I am trying to show why it is possible to accept two truths simultaneously until evidence of the exclusion of one is discovered. I figure your background in quantum physics (or at least a portion of studies) might know a better way to prove this. Any direction you can offer here?
Well, it's possible for a molecule composed of 430 atoms to be in two places at once, possible for a physical system to be measured as a wave or as a particle based on decisions AFTER measurement, and about a century or so of many-valued logics (and decades of one which is infinitely-valued) to support this idea. One of the reasons classical logic can't deal with mental state predicates like "believe" is because it leads naturally to something being true and false (or neither). My typical example is Clark Kent and Superman.
(1) Louis Lane believes that Superman can fly.
(2) Clark Kent is Superman
(3) *Louis Lane believes Clark Kent can fly
I've opted against using logical symbols and the format used in derivations because I think it this form is adequate enough. Basically, in classical logic one has the identify operator ("is", "are", "=", or any operator that equates the subject and predicate). Whenever we find something of the form "X is Y" meaning that X and Y are two labels for the same thing (e.g., one's member name here and one's actual name have the same referent), truth preserving rules of inference allow one to replace any instance in Y with X and vice versa. Thus, formal logic would (if it allowed mental state predicates like "believes") allow us to infer (3) from (1) and (2). However, (3) isn't true, and even outside of a fictional example the same logic will fail.
This can be made even more simple.
The superposition state of a molecule composed of 430 atoms I mentioned wasn't just a potentially possible realization but the experimental result of a study published in
Nature Communications. The molecule was found to be in two "legs" of the interferometer or, to simplify this just consider location X and Y. The researchers were able to create a superposition state in which a single molecule was at location X and Y at the same time. Let's say that I say I believe the molecule was in location X. Somebody tells me "you arrogant moron, it was clearly in position Y!". I tell them I believe it was in Y. They respond "you can't believe two mutually exclusive things to be true. My god what is the world coming to?". I say "Apparently, one in which we don't have to rely merely on highly abstract, arcane philosophical discussions or incredibly technical discussions because we are literally able to create macroscopic systems that are in mutually exclusive states independent of belief, such that to NOT believe both states are true would be wrong."
I then get beaten up in a dark alley.
Given that is it necessary to accept what in classical logic would be mutually exclusive statements as both being true, I would say it is certainly "possible to accept two truths simultaneously until evidence of the exclusion of one is discovered". That's without the various other motivations for many-valued logics, belief functions in subjective and/or Bayesian epistemology, etc. Interestingly, belief functions in Bayesian statistics/epistemology/analysis are formally defined as axioms as a foundation for scientific methods and discovery, and the first is that a belief that "not H" given "H is true" is merely less than or equal to the belief in F given H which is less than or equal to the belief that H is true given H is true.
