View Full Version : How Can A Paradox Exist?


Captain Canada
08-22-01, 11:00 AM
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?

Xerxes
08-22-01, 08:28 PM
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.

wet1
08-22-01, 09:50 PM
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.

Captain Canada
08-23-01, 06:18 AM
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.

Merlijn
08-23-01, 08:14 AM
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:

This message does not refer to itself
is false, so the last proposition

The previous sentences are are all true.
is also false. So,

For example, the next sentence is false.
would be true. But what to make out of

Because every sentence it contains is false.
???
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

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

Merlijn

Captain Canada
08-23-01, 10:58 AM
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)

Xerxes
08-23-01, 07:30 PM
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.

Cris
08-27-01, 08:08 PM
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

glaucon
08-27-01, 09:36 PM
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??

Cris
08-28-01, 09:31 PM
No one can answer my riddlle huh? I'm very dissapointed.

wet1
08-28-01, 10:01 PM
Sounds like a circular argument with no right answer...

Xerxes
08-29-01, 01:58 PM
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.

Captain Canada
08-30-01, 05:02 AM
Check out the problem with self-referrential propositions above. It's linguistic rather than logical.

teerum
08-30-01, 08:23 AM
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.

Captain Canada
08-31-01, 10:59 AM
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.

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.

teerum
08-31-01, 11:28 AM
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.

axel
10-01-01, 09:04 AM
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

teerum
10-01-01, 09:15 AM
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.

Captain Canada
10-01-01, 10:45 AM
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?

axel
10-01-01, 10:57 AM
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

glaucon
10-01-01, 11:12 AM
Intuitively, it is of course difficult for us to grasp the notion of the contradictory. That's because we do not experience the world through Propositional Logic. Strictly speaking, contradiction can only obtain in a realm where Tautologies exist. A = -(-A)
The denial of which, truth functionally speaking, would be a contradiction. Since this does not necessarily accord with our daily life, Modal Logic was sprung on us. This takes into account truth functional variables and implicative conditionals (if...then..).
Just remember, contradiction only exists within a specific descriptive structure.

Stryder
10-15-01, 03:27 PM
Paradoxes???

Okay how about:
"I'm a Vegetarian and Work as a Butcher"
Or
"I don't clean plates, unless you pay me"

Paradoxes are on of the most tediously absurd things that occur, and fortunately a preportion of study within artificial intelligence systems that deal with Words and their contexts.

"I drempt of waking"

My personal favourite, for when someone asks you to do something and you reply...

"In a minute/second!"

"that nearly hit you!" (Is there such thing as nearly hit, it didn't hit, so it must have missed, meaning it wasn't even close to hitting you)

"If you can find proof of his guilt, we will hand him over" Taliban paradox.

"Have you ever noticed when you find what you are looking for, it's always in the last place you look!"

"I took the fish for a walk!"

"What goes up, must come down!"

I think that's all I need to type to point out there is paradoxes out there :D

machaon
10-15-01, 11:18 PM
Knowing the definition of words allows us to formulate sentences describing things that are in conflict with the conceptial templates that define the contrast between that which can be achieved and that which can not. One way to validate this claim would be to examine whether or not paradoxes existed before launguage and the written word were invented.

Bambi
10-19-01, 10:50 PM
Machaon,

Sure paradoxes exist outside of language. For example, many Escher drawings show impossible objects or impossible situations.

Cris pretty much nailed the issue:



It is easy to create a circular argument or reference, but that does not mean that there is a paradox, <b>just that someone made a mistake</b> and didn't check whether the words made sense.


This applies to nonverbal paradoxes as well. They are merely results of mistakes stemming from incomplete understanding or from faulty analysis.

Stryder
10-20-01, 11:38 AM
I can see this topic beginning to parallel that of one of the topics involving "What do you call art?"
I checked out what Bambi had mentioned:

M.C.Escher (1898-1972) and his Artwork that spanned his life (some of which I'm sure relativity students might have studied).

rather than placing all the images that I found involving his lithographs, I'm going to place the anchors to some two sites I came across, one that is a paper about him and some of the other types of paradoxes, and the other at an Art site that you can get to see all his work (and even get extremely large versions of the image for printing)

http://www2.bc.edu/~schiavop/escher.html
A paper

http://www.artchive.com/artchive/E/escher.html
The Art gallery with poster sized versions.

I'm sure if you take a look you will realise that you've seen some of his work before, but probably didn't realise.

Tom
10-21-01, 02:37 PM
in everything and everyone theres true & false, there is no 'its all inncorrect' its either true or false.

No one says im wrong, you think im wrong, send in a post. :mad: :)

SeekerOfTruth
10-22-01, 08:08 AM
Originally posted by Captain Canada
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.



I disagree. There can be "degrees of truth". Those degrees are based upon the context of the arguements of truth you are interested in discovering. For example. Is it a true statement to say "stealing is wrong"? In the context of someone who has the potential to earn their living, then you could argue that stealing is wrong. But what about the context of someone who has no job, no ability to get a job, and has to support their family in some way. If their family is starving to death, is it then wrong to steal?

Truth is based on the context in which the truth is written. The truths of today are not the truths of yesterday and will probably not be the truths of tomorrow.....

machaon
10-23-01, 12:09 AM
Sure paradoxes exist outside of language. For example, many Escher drawings show impossible objects or impossible situations.

I was one of the first people in line when the M.C. Escher exhibit came to Knoxville, Tennessee(USA). I have personally seen his works and was duly impressed by his artistic genius. However, his works demonstrate what IS possible in reference to how images are portrayed in two dimensions. They also, in my opinion, represent how it is possible for ideas to be communicated that are in conflict with what we observe about the world. The paradox arises from the fact that his art describes visually what sentences can describe verbally, they describe the ability to express that which can not be intergrated into functional ideas based on the conceptialization of reality as we can utilize it in a meaniful way. It outlines the limits of what we CAN believe against the background of what CAN be believed.

MuliBoy
10-23-01, 08:49 AM
ON or OFF. True or false. These are facts. Everything else is grayzone stuff and excists in a state of uncertainty. Mutating and formable into whatever you like. A paradox does not excist, it is merely a idea that counteracts itself.
Loopholes in the programming of reality.
Just reboot :)

James R
10-23-01, 11:45 AM
In classic propositional calculus, every statement is either true or false (or possibly undeterminable). But that's not the only possible type of logic. For example, "fuzzy logic" assigns truth values on a continuum from 0 to 1, according the probability that the given statement is true. A statement with a value of 1/2 is neither true nor false. A statement with a value of 0.9 is mostly true.

Statements such as:
This statement is false.are sometimes called <i>meta-</i>statements. They are statements about statements. The paradoxes of such statements arise from their self-referential nature. We can avoid the paradoxes in a technical way by not allowing a meta-statement to refer to a statement at the same meta-level (including itself). However, in the ordinary usage of language such paradoxes cannot be avoided. Perhaps the quoted statement is a good candidate for a fuzzy truth value of 0.5?

Tom311
11-28-01, 06:21 PM
How could a human be a paradox. Me in general. My teacher called me a paradox. How can this be?


The paradox definitin is a paradox by its very own definition.

Chagur
11-28-01, 09:34 PM
Re. 'Degrees of Truth'

I wasn't much more than an ankle-biter when the following (more
or less) was related to me to help me understand the inter-
relatedness of 'truth', 'justice', and 'compassion' ...

The Prince, who had been captured and raised as the son of a far
distant Lord returned to his native land and unwittingly slew his
father. The law at the time required that a son who slew his
father was to be drawn and quartered.

Upon hearing the circumstances, the magistrates of the Emperor
allowed the Prince to be drawn and quartered facing the sky in
recognition of his not having known it was his father whom he
had met and slain on the field of battle.

;)

Merlijn
11-29-01, 06:23 AM
James R,
You write about fuzzy logic. There seems to be something fuzzy about your logic

For example, "fuzzy logic" assigns truth values on a continuum from 0 to 1, according the probability that the given statement is true. A statement with a value of 1/2 is neither true nor false. A statement with a value of 0.9 is mostly true.
The problem here is that "the probability that statement A is true" does not equal "the truth value of statement A".

This means that your " A statement with a value of 0.9 is mostly true." is misconceived. It should be something like " A statement with a value of 0.9 is most likely to be true."
Thus, there are still no half-truths, no so-called 'gray areas'.

I the line of machaon's remarks on Escher's work: well just as I pointed out in my earlier piece in this thread, it is all about representations. These just happen to be visual, not linguistic.

SeekerOfTruth,

Truth is based on the context in which the truth is written.
Do you really think that truth is a value that is defined by the limited capabilities of those who are investigating it? This would mean that the truth is the insight one has on a particular moment.
If that were so, then there is no point in investigating. If you do not investigate, the truth is what you believe it to be.
Makes me wonder, where did you get your name?

Live long and prosper.
Merlijn

Riomacleod
11-29-01, 08:38 AM
Ok, far be it from me to disagree that Descartes was a crackpot, but I suddenly feel myself compelled to defend him.

Here is his argument, boiled down. He starts by assuming nothing exists, and nothing is true.

1 Thoughts are.
Edit:1.5 Thoughts are percieved through this particular stream of conciousness.
2 These thoughts whether poured into me or created myself are posessed, however transiently, by this stream of conciousness.
3 If these thoughts are pushed into this stream of conciousness by a foreign entity, I exist.
4 If these thoughts are created within this stream of conciousness, I exist.
5 If ~3 then 4.
6 If ~4 then 3.
7 Therefore, I exist.
8 Thus: I think, I am.

Generally speaking, paradoxes exist because of imperfections. Language has imperfections, so we can have bizarre statements with a true and false value. Escher can make fascinating visual paradoxes because it is not really possible to represent a three dimensional reality in a 2 dimensional projection. If anyone could build any of the things which Escher drew, that then would be a true paradox because it would have an underlying reality behind it. Words and pictures have no fundamental reality, they are tools which we use to express our understanding OF fundamental reality... I'm pretty much behind Merlijn on the rest of it.

Merlijn
11-29-01, 08:49 AM
Thanks Riomacleod ,

Te thing I was referring to earlier was that

5 If ~3 then 4.
6 If ~4 then 3.
7 Therefore, I exist.
8 Thus: I think, I am.
is such a self referential system. The problem I wanted to point out is that the truthvalue of self referential systems cannot be determined.

Note however, that a self-referential system is paradoxal per se!
For example:

This example has two lines, this one and the next.
The first line of the example is true.
there is nothing paradoxal here.

Riomacleod
11-29-01, 09:13 AM
No no! They are not self referential statements.

6 is not technically important to the proof, but is added to eliminate any other possibilities.

Line 5 can also read "these thoughts are either created by myself or created by something else"

Once you prove something as true, anything that logically flows from it is also true. This is why we have lemmas in mathematics.

James R
11-29-01, 06:37 PM
Merlijn,

<i>The problem here is that "the probability that statement A is true" does not equal "the truth value of statement A".</i>

I apologise for my perhaps rushed and misleading explanation. To use fuzzy logic you really need to throw away the probability idea and just talk about the truth vales of statements. The thing about probability was to give you something convenient to hang on to while you were getting the idea.

Merlijn
11-30-01, 06:26 AM
James R,
I have nearly no knowledge of Fuzzy Logic. It may very well be that you are right. But then again, what do we do with it?
I for one have serious trouble with the notion of continuous truth values, I prefer the 0,1, undecided system. It's nice that the possibility of such a calculus exists, but does it add to the understanding of the nature of our universe?
I can imagine that in some (strange) multiverse theory it can provide a meaningfull description of things... I think you get my drift here. But I am not too fond of the multi-universe idea of Deutsch (and others). Even though such a theory would, I guess, in principle be able to shed some light on paradoxes.
Hmm, maybe somebody with a more thourough knowledge of the theory can tell us more about this.

Riomacleod,
'Line 5 can also read "these thoughts are either created by myself or created by something else" '
I knew what line 5 (and 6) means.... I think it is the beauty of Descartes insight.
My problem is more on a meta-level. The notions of 'thoughts', 'consciousness' and 'I' cannot be separated.
Thus, it all comes down to line/assumption (1)"Thoughts are". One cannot proof 'I' exist(S) from there, because that would mean one has to proof their assumption (1).
the notion of "I" is a thought of a consciousness. And "thoughts" are what constitutes "consciousness" (does this make sense?).
It is like "Consciouness" is a collection and "Thoughts" and "I" are elements of the collection.
It's tricky. I am going to rethink it all. I'll let you know what I have come up with.

Live long and prosper.
Merlijn

Rick
11-30-01, 06:42 AM
Originally posted by Cris
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
Hi,
it depends upon the side you first take a look.eg if you take a look at first side,where it is written the statement on other side is true,then the other side on the second look you find that NOW the statement has become false,until now it was true.the statements are interdependent and also dependent on instances you look at.
bye!.

James R
11-30-01, 10:12 PM
Merlijn:

<i>I for one have serious trouble with the notion of continuous truth values, I prefer the 0,1, undecided system. It's nice that the possibility of such a calculus exists, but does it add to the understanding of the nature of our universe?</i>

I've been thinking about this a fair bit recently, and I think that most scientific statements do not fall easily into a binary logic. Let me give you one example:

Scientists estimate the distances to certain stars called Cepheid variables using different methods. At this stage, we think we know how to measure the distance to certain Cepheids with a 15% degree of accuracy. For example, our best estimate of the distance to a particular Cepheid might be 100 light years plus or minus 15 light years.

Now, ask yourself: Is it true that this Cepheid is 100 light years away? If you say "Yes", what happens if it turns out to be 107 light years away when we get better data? If you say "No", then is it equally valid to say it could be 200 light years away? That's the problem with the true/false dichotomy. What we need (possibly) is an idea of "how true" something is. In the example, I would say it is "more true" to say the star is 100 light years away than to say it is 120 light years away, even though the 100 light year figure might not be spot on.

I realise that there are ways around this, but only at the expense of multiplying the number of binary statements we need to make. Even that doesn't necessarily solve all the problems.

Merlijn
12-01-01, 07:16 AM
Actually I was referring to the "TRUE" nature of the world, not to the "PERCEIVED" nature. We do not have perfect knowledge of the world, that's neither news nor something that should make us doubt wether there is at all a 'truth'.

Riomacleod
12-03-01, 09:33 AM
Scientists estimate the distances to certain stars called Cepheid variables using different methods. At this stage, we think we know how to measure the distance to certain Cepheids with a 15% degree of accuracy. For example, our best estimate of the distance to a particular Cepheid might be 100 light years plus or minus 15 light years.

There is a difference between accuracy of numbers and truth value, because with the data you've given, it's FALSE to say that the Cepheid is 100 light years away. it's only true to say that it is 100 light years, +/- 15%. (BTW, that's what real scientists do.)


I realise that there are ways around this, but only at the expense of multiplying the number of binary statements we need to make. Even that doesn't necessarily solve all the problems.
I also shudder at any system that sacrifices whole truth for the sake of convenience.

Merlijn
12-03-01, 09:41 AM
Hear hear!

Alpha
12-07-01, 12:04 PM
Okay how about:
"I'm a Vegetarian and Work as a Butcher"
Or
"I don't clean plates, unless you pay me"

"I drempt of waking"

"In a minute/second!"

"that nearly hit you!" (Is there such thing as nearly hit, it didn't hit, so it must have missed, meaning it wasn't even close to hitting you)

"If you can find proof of his guilt, we will hand him over" Taliban paradox.

"Have you ever noticed when you find what you are looking for, it's always in the last place you look!"

"I took the fish for a walk!"

"What goes up, must come down!"

I think that's all I need to type to point out there is paradoxes out there.There wasn't a single paradox in there.

There is no such thing as a paradox. The idea of a paradox only exists as an abstract thought. Everything in the universe makes sense. There are no contradictions in the universe. Truth is absoulute, either something is true, or it is not. Simple as that. Paradoxes and contradictions and "shades of grey of the truth" only exist in abstract because of imperfections.

Riomacleod
12-07-01, 12:16 PM
There is no such thing as a paradox. The idea of a paradox only exists as an abstract thought. Everything in the universe makes sense. There are no contradictions in the universe. Truth is absoulute, either something is true, or it is not. Simple as that. Paradoxes and contradictions and "shades of grey of the truth" only exist in abstract because of imperfections.
Because of imperfections in lagnuage/communication.

Xelios
12-07-01, 06:44 PM
How Can A Paradox Exist?

Easy, you go back in time and kill your grandmother. If she died before givin birth to your mother, then she could never have given birth to you. Therefor you could never have gone back in time to kill your grandmother.

There's one right there ;)

Alpha
12-08-01, 12:38 PM
Originally posted by Xelios


Easy, you go back in time and kill your grandmother. If she died before givin birth to your mother, then she could never have given birth to you. Therefor you could never have gone back in time to kill your grandmother.

There's one right there ;) I'll assume you're not trying to be funny in case someone might actually think that's a paradox.

1 - You can't go back in time.
2 - If you could, you would end up in another timeline and you would be altering that timeline, not your own. What's happened has happened. There's no way to change it.

Captain Canada
12-10-01, 07:47 AM
1 - You can't go back in time.
2 - If you could, you would end up in another timeline and you would be altering that timeline, not your own. What's happened has happened. There's no way to change it.

If 1 is true that's all you need. How do you get 2? What's the justification for 1?

I expect you justify the two statements by stating, essentially, a paradox cannot exist. That's just begging the question.

Why can't I go back in time? And if you're so certain that you can't, why do you think that if you could you'd enter another timeline? I don't follow.

Alpha
12-11-01, 04:32 PM
If you go back in time there would be a paradox, which is impossible, so the assumption is that if time travel were possible you would have to enter another timeline in order to avoid a paradox.
That you can't go back in time is really just my personal belief, but I really don't think I'll be proven wrong.

Myles
11-08-07, 04:06 PM
We can't go back in time because doing so would contravene the laws of thermodynamics. If I broke a plate yesterday a certain amount of energy will have been dissipated in the proces. To go back to one minute before I broke the plate would entail finding the plate whole. But to find the plate whole would mean that the energy expended in breaking it would be available to put it together. But that energy is no longer available; it has been dissipated. Hence I cannot go back and find the plate whole because the energy books would not balance , so to speak.

granpa
11-10-07, 12:24 PM
fuzzy logic is not about probablity. if that were true then %100 sure in fuzzy logic would be the same as true. but its possible to be completely sure that something is true yet be wrong.

fuzzy logic is about the degree to which one believes something to be true. or the amount of evidence that one has that something is true. its more of a guess than a probability.


as for the assertion that paradoxes cant occur in reality, what about the prisoners dilemma?

the judge orders that the prisoner be executed within one year. the sheriff wishes to make the prisoner suffer so he tells him that he will hang him on a day that he doesnt expect it. the prisoner asks himself 'what is the last day that the sheriff can hang me on and still keep his word'?

the dilemma is that if the prisoner deduces that day x is the last day then when that day arrived he would be expecting to be hanged therefore the sheriff cant hang him on that day and still keep his word. ie its self-referrential. its unknowable (from the prisoners point of view).

DeepThought
11-10-07, 06:52 PM
Is the problem a linguistic or conceptual one? Or is it not a problem at all.


It's a constitutional problem.

Resulting from an over sized brain.

Cyperium
11-24-07, 08:16 PM
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.


"This statement is false" isn't a paradox.

Paradoxes open up a scenario where we can understand that we lack understanding.

Schrödingers cat, for example. How can it be both dead and alive. If the cat is dead then it didn't collapse the wavefunction. But if it was alive it did collapse the wavefunction and then there is still a 50/50 chance of it being dead or alive...

Hmmm...perhaps the solution is that the cat wouldn't die, since it would never observe the consequences that caused it to die, but only the consequences that caused it to stay alive?

Myles
12-01-07, 10:42 AM
Not enough food, water, air in the box ? Any of those could be a cause of death. The cat would collapse.

draqon
12-01-07, 10:51 AM
"this statement is false."

there are different realities of something...different dimensions of realities. It just happens that some realities resemble the others. That statement I wrote has two realities to it, one speaks of itself by existing itself and the other serves its function in being a statement.

TruthSeeker
12-01-07, 11:48 AM
Paradox is the essence of the universe.

wesmorris
12-03-07, 05:40 PM
the thing i seem to have arrived at is this:

paradoxes can exist no problem in mind, as there is nothing to prohibit them except in the long term, as they tend to screw up a mind's capacity to interface with "reality".

in "reality" however, the physical part - paradoxes don't seem to be allowed.

greenberg
12-03-07, 05:48 PM
Paradoxes open up a scenario where we can understand that we lack understanding.

The simplest way to enslave an honest and well-intended mind is to feed it a paradox.

Feed it a paradox, and the poor thing will then think that if it doesn't understand something, it is its own fault.

Upon which it will realize the need to declare itself faulty and evil.

After that, it is easy to break it and make it grant the paradox the status of The Truth.

elsyarango
12-03-07, 07:22 PM
"This statement is false" isn't a paradox.

Paradoxes open up a scenario where we can understand that we lack understanding.

Schrödingers cat, for example. How can it be both dead and alive. If the cat is dead then it didn't collapse the wavefunction. But if it was alive it did collapse the wavefunction and then there is still a 50/50 chance of it being dead or alive
why is that statement not a paradox?
i dont think shrodingers cat is a paradox. its either dead or alive. if nobody can observe the interior to find out, too bad for them.

Ogmios
12-04-07, 01:40 PM
Post quick, no time to read!

Paradox is (="defined by me") a proof that the premises of the statement are wrongly constructed.

Say, for one, what happens when an unmovable objects gets hit by an unstoppable force?

The simple answer is simply that there can not be an unstoppable force in the same reality as an unmovable object. Unstoppable force must, by necessity, have infinite amount of energy. Unmovable object must, likewise, have a depository of infinite energy; Otherwise they could be stopped, or moved, by some excessive amount of energy.

And you cannot have two times infinite amount of energy; one might argue that you cannot even have one (if you assume that energy must be finite in the universe). But, by definition, infinite is at least "everything within a system"; and it cannot be divided or multiplied without changing the amount of energy it has.

Therefore the paradox cannot be solved, but can be made irrelevant by changing the definitions of the statement to something more sensible.

Katalyst
01-03-08, 12:27 AM
I see it as this. Anything can be true and anything can be false. Theres no rule that says "This has to be true and this has to be false." Therefore a Paradox can exist. More so, they do exist.

Pronatalist
01-03-08, 12:41 AM
How many so-called "paradoxes" exist, merely because of our poor understanding of them?

For example, what happens if an irresistable force meets an unmovable object? What was that? Xeno's paradox? They played with that one, on Knight Rider, TV show. K.I.T.T. is supposedly an "indestructable" talking futuristic car, so what happens when he runs into his evil twin, K.A.R.R., also a computerized "indestructable" car? Well judging by the outcome of that episode, and by that monster semi- truck that Michael Knight's evil brother (same actor, but of course) drove, that had applied the same secret "Indestructable" formula, K.I.T.T. and K.A.R.R. weren't actually indestructable after all, just nearly so.

Actually, K.I.T.T.'s indestructability, was both kind of funny, and tragically sad. When Michael Knight found himself the willing victim of some car-theft scam, in which a woman would "accidently" rear-end him, then make off with his car, Michael said to K.I.T.T. something about think how it is for ordinary cars. "They dent." The lady was shocked that her car was messed up some, but K.I.T.T. didn't have even a scratch. Michael made up some excuse about maybe there's internal damage, so as they make to exchange insurance information, she makes off with K.I.T.T. K.I.T.T. of course, has so much technology, that K.I.T.T.'s theft easily leads them to where the stolen cars are being stashed.

Another time, some evil lady tried to shoot Michael through his closed car window. He tried to warn her, that the windows are bulletproof, but she shot herself with the ricocheted bullet anyway.