How Can A Paradox Exist?

Always wondered. Something which is both true and false - how can it possibly exist? It breaks the first rule of philosophy - a thing is a thing and not another thing - or at least appears to. Is the problem a linguistic or conceptual one? Or is it not a problem at all.

The classic example:

This statement is false.


How can I say this? Doesn't this confuse our view of the world?


Thoughts anyone?

 

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think of this.....

This is my personal belief:

everything in the universe is a paradox... nothing is completely true or false. True this statement is stupid but it is also smart and observant. Its like falsehoods in materialism. Mass is just alot of energy and when you break the mass down you got nothing but alot of energy.

So basically I'm saying that something only exists in any way, in the prescence of something else and because things always have an opposite like cold and hot, you would be viewing anything and everything as a paradox in someway or another. Basically the only way something can exist is as a paradox.

 

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I think you will find that there are a lot of items which fall into the all white or all black such as mathematics. But most will fall into the grey area, half true (more or less). Life does not exist to provide us with neatly boxed catagories that fit into our thoughts of how the world should be.

 

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There cannot be degrees of truth. A thing is either true, false, or (some argue) indeterminate. What does partly true mean? If a proposition is not wholly true, it is false in terms of propositional logic. And it is through proposition that we convey concepts - it is the framework of understanding.

If everything in the universe is neither one thing or another, then there is no meaning (in the strict, Wittgensteinian sense) to language or concepts. I do not think this can be what you are saying.

The paradox is more of a problem than I think is realised. We can dismiss it as a linguistic contrivance (as, again, Wittgenstein did) but I am not fully convinced.

Speaking in broad terms, yes there are 'grey' areas. Moral and ethical issues. But I'm talking about the structure of a strict proposition, the structure of logic and the function of language in conveying concepts.

Can you conceive of something which is both white and not white at the same time? It is logically impossible if there is a genuine conception of 'whiteness'. Again, a thing is a thing and not another thing - this applies to all physical objects (quantum theory possibly bringing this into question).

It is the existence of a logical impossibility that concerns me about the paradox.

 

Hi
This message does not refer to itself. Because every sentence it contains is false. For example, the next sentence is false. The previous sentences are all true.
etc. etc.

This is not an example of a paradox, in the sense of being both true and false. It is neither: it is undetermined. Here is the deal: a proposition holds some truth-value about something. For example "Merlijn is Dutch for Merlin" is true, it refers to something else (i.e. "Merlijn").
Propositions can also refer -directly or indirectly- to themselves. In which case things get all messy, as shown in the story above:

is false, so the last proposition

is also false. So,

would be true. But what to make out of

???
Thus: in self referring propositional systems it is not always possible to determine the truth-value (maybe it doesn't even exist).
To me the great question is, what do we make out of René Descartes famous

??? the proposition is indirectly self-referring. Does it hold any truth-value about 'I'?

Merlijn

 

Merlijn

That's the spirit! Liked the post!

You're quite right! Self-referential propositions are the problem. It is, essentially, a linguistic difficulty with self-referential propositions that leads to statements which are (I would agree with Wittgenstein) ultimately meaningless (I am assuming that propositions with no truth value are meaningless). But does a genuine paradox exist?

As for Descartes. From my perspective the argument is flawed due to its circularity.

'I think therefore I am'

He is attempting to prove the existence of 'I', but assumes that existence in the premise. He cannot assume to be true that which he is seeking to logically prove, thus the argument is invalid (has no truth value).

The only argument (if it is one) that I believe he can make is:

There is thought.

And thus we reach the limits of what deductive logic can tell us about the world! Okay, I exagerate.

Induction, now there's another story.

(related question that has always interested me is Schroedlinger's cat)

 

what

I still hold true to my belief.

what is logic anyway? Isnt it the ideaology that something must be someway specific or it is false. Isn't that Ideaology somewhat of a paradox in itself. I dont think you can have logic that is actually logical because then there should be no limits or constrictions to the logic of something. Its just not logical.

Now I'm confusing myself?!?!?! I cant understand what I just wrote, anymore. I hope you guys can.

 

A paradox describes an impossibility, so while the description of the paradox can exist, the paradox so described cannot exist, otherwise it would not be a paradox.

I hope that is clear.

The fact that one can describe impossibilities by plays on words defies the sense of the words. It is easy to create a circular argument or reference, but that does not mean that there is a paradox, just that someone made a mistake and didn't check whether the words made sense.

Take a card and write on one side -

The statement on the other side of this card is true.

on the other side write -

The statement on the other side of this card is false.

Is there a paradox? Which statements are true and which false?

Cris

 

Actually, the first rule of philosophy is: seek wisdom.

You're referring to the logical rule of Identity. This is a syllogistic rule, not a philosophical rule. While we may make use of logic to assist us in understanding, it is not always the case that logic leads us to the truth. By the way, even in logic, the Law of Identity can be broken; look into Modal Logic.

In any case, more often than not, a paradox is generated by our perception; whether it be something physical ( gee, I thought that pencil was straight, but now that it's sitting half way in that glass of water, it's bent), or something conceptual ( everything is relative), 'apparent' paradoxes represent how poorly we understand our world. Admittedly, the majority of paradoxes are created through our use of language. If you're interested in this angle, check out Gottlob Frege, or WVO Quine. Suffice it to say, paradoxes are particular to the human mind. What does that tell you??

 

No one can answer my riddlle huh? I'm very dissapointed.

 

Sounds like a circular argument with no right answer...

 

you want an answer to your riddle?

You want an answer to your riddle, alright.

There is no technical paradox in your riddle. both statements are true. It's like someone calling you an idiot (i'm not calling you an idiot.) and you saying your right. You're know that your stupid and your just admitting it. You don't have to be smart to say so.

 

Cris

Check out the problem with self-referrential propositions above. It's linguistic rather than logical.

 

I am not sure I follow what you mean Captain, but I am just getting involved in this one.

In the grand scheme, I believe there is a truth, to get there is the paradox. I believe, that the paradox lies in the path to the truth.

However, there are also different truths, depending on what one is dealing with, does a paradox exist in two different truths? Of course I am speaking in generalities. but to approach this it needs to be done from the top down.

For example: Lets say that one day we find out that God as we have pereceived is actually a creation born out of the imagination of each of us. We both die tomorow, I find out that my GOD does exist, you find out that your God does exist. They are both real, however is the force that has caused us to imagine our reality the REAL truth???

You know what? I just confused myself, I don't know what the hell I am talking about..........

No I say a paradox cannot exist. It is only a perception of true reality.

 

Not quote sure what you're getting at here Teerum. I think you might be confusing subjective and objective truth.

This ultimately becomes a different question - can we ever perceive an objective truth? (the problem - all humans experience the world through perception - perception necessarily implies subjectivity).

Simply put, my conception (and I believe the right one) of a paradox is a thing which is both entirely true and entirley false, judged against one criteria (any one) of what truth is. We are assuming a common definition of truth for this purpose.

The paradox springs (the modern version) from Bertrand Russell and set theory where he discovered that Frege's system of logic was flawed under certain conditions as a proposition would become true if and only if false, and false if and only if true.

A couple of ways out were offered, but there is as yet no accepted answer. I tend to lean towards the idea that the paradox emerges from self referrential propositions, suggesting that a statement referring to its own truth value is meaningless in any propositional system of logic.

It does remain a little bit unsettling though. So after all that, I'd agree with you that a paradox cannot exist outside of a flawed system (I would suggest that the emergence of a paradox indicates a systemic problem rather than a deeper, logical one). For me, the problem is linguistic.

 

I must admit Captain I am a bit at a loss for some things you commented on, my fault not yours.

I guess I am approaching the topic in less of an idealistic sense in terms of the paradox itself.

I mean to bring the issue further into the realm of reality and our existance. I believe that while there may be different realities for different individuals. In the end the only paradox is like you have stated, one which is created by flaws.........I don't know....

all I know is that I am off to the Colorodo Rockies,,,,,,,this weekend, we will see what reality lies ahead for me there.

 

Paradoxes don't exist, there is just a gap in understanding of the finite rules of existance.

500 years ago Europe beleived the world was flat. There was no empirical proof to disagree.

A Pope agreed with this, because he said, when Jesus did his second coming thing he would go from heaven to jeruselem and everyone would see him.

The beleifs of the common man, were eeven more basic, water runs off slopes, ergo if the world wasn't flat, the sea would fall off the edge.

People didn't understand, so they made stuff up.

Sub atomic physics. The imaginary particles that don't exist but must exist to make the math balance.

Things are not black or white, just a myriad shade of greys.

XL

 

I agree Axel.......it does not exist.......and anyway the borders of insanity are present enough with out creating some imaginary reality. We may not know or understand the truth, but there is only ONE......truth. In my opinion.

 

Welcome to the Forum axel, and greetings teerum.

axel:
what you describe in regard to a belief that the earth was flat is a problem of knowledge rather than a paradox. But I think I see what you are getting at. You are saying that contradiction cannot exist - if it does then there is simply a gap in our knowledge. It seems to me that this suggests that everything is black and white, just that our limited vision allows us only to see shades of grey. Or are you saying that there is no objective Truth? Or that we cannot see the Truth?

teerum:
You seem to be reading axel the same way - that there is no contradiction in the universe, simply an inability on our part to acquire the Truth.

I tend to agree - we would have to seriously alter our outlook if a paradox could exist, wouldn't we?

 

Black or White?

One or Zero?

Nothing runs on 1 bit values, (apart from crap pieces of my code)

I believe everything can be devolved to a binary status, okay a 3million bit value is of no use to man nor beast but it works, we just skip over the irrelevant detail.

At a guess you are human, that means I can skip over all the Animal, vegetable Mineral stuff and all the animal stuff, to get to where you are in my perception system.

I've probably spent too much time programming with IfElseThen

Xl