An Illogical Universe?

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snow5379
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An Illogical Universe?

Postby snow5379 » Sun Jul 10, 2011 9:17 pm UTC

A is (A and (B xor !B))

1. Can a universe exist with the above statement as false?
2. Can a universe exist with the above statement as sometimes true and sometimes false?

I hear a lot of people talk about universes without logic. The only way I can imagine such a universe is with A and B being random values. Thus A is A wold only sometimes be true. Do you think an illogical universe could exist?

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Re: An Illogical Universe?

Postby Greyarcher » Sun Jul 10, 2011 9:41 pm UTC

I have no strong reason to think it can't exist. I only have experience with one universe after all. Extrapolating about other universes from only that would, probably, be lousy methodology.
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Re: An Illogical Universe?

Postby Fedechiar » Sun Jul 10, 2011 9:49 pm UTC

What do you mean with "A is A"? You have to define A first! Logic is a mode of thought, a systematic environment created from a few principles (one of which is, obviously, A=A); you can't say with any certainty this universe is logical; to do it, you would have to fit everything into a completely logical and rational framework. Even accepting your definition of a logical universe, there is a whole branch of logic (fuzzy logic) that deals with variables that have more than two states (p.e., true, false, unknown, probably true, probably false).

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Re: An Illogical Universe?

Postby CorruptUser » Sun Jul 10, 2011 11:59 pm UTC

Wait, is that xor a typo? Assuming a typo, by definition, (B or !B) is equivalent to S*. Either event E has occurred or not. Not getting into quantum physics and cats, of course. So the statement simplifies to "A is (A and S)". "A and S" is just A, so the statement further simplifies to "A is A".

The only way I see this as not occurring is when a certain cat** is involved. In our weird universe, quantum physics tells us that the events B and !B can both occur, or both not occur. Then, it's possible in our own universe that the statement isn't true.


*S = Set, or whole, or universe, or 1, depending who you ask.
**I can't get it to link directly to that part of Wiki~. Are ö's a problem for the [URL] function?

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Re: An Illogical Universe?

Postby Dark567 » Mon Jul 11, 2011 1:16 am UTC

Can a universe exists where 1+1=3? No. All that could be done is redefining what the symbol '3' represents, not changing the fundamental concepts of math. The same is true with logic, suddenly ending up in a different universe wouldn't change the rules of logic any more than they would change the rules of math. Math and logic transcend our physical universe.
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Re: An Illogical Universe?

Postby CorruptUser » Mon Jul 11, 2011 1:20 am UTC

Apparently you never learned non-Euclidean geometry or Complex Analysis.

Or learned about hypergraphs (basically, a graph where each edge can have more than 2 endpoints. It's weird because graph theorists argue about whether an edge can have less than 2 endpoints, let alone more).

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Re: An Illogical Universe?

Postby TheGrammarBolshevik » Mon Jul 11, 2011 1:53 am UTC

Non-Euclidean geometry revises Peano arithmetic, now?
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Re: An Illogical Universe?

Postby elasto » Mon Jul 11, 2011 1:54 am UTC

Dark567 wrote:Can a universe exists where 1+1=3? No. All that could be done is redefining what the symbol '3' represents, not changing the fundamental concepts of math. The same is true with logic, suddenly ending up in a different universe wouldn't change the rules of logic any more than they would change the rules of math. Math and logic transcend our physical universe.
Binary logic transcends our universe, it's true. That does not, however, guarantee that our universe is logical*.

On the opening post: It seems to me to be basically asking can a universe exist which is not based on binary logic. Personally, I don't see why it couldn't.



*It's better to assume it is than it isn't, since otherwise scientific progress grinds to a halt. But that's a different issue!
Last edited by elasto on Mon Jul 11, 2011 1:54 am UTC, edited 1 time in total.

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Re: An Illogical Universe?

Postby Dark567 » Mon Jul 11, 2011 1:54 am UTC

CorruptUser wrote:Apparently you never learned non-Euclidean geometry or Complex Analysis.
Well, I have. How does it apply to the above?
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Yakk wrote:The question the thought experiment I posted is aimed at answering: When falling in a black hole, do you see the entire universe's future history train-car into your ass, or not?

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Re: An Illogical Universe?

Postby Ross1 » Mon Jul 11, 2011 2:40 am UTC

I am pretty sure an illogical universe wouldnt need logic to prove that it can exist.

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Re: An Illogical Universe?

Postby doogly » Mon Jul 11, 2011 3:23 am UTC

TheGrammarBolshevik wrote:Non-Euclidean geometry revises Peano arithmetic, now?

Word. Sigh. A little bit of education is a dangerous thing, eh?
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Re: An Illogical Universe?

Postby KnightExemplar » Mon Jul 11, 2011 3:48 am UTC

Logic is a human invention. It aids in arguments and tends to predict the universe pretty well. Outside of that, the universe determines logic, not the other way around.
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Re: An Illogical Universe?

Postby TheGrammarBolshevik » Mon Jul 11, 2011 3:49 am UTC

What observation about the universe could possibly change anything about logic?
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Re: An Illogical Universe?

Postby KnightExemplar » Mon Jul 11, 2011 4:13 am UTC

TheGrammarBolshevik wrote:What observation about the universe could possibly change anything about logic?


If from today, to the end of the universe... we observe that For All A, B: ((A implies B) implies (B implies A)), then I would not be against changing the laws of logic to make that legal.
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Re: An Illogical Universe?

Postby TheGrammarBolshevik » Mon Jul 11, 2011 4:17 am UTC

You're talking about observing logical operators. How would that actually look in the physical world?
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Re: An Illogical Universe?

Postby KnightExemplar » Mon Jul 11, 2011 4:21 am UTC

TheGrammarBolshevik wrote:You're talking about observing logical operators. How would that actually look in the physical world?


In the case of (A -> B) -> (B -> A)... then we would observe that not only do "causes" create "effects", but the "effects retroactively cause its cause".

For example, In the current universe, if I squash a bug, then it is dead. (A == I squashed the Bug. B == Bug is dead). If in some universe, a dead bug implies I squashed it, then the above rule would be true in that universe. EDIT: Or perhaps, "the ability to kill a bug implies that I killed all bugs" would be an equivalent statement)

And if we wanted to make sense of that universe, then we'd have to change the rules of logic to fit into it.
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Re: An Illogical Universe?

Postby Dark567 » Mon Jul 11, 2011 4:54 am UTC

KnightExemplar wrote:
TheGrammarBolshevik wrote:You're talking about observing logical operators. How would that actually look in the physical world?


In the case of (A -> B) -> (B -> A)... then we would observe that not only do "causes" create "effects", but the "effects retroactively cause its cause".
And what exactly would that look like? I am pretty sure if "effects retroactively cause its cause" it would pretty much look exactly like it does now. Hell what your saying "effects cause its cause".... Think about that, your just switching the definitions of words. If an "effect" is causing something, its a cause. That's what the word cause mean: a thing that causes something else.

For that matter the entire idea of "observing logic" makes no sense. All science and all observation for that matter, assumes logic axiomatically. It's not possible to observe logic, because the very act of observing assumes logic already is true.

elasto wrote:On the opening post: It seems to me to be basically asking can a universe exist which is not based on binary logic. Personally, I don't see why it couldn't.
The universe isn't based on on anything of the sort. Logic is a tool we use to interpret it, but its a special tool, because its transcendent. Again look at math, could a universe exist where 1+1 didn't equal 2? What would that even entail? Again the only way around it is to change the definition of our symbols, but that meaningless for this. Math is correct because its defined that way. 3 is always 1+1+1 because it's defined as 1+1+1. A change in universe doesn't change our definitions. This also holds true for logic: logical statements are valid, not because of any objective fact of the universe, but because the definitions make it that way.
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Re: An Illogical Universe?

Postby doogly » Mon Jul 11, 2011 4:55 am UTC

http://en.wikipedia.org/wiki/Is_logic_empirical%3F
There is a discussion to be had, but your example isn't it.
Generally though, we're better off with vanilla logic and quantum probability.
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Re: An Illogical Universe?

Postby curtis95112 » Mon Jul 11, 2011 7:49 am UTC

Ross1 wrote:I am pretty sure an illogical universe wouldnt need logic to prove that it can exist.


Just wanted to emphasize this.
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Re: An Illogical Universe?

Postby Greyarcher » Mon Jul 11, 2011 10:31 am UTC

Ross1 wrote:I am pretty sure an illogical universe wouldnt need logic to prove that it can exist.
Agreed.

Until we observe more universes, I see no reason to judge the likelihood of an "illogical" universe. A limit on my ability to conceive of something is not necessarily a limit on what is actually possible.

That said, I admit an "illogical" universe sounds strange. Rather, universes aren't logical or illogical in the first place--it's inferences that are logical or illogical. It's just our way of structuring thought. So, in a way, it doesn't mean anything for a universe to be illogical. The only way for such a phrase to be meaningful is if it's not literal. The closest I can think of is a universe with no consistent chain of cause and effect, such that something like modus ponens doesn't meaningfully apply.

So I suppose an "illogical universe" could be a universe where certain logical forms don't apply. But "A and (B or !B)"...that requires basically nothing. For it to not apply, the universe would have to be empty. But that would be more of an alogical universe.

Yes...when I think about it, "a universe where 'A and (B or !B)' is false" sounds like nonsense. "A and (B or !B)" has such minimal content, what is there to be false? It's more about us saying "there's stuff, and maybe other stuff" than about the hypothetical universe.

But I could be wholly wrong about this.
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Re: An Illogical Universe?

Postby L4nce0 » Mon Jul 11, 2011 1:10 pm UTC

My two cents. When you start talking in Boolean algebra, or anything really high and thought out.. you're really talking about meta, μετά. It doesn't exist. So for such a thing to come into existence in the meta, other universe, one must also assume that there is a life form that has a brain.. or further a brain which thinks in a similar logical way. As it took humanity how many melenia to transform from drunk geek philosophers to modern scientists? It's shocking we even have these ideas ourselves. Course quite quickly we get into metaphysics and Platonism.. which there is a reason why the Greeks drank ( okay, technically previously). Drawing from the idea that ideas exist and any logical being will eventually come to the same idea. ie circle is a circle, despite the impossibility of a perfect circle in any circumstance existing, yet obviously any culture figured out a circle. I digress. Assuming a being of which could interpret the idea of boolean algebra, the next question is how could logic be changed? Your sample is layers too complex for my head to abstract from the perspective of this meta being. So binary. 11. Could meta physics produce a world where there is an on, off, and meta state? I could imagine that, but further, you change one tiny rule, such as turning binary to trinary on a basic level everything changes. Heck, change the strength of gravity by a billionth of a percent. Consider how that would percolate over an infinite amount of time with an infinite amount of particles. Or perhaps something more exciting, as dark matter acting the opposite of what we think of it.. or even more crazy, a being from whos universe is made of dark matter! The results of that would be astonishing.... When I'm presented with these questions I usually go the easier route and say, why not? Avoiding trying to encapsulate it in my brain.. So my answer is, life gets annoying when the word meta is involved.

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Re: An Illogical Universe?

Postby doogly » Mon Jul 11, 2011 1:19 pm UTC

Good reasons why not are that we can understand variations to gravity much better than you think (with telescopes!) and that cubits (with 3 or more states) can be used for computing completely in harmony with Boolean logic.
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Re: An Illogical Universe?

Postby Роберт » Mon Jul 11, 2011 2:42 pm UTC

Every single place has to follow logic. Why?

Well, let's look at the universe. Let's not assume it's all logical. Some parts of it are, some aren't.

If the part we are considering is logical, than logic always works in that part.
If the part we are considering is illogical, than logic always works in that part.

So logic always works everywhere. :mrgreen:
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Re: An Illogical Universe?

Postby curtis95112 » Mon Jul 11, 2011 3:29 pm UTC

Роберт wrote:Every single place has to follow logic. Why?

Well, let's look at the universe. Let's not assume it's all logical. Some parts of it are, some aren't.

If the part we are considering is logical, than logic always works in that part.
If the part we are considering is illogical, than logic always works in that part.

So logic always works everywhere. :mrgreen:


I had thought logically disproving an illogical universe would be inconsistent.

I... seem to have been mistaken.
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Re: An Illogical Universe?

Postby Greyarcher » Mon Jul 11, 2011 4:01 pm UTC

Роберт wrote:Every single place has to follow logic. Why?

Well, let's look at the universe. Let's not assume it's all logical. Some parts of it are, some aren't.

If the part we are considering is logical, than logic always works in that part.
If the part we are considering is illogical, than logic always works in that part.

So logic always works everywhere. :mrgreen:
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Re: An Illogical Universe?

Postby KnightExemplar » Tue Jul 12, 2011 12:02 am UTC

Dark567 wrote:
KnightExemplar wrote:
TheGrammarBolshevik wrote:You're talking about observing logical operators. How would that actually look in the physical world?


In the case of (A -> B) -> (B -> A)... then we would observe that not only do "causes" create "effects", but the "effects retroactively cause its cause".
And what exactly would that look like? I am pretty sure if "effects retroactively cause its cause" it would pretty much look exactly like it does now. Hell what your saying "effects cause its cause".... Think about that, your just switching the definitions of words. If an "effect" is causing something, its a cause. That's what the word cause mean: a thing that causes something else.

For that matter the entire idea of "observing logic" makes no sense. All science and all observation for that matter, assumes logic axiomatically. It's not possible to observe logic, because the very act of observing assumes logic already is true.


No, it does not.

For example, if a bug were to die, it could be due to a variety of causes. The bug could get eaten, or it can die of natural causes, or maybe it was poisoned.

If effects retroactively caused the causes, (ie: if ( (A->B) -> (B -> A)) ), then all effects would have a singular cause. A bug could ONLY die by getting eaten. Natural causes and poisoning would fail to kill the bug. All effects can be traced to a singular cause.

Which is just silly, at least in this universe.
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Re: An Illogical Universe?

Postby TheGrammarBolshevik » Tue Jul 12, 2011 12:12 am UTC

You're conflating implication with causation. There are probably other problems, which I might get to later.
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Re: An Illogical Universe?

Postby Qaanol » Tue Jul 12, 2011 2:26 am UTC

snow5379 wrote:A is (A and (B xor !B))

1. Can a universe exist with the above statement as false?
2. Can a universe exist with the above statement as sometimes true and sometimes false?

I hear a lot of people talk about universes without logic. The only way I can imagine such a universe is with A and B being random values. Thus A is A wold only sometimes be true. Do you think an illogical universe could exist?

Suppose 0 ≤ B ≤ 1. The statement “B xor !B” is equivalent to “(B & !!B) or (!B & !B)” which simplifies to “B or !B”, which has truth value equal to C = max(B, 1-B). Also, “A & (B xor !B)” has truth value equal to D = min(C, A). But we want D = A, meaning A = min(A, C), and thus A ≤ C. This means we need to have A ≤ max(B, 1-B) in order for that statement to be true.

Therefore, if choose A and B so that A > max(B, 1-B), the statement “A is (A and (B xor !B))” will be false. To do so, we may take B as any truth value strictly between 0 and 1, say B = 0.5, and we may take A as being true, so A = 1. Then the statement is false.

As has been mentioned, we can do this with quantum mechanics. Suppose we have an electron and measure its spin in the x direction, finding that it has spin up in the x direction. Let A represent the truth value of the statement, “The electron has spin up in the x direction.” Let B represent the truth value of the statement, “The electron has spin up in the z direction.” Now B is truly 0.5.

Bear in mind this is not simply analogous to flipping a coin in a dark room and considering the truth value of the statement, “The coin landed on heads.” In that case, the statement has a definite value of 0 or 1, we just don’t know what it is. With quantum indeterminacy, the electron truly does not have either spin up nor spin down in the z direction when its spin in the x direction has been observed in an eigenstate.

Thus, that statement can indeed be false, and in our very own universe to boot.

On the other hand, if you artificially restrict the allowed values of A and B to the boolean set {0, 1} then the statement will always be true.

Edit: In the case of a coin flip whose result is unknown, we have “B xor !B” equivalent to |B - !B| = |B - (1 - B)| = |2B - 1|. Then “A and (B xor !B)” equals A*|2B - 1|. We are considering whether A = A*|2B - 1|, which means either A = 0 or |2B - 1| = 1. In this case we can make the statement false by taking any value for A strictly greater than 0, and any value for B strictly between 0 and 1. That is to say, when A > 0 and 0 < B < 1 for probabilistic variables, the statement “A is (A and (B xor !B))” is false. This is actually an easier condition to satisfy than the one for true indeterminacy, but relies on incomplete knowledge rather than an intrinsic property of the universe.
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Re: An Illogical Universe?

Postby Whimsical Eloquence » Tue Jul 12, 2011 2:46 am UTC

All that KnightExemplar's argumentation flailing serves to do is to illustrate quite nicely why causality is a synthetic a prior - existing as a nearly universal feature of our modelling rather than as any directly observable empirical feature. All our models don't exist, even statements like "There's a laptop in front of me" is an unprovable, intangible idea. What is tangible is the empirical data which the model of "There is a laptop in front of me" seems to account for. The same is broadly through of the application of Mathematics and Logic to Science. The Universe does not dictate the terms but rather dictates the applicable terms of things such as Mathematics and Logic. Mathematics creates two systems of geometry, each with particular axioms - both equally valid. The empirical data of the universe seems to match the predictions of one of these systems - it is then useful to treat as a valid model that system's axioms and theorems. Equally for Logic - though I would argue that much of logic is merely rigorous self-consistency which is really a synthetic a priori in any Empirical Venture - regardless of the empirical particulars.
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Re: An Illogical Universe?

Postby elasto » Thu Jul 14, 2011 6:38 am UTC

Dark567 wrote:
elasto wrote:On the opening post: It seems to me to be basically asking can a universe exist which is not based on binary logic. Personally, I don't see why it couldn't.
The universe isn't based on on anything of the sort. Logic is a tool we use to interpret it, but its a special tool, because its transcendent. Again look at math, could a universe exist where 1+1 didn't equal 2? What would that even entail? Again the only way around it is to change the definition of our symbols, but that meaningless for this. Math is correct because its defined that way. 3 is always 1+1+1 because it's defined as 1+1+1. A change in universe doesn't change our definitions. This also holds true for logic: logical statements are valid, not because of any objective fact of the universe, but because the definitions make it that way.

Whimsical Eloquence's response broadly preempts mine, so mine can be a little shorter.

Firstly, you are perfectly correct that logic itself transcends universes because it's merely a set of definitions: 1+1+1 will always equal 3 because that's how it's defined, as you say.

When I talk about 'a universe existing that is not based on binary logic' I am not referring to the universe itself - so forgive me for my lazy phrasing; For, as I have pointed out repeatedly in other threads in recent days, the nature of the universe itself is and always will be unknowable. The closest we can come is to say 'the universe behaves as if it were like [Model]' - where [Model] is '1d strings moving in 11d space-time' or whatever. What I am referring to, then, is our model of the universe.

So the question I am refining the OP's question to is: 'Is it possible that a universe might exist where the model that best matches past observations and best predicts future ones is one not based on binary logic?' And my answer, as I stated, is that I don't see why not.

Course, I don't know how likely or possible it would be for such a universe to evolve intelligent life (non-determinism at a macro level in particular, if that's what this model results in, does not seem at all conducive to that), so such observation and analysis might have to take place from outside that universe.


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