not small.
Neither this is acceptable.
Hence, the assertions cause a paradox.