What if concepts are not reducible to propositions at all...? There seem to be a lot of assumptions here that could be spelled out more carefully?

@JosephWeissman I can't imagine any concept that cannot be specified using language. In fact the way that I make the analytic versus synthetic distinction is representable in language is analytic and not representable in language (direct stimulus from the sense organs) is synthetic. I am not referring to anything as specific as propositions. I am generalizing to any language relation between finite strings.

A universal conceptual language will be incoherent. You do not even need to formalize "all" relations, as long as it allows talking about truth of its own statements you'll get into semantic paradoxes. It is true that natural language does work this way, more or less, and then limits the damage by compartmentalization devices, but mimicking that is not necessarily the best way to proceed with formal systems. In any case, complete paraconsistent systems that formalize this feature are well-known, but did not gain much popularity.

@polcott Hey I recognize you! If you really think this could work it would require perhaps multiple books to actually work it through. I have no idea what you're saying in these few sentences. Instead of creating new accounts trying to convince people on here, you'd be much better off writing the darn book. If you actually know what you are talking about, you should be able to do it. Write up a few chapters and a precis and see if you can get a contract from a reputable publisher, how sweet would that be?

@Conifold In the system that I am proposing paradoxical expressions of language are excluded as not deriving a theorem. When expressions such as: "This sentence is not true" are evaluated in a directed graph, the fact that this graph contains a non-terminating cycle rejects the expression as not forming a relation between finite strings.

Yeah, that does not work. Paradoxes are not algorithmically detectable, so the language that just stipulates them out is not really a language.

@transitionsynthesis I keep reformulating my words as I get feedback of which aspects of the prior words were not understood. These most recent words eliminate several aspects of confusion from my prior words.

@Conifold The liar paradox is easily detectable from the non terminating cycle in its directed graph. Every case where a relation between finite strings cannot be formed is rejected.

If only the Liar was the only paradox, or every set of premises implying it was recognizable... I agree with @transitionsynthesis. You are wasting your time on reinventing the wheel, all of these issues are well-settled. Completeness, consistency, and recursive definability are linked by Godel's argument, one can gain one only at the expense of another.

@Conifold In any formal system that is defined to be comprised entirely of stipulated relations between finite strings Gödel's G is rejected as syntactically ill-formed because it does not satisfy any of the stipulated relations between finite strings in the formal system.

Your stipulated relations do not produce a recursive syntax, so the absence of a Gödel sentence is a triviality

@Conifold Recursive syntax is one element of an infinite set of relations between finite strings. Relations between finite strings is free to have any possible algorithm define the relation.

No, it is not, "recursive" is not meant as one of your stipulated relations here.

@Conifold I stipulate that it does. A relation between finite strings is any relation derived from any algorithm.

It makes no difference what you stipulate when it comes to how finite strings objectively behave any more than to how gravity works.

@Conifold when you apply arbitrary algorithms to finite strings they behave as their algorithm specifies.

No, they don't, that is why we have the halting problem.

@Conifold Algorithms necessarily always behave as they behave. When we ask for the Boolean answer to a question lacking a Boolean answer and we restrict the form of the answer to Boolean the lack of an answer does not indicate incompleteness. Is the following sentence true or false: "This sentence is not true". The halting problem was constructed to mimic the Liar Paradox.

In light of the extended comments, I recommend revising and clarifying your question.

I think what you need to do here is construct a proof in the stipulated language of the following sentence: "The proof of this sentence will not halt"

Also see: philosophy.stackexchange.com/a/5973/33787

How could you know that every objective fact has at any point in time been so encoded/stipulated? How do you account for possible discovery of new facts? And if a new fact contradict something already established do you then simply discount it as "I'll formed"? Apparently you think that a simple hierarchy of ontologies could be the base for a model of a useful fraction of Reality. At best you need two disparate ontological frameworks, one to describe the other, and at worst an infinite regress.

@christo183 A single knowledge ontology can consistently specify every general conceptual truth currently known and it can do this in finite space. Contradictions must be resolved. New facts can be added at any time. There is never infinite regress in any directed acyclic graph.

Is there anyone else that believe all that? - Regardless, you are going about this wrong. Both how you are going about explaining and how you are trying to construct a complete language. A complete language cannot accept new facts, but let's forget for the moment your program: look at Noah Sweber's last comment... I'll go out on a limb a state that it summarizes the community consensus. You are not communicating your idea, nor are you attaining any credibility. (Credibility comes after demonstrating a new idea) You have only insisted that you have an idea, never demonstrated it.

@christo183 "A complete language cannot accept new facts", The reason that I began with finite strings as my basis is to circumvent ridiculous preconceived notions such as this one. The only reason that I changed it was to make my words have a more intuitive and common basis. so it is back to stipulated relations between finite strings again. The body of conceptual knowledge is entirely comprised of stipulated relations between finite strings. The only possible counter-example would be a concept that is defined without using language.

Your definition of truth is vague & only applies to SCIENCE. Secondly the la gue is supposed to reflect the world not just make definitions just for the sake of GOD like powers. You put too much emphasis on authority. Who will make these concepts? The concepts should reflect what we know not the other way around.

The issue is the requirement of sense verification just like science. The axioms have no support. They cant meet tour requirements. So concepts like axioms may or may not have proof . There are types of truths. All truths are not identical. Contingent truth is an example as well as objective truth. Which do you refer to? By your definition axioms are not all provable. At best only some are but what do you do then?