> It may be interesting as a thought exercise to wonder if non-contradiction could be an emergent property. It would certainly make for an interesting model for the beginning of the universe.
Any theory of reality must have full closure. Meaning what happens when two constraints/structures collide depends on the two components, but that there is always a definite result, and it is the solution to conservation.
It isn't just that reality doesn't or can't ever "contradict" itself, but that contradiction dodging doesn't happen either. Bolted on contradiction avoidance, isn't needed when there is closure. Mixing up logic as tool, with logic as inherent reality is a category error. Things cancel, reduce, etc. All operations that happen locally where structure connects. They don't produce potential solutions, then winnow them down. We do that.
Thats what we do when we don't completely understand something, or we only have partial knowledge. Not scenarios that reality operates in. Entirely different.
> I think this would probably be contentious, I think most people believe that logical values are basically "necessary". I don't really know though.
Unknown is obviously a factor of notation, or our knowledge. Its dual is contradiction. Those concepts are foundational in terms of our ability to analyze things we only have partial knowledge of, or may be describing incompletely or inaccurately. Analysis needs that meta-level to handle all the provisionalism inherent in conjectural knowledge.
What is true, what is not?
What don't we know?
What have we incorrectly assumed?
We cannot operate on provisional/conjectural knowledge without all four of those concepts. (We rarely actually operate with just boolean true/false logic, even if unknown/contradiction are handled implicitly instead of explicitly, which only works in trivial systems. Which makes the major proofs of fundamental limitations' dependency on an excluded middle a bright red flag.)
Logic is how we analyze arbitrary structures. In that sense it is universal. Whether the artifacts we analyze have any resemblance to logic or not. We traverse them with logic as an external scaffolding that allows us to represent and operate directly on our understanding of the artifact.
Keeping those things separate sheds a lot more light on things like mathematical and computational limits. I.e. the weaknesses of starting with logic in Russell's Paradox and Gödel's theorems, instead of structure-agnostic reduction, are pretty stunning. Of course a system fundamentally restricted to true/false, without explicit "either/unknown/undetermined" or "both/contradiction/overdetermined", can't be consistent or complete.
Analysis without the four possible states of analysis inherently breaks. Whether that is a Russell set ("a set that includes all sets that don't include themselves", given sets are defined as boolean mappings), or a Gödel system (a Boolean mathematical system can't consistently handle something as simple as, "this system will say this statement is false"). Not how both of these examples pull the means of analysis into the contradictory statement loop. A set, in a set system. The mathematical system, into analysis of itself. So analysis as the subject. True, false, unknown and contradiction need to all be first class values in any study of analysis.
How would you feel if I sent you an email? I have a question but asking offline works better.
