I really like the idea that an evaluation algorithm of a proposition can either terminate or end up in a fixed point, mapping back to the evaluation algorithm itself. It unites mathematical and non-mathematical statements instead of separating them, and it allows for algorithm-dependent outcomes of propositions, which fits well into my anti-realist ontology. In this approach a lack of convergence would be an indication that a new, potentially higher-level evaluation algorithm (I call those “models”) is required.
Going by what you have presented, some basic hierarchy could be something like this:
Evaluating algorithm-1: Immediately/obviously/postulated true or false, no extra evaluation needed
Evaluating algorithm-2: Evaluated to true or false with or the evaluating algorithm-2 (your “infinite loop”)
Evaluating algorithm-3: Evaluated to one of the 2 above or to itself, if the “evaluation field” is not closed.
I really like the idea that an evaluation algorithm of a proposition can either terminate or end up in a fixed point, mapping back to the evaluation algorithm itself. It unites mathematical and non-mathematical statements instead of separating them, and it allows for algorithm-dependent outcomes of propositions, which fits well into my anti-realist ontology. In this approach a lack of convergence would be an indication that a new, potentially higher-level evaluation algorithm (I call those “models”) is required.
Going by what you have presented, some basic hierarchy could be something like this:
Evaluating algorithm-1: Immediately/obviously/postulated true or false, no extra evaluation needed
Evaluating algorithm-2: Evaluated to true or false with or the evaluating algorithm-2 (your “infinite loop”)
Evaluating algorithm-3: Evaluated to one of the 2 above or to itself, if the “evaluation field” is not closed.
Etc.