It looks to me that you may have succeeded by simply not allowing those things that are not reliably computable as part of our body of knowledge. Looks like a cheat. Sorry.
There are those who arrive with their Philosophy, and expound it at length, explaining The Way The World Is, to the benefit of every one of the unenlightened. They often seem shocked into incomprehension when someone comes back with a quibble about how their story doesn’t quite follow, contradicts itself, doesn’t match what is plain to all, or derives an “ought” from an “is”. They will complain of straw men, of trolling, or simply of rudeness, apparently being astonished that folk could be so discourteous as to be critical of their work.
But this is a philosophy forum, not a Vanity Press. If you present your thoughts here you must expect them to be critiqued. In a very central and important sense, this is what we do.
So let’s look at the idea that our “body of knowledge” being “reliably computable”.
We know that there are true statements which are not computable.
So it seems to me that your plan is problematic.
Again, what you are doing is similar to the sort of thing Russell and the Early Wittgenstein were trying to do, over a century ago, before being forced to move on.
Those elements that are ungrounded in a finite sequence of inference steps are either semantically incoherent like self-reference “paradox” or out of scope of the body of knowledge like the truth value to the Goldbach conjecture.
There are no true statements in the body of knowledge expressed in language that are: (a) not computable in finite time or (b) not stipulated to be true such as “cats are animals”
There are no true statements in the body of knowledge expressed in language that are: (a) not computable in finite time or (b) not stipulated to be true such as “cats are animals”
The truth value of the Goldbach conjecture is outside of the body of current knowledge and may be unknowable, yet definitely has a truth value, unlike expressions with pathological self-reference that are meaningless.
My thesis says that all undecidability is essentially:
(a) Expressions that are semantically incoherent.
(b) Expressions that are outside of the body of knowledge expressed in language. The truth value of the Goldbach conjecture is one example.
Again, we know that G is not computable, yet true. We know that no finite computational procedure captures all arithmetic truth. That directly contradicts your assertion.
To that we might now add that if all definitions are mere stipulations, we could never be mistaken. All empirical statements would be analytic.
And to that we might add a third problem: Consider
Is that statement the result of a calculation, or is it a mere stipulation?
If the former, present the calculation. If the latter, present some reason that we ought accept it.
That is all based on using the foundation of truth conditional semantics instead of proof theoretic semantics. G is computable in meta-math and meaningless in PA.
All of the empirical “atomic facts” are stipulations transforming them from synthetic into analytic truth. Things such as the definition of the set of natural numbers must at least have a stipulated form of encoding.
The value of PI in an inherent aspect of the concept of round, thus not merely stipulated. Some “atomic facts” would be axioms of formal mathematical systems such as the axioms of PA.
“The cat is on the mat” is the translation of empirical sense data into analytic “atomic facts” in language. That “cats are animals” can only be known by stipulation.
My plan is to only translate general empirical knowledge such as “cats are animals” into a finite list of atomic facts.
It cannot possibly be implemented as an actual algorithm unless it has a finite list of “atomic facts” and a finite list of finite string transformations rules.
To the best of my knowledge you did not point out a single mistake in my 28 year long research project. You did point out some details that needed to be filled in.
It’s a shame that you can’t see the problems. It means you cannot address them. Doing philosophy is not as simple as you suppose. Philosophy is not engineering. It is not building a system and then declaring all else meaningless. You’ve put yourself in a cage, and declared it to be the whole world.
You did not point out any actual concrete mistake. Parroting the conventional view Gödel’s 1931 incompleteness without fully taking into account utterly replacing the foundation of [truth conditional semantics] with [proof theoretic semantics] is not pointing out any actual error on my part. You did do a better job reviewing my work than any other human.
Point out one 100% concrete example where you think that I am wrong. “The cat is on the mat” was not an example of me being wrong. It was an example that needed to be further elaborated within my system. Since the purpose of my system is to provide the means for LLM systems to become completely reliable, “cats on mats” is off-topic.
Lets go back and defend my whole thesis: The entire body of knowledge that can be expressed in language can be encoded as relations between finite strings.
All empirical knowledge is first translated into expressions of language, thus becoming analytic knowledge.
(1) Lilly is defined by a GUID that identifies her as a unique object in the world and is assigned the type: “cat”
(2) Gödel sentence G has its entire incoherent foundation of truth conditional semantics utterly replaced by proof theoretic semantics. This makes it true in meta-math and meaningless in PA.
This sentence is not true: “This sentence is not true.” the outer (meta-level) sentence is true because the inner sentence is semantically meaningless.
(3) Liar sentence is as I have formalized in Prolog
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
(4) PI has the full semantic meaning of its algorithm (defining the ratio of the diameter to the circumference of a circle) and otherwise has no meaning.
(5) Knowing that an expression of language is incorrect must have some basis. Within my system all relevant empirical knowledge derived from observation is first translated into language expressions.
“The cat is on the mat”, thus requires the GPS coordinates of the 3D model of the cat and GPS coordinates of the 3D model of the mat at a point in time. If there are no common GPS coordinates at that point in time then “the cat is not on the mat”.
(2) Proof Theoretic Semantics is a different foundation for semantics than truth conditional semantics. In my augmentation to proof theoretic semantics consistent with Dag Prawitz theory of grounds G is simply ungrounded in PA. (3) Making no attempt to answer the question: “What time is it (yes or no)?” also does not answer the question (because the question is incorrect). (4) Whatever algorithms that can be used to calculate an arbitrary number of digits of PI is the only aspect of PI that is in the body of knowledge. (5) The list of “atomic facts” must be finite because it is planned that the system will be implemented.
The liars paradox is a logically invalid statement because it distorts the necessary structure of the 3 fundamental laws. It is a transitive level logical loop or glitch.
The 3D model of the cat and the mat are the visual perception, they must at least be in the same model space. I am translating empirical data into analytical data to make it computable.
It may give you a map where the cat is located on the earth. The statement “The cat is on the mat.” is not really relevant for what you are trying to do.