On 28 Jun 2017, at 16:03, John Clark wrote:
snip
>> Unicorns don't exist,
>In which theory?
Oh for christ's sake! This is really getting silly, now existence
depends on theories.
Of course not.
But *asserting* an existence depends on a theory or belief of some
subject doing the assertion.
For example, you just said to Adrian Chira: "Assuming there is a
largest prime number leads to a logical contradiction, but assuming
free will exists is like assuming Klogknee exists."
But Robinson Arithmetic, a weak but already sigma_1 complete theory
(and thus Turing universal) is consistent with "there is a biggest
prime number". You can add that axiom to RA without getting any
contradiction.
You were probably assuming Peano Arithmetic (which is Robinson
arithmetic + the induction axiom), or you were assuming the standard
model of arithmetic (which is a much stronger assumption than the
axioms of PA).
Except for the here-and-now 1p experience (consciousness), all
existence assertions presupposes some belief, that is, an unconscious
or a conscious theory.
And the unicorn certainly exists. It is the national animal of Scotland!
Bruno
John K Clark
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