[donh]

u

Godel proved that any logic that contained quantifiers, (For some, For Every) would be incomplete and inconsistent.

No, he didn't. That's an easy assumption to make, and I made it when I was younger, much to my eventual embarassment. Universal and particular Quantifiers can be used to state the axioms of plain geometry, for an obvious, not to say, classical example. Quantifiers don't necessarily imply specifiable, logically tractable sets--barbers in villages that don't shave themselves come to mind.

When you try to run the proof over a continuous domain, you find that you have no contained sets to map to the Godel strings that represent particular theorems+theirProofs. You need sets to complete the proof, and continuous domains of discourse are not about discrete sets of things, they are about continuous things. You could just try to run Godel's proof over plane geometry, instead of arguing with me about it.

Godels proof is so powerful that it blew the bottom out of mathematical logic and consigned to a sidebar in the history of Philosophy.

Um, well, it blew the bottom out of the grand project to formalize all of mathematics. As far as I can tell meta-mathematics is still alive and kicking. It's a great proof, but it ain't a universal solvent.

[beaver fever]

"As far as I can tell meta-mathematics is still alive and kicking"

You snagged me there. Meta-mathematics was in it's formative stages when I studied this stuff in 1971.

Also you have a knowledge of sets which I am very weak on.

I'm really curious at this point of your background in Philosophy.

I have to admit this is the most detailed conversation I've had on this topic on FR.

My mentor was John Woods who did battle with Willard Quine and Jakko Hintika in the early seventies so I'm probably behind on my scholarship.

Please send me a more detailed post of your objections. It is very interesting.

Links would be nice including to your own work.

It's been a long drought. I miss Philosophy

[beaver fever]

per xzins

"This thread was in the open forum.

Now the mods have moved it to the SBR, generally happens when there is bad behavior."

Consigned to the dungeon for mentioning the Phil word.

Keep in touch.

[beaver fever]

BTW as interesting as this discussion has been and I'd like to continue. Let's get together in the New Year and Merry Christmas to you and yours.

Best Regards

Beaver Fever.