Exploring the Paradoxes of Logic

[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. :rofl:

 

[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?

 

[wuliheron]

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

As Omin has just demonstrated so well, we can use natural language to split semantical hairs ad infinitum and get nowhere, or we can even redefine words willy nilly and begin spouting nonsense poetry.

Once again with emphasis, words only have demonstrable meaning according to their function in a given context. In this case, I gave a specific context, that of formal logic. The following definition will serve as well as any other for this purpose.

truth ( P ) Pronunciation Key (trth)
n. pl. truths (trthz, trths)
Conformity to fact or actuality.

 

[Imparcticle]

Symbols may only represent knowns.

How about variables? For example, in formulas like a²+b²=c², the variables a, b, and c are symbols representing unknowns.

 

[omin]

How about variables? For example, in formulas like a²+b²=c², the variables a, b, and c are symbols representing unknowns.

I once thought things could be destroyed or things could be negated. I also thought things could be created out of nothing. I now only look at all things as being positioned here or there. Forms change, but there elements are not created or destroyed.

The essential meaning of unknown may be infered with these simple logic negations of an underlying positive statement.

The subject is in the color Sienna, the copula is in Dark Olive Green and predicate is in Dark Slate Blue. The first example is the negative form and the second (in parenthesis) is the positive form it really infers! All statements in language infer only positive. All things are only inside or outside something rather than created or destroyed. It seems a play on words, but I found it helpfull because inside and outside connotes existence vs. not, un, etc which seems to connote zero or nothing concepts, which can increase confusion thorugh paradoxical type expression.

The Positive Statement
Things I know are things I sense. The statement that is said over and over in the negatives below.

The Negatives Turned To Positives
Things I don't know are things I don't sense. (Things outside my knowledge are things outside my sense.)

Things I know aren't things I don't sense. (Things I know are things outside what is outside what I sense.)

Things unknown are things I don't sense. (Things outside what I know are outside what things I sense.)

Non-things I know are things I don't sense. (Things outside my knowledge are things outside my senses.)

Etc, etc... We could go on and on.

And there is also the appeal to ignorance...what could it possible mean?

Nothing does exist because you can't prove it doesn't exist.
Nothing doesn't exist because you you can't prove it exists.

I used the paradoxal words and their definitions for conviece of explanation.