At 9:36 PM 06/17/2015, Pedro wrote:

... What if information belongs to action,

[KM] This is a good remark suggesting that information may go beyond the 
standard stipulation of first-order logic. A great advantage of mathematics 
grounded upon first-order logic is to enjoy the provability or computability of 
an inductive judgement with use of the few axiomatic primitives. This scheme, 
however, does not work for information at large, though notably except for 
Shannon's information bits. If one faces a statement like "information is 
probabilistic", it would go beyond first-order logic when the predicate "to be 
probabilistic" admits its quantification as revealed in the context-dependent 
probabilities in QM. Once we enter the higher stage of second-order logic, it 
could be possible to form an opinion of course while its provability may be out 
of reach in most cases. Nonetheless, if one wants to save something good with 
saying "information is probabilistic", a likely makeshift might be to relate 
information to action, for instance, as appealing to conditiona!
 l probabilities which are quite at home with the action of setting and 
detecting such conditions. 

   Koichiro





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