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:

Hi Rex,

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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