Is Logic Flawed by Paradoxes and Variables?

[Sikz]

Paradoxes exist in our logic. They do not exist in the real world (to our knowledge at least; no one has ever encountered proof of a pardox existing). Logic is sopposed to describe the real world. Could there be some sort of flaw in our logic then :S?

 

[Njorl]

There are physical analogs of paradoxes in the physical world. Bistable states in logic devices for instance.

There is more to what you say though. I think the simple, everyday logic we learn is not adequate for all occasions. This is not suprising. By analogy, arithmatic and algebra will let you do your household budget, but they won't put a man on the moon. The simple logic of true/false and epistemology work for most requirements, but modern mathematical logic has other states. I'm no expert, but I believe there are states like unknowable, indeterminate, and immaterial in addition to true and false.

Njorl

 

[Mentat]

Sikz,
One must remember that, as Tom has stressed before, Logic is a prescription for the Universe, not a description of it. One can deduce, from Logic, what the Universe should be like if such-and-such were true...however, the Universe is not always as one deduction says it "should be". Also, if a deduction leads to a paradox, it is pretty well impossible (just my opinion) for it to be expressed in reality...

Of course, there are those who say that QM requires paradoxes of a sort, but I think QM doesn't so much counter Logic, as it does Common Sense...as such, I think that one must use a slightly refined reasoning method, but it remains in the realm of "logic", and doesn't produce paradoxes.

 

[Yahweh]

Originally posted by Sikz
Paradoxes exist in our logic. They do not exist in the real world (to our knowledge at least; no one has ever encountered proof of a pardox existing). Logic is sopposed to describe the real world. Could there be some sort of flaw in our logic then :S?

Short answer: Logic is not a set of laws which govern the universe.

 

[Mentat]

Originally posted by Yahweh
Short answer: Logic is not a set of laws which govern the universe.

Well, you're right, of course, but what of the fact that logic is supposed to be a prescription for the Universe (anyone who can catch the intended joke here has my admiration)? If Logic shows what the Universe "should be" like, and yet it (the Universe) has no paradoxes, then Logic is doing a poor job of prescribing, isn't it?

 

[Bob3141592]

Originally posted by Sikz
Paradoxes exist in our logic. They do not exist in the real world (to our knowledge at least; no one has ever encountered proof of a pardox existing).

What? Have you never met a teenage girl?

 

[quartodeciman]

Paradox means two different things.

1. Paradox means defiance of accepted thought. The antonym of this kind of paradox is "orthodox". For example: it was long considered axiomatic that a whole entity must be greater in every way than any proper part of the entity. But the theory of transfinite sets produced a paradox that shows that the even part of the whole numbers can be mapped into an exact one-to-one correspondence with the whole set of odd and even numbers. Of course, as sets, the subset of even numbers is still properly smaller than the set of all numbers. But in at least one respect, one-to-one association, the two are equivalent. Since the acceptance of this paradox, it has been understood that this is a defining character of the transfinite.

2. Paradox means logical self-defeat. This is probably what you have in mind using the word 'paradox". A synonym that specializes this meaning is "antinomy", an outlaw conceptual entity. A famous example in the theory of transfinite sets in the set of all sets. logicians and mathematicians have learned strategies for dealing with these outlaws when they arise and avoiding their antinomous behavior. The set of all sets is a kind of class, but it is not allowed to be a member of another class.

Not all antinomous paradoxes are from set theory. Many come from troubles in semantics. Here is an ancient example:

A: Mr. X is bald. This statement should be clearly true or false.
B: Agreed.
A: First I present Mr. X with a full, lush head of hair growing out of his scalp. Is he bald?
B: No.
A: Now I cut one hair follicle off Mr. X's head. Is he now bald?
B: No.
A: Now I cut another hair off Mr. X's head. Is he now bald?
B: No.
...
A: Each time I cut one hair off Mr. X's head, it does not change the status of his baldness.
B: Correct.
A: Therefore, if I continue cutting his hair this way, he will never become bald.

This is an example of vagueness at work.

 

[master_coda]

Originally posted by Mentat
Well, you're right, of course, but what of the fact that logic is supposed to be a prescription for the Universe (anyone who can catch the intended joke here has my admiration)? If Logic shows what the Universe "should be" like, and yet it (the Universe) has no paradoxes, then Logic is doing a poor job of prescribing, isn't it?

But that's like saying that since language is supposed to describe the universe, anything that you can state using language must therefore exist within the universe.

Logic is a set of rules that tell us how reason is supposed to work in the universe. That doesn't mean that just because we can describe something with logic that the "something" must manifest itself within the universe.


Also, I don't know of any paradoxes of logic itself. The only paradoxes that I know of are ones where you assert something is true and then use logic and the assertion to derive a contradiction (a paradox). So the paradox occurs because of the assertion, rather than just logic itself.

 

[Yahweh]

Originally posted by Mentat
Well, you're right, of course, but what of the fact that logic is supposed to be a prescription for the Universe (anyone who can catch the intended joke here has my admiration)? If Logic shows what the Universe "should be" like, and yet it (the Universe) has no paradoxes, then Logic is doing a poor job of prescribing, isn't it?

Paradoxes certainly exist in the universe. It takes a bit of preperation, but any engineer or statistician is familiar with Simpson's Paradox (that link describes how a datatable can be created from legitimate study to demonstrate how those with no education in Physics perform better on Physics tests... the paradox is obvious, though the conditions which create the paradox tend to fool most people).

Other paradoxes include the familiar Liar's Paradox: This sentence is false.[/color]

Another paradox is the Birthday Paradox: If there are 23 people in the room, there is a 50/50 chance that two of them have the same birthday.

Theirs no problem in the logic. Its important to keep in mind the definition of a paradox: A paradox is an apparently true statement that seems to lead to a logical self-contradiction, or to a situation that contradicts common intuition. Not all paradoxes imply a logical contradiction.

On a note of logical contradiction and paradoxes, here is one paradox which does creates an apparent logical contradiction: Considering the concept of omniscience, you might ask "if something knows all there is to know, then that something must know something which it doesn't know". That statement creates a paradox. In the case of omniscience, the particular "know what you do not know" demonstrates the incoherency of omniscience. (Most other prefixes that start with the word "omni" to describe things - especially deities - create similar contradictions.)

(Here is a whole list of popular paradoxes: Wikipedia - Paradox)

 

[vacuum]

Originally posted by Yahweh

Theirs no problem in the logic. Its important to keep in mind the definition of a paradox: A paradox is an apparently true statement that seems to lead to a logical self-contradiction, or to a situation that contradicts common intuition. Not all paradoxes imply a logical contradiction.

So, simply put, that's a statement for which you can not determine whether its true or false?

 

[wuliheron]

Words only have demonstrable meaning according to their function in a given context. To the layperson, paradox can mean anything from a simple contradiction to an apparently insoluable puzzle. To the mathematician and logician, the word has a much more specific meaning. Hence, your assertion that paradoxes do not exist in the real world is meaningless mumbo-jumbo without a clear definition of what you mean by paradox.

 

[quantumdude]

Paradoxes exist in our logic. They do not exist in the real world (to our knowledge at least; no one has ever encountered proof of a pardox existing). Logic is sopposed to describe the real world. Could there be some sort of flaw in our logic then :S?

There is no inconsistency in the statements, "paradoxes exist in logic", "logic describes the real world", and "paradoxes exist in the real world". That is because the paradoxes of logic only arise when statements are self-referential or vague, not when they describe the observable universe.

 

[quartodeciman]

"
This dog is mine.
This dog had puppies.
So, this dog is a mother.
This dog is mine and this dog is a mother.
Therefore, this dog is my mother.
"

 

[quantumdude]

"
This dog is mine.
This dog had puppies.
So, this dog is a mother.
This dog is mine and this dog is a mother.
Therefore, this dog is my mother.
"

Very funny, but that's a fallacy, not a paradox.

 

[jeffceth]

There is a possiblity that paradoxes could exist in our physical world. Many of these are predicted by physics theorems and models. For example, a branch of superstring theory suggests that if a spaceship were traveling at just the right velocity very close to a position where two superstrings(very dense 'strings' that cruise around the universe at high speeds) crossed each other, the intense gravity would pull the path of the spaceship into a tight enough loop that the acceleration would cause it to arrive before it left. Now here's the real question:

If the spaceship arrives before it leaves, does it hit itself?

If so, it would produce a physical paradox, as indeed many time-travel situations do. Scientists are divided on what such a paradox would 'do'. Some believe it would destroy the universe, but that's rather out of a melodramatic constitution than out of any real science in my opinion. A popular opinion which possibly finds its roots in sci-fi is that it would 'rip the fabric of time-space' but this positin is also scientifically unfounded. We simply don't know what would happen.

Hope that helps,
jeffceth

 

[quantumdude]

There is a possiblity that paradoxes could exist in our physical world. Many of these are predicted by physics theorems and models.

But models are only that: models. They have no efficacy in the real world. And if a theoretical physicist were to come up with something that predicted a paradoxical effect, then the theory would most likely be modified or rejected on that basis. For instance noninteger values of the quantum number l are rejected as they lead to two different wavefunctions corresponding to the same quantum state (which would be paradoxical). Similarly, periodic boundary conditions are imposed on angular wavefunctions specifically to avoid multiply-valued wavefunctions (which would also be paradoxical).

When we encounter a paradox in theoretical physics, I think it should be viewed as a giant neon sign that says, "You are making a mistake!"

 

[wuliheron]

When we encounter a paradox in theoretical physics, I think it should be viewed as a giant neon sign that says, "You are making a mistake!"

Or your context is too vague.

For example, I could assert that life, the universe, and everything is ultimately paradoxical. However, such is the realm of philosophy rather than physics. The context is simply too broad and vague to have any demonstrable meaning in the context of physics.

 

[Les Sleeth]

When we encounter a paradox in theoretical physics, I think it should be viewed as a giant neon sign that says, "You are making a mistake!"

Yes, and when we come up against a paradox through reasoning, the same neon sign should be flashing. Or if one is reasoning correctly maybe the sign could say something like, "You are reasoning without all the information you need to resolve what merely appears to be a paradox."

 

[loseyourname]

For example, I could assert that life, the universe, and everything is ultimately paradoxical. However, such is the realm of philosophy rather than physics. The context is simply too broad and vague to have any demonstrable meaning in the context of physics.

I don't see any way you could seriously assert that everything is paradoxical. I can name plenty of things that are not.

 

[wuliheron]

I don't see any way you could seriously assert that everything is paradoxical. I can name plenty of things that are not.

Exactly my point, you can name plenty of things that are apparently not paradoxical and I could name plenty that are. For all either of us can prove life, the universe, and everything is ultimately ineffable. Without providing a specific context there is no way to meaningfully discuss the issue. Merely asserting that plenty of things are or are not apparently paradoxical proves nothing about the big picture.

 

[quantumdude]

Without providing a specific context there is no way to meaningfully discuss the issue.

But the specific context was provided in the opening post. The comparison is being drawn between formal logic, which has inherent paradoxes, and the observable universe, in which the law of excluded middle seems to never be violated. The question is, given that, how can we say that logic corresponds in any way to the universe.

I don't see what your point is.

 

[quartodeciman]

There are (at least) two types of paradox:

1. consequences that seem to violate accepted presuppositions

2. consequences that are antinomous (direct contradictions)

.

The answer to the 1 type might be to change those presuppositions (e.g. nature of infinite sets);
the answer to the 2 type might be to acquire some kind of insurance (e.g. set of all sets);
.

(Logic, as a science, must watch its own back. Some limits and restrictions might be in order. Just exactly what needs to be done for safety may remain a longterm problem.)

 

[wuliheron]

But the specific context was provided in the opening post. The comparison is being drawn between formal logic, which has inherent paradoxes, and the observable universe, in which the law of excluded middle seems to never be violated. The question is, given that, how can we say that logic corresponds in any way to the universe.

I don't see what your point is.

Ahhh, I see what you mean. Here is the original post again.

Paradoxes exist in our logic. They do not exist in the real world (to our knowledge at least; no one has ever encountered proof of a pardox existing). Logic is sopposed to describe the real world. Could there be some sort of flaw in our logic then :S?

This is a nonsensical statement by all the standards of logic. Paradoxes have no truth value whatsoever according to traditional formal logic. However, some types of formal logics, especially extentions of fuzzy logic, give them a truth value of "indeterminate" (note: much like QM.)

In addition, you cannot prove or disprove a negative. You cannot prove paradoxes do not exist any more than you can prove angels do not dance on the heads of pins. Thus, by the standards of formal logic it is impossible to prove or disprove the existence of a paradox in the real world. All we can do is note what is apparently paradoxical, and look for resolutions.

This is similar to the EPR thought experiment. Einstein, Podolsky, and Rosen could not prove paradoxes were impossible, but they could point out that QM is apparently inherently paradoxical and just how ridiculous that sounded. Likewise, I would add, it is equally ridiculous (paradoxical?) to insist everything must have some sort of rational explanation.

For all these reasons, the statement has no meaningful context. Given a specific context, then something meaningful can be said on the subject.

 

[quantumdude]

This is a nonsensical statement by all the standards of logic.

It's not nonsensical at all. Sikz made an observation about a property of logic which is well understood, and then made another observation that that same property is not evinced by any observational data. The question is then, "Is logic appropriate for describing the universe?"

I think he's misunderstanding things, for the reason I stated, but the question is perfectly intelligible.

Paradoxes have no truth value whatsoever according to traditional formal logic. However, some types of formal logics, especially extentions of fuzzy logic, give them a truth value of "indeterminate" (note: much like QM.)

But those fuzzy logics only describe quantum mechanical systems inbetween measurements. Make a measurement, and QM predicts no violation of the law of excluded middle. You will find that electron at precisely one location, not two.

In addition, you cannot prove or disprove a negative. You cannot prove paradoxes do not exist any more than you can prove angels do not dance on the heads of pins. Thus, by the standards of formal logic it is impossible to prove or disprove the existence of a paradox in the real world. All we can do is note what is apparently paradoxical, and look for resolutions.

This was acknowledged in the first post.

This is similar to the EPR thought experiment. Einstein, Podolsky, and Rosen could not prove paradoxes were impossible, but they could point out that QM is apparently inherently paradoxical and just how ridiculous that sounded.

"Sounding ridiculous" is not the same as "being inherently paradoxical".

Likewise, I would add, it is equally ridiculous (paradoxical?) to insist everything must have some sort of rational explanation.

What's this got to do with the question that Sikz asked?

For all these reasons, the statement has no meaningful context. Given a specific context, then something meaningful can be said on the subject.

Well, the first post has a perfectly meaningful context, whether you recognize it or not. The idea that logical paradoxes exist, while physical paradoxes have not been observed, is well-defined enough for anyone to be able to understand it.

 

[wuliheron]

Well, the first post has a perfectly meaningful context, whether you recognize it or not. The idea that logical paradoxes exist, while physical paradoxes have not been observed, is well-defined enough for anyone to be able to understand it.

Sorry, but this boy can not understand the statement. I will try to make myself as clear as possible.

As far as I can tell, it is either too vague to be intelligable or downright paradoxical. Logic without paradox is like up without down, patently impossible. To then say that logic describes everything we observe, but we have never observed a paradox is a contradiction.

There are two rudamentary types of paradoxes, the Heap paradox and the Liars paradox. The liars paradox is more substantiated by the rules of logic, while the heap paradox is more applicable to linguistics and concerns the vagueness of statements. Because we are talking about the "real" world, it is the heap paradox with it's emphasis on vagueness and linguistics that takes precident.

Again, words only have demonstrable meaning according to their function in a given context. Natural language is repleat with vague terms while logistics are not. Mixing the two then requires a great deal of care in order to maintain coherency.

 

[quantumdude]

As far as I can tell, it is either too vague to be intelligable or downright paradoxical. Logic without paradox is like up without down, patently impossible. To then say that logic describes everything we observe, but we have never observed a paradox is a contradiction.

But he's not saying that logic describes everything we observe. He was asking if it is right to use logic to describe what we observe, given the presence of paradoxes in logic and the absence of paradoxes in observations.

There are two rudamentary types of paradoxes, the Heap paradox and the Liars paradox. The liars paradox is more substantiated by the rules of logic, while the heap paradox is more applicable to linguistics and concerns the vagueness of statements. Because we are talking about the "real" world, it is the heap paradox with it's emphasis on vagueness and linguistics that takes precident.

I agree. My answer to Sikz was that the formal type of paradox (the "liar" type) should not concern us, because it only arises when statements refer to themselves. But when we use logical reasoning to describe the world, there is no danger in running into that sort because the statements refer to physical objects and processes. So this reduces the problem of, "Is logic appropriate for describing a non-paradoxical world?" to the question of, "Can we formulate nonvague physical theories, thereby circumventing the second type of paradox?"

I hope you can see that your ability to articulate the problem means that it is decidedly not nonsensical. If it were unintelligble, you wouldn't be able to make heads or tails of it.

 

[wuliheron]

But he's not saying that logic describes everything we observe. He was asking if it is right to use logic to describe what we observe, given the presence of paradoxes in logic and the absence of paradoxes in observations.

I agree. My answer to Sikz was that the formal type of paradox (the "liar" type) should not concern us, because it only arises when statements refer to themselves. But when we use logical reasoning to describe the world, there is no danger in running into that sort because the statements refer to physical objects and processes. So this reduces the problem of, "Is logic appropriate for describing a non-paradoxical world?" to the question of, "Can we formulate nonvague physical theories, thereby circumventing the second type of paradox?"

I hope you can see that your ability to articulate the problem means that it is decidedly not nonsensical. If it were unintelligble, you wouldn't be able to make heads or tails of it.

I don't know if that is his question at all, again, because he has not provided a specific context. Here is his original question again:

Paradoxes exist in our logic. They do not exist in the real world (to our knowledge at least; no one has ever encountered proof of a pardox existing). Logic is sopposed to describe the real world. Could there be some sort of flaw in our logic then :S?

First off, paradoxes do exist in the real world as far as we know. As I have already pointed out, the EPR experiment is one of the more famous proofs that the most successful physical theory ever is apparently paradoxical. Secondly, as I already pointed out, it is impossible to prove a paradox exists! Paradoxes do not have truth values and the proof he is talking about is I assume a logical proof!

Thus, the only conclusion I can draw is that he is speaking from a logically biased position, or he is speaking in paradoxes. Which it is I have no real clue.

 

[Les Sleeth]

First off, paradoxes do exist in the real world as far as we know. As I have already pointed out, the EPR experiment is one of the more famous proofs that the most successful physical theory ever is apparently paradoxical. Secondly, as I already pointed out, it is impossible to prove a paradox exists! Paradoxes do not have truth values and the proof he is talking about is I assume a logical proof!

Thus, the only conclusion I can draw is that he is speaking from a logically biased position, or he is speaking in paradoxes. Which it is I have no real clue.

I believe what Sikz has pointed to borders on profound. I'll try to explain.

He has noticed there are no confirmed paradoxes in the real world;that is, we cannot observe them. Before the so-called "EPR paradox" were the position-momentum paradox, the wave-particle paradox, and then, as you've pointed out, the liar's and heap paradoxes, and so on. But what is creating the paradox? I say what happens every time, without exception, is that our logic is confounded by our experience. Because of that Sikz asks if there is a flaw in our logic. I don't think so at all, and because there isn't, the implications could be profound.

Logic is grounded in math, and math symbolically represents the order and structure of physical processes and objects. The logic of a situation is completely different than the experience of a situation, so it is very clear that experience is not logic. Logic is a process of our computing mind, experience is a subjective element of conscious existence, and therein lies the confusion. We can experience reality, but it is impossible to represent all of it with math/logic. There are aspects of reality which appear distinct from other aspects, and so lend themselves to logic. But there are also aspects which are holistic, continuous, homogeneous and seemingly impossible to pull out of the whole . . . If something cannot be segmented, logic alone is going to miss it.

Back to the question of profundity and paradox. The paradox proves that "mind" (mentality) does not expose the whole of reality to us, but merely a framework. The paradox often arises when homogeneity and "parts" are put at odds mentally. Because it can't be resolved mentally/logically, we call it a paradox until, that is, we find a way to experience a situation and realize the overall thing that's going on. When that happens, something that was impossible to accept logically, like wave-particle duality, suddenly is accepted when we understand that EM is both wave and particle (in that instance, wave is the homogeneous aspect and particle is the "part" aspect). So, there is no paradox in the real world, just as Sikz says, only mental confusion.

I like this problem because I believe it demonstrates how easily we geniuses can be "in our minds." That is, to get so caught up in trying to think our way to the truth that we forget to experientially participate in life the way we need to in order to truly know reality.

 

[quantumdude]

I don't know if that is his question at all, again, because he has not provided a specific context. Here is his original question again:

What exactly are you looking for here in the way of a "specific context"? He's talking about formal logic on the one hand, and observational evidence on the other. It doesn't get any more well-defined than that.

First off, paradoxes do exist in the real world as far as we know.

That doesn't matter. The question is as to whether or not logic is an appropriate tool for describing what we observe, if we don't observe paradoxes. They may exist, but they aren't observed. And as you note later, they can't be observed--and that only makes the question more relevant, because they are observed in logic.

As I have already pointed out, the EPR experiment is one of the more famous proofs that the most successful physical theory ever is apparently paradoxical.

This is not relevant. EPR is not a real experiment, but a thought experiment, which places it on the "logic" side of the "logic-reality" dichotomy.

Secondly, as I already pointed out, it is impossible to prove a paradox exists! Paradoxes do not have truth values and the proof he is talking about is I assume a logical proof!

No, he's not talking about a logical proof at all. As I have already said, he's asking if logic is an appropriate tool for describing the real world, when paradox is manifest in the former and not in the latter. The point you raise here (that paradoxes can't be observed even in principle) only makes that question more pertinent: How can a formal system that manifestly[/color] exhibits this feature called "paradox" be an apt tool for modeling a physical reality that cannot[/color] exhibit such a feature?

 

[wuliheron]

Once again with emphasis, neither logic nor observation can prove or disprove the existence of paradoxes! Paradoxes have no truth value in logic and unless you are talking about some kind of meaningful emotional experience as observational proof, there is no way to prove paradoxes exist in the world either.

What all of you are dancing around is what Wittgenstein described, and he is widely considered perhaps the most profound philosopher of the last century. He said there are facts and the mystical. Facts such as the world being round can be spoken of coherently, but there is nothing that can said about the mystical coherently. It does not matter whether or not the mystical actually exists, the point is simply that if it really is mystical nothing coherent can be said on the subject.

As a Taoist myself, the whole point is moot in much the same fashion as Wittgenstein proposed. What matters is being accepting, open minded, and flexible. Logic can either be a straight jacket or a wonderful tool. Don't confuse the tool with the reality, that is my advice.

Tools

Thirty spokes meet at a nave;
Because of the hole we may use the wheel.
Clay is moulded into a vessel;
Because of the hollow we may use the cup.
Walls are built around a hearth;
Because of the doors we may use the house.
Thus tools come from what exists,
But use from what does not.

 

[quantumdude]

Once again with emphasis, neither logic nor observation can prove or disprove the existence of paradoxes!

Once agan with emphasis, that is not the question at hand!

The question goes to the appropriateness of logic in describing the world. It's not about proving or disproving the existence of paradoxes in the world.

Paradoxes have no truth value in logic and unless you are talking about some kind of meaningful emotional experience as observational proof, there is no way to prove paradoxes exist in the world either.

You already covered that, and I pointed out that this point actually highlights[/color] the apparent incongruity between logic and the universe. Whether or not paradoxes exist in the real world, you can't observe one, even in principle. But you can demonstrate paradoxes with logic. Thus, there is some feature of formal logic that does not map onto observation, hence the question.

 

[wuliheron]

Once agan with emphasis, that is not the question at hand!

The question goes to the appropriateness of logic in describing the world. It's not about proving or disproving the existence of paradoxes in the world.

You already covered that, and I pointed out that this point actually highlights[/color] the apparent incongruity between logic and the universe. Whether or not paradoxes exist in the real world, you can't observe one, even in principle. But you can demonstrate paradoxes with logic. Thus, there is some feature of formal logic that does not map onto observation, hence the question.

The idea that you cannot observe a paradox, even in principle, is merely a biased idea, not necessarilly the reality we live with. Again, you cannot use logic to prove or disprove anything about the ultimate nature of reality. Logic is merely a tool used to help us describe reality, not to be confused with reality itself. I no more expect logic to describe everything than I expect music or numbers to describe everything. Each tool has specific applications for which they are extremely useful, but by definition they have their limits.

From my own point of view, existence itself is apparently a paradox we live with everyday. Why is there something rather than nothing? What is the cause of existence? Any answer you might propose involves a paradox. In fact, the vast majority of humanity believes in paradoxes, such as the belief in God(s) and Divinities.

I observe paradox not only in existence in the broader sense, but in my own emotional life as well. Because of my emotional life, I can apply meaning to things such as paradoxes, logic, and this discussion we are having. Although my desktop computer can execute perfectly logical operations, it cannot apply meaning to things and, at its best, acts like an idiot savant. Ironically, because I am irrational I can be more rational.

 

[quantumdude]

The idea that you cannot observe a paradox, even in principle, is merely a biased idea, not necessarilly the reality we live with.

OK, fine. It wasn't my idea anyway, it was yours. I was merely conceding the point because you are difficult enough!

 

[wuliheron]

My idea was that it is impossible to prove an observation of a paradox, not that it is impossible to observe a paradox.

I'm sorry if this discussion seems difficult to you, it is actually a conceptually simple subject. However, my approach does differ dramatically from traditional western approaches to the subject. Both asian philosophy and modern contextualism have proven more adept at dealing with such slippery concepts outside the boundaries of formal logic.

 

[Royce]

Years ago I lived in Riverside, California and on occasion worked in Los Angeles, about 50-60 miles. If I left for home immediately after getting off work at 5 I would not get home until around 8. If I waited until 6 before starting to drive home I got home around 7. I've often wondered where I would have passed myself and why if I could pass myself why was I driving so slow when I left at five and so fast when I left at 6 that I could pass myself. This is to me a paradox that existed in the real world and in my life.
It was not just a failure or limitation of our language or thought processes, logic, but a reality that repeated itself over and over without fail.

 

[Les Sleeth]

Years ago I lived in Riverside, California and on occasion worked in Los Angeles, about 50-60 miles. If I left for home immediately after getting off work at 5 I would not get home until around 8. If I waited until 6 before starting to drive home I got home around 7. I've often wondered where I would have passed myself and why if I could pass myself why was I driving so slow when I left at five and so fast when I left at 6 that I could pass myself. This is to me a paradox that existed in the real world and in my life.
It was not just a failure or limitation of our language or thought processes, logic, but a reality that repeated itself over and over without fail.

Hi Royce. I have trouble with your interpretation (and Wuli's) because it seems you say the paradox exists in objective reality rather than in the mind. If we were to take a robotic car, have it repeat your route at the two different times, and film both excursions from a helicoptor, do you really believe we wouldn't be able to observe actual, physical reasons for the apparent mystery?

So in the end, isn't "paradox" the confounding of our logic? Intra-logic paradoxes such as the so-called "liar's paradox" are easily resolved once we switch from thinking about it, to gathering evidence about the speaker's statement; that is, in reality there is no ambiguity when a man says he is lying because the answer is either he is lying or he isn't. We might be perplexed logically, but that has no bearing on the reality his statement denotes.

Paradoxes that seem to indicate a conflict in the nature of reality (e.g., the antinomy paradox) I believe are similar in that they are usually due to lacking all the information we need to settle a problem, as when we observe only one side of some two-sided relationship without realizing its connection to the other aspect (wave-particle duality), or we create a logical conflict between the holistic view of a situation and a reductive view of the same situation, etc.

So I fall back on what I implied in an earlier post, that if someone believes reality is paradoxical, it is likely because they are confusing their mental representations of reality with actual reality.

 

[wuliheron]

So I fall back on what I implied in an earlier post, that if someone believes reality is paradoxical, it is likely because they are confusing their mental representations of reality with actual reality.

I never said reality IS paradoxical, I said existence and our emotional lives are apparently paradoxical. Whether they are really paradoxical or not, I could not care less and speculating about this seems utterly pointless and counterproductive to me. Assuming that they are rational and logical in specific contexts makes perfect sense to me, but to extend this to some sort of ultimate statement about life, the universe, and everything is patently absurd.

Because we are ignorant we may learn. Rather than preoccupying our minds with useless and counterproductive beliefs about things we have no control over and no way of proving, best to embrace our ignorance for the gift it really can be. Much simpler that way.

 

[Les Sleeth]

I never said reality IS paradoxical, I said existence and our emotional lives are apparently paradoxical.

How can existence be distinguished from reality? How can existence be equated with emotional states?

 

[loseyourname]

Years ago I lived in Riverside, California and on occasion worked in Los Angeles, about 50-60 miles.

Why? Are the home prices really that much cheaper? I've never understood the people that commute from the Inland Empire.

 

[wuliheron]

How can existence be distinguished from reality? How can existence be equated with emotional states?

Reality is but a part of existence, which includes our dreams, fantasies, fears, and nightmares among other things.

As I have already mentioned, it is because we have the power to emote that we possesses the ability to give things meaning, to place things contextually rather than merely by content. One victim of brain trauma lost the ability to emote for the most part, and with it the ability to place things contextually.

He could not hide his condition well at all. He was basically functioning on memory alone, and the slightest novel event or emotional context left him bewildered. It was as if he had become a fabulous computer programmed with all the memories of an adult, but unable to make much sense of these.

Whether existence has any intrinsic meaning or not, we certainly give it meaning. Thus our emotions tend to dominate the vague yet self-evident concept of existence, and many claim to this day that our emotions/consciousness is even the source of existence. A possibility even the most useful physical theory ever devised, QM, cannot deny.

Rather than focusing exclusively on the evidently impossible to substantiate possibility that existence has some sort of intrinsic meaning, increasingly scientists and philosophers alike are focusing on the meanings we give existence. As with the infinite and finite, vague and explicite, global and local, the vague concept of existence has proven useful in combination with more explicit concepts. Not least of all, our feelings.

For more information you may want to read up on Relational Frame Theory, Functional Contextualism, and modern pantheistic approaches to the subject of consciousness, as well as the more serious modern philosophical studies into Asian philosophies, in particular Taoism and Buddhism. In the last few decades these have all come under intense scrutiny by disciplines ranging from computer sciences to psychology and physics and have even been seriously scrutinized by the defense industry.

 

[quantumdude]

My idea was that it is impossible to prove an observation of a paradox, not that it is impossible to observe a paradox.

OK, I read you wrong. The question still stands though, because you can prove the observation of a paradox in logic. Hence, the incongruity remains.

I'm sorry if this discussion seems difficult to you, it is actually a conceptually simple subject.

Erm, I wasn't saying that the discussion was difficult, I was saying that you are difficult in that you seem to be determined not to make sense of the question asked by Sikz.

 

[endergonic]

Logic is sopposed to describe the real world.

is there a flaw in trying to describe what everyone perceives differently?
or using one meaning for another?

"Logic is the study of correct reasoning," ?

 

[wuliheron]

OK, I read you wrong. The question still stands though, because you can prove the observation of a paradox in logic. Hence, the incongruity remains.

You cannot prove the observation of a paradox in logic, paradoxes have no truth value. The Liar's paradox is considered by logicians to be almost certainly a genuine paradox, but this is not a proven fact.

 

[wuliheron]

OK, I read you wrong. The question still stands though, because you can prove the observation of a paradox in logic. Hence, the incongruity remains.

Erm, I wasn't saying that the discussion was difficult, I was saying that you are difficult in that you seem to be determined not to make sense of the question asked by Sikz.

Well, yes and no, I have been pushing a point about contextualism. Contextualism applies particularly where logic meets natural language.

I understand what seems to be his intended question, but the explicit words he used were poorly formulated. If the question was sincere, then it makes an eronious assumption that we can observe paradoxes in logic, but not in the natural world.

All this broohaha reminds me of the controversy over faster than light travel. Shadows move faster than light, but they convey no information, mass, energy, or any other property for that matter. All they convey is the absense of such things. Likewise, paradoxes have no truth value, they are neither true nor false, real nor unreal. All they seem to convey as far as anyone knows is the absense of such things.

Even the shallowest study of paradoxes will quickly reveal this simple truth. Paradoxes apparently do not tell us what is impossible, so much as what is useless to us according to the rules of logic. Being useless in a strickly logical sense, is not the same thing as being utterly useless or unreal.

 

[omin]

Turn the Page Through Finite Space

Paradoxes exist in our logic. They do not exist in the real world (to our knowledge at least; no one has ever encountered proof of a pardox existing). Logic is sopposed to describe the real world. Could there be some sort of flaw in our logic then :S?

Since paradoxes do not exist in the physical world, they cannot exist in logic. Logic, used accurately, is a symbolic representation of the physical world. All thoughts and words possible in logic derive from the physical world. Physics represents hard determinism, is the most accurate of all symbolic representation of the world, and therefore logic is a description vs. a prescription of the world.

Some say paradox only exists in logic. It is said we don't observe it in the physical world, but we see it only in logic. The mind is part of the physical and logic is thoughts of the mind, so it is observed in the physical world, as we observe our thoughts.

How can I use the word paradox then if it physically can't exist, since all thoughts derive from physical things? And how can I truly claim it doesn't exist if I understand what paradox means? Is this not a paradox itself?

I say a paradox is simply a type of confusion that when critically thought through no longer gives the mysterious psychological state of paradox. After this is realized, it makes one wonder what paradox means anymore, the confusion is gone. I usually loose what paradox means after I finally 'get' something I've wanted to 'get' for awhile. After I get it, I say, "Oh, now I get it." At that point, I don't know what paradox means. Everything I thought before just seems silly.

One definition of Paradox: When two separate physical things are said to be one or one is considered to be two. Since no two things can exist in the same place, we must go over our thoughts (logic) more carefully to debunk the paradox.

If I turn a page half way and then half that, then half that, etc., won't turning it even one inch be passing through an infinite amount of space? Doesn't this make it seem like I can't turn the page all the way, because I would have to pass through an infinite amount of space in a finite amount of time?

There is a paradox here, but that only means that something is being confused.

Space is thought of here as something that can be divided. When we divide things, we pull them apart and there is a space in between. Wow, we created space. In this example, we are driven to think space is expanding constantly when it's divided, even when those peices of space keep expanding are getting smaller and smaller. This is example of applying the multiplication principle to finite things. Space become a piece of matter that continually multiplies, but to a smaller size for each product, thus creating a permanent barrier.

The anti-thesis of the law of conservation of energy must be believed for a paradox to exist in this example.

Space is physical or isn't there to pass through. If space is something, it's very, very small and moved around the page or through the page as the page turned. And if space is physical we would have divided it, but no matter would have been created or destroyed, so no space would have been created as it divided, that's just where the page is.

All paradoxes can be debunked. I think paradox just means I'm con(fused).

 

[wuliheron]

All paradoxes can be debunked. I think paradox just means I'm con(fused).

In other words, all paradoxes are false. You know, of course, this presents yet another paradox since paradoxes have no truth value.

 

[Imparcticle]

Can you give an example, wuliheron?

In other words, all paradoxes are false.

Why?

 

[wuliheron]

Can you give an example, wuliheron?

Why?

I was paraphrasing Omin who wrote:

"All paradoxes can be debunked. I think paradox just means I'm con(fused)."

This is related to the most famous paradox of them all, the Liar's paradox:

"This statement is false."

If true, then the statement is false. If false, then the statement is true, and so on in an endless infinite regression. By the rules of formal logic, paradoxes have no truth value, they are neither true nor false. All one can really say about them is whether something seems likely to be a paradox or not.

Paraphrasing Omin's statement then: "All paradoxes are false."

If true then it is false, if false then it is true, and so on ad infinitum.

Words only have demonstrable meaning according to their function in a given context. In the case of the word paradox, it is a perfectly useful word when given a specific context, and just as meaningless as any other without a context.

"The Fish!", "The banana!", "The paradox!" are all just so much drug induced ramblings.

 

[omin]

The definition of false is a theory or some statement that asserts to represent some order of the world accurately, but produces a disorder.

This statement is false. What does it represent?

'This' means to point. The action of pointing for the purpose of associating a sign of communication to an object. The sound a person makes is associated to the physical object or actions or purely psychological state being experienced. It's how we learned new world when we were child. Our parents said 'this' alot, which was followed by the objects sound.

'Statement' means symbols, which assert to represent the physical world and brain activity is physical.

'Is' means to equate. The left side symbols represent the same as the right hand symbols in the statement represent.

'false' means a statement represents a disorder of positive elements. It represents a psychological order perfectly but are not symbols in an order that represent the physics of the objective world accurately. False, in general, means less accurate.

I can form a thought of a fire exhaling dragon, but it's a false statement in accordance to objective-physical reality, but an accurate statement of psychological-physical order, because it represents exactly what I think.

And by the way, negative is not a paradox of positive. Negative is positive. It's just a very, very small positive. Zero is also positive. It's very, very small. So is absence. Why? Prove nothing. Symbols may only represent knowns.

In and of itself the statement is a physical quantity of symbols and that's it's real value. Since there is non comparitive context that the terms reference, it's quantity of accuracy as representing some context can not be positively debated.

 

[Imparcticle]

If true, then the statement is false. If false, then the statement is true, and so on in an endless infinite regression. By the rules of formal logic, paradoxes have no truth value, they are neither true nor false. All one can really say about them is whether something seems likely to be a paradox or not.

How is a truth value defined? How is a false value defined?