Burden of proof is on Con to prove that things outside Bible exist, without using Bible or things outside Bible as proof.
Alright, so my opponent must use something which isnt using Bible nor things outside Bible, to prove that things outside Bible exist.
So my opponent cannot use anything outside Bible to prove things outside Bible.
So he is left with things which are not outside Bible, apparently Bible verses and pages.
Do Bible pages prove things outside Bible? No, Bible pages are just proof for Bible pages, which isnt outside Bible.
Bible verses are just proof for Bible verses, they dont prove anything outside Bible.
Now, my opponent suffers from two logical problems:
- Second incompleteness theorem
- Circular proof problem
Lets start with 1. Second incompleteness theorem is a famous problem in math where no system exists which can prove itself true.
this is because "A says that A is true" is not only circular, but a logically impossible statement where "A = A is true" - So A must contain more than itself to even make that statement.
Now, all truth determining systems are systems, and thus no system proves itself true. thus, even my opponent, when he assumes role of truth determinator, cannot prove himself true.
Now, lets go to 2. Circular proof problem.
For any proof system, this logic follows:
P1. A is proved by A or non-A, or not proved at all.
P1 is true by law of identity. If A is proved, it can only be proved by A or non-A.
If it is proved by A, that is circular proof.
If it is proved by non-A, then problem rises: What is non-A proved by?
Non-A, if proved by A, creates circular proof where A depends on non-A and non-A depends on A.
Non-A, if proved by Non-A, again creates circular proof, because even if we assume that a different non-A proves non-A, you eventually run out of different non-A to prove all the different non-A.
With these two problems which are alone sufficient to disprove my opponent, my opponent might try to say "truth exists", or "logic exists", as an attempt to prove something outside Bible.
However, saying that truth exists cannot be logically proved without using truth, which is again circular proof.
Saying "truth doesnt exist" is a claim which cannot be true, but that does not make opposite claim "truth exists" true, because in order to make such connection, you need to use truth, which you cannot possibly use there without creating circular reasoning.
In simple terms, truth says that truth exists, is circular reasoning. And if non-truth says that truth exists, then that is nonsense.
truth can only be proved by truth or non-truth. First is circular reasoning, second is impossible.
Same with logic. Logic can only be proved using logic or using non-logic. First is circular reasoning, second is impossible to even explain.
thus, all logic and all truth is self-contradiction, making it impossible for my opponent to prove anything here, even with great burden placed upon him.
Sources:
https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
https://en.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma
In epistemology, the Münchhausen trilemma is a thought experiment intended to demonstrate the theoretical impossibility of proving any truth, even in the fields of logic and mathematics, without appealing to accepted assumptions. If it is asked how any given proposition is known to be true, proof in support of that proposition may be provided. Yet that same question can be asked of that supporting proof and any subsequent supporting proof. The Münchhausen trilemma is that there are only three ways of completing a proof:
- The circular argument, in which the proof of some proposition presupposes the truth of that very proposition
- The regressive argument, in which each proof requires a further proof, ad infinitum
- The dogmatic argument, which rests on accepted precepts which are merely asserted rather than defended
The trilemma, then, is having to choose one of three equally unsatisfying options.
A loose equivalent can be seen in the response to a young child repeatedly applying "but why?" to answers they receive. One can either end up admitting "but why" could go on forever (regressive argument), that the "why" eventually loops back to where you started (circular argument), or that at some point the answer to why becomes "it just is" (dogmatic argument).
Gödel's second incompleteness theorem shows that, under general assumptions, this canonical consistency statement Cons(F) will not be provable in F. The theorem first appeared as "Theorem XI" in Gödel's 1931 paper "On Formally Undecidable Propositions in Principia Mathematica and Related Systems I". In the following statement, the term "formalized system" also includes an assumption that F is effectively axiomatized. This theorem states that for any consistent system F within which a certain amount of elementary arithmetic can be carried out, the consistency of F cannot be proved in F itself.[6] This theorem is stronger than the first incompleteness theorem because the statement constructed in the first incompleteness theorem does not directly express the consistency of the system. The proof of the second incompleteness theorem is obtained by formalizing the proof of the first incompleteness theorem within the system F itself.
Expressing consistency
There is a technical subtlety in the second incompleteness theorem regarding the method of expressing the consistency of F as a formula in the language of F. There are many ways to express the consistency of a system, and not all of them lead to the same result. The formula Cons(F) from the second incompleteness theorem is a particular expression of consistency.
Other formalizations of the claim that F is consistent may be inequivalent in F, and some may even be provable. For example, first-order Peano arithmetic (PA) can prove that "the largest consistent subset of PA" is consistent. But, because PA is consistent, the largest consistent subset of PA is just PA, so in this sense PA "proves that it is consistent". What PA does not prove is that the largest consistent subset of PA is, in fact, the whole of PA. (The term "largest consistent subset of PA" is meant here to be the largest consistent initial segment of the axioms of PA under some particular effective enumeration.)