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Explanation:
I know this sounds strange, but hear me out...

My ideas are the following:
(1) Logical analysis and (current) semantic analysis alone aren't equipped to express all meanings, distinguish all meaningful from meaningless expressions and prove all propositional truths.
(2) There possibly exists (or could exist) another formal tool set that takes care of cases where logical and semantic analysis fails.
(3) IF such a tool set were to exist, it would be neither syntactic nor inferential in nature but rather, semiotic and referential.
(4) Such a tool set could have the same "necessary truth-preservation" property that formal logic does without involving the notions of deduction, entailment, tautology, (syntactic) proof, etc.
I hope to articulate and make the case for these without digressing into continental gibberish or copping-out by calling it "sui generis", "unanalysable" or "primitive".

To understand my motivation, consider the following thought experiment:
Take two people arguing about moral realism, S1 (an anti-realist) and S2 (a realist).
S1 and S2 both have endless supplies of deductive arguments for their respective opposing positions.
S1 suspects he will reach a point in the debate where S2 won't be able to provide a sense for a proposition, stripping it of truth-aptness (and so collapsing their argument tree).
S2 nonetheless continues providing senses and valid arguments for each premise.
S1 then suspects that there is something awry with S2's semantics and probes for specific term meanings.
S2 responds, stating one of the pivotal normative terms ("external normative reason") is referential, and even a definite description would fail to communicate the meaning (preventing S1 from "breaking into" S2's "conceptual circle").
S2 goes on to clarifies that the normative term is nonetheless meaningful as a primitive 'tag', that statements involving it are truth-apt, that true statements involving it are stance-independent, and that the referent has the property of being a normative fact giving reason for actions.
S1 responds with two questions:
(1) What does "external normative reason" even mean? (What does it refer to? What is its truthmaker?)
(2) Even if the meaning can be communicated, how do we know that "external normative reasons" exist? (What are examples? What's the argument?)

How do we resolve this dispute if S2 states that it is primitive?

Take semantic primes like the colour purple:
In cases like this, we could fix the reference with scientific explanations of the underlying neuropsychology of visual perception and the underlying physics of photon wavelength and frequency.

But let's say we don't have a scientific explanation available to us. What then?
We can still fix the reference (albeit for someone who isn't colour blind) by describing purple as the combination of red and blue.

Now, let's say we have another primitive notion. One which resists analysis (is primitive), scientific explanation (is non-natural), and which we cannot tell whether or not a person is "colour-blind" to it, hallucinating it or whether it's just some sort of illusion (is epistemically opaque).
This is exactly the state of this moral realist's primitive terms.

So, how do we put to bed this issue?

(Option #1 - Semantic Analysis)
Through semantic analysis alone, we wouldn't be able to communicate the concept (due to its being primitive) without generating a vicious circle of term meanings.
The reason it becomes circular is because when one has to define normative terms that are purportedly about stance-independent matters, to avoid crossing the is-ought divide, one can only use further stance-independent normative terms - a process which will inevitably circle back on itself.

(Option #2 - Logical/Argument Analysis)
Through inference alone, we wouldn't be able to tell if these "normative facts" exist without generating an infinite regress.
The reason it becomes regressive is because when one has to argue the existence of a stance-independent normative fact, one has to include premises that involve a second normative notion of the same kind to avoid is-ought crossing and question-begging, which then requires a further argument for the premise containing the second normative notion, and then another involving a third, and so on, ad infinitum.

So, what the heck do we do??

Find out more in the description section of part 2. Hopefully, in the follow-up, I more clearly state the case of what the issues are, why they are, and what is required to resolve them (given we take them as problems that we want to solve).

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