[FOM] the intended model of arithmetic
Mongre at gmx.de
Fri Oct 13 04:38:12 EDT 2006
Francis Davey wrote:
>. I might believe that the godel
>sentence is true in the "intended model", but no-one has ever been able
>to explain exactly what they mean by the intended model, so I am far
>from sure about that. Maybe its a mystical ability I don't have or
>haven't appreciated (*).
>...(*) in other words - how do I know there aren't a non-standard number of
hadrons in the universe?
It is indeed possible to doubt whether we can determinately pick out
the intended model of arithmetic, i.e. to doubt whether we have a
determinate understanding of the word 'finite' (for the intended
model is the model in which each number only has finitely many
predecessors), but then you're disabled from conjecturing over
whether the number of hadrons in the universe might really be
'nonstandard' (i.e. infinite) since you won't understand
'nonstandard' either. If everything meaningful is knowable, i.e.
anything you can't know can't be meaningful (which is the radically
constructivist assumption on which such scepticism rests) then you
can't identify *what* it is that you can't know.
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