The Liar's paradox

[Tom Sawyer]

A sentence is as real as anything else.

Well, all that just over defines a paradox into meaninglessness. It may be syntactically correct, but it's as pointless as nipples on a breastplate. When you call someone a married bachelor, what do you mean? When you say an omnipotent guy can create a rock too heavy for him to lift, what do you mean? When you say "this sentence is false", what do you mean? If it can't reference anything outside of itself, it's not meaningful.

The point of logical analysis is to give us methods to be able to increase our understanding - it is a tool. If you simply assert a self-contradictory statement and then stop to congratulate yourself, you haven't increased any understanding. You know no more about anything than you did before you started and you can never use it change that.

A "real paradox" as opposed to a "theoretical paradox" would be an actual quality of the external universe which is contradictory and that would be really interesting. Making up word game just leaves you with a word game.

 

[DBT]

The liars paradox is neither true or false.

Easy to say. Please explain briefly why.

And do you think it should be possible to prove there is in fact no paradox.

My remark is self explanatory. The relationship of my remark to paradoxical statements such as the Liars Paradox needs no explanation, ie, the Liars Paradox itself is neither true or false. A paradox being neither true or false.

 

[Speakpigeon]

A sentence is as real as anything else.

Well, all that just over defines a paradox into meaninglessness. It may be syntactically correct, but it's as pointless as nipples on a breastplate. When you call someone a married bachelor, what do you mean? When you say an omnipotent guy can create a rock too heavy for him to lift, what do you mean? When you say "this sentence is false", what do you mean? If it can't reference anything outside of itself, it's not meaningful.

The point of logical analysis is to give us methods to be able to increase our understanding - it is a tool. If you simply assert a self-contradictory statement and then stop to congratulate yourself, you haven't increased any understanding. You know no more about anything than you did before you started and you can never use it change that.

A "real paradox" as opposed to a "theoretical paradox" would be an actual quality of the external universe which is contradictory and that would be really interesting. Making up word game just leaves you with a word game.

Yeah, I guess I have to broadly if only reluctantly agree with that, as long as you don't redefine our vocabulary all the time. The expressions "Real paradox" and "theoretical paradox" are not quite the thing but I grant you that it's the idea. If you can think of a better way to put it, I'd be interested.

Congratulation, it's not often that Speakpigeon grants a point!
EB

 

[Speakpigeon]

The liars paradox is neither true or false.

Easy to say. Please explain briefly why.

And do you think it should be possible to prove there is in fact no paradox.

My remark is self explanatory. The relationship of my remark to paradoxical statements such as the Liars Paradox needs no explanation, ie, the Liars Paradox itself is neither true or false. A paradox being neither true or false.

Oh, right, just another of your tautologies.

You address the case of a paradox by producing a tautology about paradoxes. That's kinda dark humour. Involuntary, I presume.
EB

 

[DBT]

My remark is self explanatory. The relationship of my remark to paradoxical statements such as the Liars Paradox needs no explanation, ie, the Liars Paradox itself is neither true or false. A paradox being neither true or false.

Oh, right, just another of your tautologies.

You address the case of a paradox by producing a tautology about paradoxes. That's kinda dark humour. Involuntary, I presume.
EB

Your conceit is showing again.

To observe that the Liars Paradox itself is neither true or false is not a tautology

''The hypothesis that (A) is false leads to the conclusion that (A) is true, another contradiction. Either way, (A) is both true and false, which is a paradox. However, that the liar sentence can be shown to be true if it is false and false if it is true has led some to conclude that it is "neither true nor false".'' - Wiki

''These statements are paradoxical because there is no way to assign them consistent truth values. Consider that if "This statement is false" is true, then what it says is the case; but what it says is that it is false, hence it is false. On the other hand, if it is false, then what it says is not the case; thus, since it says that it is false, it must be true.''

 

[untermensche]

The liars paradox is neither true or false.

Easy to say. Please explain briefly why.

And do you think it should be possible to prove there is in fact no paradox.

My remark is self explanatory. The relationship of my remark to paradoxical statements such as the Liars Paradox needs no explanation, ie, the Liars Paradox itself is neither true or false. A paradox being neither true or false.

It is not a paradox.

And it is always necessary to provide reasons for conclusions. A conclusion of truth is never "self explanatory".

Saying a sentence is true is merely a conclusion with no support for the conclusion.

It is just irrationality.

Hardly a paradox.

 

[Speakpigeon]

And it is always necessary to provide reasons for conclusions.

So, why do you never provide any reason for your litany of extraordinary conclusions?
EB

 

[untermensche]

And it is always necessary to provide reasons for conclusions.

So, why do you never provide any reason for your litany of extraordinary conclusions?
EB

You at least are beginning to see the issue here.

It is merely the stating of a conclusion about nothing.

It is drawing a conclusion based on nothing.

Irrationality.

No paradox.

 

[Speakpigeon]

And it is always necessary to provide reasons for conclusions.

So, why do you never provide any reason for your litany of extraordinary conclusions?
EB

You at least are beginning to see the issue here.

How could you possibly know I didn't "see the issue" even before starting this thread?

It is merely the stating of a conclusion about nothing.

It is drawing a conclusion based on nothing.

Irrationality.

No paradox.

Sorry, but these are merely vacuous claims without supporting reasons.

"And it is always necessary to provide reasons for conclusions", say Untermensche.
EB

 

[untermensche]

You at least are beginning to see the issue here.

How could you possibly know I didn't "see the issue" even before starting this thread?

It is merely the stating of a conclusion about nothing.

It is drawing a conclusion based on nothing.

Irrationality.

No paradox.

Sorry, but these are merely vacuous claims without supporting reasons.

"And it is always necessary to provide reasons for conclusions", say Untermensche.
EB

You want me to prove that to say something is true there must be a something?

 

[Testy Calibrate]

It is not a paradox because there is no referential for truth value. I've never seen a paradox that couldn't be resolved by clearing up the referents

- - - Updated - - -

How could you possibly know I didn't "see the issue" even before starting this thread?



Sorry, but these are merely vacuous claims without supporting reasons.

"And it is always necessary to provide reasons for conclusions", say Untermensche.
EB

You want me to prove that to say something is true there must be a something?

Exactly

 

[Speakpigeon]

How could you possibly know I didn't "see the issue" even before starting this thread?



Sorry, but these are merely vacuous claims without supporting reasons.

"And it is always necessary to provide reasons for conclusions", say Untermensche.
EB

You want me to prove that to say something is true there must be a something?

And of course it's only you who decides, then, whether you would need to support all those wild claims of yours.

So much more comfortable like that.
EB

- - - Updated - - -

It is not a paradox because there is no referential for truth value. I've never seen a paradox that couldn't be resolved by clearing up the referents

The referent is the sentence itself.

Which is why there is a paradox to begin with.
EB

 

[untermensche]

The referent is the sentence itself.

No. The sentence merely has a claim that it is true.

But sentences are not true or false in themselves. Sentences are a means in which information is potentially transmitted.

Some information contained within them is possibly true or false.

We may casually say the sentence is true when what we mean is the information in the sentence is true but lazy use of language is not an argument.

The sentence is where you possibly find referents. It is not a referent in itself. Only information of some kind within it can be referred to in terms of truth. It is a means of putting forth information.

Possibly.

 

[Testy Calibrate]

And of course it's only you who decides, then, whether you would need to support all those wild claims of yours.

So much more comfortable like that.
EB

- - - Updated - - -

It is not a paradox because there is no referential for truth value. I've never seen a paradox that couldn't be resolved by clearing up the referents

The referent is the sentence itself.

Which is why there is a paradox to begin with.
EB

What is its truth claim? I suspect some wiggles involved with definitions but I dunno. You tell me.

 

[DBT]

My remark is self explanatory. The relationship of my remark to paradoxical statements such as the Liars Paradox needs no explanation, ie, the Liars Paradox itself is neither true or false. A paradox being neither true or false.

It is not a paradox.

And it is always necessary to provide reasons for conclusions. A conclusion of truth is never "self explanatory".

Saying a sentence is true is merely a conclusion with no support for the conclusion.

It is just irrationality.

Hardly a paradox.

It is called the ''Liars Paradox''- but it is neither true or false for the given reason. Which I quoted;

'' However, that the liar sentence can be shown to be true if it is false and false if it is true has led some to conclude that it is "neither true nor false''

 

[untermensche]

My remark is self explanatory. The relationship of my remark to paradoxical statements such as the Liars Paradox needs no explanation, ie, the Liars Paradox itself is neither true or false. A paradox being neither true or false.

It is not a paradox.

And it is always necessary to provide reasons for conclusions. A conclusion of truth is never "self explanatory".

Saying a sentence is true is merely a conclusion with no support for the conclusion.

It is just irrationality.

Hardly a paradox.

It is called the ''Liars Paradox''- but it is neither true or false for the given reason. Which I quoted;

'' However, that the liar sentence can be shown to be true if it is false and false if it is true has led some to conclude that it is "neither true nor false''

It is not a paradox. I don't care what it is called.

There is no liar.

There is a sentence that makes an empty claim.

 

[Speakpigeon]

The referent is the sentence itself.

No. The sentence is where you possibly find referents. It is not a referent in itself. Only information of some kind within it can be referred to in terms of truth. It is a means of putting forth information.

That's true, no sentence refers to anything all by itself. Instead, we can only look at it, consider what we understand of it, and decide in the privacy of our mind whether we can make sense of the sentence as referring to something.

Well, me, I'm quite sure there's no problem understanding the sentence as referring to itself, and therefore most people should be able to understand it this way. Certainly, many philosophers and mathematicians have been able to do so throughout history.

The sentence is also a re-writing of the Paradox of the Liar, and in fact the sentence is still called today, somewhat confusingly, the Paradox of the Liar. And Liar just says: "I am lying". The effect is the same. The liar is referring to himself just as the sentence can be understood as referring to itself. And the two paradoxes have a same paradoxical consequences that the initial utterance implies the falsehood of it.

So, you're free to refuse to see the sentence as referring to itself but it's your unjustified choice.

The sentence merely has a claim that it is true.

But sentences are not true or false in themselves. Sentences are a means in which information is potentially transmitted.

Some information contained within them is possibly true or false.

We may casually say the sentence is true when what we mean is the information in the sentence is true but lazy use of language is not an argument.

Possibly.

That's true, sentences are never true or false by themselves. Instead, it's up to us to decide first whether we can take them as true or false, and is so, whether we think they are true or false.

With all assertive meaningful sentences, we can always decide by ourselves whether we think the sentence may possibly be true or false, and if so which.

However, in this case, although it is a meaningful sentence since it is a very simple sentence we can easily unpack, and although it is an assertive sentence, i.e. it asserts something about itself, we are apparently incapable of deciding whether it is true or false.

So, you're just wrong again.
EB

 

[Speakpigeon]

It is not a paradox because there is no referential for truth value. I've never seen a paradox that couldn't be resolved by clearing up the referents

The referent is the sentence itself.

Which is why there is a paradox to begin with.
EB

What is its truth claim? I suspect some wiggles involved with definitions but I dunno. You tell me.

No deep mystery here. No ambiguity. No issue with definitions. And I guess you can read English just like me. The truth claim of the sentence is that it is itself false.

And that's how it's been read by generations of philosophers and mathematicians.

There is a clear referent and there is a clear truth claim.

So, what is stopping you?!
EB

 

[Tom Sawyer]

A sentence is as real as anything else.

Well, all that just over defines a paradox into meaninglessness. It may be syntactically correct, but it's as pointless as nipples on a breastplate. When you call someone a married bachelor, what do you mean? When you say an omnipotent guy can create a rock too heavy for him to lift, what do you mean? When you say "this sentence is false", what do you mean? If it can't reference anything outside of itself, it's not meaningful.

The point of logical analysis is to give us methods to be able to increase our understanding - it is a tool. If you simply assert a self-contradictory statement and then stop to congratulate yourself, you haven't increased any understanding. You know no more about anything than you did before you started and you can never use it change that.

A "real paradox" as opposed to a "theoretical paradox" would be an actual quality of the external universe which is contradictory and that would be really interesting. Making up word game just leaves you with a word game.

Yeah, I guess I have to broadly if only reluctantly agree with that, as long as you don't redefine our vocabulary all the time. The expressions "Real paradox" and "theoretical paradox" are not quite the thing but I grant you that it's the idea. If you can think of a better way to put it, I'd be interested.

Congratulation, it's not often that Speakpigeon grants a point!
EB

Ya, I don't like the terms "real paradox" and "theoretical paradox" either, but I couldn't think of better terms to sum up the distinction I was making. The main point was that if you come to a conclusion which points to something fundamentally contradictory about actual properties of the universe, that's either a WOW moment or an indication that one of your premises are wrong. If all you can do is assert contradictory premises and show that this leads to contradictory conclusions, that's a word game which may get you a quick chuckle as a party trick if there's a group of philosophy students at that party, but really has no additional value.

 

[Speakpigeon]

Yeah, I guess I have to broadly if only reluctantly agree with that, as long as you don't redefine our vocabulary all the time. The expressions "Real paradox" and "theoretical paradox" are not quite the thing but I grant you that it's the idea. If you can think of a better way to put it, I'd be interested.

Congratulation, it's not often that Speakpigeon grants a point!
EB

Ya, I don't like the terms "real paradox" and "theoretical paradox" either, but I couldn't think of better terms to sum up the distinction I was making. The main point was that if you come to a conclusion which points to something fundamentally contradictory about actual properties of the universe, that's either a WOW moment or an indication that one of your premises are wrong. If all you can do is assert contradictory premises and show that this leads to contradictory conclusions, that's a word game which may get you a quick chuckle as a party trick if there's a group of philosophy students at that party, but really has no additional value.

I 100% sign to this but I have to warn you that this is effectively disagreeing with nearly all mathematicians, nearly all computer scientists, and a good chunk of philosophers interested in logic as well as our in-house local expert in mathematical logic here, Angra Mainyu. Do you have a good life insurance?
EB