Let Me Point Out the Errors of Mathematics and Others on Miss Chan's Behalf!

The forum is very lively today, all because of Miss Chan's rebuttal of Mathematics' claim that "all human thoughts can be stored in a binary computer." In the case of infinite encoding, Miss Chan's proof is already very complete. Later, Mathematics proposed another hypothesis -- that encoding is finite. Actually, the proof in this case is even simpler, so let me have a go at it too!

Since encoding bit-length is assumed finite, the number of encodable binary numbers is finite. If the maximum value of encoding bit-length is set to N, the number of encodable binary numbers is 2 to the N-th power. Due to the encoding convention, each thought -- or in more professional terms, each proposition -- corresponds to an encoding. Then the logical conjunction of all these propositions followed by logical negation is also a proposition, and this proposition is not among the previous 2^N propositions -- meaning this proposition hasn't been encoded. This is a contradiction.

Actually, the key issue lies in the universal judgment "all human thoughts can be stored in a binary computer." The generalized diagonal method is essentially logical conjunction of propositions followed by logical negation, and has nothing to do with bit-length. So attempting to make the diagonal nonexistent through finite bit-length fundamentally misunderstands the essence of the diagonal method.

In mathematical propositions, universal judgments involving "all" generally tend to fall into logical traps -- this can be seen from the "barber paradox" and "Russell's paradox." If one says "human thoughts can be stored in a binary computer" -- this proposition without the universal judgment would be valid. So nothing should be too absolute -- absolutes always lead to problems.