Fantasies about Quantum Mechanics aside, Probability and Information are distinct. Both are ways of speaking about the world. You may speak of alternatives probabilistically, but you cannot say that “information is probabilistic."
Any truth based system is necessarily flawed (Godel) and dualist. The great disadvantage of mathematics grounded upon first-order logic is also exactly what you say because it can lead to over-confidence. This is not to say that logical proof systems are not useful for checking syntactic and semantic reasoning, they are. But they cannot provide the certainty desired. Mathematical proofs are not logical proofs. Reasoning about motion and degrees of freedom in dynamic structure, be it falling bodies or social graces, is not greatly helped by first-order logic. FOL is only concerned with certain types of thinking. Arbitrary axioms are no basis for rigor. In my view, at least, only the general covariance of premises can provide a basis of scientific argument. Constructive methods are flawed if they do not consider the action of premises together. Arbitrary axioms only represent the abductions that may lead us to this. Existence is before essence, remember the prime principle of existentialism. Regards, Steven > On Jun 17, 2015, at 6:04 PM, Koichiro Matsuno <cxq02...@nifty.com> wrote: > > 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 > > > > > > _______________________________________________ > Fis mailing list > Fis@listas.unizar.es > http://listas.unizar.es/cgi-bin/mailman/listinfo/fis > _______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis