It is interesting, though hard to declare logical. The primary issue is that you have not stated what system of logic you are using. Because it is the lowest-common-denominator, I will compare it to First Order Logic (FOL):
- "'no truth' is a truth" is not a well formed statement. For FOL, the statement needs to be in the form of a predicate. I believe you are trying to say "'There is no truth' is true."
- I'm going to get a little finer detailed than this in a moment
- "'More than one truth' seems to lead to an infinity of truths, I couldn't really explain why it just seems so." may qualify as the antithesis of logic. It is provided axiomatically, so readers must accept that more than one truth leads to an infinity of truths as an axiom before admitting your logic.
- "That leaves us with one truth, which is a truth therefore the one truth. It just sounds good to me." Once again, there is a lack of logical construction. You make an axiomatic statement.
Your argument thus is reduced to:
- Assume: More than one truth leads to infinite truths.
- Declare: "There is no truth" is paradoxical (why this is paradoxical will be covered shortly)
- Result: There must be one truth.
Unfortunately we must treat the result as an axiom as well, for it does not follow from the assumptions. Nowhere does it state there cannot be infinite truths. In fact, the claim that there cannot be infinite truths is highly questionable because arithmetic suggests there are indeed infinite truths. Consider "for each a,b from Z, the set of all integers, there exists a c from Z such that a + b = c" is true. Arithmetic would claim this statement is true. From this one truth, we can create a series of truths in the form "for each b from Z, there exists a c from Z such that A + b = c is true", where we may use any integer value for A to construct this new truth. Since there are infinite potential values for A within Z, we have already constructed an infinite number of truths.
I believe you are working towards an argument Whitehead and Russel were working towards until Gödel showed their work impossible
I believe the "one truth" you are working toward is more accurately phrased as a "Formal System" of truth, and you seek "One True Formal System of the Universe". A formal system consists of:
- A finite set of symbols, the alphabet for the system, used to construct formulas (strings of symbols)
- A grammar, describing how to make "well formed" systems
- A set of axioms which are declared "true"
- A set of inference rule to manipulate formulas and prove their truthfulness.
If you combine First Order Logic and a set of axioms, you get a Formal System. If you want, you may define your own logic, instead of using FOL. However, declaring something powerful like "there is only one truth" is going to require more than a paragraph, for you will have to define the Formal System you are using.
If we can limit ourselves to FOL, all we need is a set of axioms to create a formal system. This means the search is for "The One True Set of Axioms," which is starting to sound a whole lot like your original search for one truth. This search just needs a little linguistic nudge to make it mathematical. It is easy to show that if you take a set of axioms, and add a derived truth from them as an axiom, you get a consistent Formal System. You may be looking for a "minimal set of axioms to admit all truths in the universe under First Order Logic."
And with that in mind, I'd like to give Gödel some attention.
Gödel devised a few theorems known as his Incompleteness Theorems. These are proven using the rules of first order logic as part of his approach to your paradox. "There is 'no truth'" is a Liar Paradox: "This sentence is false." Gödel sought to resolve some of these issues. The standard resolution of this paradox is simple: "This sentence" is not a valid symbol in FOL. It simply isn't. One of the rules of FOL is that you must define the symbols you use up front, and there is simply no valid FOL formula of that sorts.
Russel was approaching one such solution, which involves carefully crafting the set of symbols in a way which permits "This sentence" to be a valid predicate. In doing so, he identified the "Russel Paradox" which dealt with sets that contain themselves (tail chasing sets), vs. sets that do not contain themselves(normal sets).
While Russel was trying to do what you have been doing, finding a way to make this valid, Gödel came in and showed it impossible. Not just Russel's paradox... Gödel proved that an entire swath of potential systems had a fundamental flaw, including the system I believe you are working towards.
Gödel concerned himself with systems which could "admit arithmetic." Of course arithmetic is such a system, but any super-system which can define arithmetic and its trules (such as our universe) is bound by the law he found. He showed that any system which could admit arithmetic must have at least one of the following characteristics:
- Incomplete: it must fail to give a result for some value
- Incorrect: if must arrive at an incorrect result for some values
- Unprovable: it cannot be proven using the laws of the system
- Intractable: the laws of the system are not recursively enumerable (which is a really specific wording which can be generally translated as "can never be written down without infinite paper")
- Illogical: the system must violate its own laws
(His wording is more precise, but I find these to be the most human accessible versions. For example, his theorem does not actually include "illogical," because his proof was valid only for logical systems. I include it because non-mathematicians often make arguments which can only be described as "illogical." Also, technically he targeted ω-consistent systems, though Rosser strengthened it to all consistent systems in 1936)
His second incompleteness theorem used the first to prove a powerful statement that strikes to the core of the "no truth" argument. It is, as always, tremendously detailed mathematical speech, but Wikipedia is kind enough to gloss it:
For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent.
This is very much directed at the Liar paradox, basically stating that you can never prove your own provability (unless you target a weak system which cannot describe arithmetic).
On Monotheism
This does not disprove any argument about monotheism. It does not even make dangerous statements such as "The bible is a lie because it claims provability about itself." What it does say is that claims such as "the Bible is true, and it says so" will inherit at least one of those five characteristics (gloss: self-referential text admits Peano arithmetic, so it is in Gödel's domain. Most all "book" religious people I talk to (Jews, Christians, Muslims, etc.) choose to accept "unprovable" as their characteristic of choice. It is completely admissible by Gödel for the Bible to be true and claim so, if it is unprovable using formal logic. Likewise, those who profess to believe in the Dao can trivially prove their belief, but the cost for this is that the Dao is intractable (it is said "If you can write down the Dao, you have done it wrong").
It is also completely effective to define a non-infinite system, which cannot describe arithmetic. This avoids Gödel's incompleteness theorem as well. However, I am unaware at this time of any religious institutions that take this approach.