(“When the banished Samians reached Sparta, they had audience of the magistrates, before whom they made a long speech, as was natural with persons greatly in want of aid. When it was over, the Spartans averred that they could no longer remember the first half of their speech, and thus could make nothing of the remainder. Afterwards the Samians had another audience, whereat they simply said, showing a bag which they had brought with them, ‘The bag wants flour.’ The Spartans answered that they did not need to have said ‘the bag’.”)
That is a good point. I defeated myself. The actual measure of goodness is in terms of how many words you need to make somebody truly understand, in the shortest amount of time.
That means telling you the peano axioms would not count as having told you that the system they are defining is incomplete. Though that depends on the mind. If I tell the piano axioms to an AGI that does not know about gödel incompleteness it could probably figure it out very quickly.
You did not need the second sentence.
(“When the banished Samians reached Sparta, they had audience of the magistrates, before whom they made a long speech, as was natural with persons greatly in want of aid. When it was over, the Spartans averred that they could no longer remember the first half of their speech, and thus could make nothing of the remainder. Afterwards the Samians had another audience, whereat they simply said, showing a bag which they had brought with them, ‘The bag wants flour.’ The Spartans answered that they did not need to have said ‘the bag’.”)
That is a good point. I defeated myself. The actual measure of goodness is in terms of how many words you need to make somebody truly understand, in the shortest amount of time.
That means telling you the peano axioms would not count as having told you that the system they are defining is incomplete. Though that depends on the mind. If I tell the piano axioms to an AGI that does not know about gödel incompleteness it could probably figure it out very quickly.