Proof that Nothing is Impossible: C.R.A.P. Idea

[FZ+]

As part of my Current Relativist Amazingly Pragmatic (C.R.A.P.) Idea. I wish to make the following claim:

Nothing is Impossible.

The arguments behind this claim are:
1. Anecdotal evidence from quantum uncertainty etc.
2. All logical disproofs have inherent uncertainty due to inductive basis of logical procedures.
3. All logical disproofs, if relating to reality, must originate from inductive and hence uncertain assumptions.

Hence, it is impossible to show absolutely that an occurence is not merely of extremely low probability, and so nothing can be accepted as impossible.

Ok, anyone want to argue this?

 

[heusdens]

Originally posted by FZ+
As part of my Current Relativist Amazingly Pragmatic (C.R.A.P.) Idea. I wish to make the following claim:

Nothing is Impossible.

The arguments behind this claim are:
1. Anecdotal evidence from quantum uncertainty etc.
2. All logical disproofs have inherent uncertainty due to inductive basis of logical procedures.
3. All logical disproofs, if relating to reality, must originate from inductive and hence uncertain assumptions.

Hence, it is impossible to show absolutely that an occurence is not merely of extremely low probability, and so nothing can be accepted as impossible.

Ok, anyone want to argue this?

If "nothing" is "impossible" then it means "something" IS "possible".

I would say the impossible is impossible, the possible is possible.

We just have to think which is which...

There isn't mich to discuss, the idea is just CRAP!

 

[Hurkyl]

Actually, it would mean "all things are possible"

 

[heusdens]

Originally posted by Hurkyl
Actually, it would mean "all things are possible"

What are "all things" and what does it mean for them to be possible?

Are "all thing" the things that already do exist?
Then it is clear, since they do exist, that they are possible.

Or are "all things" all things that could in principle exist. Which is to say: things that can possibly exist, because the impossible things, can not exist.

Then, if it is possible for something to exist, and yet it doesn't exist, why doesn't it exist, if it is said to be possible?

This can easility become a boundless, baseless discussion, or form into a tautlogical debate. How can we know about all possible things, apart from those being really existent?

And since impossible things, can not exist, you only claim that possible things can possibly exist. Which is to say: the possible is possible, or all things that are possible are possible. But that is just a tautological statement.

Conclusion: your statement is void, has no content, and is tautological.

 

[wuliheron]

Originally posted by FZ+
As part of my Current Relativist Amazingly Pragmatic (C.R.A.P.) Idea. I wish to make the following claim:

Nothing is Impossible.

The arguments behind this claim are:
1. Anecdotal evidence from quantum uncertainty etc.
2. All logical disproofs have inherent uncertainty due to inductive basis of logical procedures.
3. All logical disproofs, if relating to reality, must originate from inductive and hence uncertain assumptions.

Hence, it is impossible to show absolutely that an occurence is not merely of extremely low probability, and so nothing can be accepted as impossible.

Ok, anyone want to argue this?

About the only practical application of such an argument would be to bolster support for maintaining an open mind, but it does not suggest how this is accomplished. Hence it is useless. In my opinion, you left out the most interesting, critical, and useful arguments, demonstrating that you have a firm grasp of C.R.A.P. if not pragmatism.

 

[quantumdude]

Originally posted by heusdens
Conclusion: your statement is void, has no content, and is tautological.

It is not his statement. He is just applying Logic 101 to the statement:

Nothing is impossible.

Put in standard form as a categorical statement:

No things are in the class of things that are impossble.

or

No T are I.

This is logically equivalent to:

All T are not I.

or

All things are in the class of things that are not impossible.

Since "not impossible"="possible", we have Hurkyl's statement. If his statement is void, then so is the first one. It's not his fault, cause it's all he had to work with! (C.R.A.P.)

 

[heusdens]

Originally posted by Tom
It is not his statement. He is just applying Logic 101 to the statement:

Nothing is impossible.

Put in standard form as a categorical statement:

No things are in the class of things that are impossble.

or

No T are I.

This is logically equivalent to:

All T are not I.

or

All things are in the class of things that are not impossible.

Since "not impossible"="possible", we have Hurkyl's statement. If his statement is void, then so is the first one. It's not his fault, cause it's all he had to work with! (C.R.A.P.)

I agree the truth content of both statement are the same.

But it forms a tautology, cause things which exist, have to be possible, else they would not exist. Hence to say all things are possible is a tautology.

 

[FZ+]

Now let's not get emotional, do we?

Let's rephrase, since we are limiting the concept of things to things that are existent.

All statements, no matter how absurd, have a probability of being in reality true that is greater than 0.

About the only practical application of such an argument would be to bolster support for maintaining an open mind, but it does not suggest how this is accomplished. Hence it is useless.

Not neccessarily. It is merely a claim in itself (or a proposal of one), and I think the consideration of the practical usefulness of a hypothesis is not relevant at this point. I merely ask if people agree or disagree with it.

 

[quantumdude]

Originally posted by FZ+
All statements, no matter how absurd, have a probability of being in reality true that is greater than 0.

No, for some statements it is impossible for them to be true by their logical structure. You heard Heusdens mention "tautologies", which are schemas that are true no matter what the value of the logical variables. Just negate a tautology and you get a "contradiction", which is always false.

Example:

p OR ~p

is a tautology and

~(p OR ~p)

is a contradiction.

 

[wuliheron]

Originally posted by FZ+
Now let's not get emotional, do we?

Let's rephrase, since we are limiting the concept of things to things that are existent.

All statements, no matter how absurd, have a probability of being in reality true that is greater than 0.


Not neccessarily. It is merely a claim in itself (or a proposal of one), and I think the consideration of the practical usefulness of a hypothesis is not relevant at this point. I merely ask if people agree or disagree with it.

Claim in and of itself with no obvious practical application is not pragmatic by definition of the word. In addition, expanding on what Tom already pointed out more or less, not everything is equally absurd or, if it is, discussing the idea is useless excepting possibly for spiritual purposes. In addition, some things are simply Indeterminate, and cannot be axiomatically assigned a truth value.

 

[FZ+]

Originally posted by Tom
No, for some statements it is impossible for them to be true by their logical structure. You heard Heusdens mention "tautologies", which are schemas that are true no matter what the value of the logical variables. Just negate a tautology and you get a "contradiction", which is always false.

Example:

p OR ~p

is a tautology and

~(p OR ~p)

is a contradiction.

But what if the construct with which you establish ~(p OR ~p) itself has an element of uncertainty?

 

[quantumdude]

Originally posted by FZ+
But what if the construct with which you establish ~(p OR ~p) itself has an element of uncertainty?

Let's check it.

p...~p...(p OR ~p)...~(p OR ~p)
T...F ...T.....F
F...T...T.....F

The construct is always false, no matter what the truth value of p is.

edit: fixed truth table

 

[FZ+]

No, what I meant is that (stepping into murky territory here) what if the principles behind the truth tables themselves were in fact false? Can we justify the ideas of the truth table, without reference to itself?

 

[wuliheron]

Originally posted by FZ+
No, what I meant is that (stepping into murky territory here) what if the principles behind the truth tables themselves were in fact false? Can we justify the ideas of the truth table, without reference to itself?

According to Godel's theorm, the answer is no. Any system you use must be ultimately based on faith as much as anything else. In this case, faith that the truth values we assign reflect reality meaningfully at the very least. This is partly why I keep insisting that your claim as it is stated is not terribly pragmatic.

There are actually two distinct ways to address this problem. One is to develop a logic that reflects nature as closely as possible, a kind of pantheistic logistics if modern physics are any indication. The alternative is to take the semantic route as I do. Rather than attempting some kind of rigorous Logistical TOE, I'm working on a vague natural language generalization of what such logic might be.

It seems likely to assume we may have to constantly update and refine any Logistical TOE for the indefinite future. Rather than waiting for the rigorous logic to be developed, we can take what we already know about nature and develop a gross generalization based on what we already know. Precisely because it is so vague yet ubiquitous and so much has already been written on the subject, the paradox of existence presents an excellent starting point for such a process.

 

[ahrkron]

Originally posted by wuliheron
According to Godel's theorm, the answer is no.

Godel's theorem applies only to axiomatic systems that can represent at least integer arithmetic (the exact requirements are slightly different).

The truth table in question refers to statements that need less than that (first order logic suffices), and hence Godel's theorem does not apply in this case.

 

[ahrkron]

Originally posted by FZ+
what if the principles behind the truth tables themselves were in fact false?

They cannot, since truth tables are built according to the rules we use to define the truth value of a statement. Please notice that this has nothing to do with the definition of truth itself, but with the definition of our connectives for statements.

i.e., We define the connector "and" saying that it can be applied when certain conditions apply between the truth of A, B and the phrase "A and B".

Whatever "being true" means, we say that the logical connector "AND" is to be used like so:

The statement "A AND B" is true if it simultaneously happens that
1. A is true,
2. B is true.

Can we justify the ideas of the truth table, without reference to itself?

Yes. It is a clear way of obtaining the truth value of a statement, based on the definition of the connectors it uses, plus the possible truth values of each component of the statement.

 

[wuliheron]

Originally posted by ahrkron
Godel's theorem applies only to axiomatic systems that can represent at least integer arithmetic (the exact requirements are slightly different).

The truth table in question refers to statements that need less than that (first order logic suffices), and hence Godel's theorem does not apply in this case.

In that case, his claim is even less useful than I thought since you can't even use it to do simple arithematic.

quote:
--------------------------------------------------------------------------------
Can we justify the ideas of the truth table, without reference to itself?
--------------------------------------------------------------------------------

Yes. It is a clear way of obtaining the truth value of a statement, based on the definition of the connectors it uses, plus the possible truth values of each component of the statement.

For a statement about formal logic, this is a bit vague and misleading in my opinion. As you alluded to yourself, exactly what "truth" means in this context is debatable and modern logicians often prefer to avoid the term altogether. Unless you can define the "truth" then you are not justifying the Truth Table itself, but merely its internal operations.

 

[ahrkron]

Wuli, I think you got confused.

FZ asked "Can we justify the ideas of the truth table, without reference to itself?"

to which you answered "According to Godel's theorm, the answer is no."

then I said that such principles require less than what enables the use of Godel's theorem.

Originally posted by wuliheron
In that case, his claim is even less useful than I thought since you can't even use it to do simple arithematic.

A claim does not need to be "used to do simple arithmetic" in order to apply Godel's theorem to the system in which it is built.

Also, the least requirements a claim needs, the more more powerful (or useful) it is. If a claim only needs basic logic, you can apply it to many more things than when it talks about systems that have lots of structure.

For example, the fact that "p OR ~p" is a tautology is far more useful and applicable than a theorem about the metric properties of differential manifolds with positive curvature.

Unless you can define the "truth" then you are not justifying the Truth Table itself, but merely its internal operations.

I disagree. Truth tables are justified in the way we define the connectors AND, OR, NOT, and how they relate to the truth of a statement. They cannot be "wrong" or "unjustified" since it is all definitions.

The problem is when checking the truth value of the elemental statements used, but once that is done, the truth table applies because it is just an application of our own definitions. The usefulness of truth tables comes precisely from this decoupling from the philosophical problem of truth.

 

[wuliheron]

Originally posted by ahrkron
Wuli, I think you got confused.

A claim does not need to be "used to do simple arithmetic" in order to apply Godel's theorem to the system in which it is built.

Also, the least requirements a claim needs, the more more powerful (or useful) it is. If a claim only needs basic logic, you can apply it to many more things than when it talks about systems that have lots of structure.

Yes, but simple arithmetic is a rudamentary function that presents a qualitative leap in magnetude as to how fast we can deduce things. Thus the claim that the more simple the system the more powerful it is only applies if you discount the amount of time required to use the system.

I disagree. Truth tables are justified in the way we define the connectors AND, OR, NOT, and how they relate to the truth of a statement. They cannot be "wrong" or "unjustified" since it is all definitions.

The problem is when checking the truth value of the elemental statements used, but once that is done, the truth table applies because it is just an application of our own definitions. The usefulness of truth tables comes precisely from this decoupling from the philosophical problem of truth.

Again, if you cannot define "truth" then the relationship is dubious and the conclusion is unjustifiable by your own definition. To say that how connectors relate to the truth of a statement justifies them contradicts your other assertion that you are decoupling from the philosophical problem of truth.

 

[Mohaamad]

FZ's argument makes perfect sense to me.

All logical conclusions are interdependent on other logical conclusions, eventually to an inherent conclusion (conclusions that are intrinsically sensible) and ultimately to a paradoxical conclusion.

Simply because a paradox is the only way our minds can conceptualize a logical conclusion that is absolutely inherent in and of itself. We can just accept it. As we do with the paradox of the quantum mechanics propositions. There is no possibility of manipulating the conclusion; it is untouchable and by this property alone we can propose that it is an inherent conclusion simply because: 1)we know that paradoxical conclusions exist (as with quantum theory) 2)we know that eventually we have to have a conclusion has to be inherent in and of itself (that is we know that it has to exist) 3) Thus paradoxical conclusions such as that of quantum mechanics pose a good candidate for an inherent conclusion.

 

[Mentat]

I, obviously, am going to disagree with FZ+'s statement, and with Hurkyl's variation because:

FZ+'s statement is: Nothing is impossible. This means that it is impossible for something to be impossible. But, then there is one impossibility, the impossibility of impossibilities. Basically, it's a paradox, since the statement cannot be proven true or false.

Hurkyl's statement is: Everything is possible. This runs into the same paradox because, if everything is possible, then it must be possible for something to be impossible...paradox.

 

[LogicalAtheist]

See how easily you are able to CRUSH those claims mentat? Good for you.

One builds up for who knows how long, only to be ruined in a second.

Rome took forever to build, but fell in short time!

mentat.intelligent = true

 

[Mentat]

Originally posted by LogicalAtheist
See how easily you are able to CRUSH those claims mentat? Good for you.

One builds up for who knows how long, only to be ruined in a second.

Rome took forever to build, but fell in short time!

mentat.intelligent = true

You flatter me, but thank you.

 

[FZ+]

ahrkron: I see. So you say that impossibilities exist as they are defined to be impossible? Does this then neccessarily have relation to impossibilities in reality then?

Originally posted by Mentat
FZ+'s statement is: Nothing is impossible. This means that it is impossible for something to be impossible. But, then there is one impossibility, the impossibility of impossibilities. Basically, it's a paradox, since the statement cannot be proven true or false.

Thank you. That was what I was waiting for.

 

[Mentat]

Originally Posted By FZ+
Thank you. That was what I was waiting for. [/B]

But I thought you were making a case for the idea that nothing is impossible.

 

[FZ+]

A disproof is sometimes more interesting than a long and repetitive argument, or even a dubious proof...

I wonder though if it can be valid if we create some restrictions? Ie. No statement that relates to reality can be impossible? ie. allow impossibility for purely internal ideas... Or is the problem still there?

 

[Mentat]

Originally posted by FZ+
A disproof is sometimes more interesting than a long and repetitive argument, or even a dubious proof...

I wonder though if it can be valid if we create some restrictions? Ie. No statement that relates to reality can be impossible? ie. allow impossibility for purely internal ideas... Or is the problem still there?

Yeah, there's still a problem. You are saying that the new proposition is, "No statement that relates to external reality can be impossible", right? If so, then the problem is now the fact that you are making a statement about statements about external reality. I think (though I'm not positive) that this runs into Russel's paradox.

 

[quantumdude]

Originally posted by FZ+
ahrkron: I see. So you say that impossibilities exist as they are defined to be impossible? Does this then neccessarily have relation to impossibilities in reality then?

Yes. The tautology (x OR ~x) is always true by construction.

As a concrete example:

x="The light is on".

So the compound statement is:

"The light is on or it is not the case that the light is on."

or, more colloquially,

"The light is on or the light is off."

That is true, regardless of whether the light is on or not. So negating it creates a false statement, again independent of whether the light is actually on.

 

[wuliheron]

Originally posted by FZ+
A disproof is sometimes more interesting than a long and repetitive argument, or even a dubious proof...

I wonder though if it can be valid if we create some restrictions? Ie. No statement that relates to reality can be impossible? ie. allow impossibility for purely internal ideas... Or is the problem still there?

Again, the restrictions you can put on it is called multi-value logic and semantics. Rather than settling for true or false, you expand upon the values of a logical system by adding new catagories like the "Indeterminate" or you resort to the pragmatic semantics of natural language. These two approaches are steadily converging as we speak towards a more global rational understanding of both the physical and linguistic realms at the very least.

In other words, cutting edge philosophy today is coverging on this problem and either logisticians, mathematicians, computer scientists, or physicists will beat them to the punch or not. What has emerged in the process is that the more profoundly spare Asian philosophies have become of interest to national defense industries among others. What we don't know is of more keen interest sometimes than what we do know.