paradox existence paradox

[flamebirde]

If I say " This statement is a lie", it is a paradox. But nothing happens. The universe doesn't explode. Therefore, it is possible for paradoxes to exist. But a paradox by it's very definition defies the laws that govern our universe. Something that defies a universal law cannot exist. Therefore, a paradox existing is a paradox in itself. Sorry if I did something wrong, this is my first paradox I've thought of by myself.

[phil1882]

a paradox is simply a contradictory or obtuse statement, not necessarily a physics denying one.

its quite possible for paradoxes to be stated, they just cant exist. in what sense does a statement exist?

[flamebirde]

I think that a statement exists the instant it is conceived of. If you think " I will go bowling today", then that idea is conceived and the idea then exists. And although it is true that it doesn't have to be physics denying, it is also true that some paradoxes are physics denying.

[Aaryan]

I think that a statement exists the instant it is conceived of. If you think " I will go bowling today", then that idea is conceived and the idea then exists. And although it is true that it doesn't have to be physics denying, it is also true that some paradoxes are physics denying.

I think a paradox simply cancels itself out, considering its impossibility.

On the other hand, you can assume that paradoxes are just lies because they are impossible.

[Molly Mae]

" This statement is a lie"

On the other hand, you can assume that paradoxes are just lies because they are impossible.

It's a paradox, though, and not a lie. Reconsider flame's example.

[denverdubster]

I think that a statement exists the instant it is conceived of. If you think " I will go bowling today", then that idea is conceived and the idea then exists. And although it is true that it doesn't have to be physics denying, it is also true that some paradoxes are physics denying.

Very intelligent viewing of it flamebride, and I agree a paradox isn't a lie because it could be true but proves itself false by predisposition, but predisposition is just the nueral networks of your brain coming to a conclusion on a topic of choice based off of previous experience. The cognition of the thought is real beacause the chemicals in your brain are allowing for the creation of that thought based off of old chemical imputs. So the way I like to think of it is, as you have a dual reality in your own existence. Your thoughts are real because they are chemical, but how you think of them is in nueral connections preceived in your imagination/ cognitive thought. So its plausable to have thoughts that are paradoxical because they are your neural responce, but it technically is just a streaming of constant chemical flow and those chemicals are real and follow all processes and rules of universal law. Our brains in my oppinion are the creaters of chaos because we can so easily create faulises, but in a real way. So its easy for us to trick ourselves, for the connections you draw from are momments so small in universal construction that they mean nothing in retrospect yet the universe wouldn't function without you operating the way you do so we are everything from almost nothing! I like to add this is my personal belief as to offend no one.

[flamebirde]

I competely agree. don't you find it disturbing that our every thoughts are controlled by a combination of chemicals? and a good science fiction novel could have that at the heart of it's conflict. A dictator controls everyone's thoughts by stopping the flow of a certain chemical to the brain and letting others go through.

[mmiguel]

If I say " This statement is a lie", it is a paradox. But nothing happens. The universe doesn't explode. Therefore, it is possible for paradoxes to exist. But a paradox by it's very definition defies the laws that govern our universe. Something that defies a universal law cannot exist. Therefore, a paradox existing is a paradox in itself. Sorry if I did something wrong, this is my first paradox I've thought of by myself.

I don't think that a paradox defies any law that governs our universe.

There are no physical laws that say that statements we make or thoughts we conceive are true or false.

There is no physical law saying that a statement has to be either true or false.

A paradox does not defy anything greater than itself --- it defies itself.

i.e. it is a contradiciton.

It implies something, then implies something else that cannot be true if the first thing it implied were true.

The result is either the first thing is true, or the second thing is, but we don't know which one, and due to symmetry in the way this was asserted, we can make no meaningful conclusion.

Example: A number, x, is equal to one, and it is equal to zero.

This is a paradox, but it is not an interesting one, since it is obvious where the self-inconsistency is.

Most likely, instead of thinking of this paradox as a universe destroying statement of pure contradiction, we would write it off as nonsense.

What attracts people to other paradoxes is that they are less obvious, the implications sound more familiar, and practical thinking builds up the confidence of the person thinking about the paradox, confidence that they understand what is going on. Then at the end, they come across an inconsistency, and are not sure what to believe.

There's my two cents.

[joshuagenes]

I look at paradox as two or more different competing truth about the same object that need resolved with respect to a particular perspective. There may be resolutions to them or not but they force us to look closer to the underlying truths and this is the beautiful thing about paradoxes.

[bonanova]

If I say " This statement is a lie", it is a paradox. But nothing happens. The universe doesn't explode. Therefore, it is possible for paradoxes to exist. But a paradox by it's very definition defies the laws that govern our universe. Something that defies a universal law cannot exist. Therefore, a paradox existing is a paradox in itself. Sorry if I did something wrong, this is my first paradox I've thought of by myself.

It may or may not be a paradox. It may or may not be decidable. It may be an ill-constructed statement. It may be inadmissible to logical scrutiny. All depends on what your rules of logic, decidability and semantics are. Here are some ways out of the perceived dilemma.

1. Do not permit self-referential statements. Tarksi's approach.

   Envision levels of languages, and permit statements in one level only to refer to other statements

   on the same level or a lower one.

   Simply put, "This statement is a lie" would not be permitted: it violates our rules for statements.

2. Attach to every declarative statement the prefix: "It is true that ... " or "It is the case that ..."

   And have the prefix apply to the entire statement.

   Then we have an equivalence between these statements:

   [a] This statement is false

   This statement is true, and this statement is false.

   The paradox thus transforms to a contradiction.

   The truth value of a contradiction is False.

3. Conclude that the sentence is not decidable. We can't determine its truth value.

   The strength of the liar paradox is seen in Godel's first incompleteness theorem,

   which kind of boils down to a crushing proof of severe limitations on mathematical logic's

   ability to decide things.

So this thing might be escaped through linguistic dodges; it certainly challenges us to understand the meaning of statements; and, in concord with many who hated Godel for his contributions, it leaves us a little less satisfied with the richness of our analytical toolbox.