[Fis] Krassimir's Notes . . .

[Koichiro Matsuno]

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 conditional probabilities which are quite at home with the action of setting and detecting such conditions. 

   Koichiro