Exploring Chaos: Finding Logic in Illogic

In summary, the conversation discusses the concept of logic and its role in understanding the universe. The original poster suggests that it may be beneficial to consider the possibility that the universe does not behave logically, as there is no definitive evidence to support the idea that logic is essential. Some participants argue that the universe does behave logically and cite historical examples to support this belief. Others question the validity of using logic to understand the universe and suggest that human error may play a role in logical reasoning. Ultimately, the conversation highlights the limitations of relying solely on logic to understand the universe.
  • #1
Mentat
3,960
3
I'm sure most of us would claim to be open-minded. In fact, most people I've spoken to would consider it an insult to be called "closed-minded". Well, I'm going to put everyone's open-mindedness to the test, with this thread.

(BTW, I would like to give credit for this thread to Manuel_Silvio. I've opened my mind greatly, after having debated with him for many posts).

Philosophy, Science, and Mathematics all hinge on one thing: Logic. One must believe that there is some logic to the Universe's behavior, in order to be in any of those fields. However, have you ever considered the possibility - left open by logic itself - that the Universe does not behave logically?

I'm not saying that I believe that the Universe is illogical, I just think it's a good idea to open our minds to the possibility. Why? Because there is nothing logically conclusive to cause one to tend toward logic.

For example, Inductive reasoning is to try an approach as many times as possible, and then make a conclusion, based on empirical patterns observed (correct me if I'm wrong about that, btw). However, common sense will tell one that Inductive logic cannot be trusted; as one can never try something an infinite amount of times. This means that everything that we have observed to be an empirical pattern could just as easily have been a coincidence, every time.

I welcome any argument/correction/comment/etc, that anyone would care to provide.

I also wish to remind you all that this post is not intended to invalidate logic (as one could not "logically" do so :wink:). No, it is intended to open one's mind to the fact - that, through ignorance, we "knew", when we were young children - that logic is not essential, provable, even demonstrable (if one's mind is open enough).
 
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  • #2
I think the very question is "illogical" :wink: because logic is not an attribute of the universe, but instead is our means of understanding the universe, while the universe itself has nothing to do with logic. For expample, imagine a person who for the first time in his life is exposed to Heisenberg's uncertainty principle. To that person, until he comes to accept QM, the universe would seem illogical. Notice the word seem, as logic only exists in human perception and is not a universal fact.
 
  • #3
this is an excellent thread and really makes one think but in my opinion: the universe does behave logically. i justify this by reminding my self of the times in history when we have made logical reasoning and, upon later observation, found it to be true. one could make the agrument that the universe behaves logically only in certain places or that the only way we understand it is by logical translation, but to me to it seem that to say that the universe is illogical is contradictive to science as a whole and would go against everything we've done. in other word: we must believe it is logical because if we don't we are no better off on our understanding of it.
 
  • #4
Originally posted by C0mmie
I think the very question is "illogical" :wink: because logic is not an attribute of the universe, but instead is our means of understanding the universe, while the universe itself has nothing to do with logic. For expample, imagine a person who for the first time in his life is exposed to Heisenberg's uncertainty principle. To that person, until he comes to accept QM, the universe would seem illogical. Notice the word seem, as logic only exists in human perception and is not a universal fact.

This is an interesting perspective (though I should warn you of Alexander's belief, which he will, no doubt, bring up soon ).

Also, remember what I said in my first post: The observation of empirical patterns is what has lead to - at least some forms of - Logic (if it's a human invention, that is). These empirical patterns could just as easily have just been coincidence, every time.
 
  • #5
Originally posted by maximus
this is an excellent thread and really makes one think but in my opinion: the universe does behave logically. i justify this by reminding my self of the times in history when we have made logical reasoning and, upon later observation, found it to be true. one could make the agrument that the universe behaves logically only in certain places or that the only way we understand it is by logical translation, but to me to it seem that to say that the universe is illogical is contradictive to science as a whole and would go against everything we've done. in other word: we must believe it is logical because if we don't we are no better off on our understanding of it.

Yes, this last sentence sums up the typical human inability to see beyond logic. But I must ask you (in Manuel_Silvio-ish style :smile:) why would you attempt to understand it?
 
  • #6
Originally posted by Mentat
Philosophy, Science, and Mathematics all hinge on one thing: Logic. One must believe that there is some logic to the Universe's behavior, in order to be in any of those fields. However, have you ever considered the possibility - left open by logic itself - that the Universe does not behave logically?
That would be totally illogical! ... Or would it?

Meaning, how can you answer this very question without the "means" of logic?
 
  • #7
Originally posted by Mentat
Yes, this last sentence sums up the typical human inability to see beyond logic. But I must ask you (in Manuel_Silvio-ish style :smile:) why would you attempt to understand it?


that's why we're all here, isn't it?
 
  • #8
i justify this by reminding my self of the times in history when we have made logical reasoning and, upon later observation, found it to be true.

What about all of the times in history where logical reasoning lead to poor, and even patently absurd conclusions?
 
  • #9
human error, usually. cold hard logic rarly fails. (and when it does is usually means we don't have all the facts) Mentat should know what I'm talking about. in DUNE weren't the Mentats only able to funtion with all the possible facts, and even then weren't perfect?
 
  • #10
Originally posted by Mentat
However, have you ever considered the possibility - left open by logic itself - that the Universe does not behave logically?

I'm not saying that I believe that the Universe is illogical, I just think it's a good idea to open our minds to the possibility. Why? Because there is nothing logically conclusive to cause one to tend toward logic.
everything that we have observed to be an empirical pattern could just as easily have been a coincidence, every time.
One might try to define all that logic is, and then imagine all that would not be it. Then extend that to extremes and try to sustain that in your mind to no limits, trying to insist that all of universe is Like That. Dangerous attempt, for to truly succeed, one must past beyond 'point of no return', ie. go nuts (nihilism). The only way left is to touch the subject gently, 'from a distance'.

Note that, "coincidence, every time" = logic. Not necessarily aristoteles logic we are used to, but still logic. Fundamental property of logic is its consistency, all else is its 'form'. We may argue that universe does not behave according to logic we are used to, but to ask if it behaves logically is infact asking if universe is consistent.

Empirical pattern of coincidence, every time, is consistency, infinite faultless demonstration of logic. Which our known universe precisely is.

Yet, if you go further, and try to consider universe that is infinitely inconsistent, being infinite faultless demonstration of ill-logic, you face a dilemma: infinite inconsistency and faultless demonstration of that are not compatible. This means, that to be truly inconsistent 'every time', this must apply to 'inconsistency' Itself aswell, or, it can't be 'faultless' in demonstration 'every time'. It must be inconsistent in demonstration of inconsistency aswell.

You start thinking about what is 'right' proportions of inconsistency and faultless demo of it so that it makes least sense. And you find that 'best' case you get is when its ideally undetermined, ie when probability of either is exactly 50%. Thats about max inconsistency you could possibly get, imho. And that applies to about anything, even existence itself. If outcome of same interaction is never the same, its consistency. Thus to be least consistent, probability of same outcome to any interaction must be 50%. And even that is consistent. You enter endless tailchase and find that its nearly impossible to sustain complete inconsistency, however hard you try, some kind of pattern emerges nevertheless.

One might even imagine that our known universe is based on those 'snapshots' of existence when probability of consistent events turned out to be the case, and that 'inbetween' other universes have their chance. In overall, it may be inconsistent, we just can't observe that, its too far off our reach. We might exist above parts of its patterns of inconsistency, in patterns of coincidence that we consider perfectly logical. One might even attribute that to cause of Planck time, we just happen to coincidently exist 'at the same time'

Though, even here we have this 'duality', any fundamental claim has no more than 50% probability of being 'the truth'.
 
  • #11
Originally posted by Mentat
I'm sure most of us would claim to be open-minded. In fact, most people I've spoken to would consider it an insult to be called "closed-minded". Well, I'm going to put everyone's open-mindedness to the test, with this thread.

(BTW, I would like to give credit for this thread to Manuel_Silvio. I've opened my mind greatly, after having debated with him for many posts).

Philosophy, Science, and Mathematics all hinge on one thing: Logic. One must believe that there is some logic to the Universe's behavior, in order to be in any of those fields. However, have you ever considered the possibility - left open by logic itself - that the Universe does not behave logically?

I'm not saying that I believe that the Universe is illogical, I just think it's a good idea to open our minds to the possibility. Why? Because there is nothing logically conclusive to cause one to tend toward logic.

For example, Inductive reasoning is to try an approach as many times as possible, and then make a conclusion, based on empirical patterns observed (correct me if I'm wrong about that, btw). However, common sense will tell one that Inductive logic cannot be trusted; as one can never try something an infinite amount of times. This means that everything that we have observed to be an empirical pattern could just as easily have been a coincidence, every time.

I welcome any argument/correction/comment/etc, that anyone would care to provide.

I also wish to remind you all that this post is not intended to invalidate logic (as one could not "logically" do so :wink:). No, it is intended to open one's mind to the fact - that, through ignorance, we "knew", when we were young children - that logic is not essential, provable, even demonstrable (if one's mind is open enough).

Logic is a tool of the mind, and the way we (in a structural way) reason about the world, the universe.

But there is nothing mandatory to the universe, the material world itself to behave this or that way. Logic has no meaning to the material world.

Let me give some examples, that maybe can lead to the conclusion that the universe itself knows nothing about logic.

For example, let us try the most basic law of logic, and see how that fits on the world. The most basic las of logic is the law of identity (A = A). At first instance, we would claim that the universe is behaving according to this law. An electron is for sure an electron, isn't it?
If we take a macroscopic object, for instance a pound of sugar, then let us think of what to make of this law. Is a pound of sugar equal to a pound of sugar?
At first instance we would say yes. Both pounds of sugar have the same taste, same weight, are made of the same stuff, etc.
Yet, when we have a closer inspection, we might notice differences. All sugar crystals have their own specific shapes, and not one is exactly like any other. So a pound of sugar is not exactly equal to a pound of sugar. Never.

But let us go on, and try for more basic things. Like a proton. A proton would seem to us equal to any other proton.
Yet we know of protons mostly as the nucleons inside atoms. Protons and neutron are holding there the nucleus, and interchange force particles (carriers of the strong nuclear force). This interchanging of force particles, caauses a proton to change into a neutron and then back into a proton. So, a proton then is not equal to a proton, cause a proton changes everytime. But perhaps a proton without change, that is a proton outside of time, is equal to a proton?

Well then perhaps the idea of a proton is equal to the idea of a proton, but the proton outside of time, that is a proton that does not change/interact, is not existing.

Conclusion: the law of identity is not applicable to the real world.
 
  • #12
Examine the statement "Logic does not govern that." You are making a statement that requires logic. A statement assumes the truth of itself (a logical property) and makes a true/false distinction (logic) about something. This is statement is applying logic to "that". But if "that" is not affected by logic, then this statement cannot be applied to "that".
 
  • #13


Originally posted by Iacchus32
That would be totally illogical! ... Or would it?

Meaning, how can you answer this very question without the "means" of logic?

Yes, it would be completely illogical.

Also, it really isn't possible to leave the framework of logic, for a logical reason. That would be paradoxical. So, what I am proposing is not that one entirely leave the framework of logic, but that one see the possibility of the Universe without Logic.
 
  • #14
Originally posted by maximus
that's why we're all here, isn't it?

Is that a logical conclusion? Think about it, logic itself tells one that logical conclusions are unusable in an illogical Universe. Thus, if you say that the reason we are here is to progress in our knowledge/understanding, then you are bound to logic.
 
  • #15
Originally posted by maximus
human error, usually. cold hard logic rarly fails. (and when it does is usually means we don't have all the facts) Mentat should know what I'm talking about. in DUNE weren't the Mentats only able to funtion with all the possible facts, and even then weren't perfect?

Yes, but you are contradicting yourself by mentioning the margin of error in any Mentat's conclusion. Do you see why?
 
  • #16
i quote Ludwig Wittgenstein on this one:

"What is the use of philosophy, if all it does is enable you to talk...about some abtruse questions of logic, ect., and it does not improve your thinking about the important questions of everyday life?"
 
  • #17


Originally posted by heusdens
Logic is a tool of the mind, and the way we (in a structural way) reason about the world, the universe.

But there is nothing mandatory to the universe, the material world itself to behave this or that way. Logic has no meaning to the material world.

I agree. However, my point is that humans look for logic in the behavior of the Universe (and invent such things as Causality), when there may be none there at all.

Let me give some examples, that maybe can lead to the conclusion that the universe itself knows nothing about logic.

For example, let us try the most basic law of logic, and see how that fits on the world. The most basic las of logic is the law of identity (A = A). At first instance, we would claim that the universe is behaving according to this law. An electron is for sure an electron, isn't it?
If we take a macroscopic object, for instance a pound of sugar, then let us think of what to make of this law. Is a pound of sugar equal to a pound of sugar?
At first instance we would say yes. Both pounds of sugar have the same taste, same weight, are made of the same stuff, etc.
Yet, when we have a closer inspection, we might notice differences. All sugar crystals have their own specific shapes, and not one is exactly like any other. So a pound of sugar is not exactly equal to a pound of sugar. Never.

I could find fault with this illustration (by, perhaps, pointing out that a pound of sugar is a weight of the whole - not a property of all of the constituents) but I understand what you are trying to say.

But let us go on, and try for more basic things. Like a proton. A proton would seem to us equal to any other proton.
Yet we know of protons mostly as the nucleons inside atoms. Protons and neutron are holding there the nucleus, and interchange force particles (carriers of the strong nuclear force). This interchanging of force particles, caauses a proton to change into a neutron and then back into a proton. So, a proton then is not equal to a proton, cause a proton changes everytime. But perhaps a proton without change, that is a proton outside of time, is equal to a proton?

Actually, one could easily assume that a proton is only a proton if it is constantly indeterminable. However, I still think I see what you are trying to say, and so I needn't present any argument against which particular analogy you use. The point is that the law of identity is not perfect (and, according to the truly open mind, needn't exist at all), and I definitely agree.

P.S. Forgive my having argued with the analogies, inspite of having shown why it was unnecesarry. Bad personality trait, I guess.
 
  • #18
Originally posted by Dissident Dan
Examine the statement "Logic does not govern that." You are making a statement that requires logic. A statement assumes the truth of itself (a logical property) and makes a true/false distinction (logic) about something. This is statement is applying logic to "that". But if "that" is not affected by logic, then this statement cannot be applied to "that".

And yet you have also just applied logic to the attempt at invalidating logic. Why should I believe that "making a statement requires logic". That is a logical conclusion, and is thus outside the realm of the illogical Universe. Of course, what I am saying here is also a series of logical statements...

I guess it all goes back to the fact that one cannot logically look outside of logic, but one can, nonetheless, do so. We just don't know how, I guess.
 
  • #19
Originally posted by maximus
i quote Ludwig Wittgenstein on this one:

"What is the use of philosophy, if all it does is enable you to talk...about some abtruse questions of logic, ect., and it does not improve your thinking about the important questions of everyday life?"

He's just making my point: Philosophy is of no use, if it doesn't enable you to improve your thinking; and you still haven't explained why you are intent on improving your thinking.
 
  • #20
Is no one going to address my post?
 
  • #21
i got your back dan

Originally posted by Dissident Dan
Examine the statement "Logic does not govern that." You are making a statement that requires logic. A statement assumes the truth of itself (a logical property) and makes a true/false distinction (logic) about something. This is statement is applying logic to "that". But if "that" is not affected by logic, then this statement cannot be applied to "that".


it is a good point dan. (hope you don't mind me calling you dan). we are using logical processes such as inductive and deductive reasoning to convey these points about an illogical subject. one would imagine it could taint our point, but we have very few words to describe something completely illogical that aren't themselfs logical or at least a comparison to logic.
that doesn't make that much sense, does it?
 
  • #22
Call me whatever you want, as long as it's not derogatory.

Not only is it that our language is a logical system, but that ascribing or having a value of true or false and any kind of statement-like idea involves logic, regardless of a human being expressing it as language.
 
  • #23
Originally posted by Dissident Dan
Call me whatever you want, as long as it's not derogatory.

Not only is it that our language is a logical system, but that ascribing or having a value of true or false and any kind of statement-like idea involves logic, regardless of a human being expressing it as language.


that it does. but this is the way the human mind works. in truth i don't think we can understand what illogic is. the very distinction between the two is a logical deduction.
EXAMPLE= if the universe is not one it (therefore) must be the other.

in a true illogical universe this logical statement would break down to maybe- the universe is both. that's certainly illogical. but by this statement there must be logic whcih is imposible if there is no logic. and wait! i just used a logical deduction! you see- we are unable to understand illogic without using some medium of logic and without running into a paradox.
 
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  • #24
Paradox is manifestation of illogic. We stop right there.
 
  • #25
Originally posted by Dissident Dan
Is no one going to address my post?

Sincerest apologies, I guess I missed it, past all the other posts.

You said:
Examine the statement "Logic does not govern that." You are making a statement that requires logic. A statement assumes the truth of itself (a logical property) and makes a true/false distinction (logic) about something. This is statement is applying logic to "that". But if "that" is not affected by logic, then this statement cannot be applied to "that".

My response is:
Do you see the paradox in what you've said here? (Just checking, as some of the members post paradoxical statements on purpose.)

You are attempting to explain why the fact that something is no affected by logic, doesn't allow one to say that something is not affected by logic. Yet, in order to explain this, you have first assumed that which you were saying was impossible. Does that make sense (I can re-word it, if you'd like)?
 
  • #26
Greetings Mentat !
Originally posted by Mentat
I'm sure most of us would claim to be open-minded. In fact, most people I've spoken to would consider it an insult to be called "closed-minded". Well, I'm going to put everyone's open-mindedness to the test, with this thread.

(BTW, I would like to give credit for this thread to Manuel_Silvio. I've opened my mind greatly, after having debated with him for many posts).

Philosophy, Science, and Mathematics all hinge on one thing: Logic. One must believe that there is some logic to the Universe's behavior, in order to be in any of those fields. However, have you ever considered the possibility - left open by logic itself - that the Universe does not behave logically?

I'm not saying that I believe that the Universe is illogical, I just think it's a good idea to open our minds to the possibility. Why? Because there is nothing logically conclusive to cause one to tend toward logic.
Congratulations Mentat ! :smile:
(It only took several hundred philosophy posts...:wink: )

I'd also like to mention what others here mentioned too
in general ways, the word logic that we use is intended
to identify the most successful reasoning system we have
at the time the word's being used. The actual precise
meaning of Logic has changed many times throughout
the history of science and before it was officialy born.

Peace and long life.
 
  • #27
I'm surprised nobody has brought up intuition.
 
  • #28
Originally posted by Hurkyl
I'm surprised nobody has brought up intuition.

You know, it's impossible to say that, without creating a paradox.

Anyway, it falls on he who has mentioned it, to expound on it.
 
  • #29
I should refrain from comment, but I can't help it. Human Nature, you know.

It seems to me we are 'hobbled', if you will, by Logic itself:
Both Aristotelian and Platonic Logic are flawed. One makes a priori assumptions, which may not be "true." The other makes an observation, and then looks for reasons to prove or disprove the observative conclusion.

There may be philosophical theories, but there is no philosophical Law.

Then there is Mathematics: An arbitrary, iterative system for measuring things.

I may be wrong, but I believe the attempt to fuse Mathematics with Philosophy have so far failed.

So what do we do? We do the best we can.
 
  • #30
I'm not sure why intuition is a paradox. It's pretty clear that the thought processes of mankind are driven primarily by intuition... even in the sciences. "Rigor" is simply a measure of how little a proof depends on intuition.

Even in formal logic, intuition plays a part. For obvious reasons one cannot be 100% sure that any proof is correct; one must rely on their intuition to some extent when accepting a proof, no matter how detailed and careful the proof is. And, of course, any logical theory must start with some axioms that are simply accepted true without proof; a.k.a. things which our intuition leads us to accept as true. And we must even intuit which formal logic to accept; for example, should we accept the usual logic, or should we reject the law of the excluded middle?

And it's fairly clear that formal logic is heavily based on the intuitive language structures that mankind has developed; it's meant to model intuitive things like "and", "or", "if", "true", and "false".

The problem with intuition is that my intuition may conflict with your intuition. That's why we have logic; if we can agree on a set of rules from which we can prove things, it reduces the likelihood of a conflict.
 
  • #31
Mentat we seem to cross paths again. You are a good thinker.

I have actually given my response to a question of this nature in another post. Here is my answer.

__________

(logic, wrong or right, because to think IS to use logic. To think does not imply that YOU thought about it.) logic is not a THING,...logic is an inherant property of the universe which is taken advantage of by nature ( in humans in particular) to futher biological surviaval (but it is not the only property and so can't be used to handle ALL situations. --therefore the universe in some case is irrational, and uncertatain. As for humans there is no such thing as rational human thought without the use of logic!)

__________

Logic is an imprtant ( for us ) proprety of the universe, but we can hardly expect that ALL of reality will fall under its rein. I am am sure that there are many instance where the universe resolves itself into an irrational mess. Logic is yes an imprtant tool, but it by no means is the only tool. And for those who know Quantum Mechanics will agree that what is logical is not nessacrrily what is right.
 
  • #32
Originally posted by Hurkyl
I'm not sure why intuition is a paradox. It's pretty clear that the thought processes of mankind are driven primarily by intuition... even in the sciences. "Rigor" is simply a measure of how little a proof depends on intuition.

Even in formal logic, intuition plays a part. For obvious reasons one cannot be 100% sure that any proof is correct; one must rely on their intuition to some extent when accepting a proof, no matter how detailed and careful the proof is. And, of course, any logical theory must start with some axioms that are simply accepted true without proof; a.k.a. things which our intuition leads us to accept as true. And we must even intuit which formal logic to accept; for example, should we accept the usual logic, or should we reject the law of the excluded middle?

And it's fairly clear that formal logic is heavily based on the intuitive language structures that mankind has developed; it's meant to model intuitive things like "and", "or", "if", "true", and "false".

The problem with intuition is that my intuition may conflict with your intuition. That's why we have logic; if we can agree on a set of rules from which we can prove things, it reduces the likelihood of a conflict.

But is not this last observation an intuitive one?
 
  • #33
Originally posted by Preator Fenix
Mentat we seem to cross paths again. You are a good thinker.

Thanks.

(logic, wrong or right, because to think IS to use logic. To think does not imply that YOU thought about it.) logic is not a THING,...logic is an inherant property of the universe which is taken advantage of by nature ( in humans in particular) to futher biological surviaval (but it is not the only property and so can't be used to handle ALL situations. --therefore the universe in some case is irrational, and uncertatain. As for humans there is no such thing as rational human thought without the use of logic!)

Well, I'm not sure about that last point (though I agree with most of the rest of it). You see, if I say "purple cows are plotting against me", there is no logic to my statement - since logic is the use of reasoning systems, and I haven't reasoned here, at all.
 
  • #34
Logic by its very nature is nothing more than what is possible. Because we know or assume this universe to be possible, as we all exist in it and experience the very possibilities, which do happen, we must know that the universe is inherently logical. No part of the universe is illogical, NOT because it all must make sense, but because it all is possible, as it happens. It’s own existence defines its possibility and thus makes it logical. There may be a great deal of the universe that seems quite illogical, but this is merely either our inability to process such complex logical thought, or our lack of sufficient data to formulate an accurate view. When things happen that don’t seem right or make no sense, it hardly means that they are illogicall, it merely means that we do not understand them. I believe the word “logic” is too often used synonymously with “makes sense.” You see, when I say: “All cows are red” and then I say: “I have a cow” I know by logic, that my cow is red. To say that all cows are red and then say I have a cow that is not red is impossible. That is what logic is.

Now! I believe the initiator of this thread made an interesting suggestion that a universe may not run logically. My response to such an idea is that it could indeed be so. But! We know that THIS universe (as it is possible) is entirely logical. There may however be an infinite number of other universes, which run illogically, but are therefore impossible. Where are they? They are impossible.

I think the question posed from this information is how and if we know what is possible. Of course that is another conversation entirely.
 
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  • #35
Welcome to the PFs, Maverick! :smile:

Originally posted by Maverick
Logic by its very nature is nothing more than what is possible.

Actually, logic can be used to make the distinction between the possible and the impossible (much like you did in the statement (quoted)). Thus it doesn't just deal with things that are possible.

Because we know or assume this universe to be possible, as we all exist in it and experience the very possibilities, which do happen, we must know that the universe is inherently logical. No part of the universe is illogical, NOT because it all must make sense, but because it all is possible, as it happens.

So, because something is possible, it's logical? Then how would one make the distinction between things that are possible and impossible (if not through the use of logic (which only deals with possible things - according to you))?

Now! I believe the initiator of this thread made an interesting suggestion that a universe may not run logically. My response to such an idea is that it could indeed be so. But! We know that THIS universe (as it is possible) is entirely logical. There may however be an infinite number of other universes, which run illogically, but are therefore impossible. Where are they? They are impossible.

Well, actually, they either exist or they don't - and if they are impossible, then they can't exist (thus there is no "they" to speak of).
 
<h2>1. What is chaos theory and how does it relate to exploring chaos?</h2><p>Chaos theory is a branch of mathematics and science that studies complex systems and their behavior. It explores how seemingly random and unpredictable patterns can emerge from simple and deterministic systems. Exploring chaos involves analyzing and understanding these patterns in order to find underlying logic and order.</p><h2>2. What are some real-world applications of exploring chaos?</h2><p>Exploring chaos has many practical applications in fields such as meteorology, economics, and biology. It can help predict and understand weather patterns, stock market fluctuations, and biological systems such as the human brain.</p><h2>3. How is exploring chaos different from traditional scientific methods?</h2><p>Exploring chaos often involves non-linear thinking and the use of computer simulations and visualizations to understand complex systems. It also relies on the idea that small changes in initial conditions can lead to vastly different outcomes, rather than a linear cause-and-effect relationship.</p><h2>4. Can chaos theory help us make predictions about the future?</h2><p>While chaos theory can provide insights into the behavior of complex systems, it is not a predictive tool. The inherent unpredictability of chaotic systems makes it difficult to make accurate predictions about the future.</p><h2>5. How can exploring chaos help us better understand the world around us?</h2><p>By studying and analyzing chaotic systems, we can gain a deeper understanding of the underlying patterns and order in seemingly random phenomena. This can lead to new insights and discoveries in various fields, and ultimately help us better understand the world we live in.</p>

1. What is chaos theory and how does it relate to exploring chaos?

Chaos theory is a branch of mathematics and science that studies complex systems and their behavior. It explores how seemingly random and unpredictable patterns can emerge from simple and deterministic systems. Exploring chaos involves analyzing and understanding these patterns in order to find underlying logic and order.

2. What are some real-world applications of exploring chaos?

Exploring chaos has many practical applications in fields such as meteorology, economics, and biology. It can help predict and understand weather patterns, stock market fluctuations, and biological systems such as the human brain.

3. How is exploring chaos different from traditional scientific methods?

Exploring chaos often involves non-linear thinking and the use of computer simulations and visualizations to understand complex systems. It also relies on the idea that small changes in initial conditions can lead to vastly different outcomes, rather than a linear cause-and-effect relationship.

4. Can chaos theory help us make predictions about the future?

While chaos theory can provide insights into the behavior of complex systems, it is not a predictive tool. The inherent unpredictability of chaotic systems makes it difficult to make accurate predictions about the future.

5. How can exploring chaos help us better understand the world around us?

By studying and analyzing chaotic systems, we can gain a deeper understanding of the underlying patterns and order in seemingly random phenomena. This can lead to new insights and discoveries in various fields, and ultimately help us better understand the world we live in.

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