Quote from: CoinCube on October 03, 2018, 02:42:30 AM

Quote from: af_newbie on October 03, 2018, 01:32:00 AM

Read my previous post. Our universe cannot be represented by the "elementary arithmetic". We have infinities and quantum effects that we know cannot be represented in a Turing automaton.

The above deduction is invalid. Full stop.

You are misrepresenting my statement. I only need to show that the universe is capable of expressing elementary arithmetic to show that it is incomplete.

I never said the universe can be entirely represented with elementary arithmetic. If the universe can be entirely represented mathematically such math is far beyond human understanding.

Here is the entirety of my first argument.

An Argument for God

Quote from: CoinCube on May 03, 2018, 10:33:55 PM

Claim #1 There are things in this universe that are true yet cannot ever be proven true no matter how much knowledge or technology advance.

This first step is a general statement about the possibility of truths that can never be proven and it can be derived from mathematical deduction.

Gödels theorem proved that any generated system capable of expressing elementary arithmetic cannot be both consistent and complete. What this means is that in any created system that determines basic arithmetical truths/answers, there is at least one statement that is true, but not provable in the system.

The universe is a non-trivial computational system. We know this from the Church-Turing thesis which tells us that physical systems can express elementary arithmetic. ~~It is a system capable of expressing elementary arithmetic.~~

~~Thus we can conclude that the universe is incomplete.~~

There is at least one thing in the universe that is true but cannot ever be proven from inside the universe. Optimal understanding of the universe necessitates we develop a way of evaluating concepts that are possibly true yet forever unprovable.

We know that we can prove some truths and we know that we cannot prove all truths. Therefore we must develop a theory of truth that allows us to prove the truths we can and infer the truths we cannot.

Just because you can express some physical system using arithmetic, and such physical system is part of the universe, it does not mean that the universe can be used in the Gödels incompleteness theorem. Why not? Because this theorem applies to the system of arithmetic axioms.

If you want to prove that the universe is an incomplete system that has some axioms that are true but cannot be proven, you have to represent the universe as a system of such axioms, then the use of the theorem would be valid.

You are playing with "capable" and "can" words.