On 11 Sep 2008, at 19:06, Brent Meeker wrote:


>> I think we are due for yet another extension to logic, one which will
>> contain Bayesianism as a special case.
> But logic is also the manipulation of sequences of propositions.  No  
> matter how
> clever, you still need to something else to supply meaning.  I think  
> meaning
> only arises in relation to action within an environment.

That is a magical move, unless you put some infinities perhaps.
Selection among an infinity of environment
would explain a little more, yet it is not enough.

>> I think Bruno had it right, it's all Category Theory-  and make the
>> next big leap forward in logic, we need to start using the concepts
>> from Category Theory and apply them to logic, to develop a new logic
>> capable of going beyond Bayesianism and dealing with the semantics of
>> information.  But how?  Listen to this:
>> <b>Given two categories C and D a functor F from C to D can be  
>> thought
>> of as an *analogy* between C and D, because F has to map objects of C
>> to objects of D and arrows of C to arrows of D in such a way that the
>> compositional structure of the two categories is preserved.</b>
> No meaning there either.

Caterorial logician and algebraist would differ with you on this.  
Again I don't think
it is enough, but at least category theory gives a frame for the  
notion of reductive meaning,
that is, when meaning is given by a faithful embedding of some unknown  
into something we
already know "meaningfully".


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