Hal Ruhl wrote:

At 09:35 PM 12/12/2004, you wrote:

Godel's theorem would also apply to infinite axiomatic systems whose axioms are "recursively enumerable" (computable). But sure, if you allow non-computable axiomatic systems, you could have one that was both complete and consistent.

A complete axiomatized arithmetic would be I believe be inconsistent as supported by to Bruno' post. http://www.escribe.com/science/theory/m5812.html

No, I'm sure Bruno was only talking about recursively enumerable axiomatic systems. He said himself that the set of all true statements about arithmetic would be both complete and consistent, so if you allow non-computable sets of axioms you could just have every true statement about arithmetic be an axiom.

If you don't believe me, though, you can ask him about this.

So, again, you don't have any way of showing to a person who doesn't share your theoretical framework in the first place that "everything", i.e. the All, need be inconsistent.

I expect that this is a common problem for anyone's ideas.

Not really, usually when people try to convince others of new ideas they appeal to some common framework of beliefs or common understanding they already share--that's why people are capable of changing each other's mind through reasoned arguments, rather than everyone just making arguments like "if you grant that the Bible is the word of God, I can use passages from the Bible to show that it is indeed the word of God."

Well ideas of this nature then where the framework shifts.

Since I don't understand your ideas I can't really comment. But I can't think of any historical examples of new mathematical/scientific/philosophical ideas that require you to already believe their premises in order to justify these premises.

But you do not understand my ideas so how does this apply?

Because when you said "well ideas of this nature then where the framework shifts", I assumed you meant that your ideas *cannot* be justified in terms of any common framework, that you can only justify your theory in the terms of the theory itself. So I don't need to understand your theory to see that it is "circular" in this way, I just need to take your word for it. And like I said, I can't think of any past cases in math, science or philosophy of new theories that gained acceptance without appealing to a common framework or common understanding. So when you said "well ideas of this nature then where the framework shifts", it seems there are no other ideas in history that were of that "nature".

I disagree. "X AND Y -> X" does not imply that first you have "X AND Y" and then it somehow transforms into X at a later date, it just means "if it is true that statements X and Y are both true, then statement X must be true".

You miss my point. As I said in earlier posts the information is static, the process of uncovering it is not.

So why couldn't the static ideas expressed by the laws of logic be timelessly true, even if we can only see the relationships between these truths in a sequential way?

You still miss what I am saying. The laws of logic are designed to discover preexisting information. The preexisting information is static. Discovery is a time dependent process. It assumes time exists. Why that? How is it justified?

The laws of logic need not be thought of as rules of "discovery", they can be thought of purely as expressing static relationships between static truths, relationships that would exist regardless of whether anyone contemplated or "discovered" them. For example, in every world where X and Y are simultaneously true, it is also true that X is true, even if no one notices this.

If you don't think the laws of logic can be taken for granted, you could just solve the information problem by saying it is simultaneously true that there is "something rather than nothing" and also "nothing rather than something", even though these facts are contradictory.

There would still be the information contained in the existence of the contradiction which divides it from systems that are not contradictory.

No it wouldn't, because if you abandon the laws of logic you can say that it is also true that this system is not contradictory--in other words, although it's true that both these contradictory statements are true (so the 'system' containing both is contradictory), it's also true that one is true and one is false (so the system containing both is not contradictory). Of course, you can now say the meta-system containing both the statements I just made is contradictory, but I can apply the exact same anti-logic to show this meta-system is not contradictory. And you can also use anti-logic to show that every statement I have made in this paragraph about the implications of anti-logic is false, including this one. Once you abandon the principle that if a statement is true, its negation must be false and vice-versa, then anything goes.

And why is "anything goes" a problem? Anything goes includes universes such as ours.

The contradictory truths aren't truths about different domains, like different "universes"--then they really wouldn't be contradictory, since there's no contradiction involved in saying "X is true in universe #1 but false in universe #2".

Fine. See below.

I am talking about contradictory truths in a single domain, like it being simultaneously true that *our* universe contains stars and true that our universe does not contain stars.

I see no reason to exclude self counterfactual structures such as a two wheeled tricycle. However, I am not ready to include a two wheeled tricycle that is simultaneously a one, three, or four wheeled tricycle.

Then it seems you are not really expressing a contradiction with the phrase "two wheeled tricycle", if you are not ready to "include" an object that simultaneously has two and three wheels--you're just changing the definition of the word "tricycle" to encompass a two-wheeled vehicle.

In any case, would you agree it is true in all possible worlds that there can be no vehicle that simultaneously has one, three and four wheels?

Anyway, are you now agreeing that if you abandon the laws of logic, you can solve the "information problem" by saying it is both true that there is "something rather than nothing" (either a single universe, or multiple universes) and also true that there is "nothing rather than something" (not just that there is a universe containing nothing, but that there are no 'universes' or 'states' or anything at all in any part of reality)?

Does that not as you say solve the information problem by cancelling out the "rather" at the global level? Then change Something to the All and it seems to be what I am saying if I understand you. After all the information re the Nothing is in the All so they are infinitely nested.

I don't understand much of the paragraph above. But if you abandon the idea that the laws of logic are universal (and I am not sure you really do, based on your comment about the tricycle above), then would you agree that statements you believe are true of reality as a whole, such as "the information re the Nothing is in the All so they are infinitely nested", must also be false, so that "the information re the Nothing is not in the All so they are not infinitely nested" could also be a true statement?


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