On Sun, Nov 14, 2010 at 6:26 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 14 Nov 2010, at 22:17, Rex Allen wrote:
>> On Sun, Nov 14, 2010 at 10:27 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:
>>>
>>> We have good reason to believe that our brains are not so bad dynamical
>>> mirror of the most probable consistent neighborhoods.
>>
>> Why only consistent neighborhoods?  Why couldn’t inconsistent
>> neighborhoods (a la Graham Priest) have role in determining the nature
>> of reality?
>
> Priest handles paraconsistency, not arithmetical inconsistency. Priest can
> be modeled in arithmetic by a sentences of the type Bf (not on the type f).
> This is because G* proves DBf (the consistency of the provability of the
> false).

"Though the construction of inconsistent mathematical theories (based
on adjunctive paraconsistent logics) is relatively new, there are
already a number of inconsistent number theories, linear algebras,
category theories; and it is clear that there is much more scope in
this area. The theories have not been developed with an eye to their
applicability in science—just as classical group theory was not. But
once the paraconsistent revolution has been digested, it is by no
means implausible to suggest that these theories, or ones like them,
may find physical application—just as classical group theory did."

-- Graham Priest

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