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>There is no algorithm that can determine the truth of any proposition in arithmetic (for example). It is impossible, in principle, to construct such an algorit
by hackinthebochs 14y ago
>There is no algorithm that can determine the truth of any proposition in arithmetic (for example). It is impossible, in principle, to construct such an algorithm. But given any proposition in arithmetic, the mind can decide its truth value.
These two statements seem to contradict, unless you grant that the mind either fudges the proof or constructs new axioms such that the proof can be valid. Why do you assume a program can never do this?
- leephillips 14y agoBecause the program that does it would itself be an algorithm with its own finite set of axioms. There would be undecidable propositions unreachable by the program.