This was helpful to me, thank you. I didn’t realize until reading it that the fact this argument relies on axioms doesn’t make it self-contradictory.

]]>You mean if it is not *refutable* then it is true.

Probabilities (or rather, events in a probability space) really are elements of a boolean lattice as are most spaces stable under intersection, union and complement, but I’m not sure my suggestion isn’t junk, as I don’t think the “classical” point of view brings much more to the table than the usual analysis of modal logic in S4.

]]>I agree that it would be great to connect the two concepts as precisely as possible. Are probabilities really elements of a Boolean lattice? Or did you mean something else? I’m getting a bit confused…

]]>I think this work is interesting! My question is this: what is the difference with working with a probabilistic assignment of truth and the more “standard” provability predicate? It seems that both assign a value to each sentence into some (boolean) lattice. Is there a way of connecting both points of view?

]]>Thank you. ]]>

Domenico wrote approximately:

I thought that each mathematical demonstration can be translated into boolean algebra,

Each statement in the propositional calculus can be translated into boolean algebra, but I doubt this is true for the predicate logic.

]]>If the value of the truth of a sentence is a spin value (spin up and down), then with a quantum computer there is not more inconsistence, because there is a quantum value for each node of the net, and it is possible deduce theorem from flip flop outputs: there is an overlap between boolean net (without incongruence) and quantum spin net (the truth tables are the same).

The boolean net have two state of truth, with an oscillation between the two state, but I am thinking that the quantum computer have a single quantum equilibrium state for a boolean net, and there is not more incongruence (intermediate values). ]]>