Posted on 07/25/2016 10:51:24 AM PDT by SoFloFreeper
Goedel’s theorem shows that Hilbert’s program is impossible and that mathematics itself is built upon faith assumptions, the axioms that we find that we have to use. There are no closed, self-defining systems. “logical systems of arithmetic can never contain a valid proof of their own consistency.”
The real field is complete in the sense of Goedel.
“logical systems of arithmetic can never contain a valid proof of their own consistency.”
But you're not talking about peano arithmetic, are you? So why not simply leave Goedel out of this?
“So why not simply leave Goedel out of this?”
Because Goedel is ultimately about epistemology.
http://theor.jinr.ru/~kuzemsky/JakiGodel.pdf
Well, no. It's ultimately about arithmetic. You should leave Goedel (and Hilbert) out of this. It just sounds ridiculous to drop those names in the context of some argument about religion and faith.
“Well, no. It’s ultimately about arithmetic. You should leave Goedel (and Hilbert) out of this. It just sounds ridiculous to drop those names in the context of some argument about religion and faith.”
Stanley Jaki held doctorates in physics, philosophy and theology. He wrote twenty some books on the philosophy and history of science, often dealing with its relationship to Christianity. Goedel’s theorem was one of his special interests and I think I’ll continue to go with his opinion that Goedel is highly relevant to the discussion.
Go for it. Make yourself out to look stupid if you so desire.
” Go for it. Make yourself out to look stupid if you so desire. “
Boy, that’s a real convincing argument for your position. Does that work with whatever crowd you like to hang with and discuss, oh epistemology and the like? Somehow I get the impression that you don’t even know what that is.
What I do know is what Jaki’s education and field of expertise was- so let’s hear yours. Do you have a doctorate in philosophy? A PhD in physics? Do you have books published on the theory of knowledge and the history of science? There is someone on this thread making himself look stupid, it just doesn’t happen to be me.
Look, why don't you give it a little though on your own? Goedel's theorem is a a statement about arithmetic. Not even that, but a formalization of arithmetic. It hasn't even been convincingly demonstrated that this formal arithmetic is equivalent to the "arithmetic" that mathematicians study anyway.
If you want to say that lots of things can't be proved in math or are very hard to prove, or require some techniques for which formal methods are useless, just say so. Although even that has pretty much zero relevance to whatever point you are making regarding faith and reason.
But leave Goedel's theorem out of this, it continues to be run through the mud in every sort of debate for which it is utterly irrelevant about a thousand times a day on the internet. Do we need more?
“Look, why don’t you give it a little though on your own? Goedel’s theorem is a a statement about arithmetic. “
There is no point in pursuing the issue with you because you obviously have no knowledge of epistemology and the philosophical implications of Goedel’s theorem, which is why you think Goedel is only about arithmetic.
Jaki had a PhD in philosophy as well as physics which is why he could write extensively on aspects of Goedel that you don’t even know exist. Or apparently believe are threatening since you repeatedly insist that it not even be discussed. Nothing is as convincing as demanding that a subject be stifled because you don’t approve of it. Good luck with that campaign.
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