hammegk said:
My invocation of Godel is somewhere between your worries of lumpen mathematics and
Courtesy of http://www.evanwiggs.com/articles/GODEL.html
This gibberish confirms that you have no understanding of Godel's theorems, in that you are willing to present it without embarassment in support of your position.
Examining that quote in detail:
Kurt Godel proved two extraordinary theorems. Accepted by all mathematicians, they have revolutionized mathematics, showing that mathematical truth is more than logic and computation. Does Godel's work imply that someone or something transcends the universe?
The first statement is true. The second statement is false (he did not, in fact, show that mathematical truth is more than logic and computation). The closing question is simply answered "no."
In more detail. The cited article is written by "Daniel Graves, MSL." The standard expansion of "MSL" is "Master of Science in Law," hardly an auspicious beginning for an article that purports to be jointly about Godel's theories and theology. Of course, he might be a brilliant mathematician in his spare time, so let's examine his reasoning in detail.
First, Godel shattered naive expectations that human thinking could be reduced to algorithms. An algorithm is a step-by-step mathematical procedure for solving a problem. Usually it is repetitive. Computers use algorithms. What it means is that our thought cannot be a strictly mechanical process. Roger Penrose makes much of this, arguing in Shadows of the Mind that computers will never be able to emulate the full depth of human thought. But whereas Penrose seeks solutions in quantum theory, Christians see man as a spiritual being with understanding that springs not just from the physical organ of the mind but also from soul and spirit.
This is simply an argument from ignorance that reflects a basic misunderstanding of Godel's theorems. Godel's theorems, as the author correctly pointed out, applies to formal systems : "Godel proved that any formal system deep enough to support number theory has at least one undecidable statement." Even here, he didn't get the statement right. A better formulation would be that Godel proved that formal system deep enough to support number theory has at least one undecidable statement
or is inconsistent. Since humans are known to be inconsistent reasoners (see the work of Kahneman and Tversky for a stunningly long list of examples), human reasoning could still be described by a formal system.
But, for other reasons, we should doubt the application of this theorem -- again, as the author points out in the opening paragraphs, "there are many systems of math and logic. One kind is called a formal system." In direct contrast to the quotation you presented,
there are other systems of logic that are not formal systems, to which Godel's theorems do not apply. So, yes, Graves is right that our thought may not be "a strictly mechanical process," but in this case Godel's theorem has no application.
Graves' metaphysics are similarly ludicrous. He writes, for example, "had Godel been able to affirm that a complex system is able to prove itself self-consistent, then we could argue that the universe is self-sufficient." This statement is unsupported and unsupportable. Or, more accurately, we could still argue (if we wanted) that the universe is self-sufficient, because the universe is not a formal system of logic. Godel's theorem has no relevance to the question of whether or not the universe is self-sufficient, and Graves has provided no evidence or argumentation that it does.
Hmm. Do I think myself capable of discussing Godel's work with a good mathematician? No.
Obviously not. And, incidentally, thank you for proving my prediction correct by providing that postmodern bafflegab from Graves. Drinks are on me, Hawk.
