On 20 May 2011, at 22:18, meekerdb wrote:
On 5/20/2011 3:59 AM, Bruno Marchal wrote:
On 18 May 2011, at 19:47, Stephen Paul King wrote:
A very good point! There must be a place for "false memories" in
our modal logics.
Indeed. and G* proves DBf. Lies and falsities abounds in the mind
of the average Löbian machines.
An interesting statement (although I doubt you mean it). A lie
means to state something you know to be false. Can a mind to this?
Yes, and the point is that it can remain consistent. It becomes unsound.
A correct Löbian machine can lie. But never does (by definition).
Careful, G* says that correct machine can lie, in a more general sense
that your's above. Also, once the machine lies, or is non correct; G*
does no more applies to it.
A bad news is that even in arithmetic, false but consistent theory can
be more efficacious, in proving correctly true statement of
arithmetic, that sound theories.
I am not a long way from believing that a statement like 'real numbers
exist' is a lie. Even if provably useful in arithmetic. It is a point
on which I do not insist, but falsities an lies does have a positive
role in the building of realities and in our surviving there.
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