At 11:41 PM 12/18/2004, you wrote:Hal Ruhl wrote:
'The laws of logic need not be thought of as rules of "discovery", they can be thought of purely as expressing
"Expressing" seems to be a time dependent process.
I don't think it needs to be. When we say a certain set of symbols "expresses" something, in the most abstract sense we're just saying there's a mapping between the symbols and some meaning.
That would be static information within a kernel.
So are you agreeing it makes sense to talk about the laws of logic "expressing" some truths without this being a time-dependent process?
static relationships between static truths, relationships that would exist regardless of whether anyone contemplated or "discovered" them.
As are my kernels of information.
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.'
Sure, That is a kernel. Observation does not make a kernel a kernel.
OK, but this isn't really relevant to my question, namely, why does any of this require time?
A kernel does not need a set of rules to make the informational relationships within it what they are. The very words "rules", "laws" and the like carry the implication of a process where the rules and laws are consulted and followed. This is a hidden assumption of some ordered sequence - time. I do not know how to be clearer than that.
I agree that world/kernels don't need to consult the "laws of logic" in order to avoid logical contradictions. I'm just saying that if you look at the facts of each world/kernel and translate these facts into propositions like "all ducks have beaks" (within this particular world/kernel), then you will find that no proposition or collection of propositions about a single world/kernel violate the laws of logic--for instance, you won't find that a proposition and its negation are *both* true of a single world/kernel, in exactly the same sense (ie applying to the same 'domain' like I talked about earlier).
Likewise, you didn't address my point that "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",
I do not believe that Cantor would be sympathetic with that. I think you need to believe in infinity in order to justify working to understand it and thus justify it.
Why do you say that? Cantor's ideas about infinity could be justified in terms of existing commonly-accepted mathematical notions. For example, mathematicians already thought the idea of sets made sense, so he defined the notion of special sets called "ordinals", each of which was a set of smaller ordinals, with the smallest ordinal being the empty set. Then, since there seems to be no obvious contradiction in considering the "set of all countable ordinals", it's easy to see that this set is itself an ordinal but cannot be a countable one, so its cardinality must be higher than the countable ordinals--he defined this cardinality as "aleph-one". Then if you consider the set of all ordinals with cardinality aleph-one, this must be an ordinal with cardinality higher than aleph-one, which he called aleph-two, and so on. See my post at http://www.escribe.com/science/theory/m4919.html for a little more explanation. All this could be described in terms of preexisting ideas about set theory, he wasn't requiring anyone to already believe his ideas about infinities in order to prove them.
I believe Bruno said that some information systems included a set of beliefs. As I recall the "premises" are these beliefs. Justification comes from emotions [based on other beliefs] surrounding the resulting system such as simplicity, elegance of apparent explanation etc. So it seems to me that justification is part of belief.
My point is that if I want to demonstrate the truth of some statement X to you (without appealing to new empirical evidence), I look for some set of premises that we *already* share, and then try to show how these premises imply X. I can't think of any historical example where someone's new idea is accepted by other people without the person appealing to common premises they already share. Can you?
See above re "infinity".
Well, see my comments above, I don't think that's a valid example.
and you didn't address my question about whether you think there could be a world/kernel where a vehicle simultaneously
Again time inserts itself as the notion of "simultaneously".
"Simultaneously" shouldn't be taken too literally, "X and Y are simultaneously true" is just a shorthand way of saying that X and Y are truths that both apply to exactly the same domain, whether "same domain" means "same universe", "same time", or whatever. For example, if I say "Ronald Reagan was President of the U.S. in 1985" and "Bill Clinton was President of the U.S. in 1995", these are two non-contradictory truths that apply to the domain of "U.S. history in our universe", so in that sense they are "simultaneous" truths about this domain even though they refer to different dates. On the other hand, if I said "Ronald Reagan was President of the U.S. in 1985" and "Lex Luthor was President of the U.S. in 1985", and both applied to the domain of "U.S. history in our universe", then this would be a contradiction. But if I made clear that the first statement applied to the domain of "U.S. history in our universe" and the second applied to the domain of "U.S. history in an alternate universe" then there would no longer be any contradiction in these statements.
had different numbers of wheels,
If the world was a CA and half the applicable cells were in a two wheel state and half in a three wheel state what would that be?
I can't really picture a CA where the state of a cell specified a number of wheels, but never mind--this would clearly involve no contradiction, because the statements "the cell is in a 2-wheel state" and "the cell is in a 3-wheel state" would not apply to the same domain, since they refer to two *different* cells. There is only a logical contradiction here if both apply to exactly the same domain--in this case, the same cell in the same "world" at a single time.
My intent in the above was for both kinds of cells to be in the same universe. If cells are on the order of the Plank distance in diameter and half of the applicable states were in a two wheel state and the rest in a three wheel state then what would an observer many orders of magnitude larger observe?
Like I said, I don't know what you even mean in saying a cell expresses "number of wheels"--what exactly would an observer measure when he looked at these cells? Would the cells just have little number-labels on them? If so, if they were too small to read, the observer just wouldn't be able to tell what state they were in, he wouldn't somehow conclude a single cell was in two different contradictory states. Likewise, if we think of cells that can be either black or white like in the "Game of Life" cellular automata, if the cells were too small to see then we would just see various shades of gray, we wouldn't believe a single cell was in two contradictory states. If you're imagining he's measuring the states of cells in some other way besides examining them visually, you need to specify what kind of measurement you're talking about. In any case, I can't imagine *any* type of measurement that would lead a reasonable observer to think he had observed a logical contradiction, so if you think this idea makes sense you'll have to flesh out the scenario a bit.
In any case, even if an observer *mistakenly* concludes two contradictory statements about states are true, the fact remains that within this world/kernel, there are no *actual* contradictions in the set of true propositions about the states of different cells at different times. So you're still not really addressing the main issue, which is whether you believe a world/kernel can contain a genuine contradiction, two contradictory truths about precisely the same domain within this world/kernel that are both true.
Do you think it could be possible for two contradictory statements about the state of a single cell at a single moment in a single world to *both* be true?
I still think that Bruno has allowed for such a case - see above re "Loebian machine".
I don't understand exactly what Bruno was talking about here, but I suspect he just means that a Loebian machine can "believe" or print out two contradictory statements, I'm confident he doesn't mean that the world containing this machine would be inconsistent, or that a third-person observer would actually see any inconsistent truths about what the machine was doing or saying. In other words, the observer might see a machine that at 4 o' clock says "X is true" and then at 5 o' clock says "X is false", but this is not a contradiction from the observer's point of view, there is still a single definite truth about what the machine was doing at any given moment. An actual contradiction would be if the observer saw it was true that at 4 o' clock the machine printed out "X is true" but also saw it was true that at 4 o' clock the machine did *not* print out "X is true".
We've already been through this issue before in the context of axiomatic systems--the fact that an axiomatic system or Turing machine may print out statements whose *meaning* (in terms of some model) is contradictory does not prove that the universe is contradictory, it just proves that it's possible to create axiomatic systems/Turing machines which print out false statements as well as true ones. Only if you were arguing that any set of statements printed out by an axiomatic system/Turing machine must correspond to sets of truths in an actual world in "the All" would this show that the All is contradictory, but of course there's no need to believe this.
From the inside perspective we are forced to be in, all we have to justifyShould we have the hubris to impose this somewhat questioned concept on all other universes? In my view the states of all universes preexist in the All [as some of the kernels] and "Physical Reality" washes over them in some sequentially inconsistent way.
So do believe the statement "the states of all universes don't preexist in the All, and 'Physical Reality' does not wash over them in any sequentially inconsistent way" would be false? If so, it seems that you yourself have the "hubris" to apply the logical law of noncontradiction to statements about reality as a whole.
I am just try to think of the simplest system that contains no information and yet has a dynamic that could support what might be the universe some may believe they inhabit.
But then is there really a process like "think"?
The All as I defined it [my current proposed belief] contains a kernel for the Nothing as well as a kernel for the All thus the nesting.such a belief system is our own beliefs re efficiency, beauty, etc. etc. so our beliefs justify our beliefs. Is this not self referential? I do not intend to impose that on the system as a whole.
You didn't really answer my question above. What I'm asking is, every time you make a statement about reality as a whole, do you intend to deny that the negation of your statement is true? For example, above you say that "The All contains a kernel for the Nothing as well as a kernel for the All." If I make the statement "The All does *not* contain a kernel for the Nothing *or* a kernel for the All", would you then say my statement is false? Please give me a yes-or-no answer to this question, if at all possible.
One has to at least stick with the definitions that establish the system. A zero net information system that actually contains all information would have to contain all kernels. Within the context of my beliefs [permises] then I would answer yes since your statement violates this premise. This is not a matter of the "Laws of Logic" but rather an informational relation within the system.
I think this is ducking the issue, since you're just saying that statements about "informational relations within the system" cannot be contradictory, which means you are demanding that these statements obey the laws of logic, even if you don't justify this demand in terms of "the laws of logic". Call it whatever you want, it still amounts to the same thing.
I do not agree with your "rather" based cancelation of the residual information issue since I see it as an unnecessary complication of my own method.
I'm not sure what you mean by "rather based cancellation." If you're talking about my point that every statement could be simultaneously true and false if you throw out the laws of logic, obviously *I* don't believe this is a good way to solve the "residual information issue", since I think it's nonsensical to allow logical contradictions. But since you seem to be saying the laws of logic aren't absolute, I was just pointing out that you would have no basis for denying that statements about reality can be simultaneously true and false. If you say that it is an "unnecessary complication" to allow statements about reality as a whole to be both true and false, then you are in effect saying it would be an unnecessary complication to claim that the laws of logic don't apply to reality as a whole!
I just believe in my own sense of neatness. You gave two apparently contradictory statements which when put in the same pot seem to sum to what I propose for the whole system absent the "rather". I wish to avoid including our "laws of logic" as a necessary component of a kernel.
But if you "wish to avoid" allowing statements about reality to be both true and false, that means you "wish to avoid" allowing reality as a whole to contain logical contradictions! The two ideas are exactly equivalent.
What has that got to do with what I said above?
Sorry, I misread what you were referring to in the "wish to avoid" statement there. But again, it's irrelevant whether you think of "the laws of logic" as some separate thing which must be "included" in a kernel, that's not what I've been arguing. I'm just arguing that that if you list the complete set of true propositions about a given kernel, you will find that these propositions do not violate the laws of logic. Are you disagreeing with that? Are you saying there could be kernels where "X is true" would be a true statement about the kernel, but "X is false" would also be a true statement about the kernel, with the understanding that both statements apply to exactly the same "domain" within the kernel?
Would both of your statements not be in the same meta system? I can in fact - as I said - accept both because in my opinion they add up to what I am saying.
When you say "both of your statements", which two statements of mine are you referring to?
My point is that it is more pleasing to think of the dynamic as being inconsistent [each state has no cause effect link of any sort to any other state] if there are other components of the All that are inconsistent. But these are not really the same thing and I begin to think the latter is a side bar issue.
There is nothing "inconsistent" in a logical statement about having no causal links between states--such an idea does not imply any logical contradictions (ie it doesn't imply that two contradictory statements can both be true in precisely the same domain).
I said exactly this when I said "But these are not really the same thing and I begin to think the latter is a side bar issue." right above.
But you said the statements are "inconsistent", I disagree with your use of that word to describe a lack of causal links between states, just like I disagree with the idea that if a machine prints out two inconsistent statements, that would somehow show that the world/kernel containing the machine was inconsistent. I am using "inconsistent" solely to refer to actual logical contradictions in the set of true statements about a single world/kernel.
indicated that as much
I think you are misunderstanding what the "laws of logic" really mean, examples like different cells of a cellular automata having different states
See above: Its in the eye of the beholder.
I disagree, there will be no situation where a reasonable observer would conclude that two inconsistent statements were both true, in exactly the same sense.
or different states in a series
Where did "series" come from?
From your own comments about a series of states with no causal connection to
each other.
having no causal relationship to one another don't contradict the laws of logic in any way.
I was not talking about the "laws of Logic" I was asking if the universe in question did not in fact have a vehicle with both two wheels and three wheels from the point of view of an observer much larger than a cell.
Truths about a world do not depend on what an observer thinks. If I believe that the sky is green, it's still true that the sky in this world is actually blue.
Does that mean you say the statement "each state of the dynamic is completely dependent on the current state" is false?
I believe we should avoid applying logic to a zero internal information entity such as the All. I believe this causes problems.
You didn't answer my question. Would you say the statement "each state of the dynamic is completely dependent on the current state" is false, or would you say it's true, or would you say it is neither true nor false, or what?
How do you justify the question?
I'm just asking whether, when you make statements about reality as a whole, you are assuming that the negation of these statements are false. If you are, then your statements about reality as a whole obey the laws of logic, even if you are for some reason hesitant to use the words "laws of logic" to describe this feature of your statements.
My quest is zero information in the whole system. I established a system I believe meets this criteria. Its premises could I suppose be taken as "true" without proof in the usual manner. However, if my system indeed has no information how do the "laws of logic", "truth", "contradiction", etc apply to no information by any justification?
If you believe the laws of logic are "information" (I don't agree), and yet statements about your system never violate these laws (ie if a given statement about your system is true, the negation is always false), then one of your premises must be false--either the premise that requiring a set of statements to obey the laws of logic introduces additional "information" into the system, or the premise that you have indeed succeeded in devising a system that contains zero information.
Any other premise set establishes an alternate system. Am I to presuppose that there is not a meta system that has more than one zero information system in it or that such a system could not somehow contain a negation of one or all of my premises? See also above.
I don't understand what you mean by "a meta system" here, or what relation that has to what we were talking about above.
Jesse
