Sujet : Re: how
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.mathDate : 13. Jun 2024, 14:16:13
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <07225a5f-8007-4fbb-a8fa-c741797d2b65@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
On 6/13/2024 6:55 AM, WM wrote:
Le 12/06/2024 à 23:12, Jim Burns a écrit :
If any natural number is undefinable, then
the first undefinable has a definable predecessor.
>
That is your error.
Proposal 1.
Definitions are only
statements of _what the definer means_
Without evidence to the contrary,
the definer is presumed to be
honest and aware of what they mean, and
definitions are presumed to be
true statements of what they mean.
On questions beyond what the definer means,
their definitions do not receive
a presumption of truth,
but they remain free to argue their POV.
The definable numbers are definable and
have definable successors.
The minimal inductive set contains
all and only finite von Neumann ordinals.
You will never get into the dark numbers by counting or defining.
There is no final finite von Neumann ordinal.
By 'natural number' I mean
'finite von Neumann ordinal'.
By ℕ I mean
minimal inductive set.
…