I was reading this page of posts and am curious if any of you have considered Godel's proof?
"Godel showed that all efforts to prove arithmetic to be free from contradictions are doomed to failure. Arithmetic cannot be proven consistent. In fact, no system powerful enough to include arithmetic is capable of proving itself consistent, unless the proof uses rules of inference from "outside the system" whose own internal consistency is as much open to doubt as is the consistency of arithmetic itself. In short, one monster is slain only by creating another; the proof is never completed." Quote from Nagel on Godel's Proof
IF you've ever read Bertrand Russell (happen to have his book, Portraits of Memory" , he laments about the lack of certainty in mathematics. I find his comments so obviously related to evolutionary delusions.
"I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. Yet I found it full of fallacies, and that, if certainty were discoverable in math, it would be in a new field of math. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and thus constructed a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after many years of toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable."
You see, for millennia, mathematicians had relied on the axiomatic method. Any mathematical statement that is true could be proven to be true. But Godel destroyed this notion. He showed there exists mathematical truth that can never be proven true. There exists truth forever out of reach of the axiomatic method. Yet Godel showed the existence of unprovable truth.
He proved that arithmetic cannot be proven to be consistent. Then he proved arithmetic is either inconsistent or incomplete - one of the other must be true.
Obviously , mathematicians had a dilemma. If arithmetic was inconsistent then the entire structure of math and logic would collapse . So to avoid self-contradiction, mathematicians were forced to acknowledge that arithmetic is incomplete. Logical self-consistency demanded it.
Some true theorems can never be proven true and they are called BELIEVE IT OR NOT - Supernatural Theorems.
The point? one would be that the Supernatural is a friend of Science
Many scientists feel science can only study the natural and can never hope to determine anything about the supernatural. Evidence from mathematics suggests the contrary. Studies of mathematics and logic have shown the hidden hazards of self-reference. Evolutionists claim that science must understand nature in terms of nature. This is a task of self-reference. It is not too difficult to show the inconsistencies and self-contradictions if one dare admit - perhaps they are illusions. Behe talked about this when he described the elephant in the room that science wanted to ignore.
Godel's Incompleteness Theorem is not quite the bludgeon some people (like Roger Penrose) think it is. It relies on certain assumptions that are not universally true in practice.
Thanks for that post.
Time to throw some Belloc into the mix.
"...the absolute powers ascribed to reason [would] lead to the exclusion of truths which the reason might accept but could not demonstrate."
From The Great Heresies, IIRC.
Cheers!