[deltasixeight]

>Not going to address your weird attempt at wordplay

There's absolutely zero need to be rude. There is no "wierd" word play here just misunderstandings and impoliteness by you.

>Also, axiom can be just a rule in a rewriting system. Doesn’t have to be an assumption/opinion as it is just a proposition (or higher order predicate) that is true within some system (not necessarily related to anything that exists).

This is obvious. You're just restating what I said and coming up with a circular argument. A rewriting system is a universe you create, not dissimilar to our own universe that we live in. An axiom in this system is an statement made by you stating something is true without any proof. A statement made without proof IS an assumption. Now this explanation may seem like word play to you but it is not. The exact identical words "assumption" and "axiom" serve to confuse your reasoning and blind you from the actuality of the concept at hand. What I am doing is unraveling your misunderstanding in attempt to explain your confusion but you are unable to see it and you view the argument as "word play." Axiom and Assumptions are two words that mean the exact same thing. There is one concept at hand and two words for that same concept that are confusing you.

>subjective logic, which you linked, is equivalent to propositional (in a sense you can express any statement in subjective logic via a set of propositions, eg Ap distributions make this connection), and does not embed predicate logic (eg any statement of this system can be expressed in predicate logic, but not vice versa)…

This system has axioms and theorems that use predicate logic. It is built off of predicate logic.

I recommend reading this: https://projecteuclid.org/journals/statistical-science/volum...

When you set the subjectivity to 100% the result is something equivalent to predicate logic. So logic is both a special case of probability as well as foundational building blocks for subjective probability itself. You can arbitrarily pick and choose which came first and which one is axiomatic. Probability or Logic.

You are indeed wrong here. Please politely admit it without calling my statements weird. If you disagree there is no need to resort to derogatory statements.