Transcendental Argument for the Non existence of God
1.) If Logic/Mathematics is from God, it would be perfect.
2.) Logic/Mathematics is not perfect.
3.) Therefore Logic/Mathematics is not from God.
I do not think that I get any argument against premise 1. from Christians or other monotheist believers.
According to Christians and other theists, God is perfect in every way, therefore, if logic came from God, it would be perfect.
Now, premise 2. is where I have to do the heavy lifting. On the surface it looks like, that it is an impossible task to defend premise 2. One could even say it is madness. How can you prove using logic, that logic is not perfect. Well, I get a lot of help from, that is, it has been done for me, by much smarter people than I am.
Search for infinity.
In the 19th century Georg Cantor, a good Christian, felt called by God to find out how big is infinity. Well, the problem really started back in the 17th century, when Galileo found out, that not all infinities are the same size. E.g. in the case of two concentric circles, both contains an infinite number of points, but it appears that the lager one has more. Galileo dodged the issue, but Cantor did not compromised. He wanted to find it out. This led him to the discover, that some infinities are infinitely larger than others. Cantor ended mad and died in a mental sanatorium. Be aware! Thinking about the infinities can make you crazy, or worse, kill you. This is the first, the last and your only warning. So, you had three warnings (jk).
The call to fix up mathematics.
Then in 1920, came the famous hotel owner David Hilbert and put out the call to mathematics to be formulated on a solid and complete logical foundation.
1. All of mathematics follows from a correctly chosen finite system of axioms; and
2. that some such axiom system is provably consistent through some means such as the epsilon calculus.
This call demonstrated that mathematics was (is) not on a solid ground or complete therefore not perfect.
Who shaving whom.
Gottlob Frege was one who heeded the call and started to work on his Set Theory. He thought he got it made, when our friendly atheist Bernard Russell wrote to him, pointing out that there was a tiny problem with his book, which made the whole of his Set-theory wrong. Frege did not publish his book about Set Theory. This was a great set back to Set Theory and Set Theory had to be cut down to size, to avoid Russell’s Paradox.
One version of this paradox is: In a town the only barber shaves everyone who does not shave himself. The question is, does the barber shave himself.
You cannot prove anything, accept that you cannot prove anything.
The Russell Paradox fiasco, was a big blow to mathematics, but it seemed to be localised. They patched up Set Theory see: Zermelo-Fraenkel Set Theory. And, mathematicians went their marry ways calculating, like nothing happened. But, then came all times greatest logician, mathematician, a true theist, unlike his friend Einstein, Kurt Godel. He delivered two fatal blows, with his Incompleteness Theorems. And, that is why many of you never heard of him.
The first incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example Peano arithmetic), there are true propositions about the naturals numbers that cannot be proved from its axioms.
1. If the system is consistent, it cannot be complete.
2. The consistency of the axioms cannot be proven within the system.
The incompleteness theorems also imply that not all mathematical questions are computable.
We do not know when to stop.
Finally Alan Turing, showed us that computers are no better than us, with the Turing Completeness. They do not know when to stop. See: halting problem.
We always knew it.
We always knew that logic is not perfect, because of the paradoxes. The most important of these paradoxes is the liar paradox. “This statement is false.” This paradox is the bases of Godel’s incompleteness theorems.
Theists always like to hide these things. There is a legend that Pythagoras followers killed the guy who discovered, that the square root of 2 is an irrational number. Done this, because the existence of irrational numbers was against their believe system.
Another example of imperfection is, that the Euclidean Geometry’s 5th Postulate, the Parallel Postulate, never been proven. In fact, we got Non-Euclidean Geometric, from mathematicians who (among them the Hungarian Bolyai) tried to prove it without success.
So, we can see that Logic/Mathematics is not complete or consistent, therefor Not Perfect!!!
To refute this argument, my opponent has to disprove Godel’s Incompleteness Theorems. Prove the parallel postulate of Euclid and resolve all logical paradoxes. It worth to try, as you would receive at least one Nobel prize as a minimum.
Failing this, my opponent needs to accept that God most likely does not exists. Or at least stop using the Transcendental Argument and Presuppositional apologetic for God.