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cousin_it comments on Logic as Probability - Less Wrong
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If you want quantifiers, you can just program your robot to respond to the symbol "for all" so that when it sees "for all x, x=y" it writes all the implications in the notebook, and when x=y for all x, it writes "for all x, x=y". This is an infinite amount to writing to do, but there was always an infinite amount of writing to do - the robot is infinitely fast, and anyway is just a metaphor for the rules of our language.
Sorry, I should've said "statements that are provable or disprovable from the axioms", mentioning quantifiers was kinda irrelevant. Are you saying that your robot will eventually write out truth values for statements that are independent of the axioms as well? (Like the continuum hypothesis in ZFC.)
I feel like the robot metaphor may be outside of its domain of validity by now. Anyhow, I replied over in the other branch.