Truth-Only Logic

Read: Further Notes and Paper Draft.

Inspiration

I was originally inspired to begin work on this idea by an outstanding Quora post. I believe the original post author was Jim King and his question was originally "Is Truth Made Up of Truths?"

I reached out to the author several months ago (perhaps over half a year ago now) to thank them and encourage more discussion (since the original post seems to have either moved or been merged). I believe all of these comments are viewable publicly (on Quora) but would prefer to make note of them here as well.

I believe my original reply (to the original post) is that one treatment of Truth (that is standard) is that the sum totality of all Truths of a certain kind (say expressions of Physical Law - physics, chemistry, etc.) can be conjoined to form a gigantic set of conjunctions.

While that's correct, there is certainly something much more interesting being asked.

After a brief amount of research and some skimming through Mathematical Logic, Philosophical Logic, and Logic and Computation journals I found no articles on what has previously been loosely called "comparative theories of truth" which have been discussed only in reference to Buddhist texts but which lack any mathematical formalization (unlike well-understood Indian logics).

I think this represents a great opportunity to provide a first (to my knowledge) formal definition and mathematical analysis of the concept.

Survey

1. There are two-valued logics.
2. There are three-valued logics.
3. There are many-valued logics.

What about single-valued logics?

Would that be trivial?

Comparative Theory of Truth

1. There are no falsehoods only truths.
2. Some truths contain more information - are more comprehensive truths.
3. Truth is not binary. Rather, some truths are strictly better (to be further specified) than others (due to their accuracy expressed through isomorphism or homomorphism, etc).
4. Alternatively, truth is ordered. Some truths are more true than others.
5. Lesser truths are contained in greater truths.
6. A growing body of increasingly accurate information accreates and aggregates into greater overall truth over time.