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Resolution of the Liar's Paradox

dylancatlow
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12/9/2015 7:00:45 PM
Posted: 1 year ago
In its simplest formulation, the Liar's Paradox runs as follows:

Take the statement "This sentence is false".

If the statement is true, then it is false, since that's what it's claiming to be the case.
But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.

How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.

It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.
ShabShoral
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12/9/2015 7:25:23 PM
Posted: 1 year ago
At 12/9/2015 7:00:45 PM, dylancatlow wrote:
In its simplest formulation, the Liar's Paradox runs as follows:

Take the statement "This sentence is false".

If the statement is true, then it is false, since that's what it's claiming to be the case.
But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.

How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.

It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.

How does this solve anything? If it's merely saying two different things, you should be able to isolate those things and give the truth values of each individually. The problem is that, if you try to do so, you end here:

"This statement is false"
and
"This statement is true"

Which resolves nothing; you've just produced another contradiction and a tautology.
"This site is trash as a debate site. It's club penguin for dysfunctional adults."

~ Skepsikyma <3

"Your idea of good writing is like Spinoza mixed with Heidegger."

~ Dylly Dylly Cat Cat

"You seem to aspire to be a cross between a Jewish hipster, an old school WASP aristocrat, and a political iconoclast"

~ Thett the Mighty

"fvck omg ur face"

~ Liz

"No aspect of your facial structure suggests Filipino descent."
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dylancatlow
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12/9/2015 7:35:23 PM
Posted: 1 year ago
At 12/9/2015 7:25:23 PM, ShabShoral wrote:
At 12/9/2015 7:00:45 PM, dylancatlow wrote:
In its simplest formulation, the Liar's Paradox runs as follows:

Take the statement "This sentence is false".

If the statement is true, then it is false, since that's what it's claiming to be the case.
But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.

How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.

It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.

How does this solve anything? If it's merely saying two different things, you should be able to isolate those things and give the truth values of each individually. The problem is that, if you try to do so, you end here:

"This statement is false"
and
"This statement is true"

Which resolves nothing; you've just produced another contradiction and a tautology.

By showing that the statement is paradoxical, I show that logic does not lead to paradox, but merely transforms a paradox into another paradox, which is not a problem for logic. Paradoxical implications of a paradoxical statement do not prove that logic is flawed.

Of course, it is easy to assign truth values to the two opposing statements.

"This statement is false" - true, because contradictory

"This statement is true" - false, because contradictory
ShabShoral
Posts: 3,245
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12/9/2015 7:39:10 PM
Posted: 1 year ago
At 12/9/2015 7:35:23 PM, dylancatlow wrote:
At 12/9/2015 7:25:23 PM, ShabShoral wrote:
At 12/9/2015 7:00:45 PM, dylancatlow wrote:
In its simplest formulation, the Liar's Paradox runs as follows:

Take the statement "This sentence is false".

If the statement is true, then it is false, since that's what it's claiming to be the case.
But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.

How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.

It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.

How does this solve anything? If it's merely saying two different things, you should be able to isolate those things and give the truth values of each individually. The problem is that, if you try to do so, you end here:

"This statement is false"
and
"This statement is true"

Which resolves nothing; you've just produced another contradiction and a tautology.

By showing that the statement is paradoxical, I show that logic does not lead to paradox, but merely transforms a paradox into another paradox, which is not a problem for logic. Paradoxical implications of a paradoxical statement do not prove that logic is flawed.
The existence of a paradox in the first place is logically impossible, for a paradox has conflicting truth-values. A or not-A - there is no alternative in logic, no matter how "contained" you would like to believe the contradiction is.
Of course, it is easy to assign truth values to the two opposing statements.

"This statement is false" - true, because contradictory
Did you not just say that "This statement is false" could not be given a truth value because it is really saying two different things?
"This statement is true" - false, because contradictory
The statement, by your own admission, is true. No paradox has been resolved.
"This site is trash as a debate site. It's club penguin for dysfunctional adults."

~ Skepsikyma <3

"Your idea of good writing is like Spinoza mixed with Heidegger."

~ Dylly Dylly Cat Cat

"You seem to aspire to be a cross between a Jewish hipster, an old school WASP aristocrat, and a political iconoclast"

~ Thett the Mighty

"fvck omg ur face"

~ Liz

"No aspect of your facial structure suggests Filipino descent."
~ YYW
dylancatlow
Posts: 12,255
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12/9/2015 7:43:00 PM
Posted: 1 year ago
At 12/9/2015 7:39:10 PM, ShabShoral wrote:
At 12/9/2015 7:35:23 PM, dylancatlow wrote:
At 12/9/2015 7:25:23 PM, ShabShoral wrote:
At 12/9/2015 7:00:45 PM, dylancatlow wrote:
In its simplest formulation, the Liar's Paradox runs as follows:

Take the statement "This sentence is false".

If the statement is true, then it is false, since that's what it's claiming to be the case.
But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.

How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.

It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.

How does this solve anything? If it's merely saying two different things, you should be able to isolate those things and give the truth values of each individually. The problem is that, if you try to do so, you end here:

"This statement is false"
and
"This statement is true"

Which resolves nothing; you've just produced another contradiction and a tautology.

By showing that the statement is paradoxical, I show that logic does not lead to paradox, but merely transforms a paradox into another paradox, which is not a problem for logic. Paradoxical implications of a paradoxical statement do not prove that logic is flawed.
The existence of a paradox in the first place is logically impossible, for a paradox has conflicting truth-values. A or not-A - there is no alternative in logic, no matter how "contained" you would like to believe the contradiction is.

Constructing a sentence with conflicting claims is not impossible. Hence, Paradoxical statement. But you are right that paradoxes can't exist in the sense of being manifested in reality.

Of course, it is easy to assign truth values to the two opposing statements.

"This statement is false" - true, because contradictory
Did you not just say that "This statement is false" could not be given a truth value because it is really saying two different things?

That's why I separated it into its two components. See below.

"This statement is true" - false, because contradictory
The statement, by your own admission, is true. No paradox has been resolved.

What.
000ike
Posts: 11,196
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12/9/2015 7:45:09 PM
Posted: 1 year ago
At 12/9/2015 7:00:45 PM, dylancatlow wrote:
In its simplest formulation, the Liar's Paradox runs as follows:

Take the statement "This sentence is false".

If the statement is true, then it is false, since that's what it's claiming to be the case.
But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.

How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.

It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.

So your solution to the paradox is that the sentence makes no coherent propositional sense (i.e. it's a paradox).....
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
ShabShoral
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12/9/2015 7:45:38 PM
Posted: 1 year ago
At 12/9/2015 7:43:00 PM, dylancatlow wrote:
At 12/9/2015 7:39:10 PM, ShabShoral wrote:
At 12/9/2015 7:35:23 PM, dylancatlow wrote:
At 12/9/2015 7:25:23 PM, ShabShoral wrote:
At 12/9/2015 7:00:45 PM, dylancatlow wrote:
In its simplest formulation, the Liar's Paradox runs as follows:

Take the statement "This sentence is false".

If the statement is true, then it is false, since that's what it's claiming to be the case.
But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.

How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.

It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.

How does this solve anything? If it's merely saying two different things, you should be able to isolate those things and give the truth values of each individually. The problem is that, if you try to do so, you end here:

"This statement is false"
and
"This statement is true"

Which resolves nothing; you've just produced another contradiction and a tautology.

By showing that the statement is paradoxical, I show that logic does not lead to paradox, but merely transforms a paradox into another paradox, which is not a problem for logic. Paradoxical implications of a paradoxical statement do not prove that logic is flawed.
The existence of a paradox in the first place is logically impossible, for a paradox has conflicting truth-values. A or not-A - there is no alternative in logic, no matter how "contained" you would like to believe the contradiction is.

Constructing a sentence with conflicting claims is not impossible. Hence, Paradoxical statement. But you are right that paradoxes can't exist in the sense of being manifested in reality.
Constructing such a sentence with any sense is impossible, and, if a sentence has no sense, it has no truth-grounds in the first place, therefore leaving no room for a paradox.
Of course, it is easy to assign truth values to the two opposing statements.

"This statement is false" - true, because contradictory
Did you not just say that "This statement is false" could not be given a truth value because it is really saying two different things?

That's why I separated it into its two components. See below.
""This statement is false" - true"
That looks an awful lot like giving it a truth value to me...
"This statement is true" - false, because contradictory
The statement, by your own admission, is true. No paradox has been resolved.

What.

""This statement is false" - true"

If it is true, then "this statement is true" is true.
"This site is trash as a debate site. It's club penguin for dysfunctional adults."

~ Skepsikyma <3

"Your idea of good writing is like Spinoza mixed with Heidegger."

~ Dylly Dylly Cat Cat

"You seem to aspire to be a cross between a Jewish hipster, an old school WASP aristocrat, and a political iconoclast"

~ Thett the Mighty

"fvck omg ur face"

~ Liz

"No aspect of your facial structure suggests Filipino descent."
~ YYW
dylancatlow
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12/9/2015 7:49:59 PM
Posted: 1 year ago
At 12/9/2015 7:45:09 PM, 000ike wrote:
At 12/9/2015 7:00:45 PM, dylancatlow wrote:
In its simplest formulation, the Liar's Paradox runs as follows:

Take the statement "This sentence is false".

If the statement is true, then it is false, since that's what it's claiming to be the case.
But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.

How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.

It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.

So your solution to the paradox is that the sentence makes no coherent propositional sense (i.e. it's a paradox).....

The sentence makes two coherent but opposed claims at once. It begins as a paradox, so attempting to assign a single truth value to it invariably leads to a paradox because a single truth value will make sense for one of the components but not the other.
000ike
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12/9/2015 7:55:22 PM
Posted: 1 year ago
At 12/9/2015 7:49:59 PM, dylancatlow wrote:
At 12/9/2015 7:45:09 PM, 000ike wrote:
At 12/9/2015 7:00:45 PM, dylancatlow wrote:
In its simplest formulation, the Liar's Paradox runs as follows:

Take the statement "This sentence is false".

If the statement is true, then it is false, since that's what it's claiming to be the case.
But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.

How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.

It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.

So your solution to the paradox is that the sentence makes no coherent propositional sense (i.e. it's a paradox).....

The sentence makes two coherent but opposed claims at once. It begins as a paradox, so attempting to assign a single truth value to it invariably leads to a paradox because a single truth value will make sense for one of the components but not the other.

"the sentence makes two coherent but opposed claims at once"....that's literally how a paradox is defined.... you're basically describing the contradiction not resolving it. Perhaps in conceiving it as two separate claims your idea is that we assess their truth value independently rather than simultaneously,.... but that's kind of absurd given that the sentence doesn't allow that independent assessment. If the statement is true, then that means the statement is false, which means it's true, and so on.
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
ShabShoral
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12/9/2015 7:58:42 PM
Posted: 1 year ago
At 12/9/2015 7:55:22 PM, 000ike wrote:
"the sentence makes two coherent but opposed claims at once"....that's literally how a paradox is defined.... you're basically describing the contradiction not resolving it. Perhaps in conceiving it as two separate claims your idea is that we assess their truth value independently rather than simultaneously,.... but that's kind of absurd given that the sentence doesn't allow that independent assessment. If the statement is true, then that means the statement is false, which means it's true, and so on.

Have I told you that I love you recently?

I love you.
"This site is trash as a debate site. It's club penguin for dysfunctional adults."

~ Skepsikyma <3

"Your idea of good writing is like Spinoza mixed with Heidegger."

~ Dylly Dylly Cat Cat

"You seem to aspire to be a cross between a Jewish hipster, an old school WASP aristocrat, and a political iconoclast"

~ Thett the Mighty

"fvck omg ur face"

~ Liz

"No aspect of your facial structure suggests Filipino descent."
~ YYW
000ike
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12/9/2015 8:06:52 PM
Posted: 1 year ago
At 12/9/2015 7:58:42 PM, ShabShoral wrote:
At 12/9/2015 7:55:22 PM, 000ike wrote:
"the sentence makes two coherent but opposed claims at once"....that's literally how a paradox is defined.... you're basically describing the contradiction not resolving it. Perhaps in conceiving it as two separate claims your idea is that we assess their truth value independently rather than simultaneously,.... but that's kind of absurd given that the sentence doesn't allow that independent assessment. If the statement is true, then that means the statement is false, which means it's true, and so on.

Have I told you that I love you recently?

I love you.

lol just calling it as I see it.
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
dylancatlow
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12/9/2015 8:09:13 PM
Posted: 1 year ago
At 12/9/2015 7:55:22 PM, 000ike wrote:
At 12/9/2015 7:49:59 PM, dylancatlow wrote:
At 12/9/2015 7:45:09 PM, 000ike wrote:
At 12/9/2015 7:00:45 PM, dylancatlow wrote:
In its simplest formulation, the Liar's Paradox runs as follows:

Take the statement "This sentence is false".

If the statement is true, then it is false, since that's what it's claiming to be the case.
But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.

How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.

It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.

So your solution to the paradox is that the sentence makes no coherent propositional sense (i.e. it's a paradox).....

The sentence makes two coherent but opposed claims at once. It begins as a paradox, so attempting to assign a single truth value to it invariably leads to a paradox because a single truth value will make sense for one of the components but not the other.

"the sentence makes two coherent but opposed claims at once"....that's literally how a paradox is defined.... you're basically describing the contradiction not resolving it. Perhaps in conceiving it as two separate claims your idea is that we assess their truth value independently rather than simultaneously,.... but that's kind of absurd given that the sentence doesn't allow that independent assessment. If the statement is true, then that means the statement is false, which means it's true, and so on.

No it's not. A paradox is defined as "A seemingly true contradiction". It begins as a contradiction, but ends up as a paradox because people forget that it began as a contradiction. Logic did not create the paradox. The paradox originates from the fact that logic is being applied to two statements as though they were one. That is not the fault of logic, but of those applying it.

I am therefore "resolving" the paradox in the sense that I'm showing that logic only leads to contradiction if applied to contradictory statements, which hardly proves that logic is flawed.
dylancatlow
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12/9/2015 8:21:24 PM
Posted: 1 year ago
It would be a paradox if we started with a non-contradictory statement, applied logic to it, and end up with a contradiction, because in that case it at least seems like the contradiction is true. But since the Liar's Paradox begins with a contradiction, logic cannot be faulted for the contradictory conclusion it reaches. In fact, it would be contradictory if a contradictory statement didn't logically have contradictory implications.
000ike
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12/9/2015 8:22:35 PM
Posted: 1 year ago
At 12/9/2015 8:09:13 PM, dylancatlow wrote:

No it's not. A paradox is defined as "A seemingly true contradiction". It begins as a contradiction, but ends up as a paradox because people forget that it began as a contradiction. Logic did not create the paradox. The paradox originates from the fact that logic is being applied to two statements as though they were one. That is not the fault of logic, but of those applying it.

I am therefore "resolving" the paradox in the sense that I'm showing that logic only leads to contradiction if applied to contradictory statements, which hardly proves that logic is flawed.

That's the colloquial definition of a paradox (e.g. The GOP is concerned about excessive federal spending, yet proposes to arrogate more funds to the defense budget, what a paradox). A paradox in a logical sense is precisely the sentence we're discussing.

Let's be clear. The sentence makes only 1 claim, but has an assumption in conflict with its claim. You cannot separate the assumption from the claim. Every time the claim is made the assumption accompanies it. The sentence is a paradox by virtue of the fact that the assumption is fundamentally inseparable from the claim.

Your conception of the paradox is that it makes two claims in the same way that "This shape is a square. This shape is a circle" is a pair of separate statements that cannot both be true. What you're neglecting is that the pair of statements I just quoted have no necessary connection, and therefore it would be an analytical error to claim that they're a paradox. What makes "this statement is false" a paradox is that there IS a necessary connection ... they're not separable.
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
SM2
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12/9/2015 8:25:14 PM
Posted: 1 year ago
At 12/9/2015 7:00:45 PM, dylancatlow wrote:
It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.

This hits the nail on the head, and is an example of how we can twist language to describe stuff that isn't real.
dylancatlow
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12/9/2015 8:28:48 PM
Posted: 1 year ago
At 12/9/2015 8:22:35 PM, 000ike wrote:
At 12/9/2015 8:09:13 PM, dylancatlow wrote:

No it's not. A paradox is defined as "A seemingly true contradiction". It begins as a contradiction, but ends up as a paradox because people forget that it began as a contradiction. Logic did not create the paradox. The paradox originates from the fact that logic is being applied to two statements as though they were one. That is not the fault of logic, but of those applying it.

I am therefore "resolving" the paradox in the sense that I'm showing that logic only leads to contradiction if applied to contradictory statements, which hardly proves that logic is flawed.

That's the colloquial definition of a paradox (e.g. The GOP is concerned about excessive federal spending, yet proposes to arrogate more funds to the defense budget, what a paradox). A paradox in a logical sense is precisely the sentence we're discussing.

It's the other way around actually. If paradox simply meant contradiction, they wouldn't be worth discussing. I mean take the notion of a circular square. Is that really in need of resolution? No.


Let's be clear. The sentence makes only 1 claim, but has an assumption in conflict with its claim. You cannot separate the assumption from the claim. Every time the claim is made the assumption accompanies it. The sentence is a paradox by virtue of the fact that the assumption is fundamentally inseparable from the claim.


That's kind of the point. In order to make a claim, one must take take on board the idea that one is asserting truth. It's unavoidable. That's why it's a paradox, because merely by being a statement it's self-contradictory.

Your conception of the paradox is that it makes two claims in the same way that "This shape is a square. This shape is a circle" is a pair of separate statements that cannot both be true. What you're neglecting is that the pair of statements I just quoted have no necessary connection, and therefore it would be an analytical error to claim that they're a paradox. What makes "this statement is false" a paradox is that there IS a necessary connection ... they're not separable.

They're inseparable in the sense that one invariably implies the other, but one can separate them in the sense of identifying them as distinct yet mutually supportive claims. If that weren't possible, you wouldn't be able to make the argument you are now making.
000ike
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12/9/2015 8:30:16 PM
Posted: 1 year ago
At 12/9/2015 8:21:24 PM, dylancatlow wrote:
It would be a paradox if we started with a non-contradictory statement, applied logic to it, and end up with a contradiction, because in that case it at least seems like the contradiction is true. But since the Liar's Paradox begins with a contradiction, logic cannot be faulted for the contradictory conclusion it reaches. In fact, it would be contradictory if a contradictory statement didn't logically have contradictory implications.

That's the most absurd thing I've ever heard (and that's not hyperbole -- I mean it). You're confusing the epistemic evolution that arises from the temporal nature of logical analysis with an ontological fact about what the statement in question is.

A non-contradictory statement does not become contradictory. It was either contradictory from the start or it wasn't.

Now I really don't know what you mean with this talk of "faulting logic".... but that has little to do with whether the statement is a paradox or it isn't.
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
dylancatlow
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12/9/2015 8:43:23 PM
Posted: 1 year ago
At 12/9/2015 8:30:16 PM, 000ike wrote:
At 12/9/2015 8:21:24 PM, dylancatlow wrote:
It would be a paradox if we started with a non-contradictory statement, applied logic to it, and end up with a contradiction, because in that case it at least seems like the contradiction is true. But since the Liar's Paradox begins with a contradiction, logic cannot be faulted for the contradictory conclusion it reaches. In fact, it would be contradictory if a contradictory statement didn't logically have contradictory implications.

That's the most absurd thing I've ever heard (and that's not hyperbole -- I mean it). You're confusing the epistemic evolution that arises from the temporal nature of logical analysis with an ontological fact about what the statement in question is.


Nothing I'm saying should be controversial.

A non-contradictory statement does not become contradictory. It was either contradictory from the start or it wasn't.

That's exactly why all paradoxes have resolutions.


Now I really don't know what you mean with this talk of "faulting logic".... but that has little to do with whether the statement is a paradox or it isn't.

In order for there to be a paradox, one must show that logically speaking, a contradiction is implied to be true. Just because you can describe a contradiction doesn't mean logic implies that it is true (or appears to at least). Thus, in order to maintain that the Liar's Paradox is unresolvable, you have to show that logic is being correctly applied to a non-contradictory statement. If logic is being correctly applied to a contradictory statement, then any "logical implications" are meaningless and don't prove that there is a true contradiction anywhere.
Not sure why you and bossy aren't getting it.
dylancatlow
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12/9/2015 8:51:19 PM
Posted: 1 year ago
So in other words, "This sentence is false" is both true and false at the same time, but only because it's saying two different things entirely. That doesn't prove that there's a "true contradiction" anymore than the idea of a circular square does.
000ike
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12/9/2015 8:55:35 PM
Posted: 1 year ago
At 12/9/2015 8:43:23 PM, dylancatlow wrote:
At 12/9/2015 8:30:16 PM, 000ike wrote:
At 12/9/2015 8:21:24 PM, dylancatlow wrote:
It would be a paradox if we started with a non-contradictory statement, applied logic to it, and end up with a contradiction, because in that case it at least seems like the contradiction is true. But since the Liar's Paradox begins with a contradiction, logic cannot be faulted for the contradictory conclusion it reaches. In fact, it would be contradictory if a contradictory statement didn't logically have contradictory implications.

That's the most absurd thing I've ever heard (and that's not hyperbole -- I mean it). You're confusing the epistemic evolution that arises from the temporal nature of logical analysis with an ontological fact about what the statement in question is.


Nothing I'm saying should be controversial.

A non-contradictory statement does not become contradictory. It was either contradictory from the start or it wasn't.

That's exactly why all paradoxes have resolutions.


Now I really don't know what you mean with this talk of "faulting logic".... but that has little to do with whether the statement is a paradox or it isn't.

In order for there to be a paradox, one must show that logically speaking, a contradiction is implied to be true. Just because you can describe a contradiction doesn't mean logic implies that it is true (or appears to at least). Thus, in order to maintain that the Liar's Paradox is unresolvable, you have to show that logic is being correctly applied to a non-contradictory statement. If logic is being correctly applied to a contradictory statement, then any "logical implications" are meaningless and don't prove that there is a true contradiction anywhere.
Not sure why you and bossy aren't getting it.

You didn't actually respond to the substance of what you quoted.

It makes no sense to say that we have to apply logic to a non-contradictory statement and see if contradiction emerges. Whether the statement is contradictory or not is epistemically inaccessible prior to at least a cursory application of logic. Like I said, you're confusing the epistemic evolution that accompanies logical analysis with facts about the nature of the statement in question. Nothing you've said even attempts to address this point...
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
dylancatlow
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12/9/2015 9:06:29 PM
Posted: 1 year ago
By showing that the statement is paradoxical, I show that logic does not lead to paradox, but merely transforms a paradox into another paradox, which is not a problem for logic. Paradoxical implications of a paradoxical statement do not prove that logic is flawed.

Of course, it is easy to assign truth values to the two opposing statements.

"This statement is false" - true, because contradictory

"This statement is true" - false, because contradictory

*I guess this was pretty confusing, since I used paradox somewhat incorrectly. It should read:

By showing that the statement is contradictory, I show that logic does not lead to paradox, but merely transforms one contradiction into another, which does not prove that the second contradiction is any more logically "implied" than the first. It only appears like a real contradiction because logic leads us in that direction. But since logic is being applied to a contradictory statement, contradictory implications do not prove that they are actually logically supported, merely that they logically follow from contradictory statements, which is not the same thing. Merely because you can describe a contradictory statement and use logic to extract contradictory implications does not prove that those implications are logically justifiable, and thus you have not demonstrated the existence of a paradox.

I hope this makes sense, because that's as clear as I can make it.
ShabShoral
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12/9/2015 9:12:36 PM
Posted: 1 year ago
At 12/9/2015 9:06:29 PM, dylancatlow wrote:
By showing that the statement is paradoxical, I show that logic does not lead to paradox, but merely transforms a paradox into another paradox, which is not a problem for logic. Paradoxical implications of a paradoxical statement do not prove that logic is flawed.
You're literally assuming that a paradox exists to be transformed, WHICH IS THE PROBLEM THAT NEEDS TO BE RESOLVED.
Of course, it is easy to assign truth values to the two opposing statements.

"This statement is false" - true, because contradictory

"This statement is true" - false, because contradictory

*I guess this was pretty confusing, since I used paradox somewhat incorrectly. It should read:

By showing that the statement is contradictory, I show that logic does not lead to paradox, but merely transforms one contradiction into another, which does not prove that the second contradiction is any more logically "implied" than the first. It only appears like a real contradiction because logic leads us in that direction. But since logic is being applied to a contradictory statement, contradictory implications do not prove that they are actually logically supported, merely that they logically follow from contradictory statements, which is not the same thing. Merely because you can describe a contradictory statement and use logic to extract contradictory implications does not prove that those implications are logically justifiable, and thus you have not demonstrated the existence of a paradox.

I hope this makes sense, because that's as clear as I can make it.

You cannot even speak of contradictions. If, as you're asserting, there is no logical problem with paradoxes that are "self-contained" (whatever the hell that means), then you're destroying any claim to reasonability you might otherwise have.
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ShabShoral
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12/9/2015 9:13:13 PM
Posted: 1 year ago
At 12/9/2015 8:30:16 PM, 000ike wrote:
At 12/9/2015 8:21:24 PM, dylancatlow wrote:
It would be a paradox if we started with a non-contradictory statement, applied logic to it, and end up with a contradiction, because in that case it at least seems like the contradiction is true. But since the Liar's Paradox begins with a contradiction, logic cannot be faulted for the contradictory conclusion it reaches. In fact, it would be contradictory if a contradictory statement didn't logically have contradictory implications.

That's the most absurd thing I've ever heard (and that's not hyperbole -- I mean it). You're confusing the epistemic evolution that arises from the temporal nature of logical analysis with an ontological fact about what the statement in question is.

A non-contradictory statement does not become contradictory. It was either contradictory from the start or it wasn't.

Now I really don't know what you mean with this talk of "faulting logic".... but that has little to do with whether the statement is a paradox or it isn't.

<3
"This site is trash as a debate site. It's club penguin for dysfunctional adults."

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"Your idea of good writing is like Spinoza mixed with Heidegger."

~ Dylly Dylly Cat Cat

"You seem to aspire to be a cross between a Jewish hipster, an old school WASP aristocrat, and a political iconoclast"

~ Thett the Mighty

"fvck omg ur face"

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"No aspect of your facial structure suggests Filipino descent."
~ YYW
dylancatlow
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12/9/2015 9:14:31 PM
Posted: 1 year ago
At 12/9/2015 9:12:36 PM, ShabShoral wrote:
At 12/9/2015 9:06:29 PM, dylancatlow wrote:
By showing that the statement is paradoxical, I show that logic does not lead to paradox, but merely transforms a paradox into another paradox, which is not a problem for logic. Paradoxical implications of a paradoxical statement do not prove that logic is flawed.
You're literally assuming that a paradox exists to be transformed, WHICH IS THE PROBLEM THAT NEEDS TO BE RESOLVED.

I'm not assuming that it exists, I'm assuming that it is described in the sense that a sentence with contradictory claims has been constructed. What about that do you not understand?

Of course, it is easy to assign truth values to the two opposing statements.

"This statement is false" - true, because contradictory

"This statement is true" - false, because contradictory

*I guess this was pretty confusing, since I used paradox somewhat incorrectly. It should read:

By showing that the statement is contradictory, I show that logic does not lead to paradox, but merely transforms one contradiction into another, which does not prove that the second contradiction is any more logically "implied" than the first. It only appears like a real contradiction because logic leads us in that direction. But since logic is being applied to a contradictory statement, contradictory implications do not prove that they are actually logically supported, merely that they logically follow from contradictory statements, which is not the same thing. Merely because you can describe a contradictory statement and use logic to extract contradictory implications does not prove that those implications are logically justifiable, and thus you have not demonstrated the existence of a paradox.

I hope this makes sense, because that's as clear as I can make it.

You cannot even speak of contradictions. If, as you're asserting, there is no logical problem with paradoxes that are "self-contained" (whatever the hell that means), then you're destroying any claim to reasonability you might otherwise have.
dylancatlow
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12/9/2015 9:16:29 PM
Posted: 1 year ago
At 12/9/2015 9:13:13 PM, ShabShoral wrote:
At 12/9/2015 8:30:16 PM, 000ike wrote:
At 12/9/2015 8:21:24 PM, dylancatlow wrote:
It would be a paradox if we started with a non-contradictory statement, applied logic to it, and end up with a contradiction, because in that case it at least seems like the contradiction is true. But since the Liar's Paradox begins with a contradiction, logic cannot be faulted for the contradictory conclusion it reaches. In fact, it would be contradictory if a contradictory statement didn't logically have contradictory implications.

That's the most absurd thing I've ever heard (and that's not hyperbole -- I mean it). You're confusing the epistemic evolution that arises from the temporal nature of logical analysis with an ontological fact about what the statement in question is.

A non-contradictory statement does not become contradictory. It was either contradictory from the start or it wasn't.

Now I really don't know what you mean with this talk of "faulting logic".... but that has little to do with whether the statement is a paradox or it isn't.

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000ike
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12/9/2015 9:18:16 PM
Posted: 1 year ago
At 12/9/2015 9:06:29 PM, dylancatlow wrote:
By showing that the statement is paradoxical, I show that logic does not lead to paradox, but merely transforms a paradox into another paradox, which is not a problem for logic. Paradoxical implications of a paradoxical statement do not prove that logic is flawed.

Of course, it is easy to assign truth values to the two opposing statements.

"This statement is false" - true, because contradictory

"This statement is true" - false, because contradictory

*I guess this was pretty confusing, since I used paradox somewhat incorrectly. It should read:

By showing that the statement is contradictory, I show that logic does not lead to paradox, but merely transforms one contradiction into another, which does not prove that the second contradiction is any more logically "implied" than the first. It only appears like a real contradiction because logic leads us in that direction. But since logic is being applied to a contradictory statement, contradictory implications do not prove that they are actually logically supported, merely that they logically follow from contradictory statements, which is not the same thing. Merely because you can describe a contradictory statement and use logic to extract contradictory implications does not prove that those implications are logically justifiable, and thus you have not demonstrated the existence of a paradox.

I hope this makes sense, because that's as clear as I can make it.

I would appreciate it if you did away with the condescension. I can see your argument and it's particular flaw with sharp clarity. This is your second time dodging conversation with the particular point I'm making only to reassert your position.

Logical analysis is an epistemic tool, and as such has temporal limitations. You cannot know whether a statement is self-contradictory or not until you've analyzed it in some capacity. To define a paradox as a statement that is non-contradictory but turned contradictory by deductive inference is to assume its status as a contradiction is known without any logical analysis in the first place --- and that's simply absurd. Logic does not change what a statement is (i.e. self-contradictory or not)... logic reveals what a statement is to us.

The upshot is that saying that logic is not at fault for producing a contradictory statement because we started out with a contradictory statement, is simply absurd on its face....a kind of incoherent double-speak.

So It would be much appreciated if you addressed this argument directly. Don't repeat yourself. Answer the specific objection that has just been raised. And if you find it unanswerable (as will most certainly be the case), then concede.
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
dylancatlow
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12/9/2015 9:21:39 PM
Posted: 1 year ago
At 12/9/2015 9:18:16 PM, 000ike wrote:
At 12/9/2015 9:06:29 PM, dylancatlow wrote:
By showing that the statement is paradoxical, I show that logic does not lead to paradox, but merely transforms a paradox into another paradox, which is not a problem for logic. Paradoxical implications of a paradoxical statement do not prove that logic is flawed.

Of course, it is easy to assign truth values to the two opposing statements.

"This statement is false" - true, because contradictory

"This statement is true" - false, because contradictory

*I guess this was pretty confusing, since I used paradox somewhat incorrectly. It should read:

By showing that the statement is contradictory, I show that logic does not lead to paradox, but merely transforms one contradiction into another, which does not prove that the second contradiction is any more logically "implied" than the first. It only appears like a real contradiction because logic leads us in that direction. But since logic is being applied to a contradictory statement, contradictory implications do not prove that they are actually logically supported, merely that they logically follow from contradictory statements, which is not the same thing. Merely because you can describe a contradictory statement and use logic to extract contradictory implications does not prove that those implications are logically justifiable, and thus you have not demonstrated the existence of a paradox.

I hope this makes sense, because that's as clear as I can make it.

I would appreciate it if you did away with the condescension. I can see your argument and it's particular flaw with sharp clarity. This is your second time dodging conversation with the particular point I'm making only to reassert your position.

Sorry, I didn't mean it like that. I meant that I'm not going to expend much more effort explaining myself, because everything I need to say is contained in that paragraph. Thus, I "hope" it makes sense because that's the last time I'm explaining it.


Logical analysis is an epistemic tool, and as such has temporal limitations. You cannot know whether a statement is self-contradictory or not until you've analyzed it in some capacity. To define a paradox as a statement that is non-contradictory but turned contradictory by deductive inference is to assume its status as a contradiction is known without any logical analysis in the first place --- and that's simply absurd. Logic does not change what a statement is (i.e. self-contradictory or not)... logic reveals what a statement is to us.

The upshot is that saying that logic is not at fault for producing a contradictory statement because we started out with a contradictory statement, is simply absurd on its face....a kind of incoherent double-speak.

So It would be much appreciated if you addressed this argument directly. Don't repeat yourself. Answer the specific objection that has just been raised. And if you find it unanswerable (as will most certainly be the case), then concede.
mrsatan
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12/9/2015 9:46:56 PM
Posted: 1 year ago
At 12/9/2015 7:00:45 PM, dylancatlow wrote:
In its simplest formulation, the Liar's Paradox runs as follows:

Take the statement "This sentence is false".

If the statement is true, then it is false, since that's what it's claiming to be the case.
But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.

How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.

It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.

It's a good resolution, although I would say it's better explained on Wikipedia.

https://en.m.wikipedia.org...

It's in the possible resolutions under the header Arthur Prior.
To say one has free will, to have chosen other than they did, is to say they have will over their will... Will over the will they have over their will... Will over the will they have over the will they have over their will, etc... It's utter nonsense.
000ike
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12/9/2015 10:04:03 PM
Posted: 1 year ago
At 12/9/2015 9:46:56 PM, mrsatan wrote:
At 12/9/2015 7:00:45 PM, dylancatlow wrote:
In its simplest formulation, the Liar's Paradox runs as follows:

Take the statement "This sentence is false".

If the statement is true, then it is false, since that's what it's claiming to be the case.
But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.

How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.

It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.

It's a good resolution, although I would say it's better explained on Wikipedia.

https://en.m.wikipedia.org...

It's in the possible resolutions under the header Arthur Prior.

I just read that out of curiosity, and his argument is quite flawed as well.

In the first example, he introduces (correctly) that every statement is implicitly prefixed with the phrase "it is true that...." but then in his analysis of the relevant paradox he illicitly morphs the precursor phrase to "This statement is true and..." which is what makes his characterization of the phrase as a simple contradiction "A and not A" seem plausible. The legerdemain behind that maneuver is fairly easy to detect. "It is true that" is a connective phrase; it intends to describe the subordinate clause that follows, which means that the claim to truth is an inseparable aspect of the following proposition. "this statement is true and..." conversely sets up two parallel and independent claims, and as such does not accurately model the original paradox.
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
dylancatlow
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12/9/2015 10:11:00 PM
Posted: 1 year ago
At 12/9/2015 10:04:03 PM, 000ike wrote:
At 12/9/2015 9:46:56 PM, mrsatan wrote:
At 12/9/2015 7:00:45 PM, dylancatlow wrote:
In its simplest formulation, the Liar's Paradox runs as follows:

Take the statement "This sentence is false".

If the statement is true, then it is false, since that's what it's claiming to be the case.
But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.

How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.

It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.

It's a good resolution, although I would say it's better explained on Wikipedia.

https://en.m.wikipedia.org...

It's in the possible resolutions under the header Arthur Prior.

I just read that out of curiosity, and his argument is quite flawed as well.

In the first example, he introduces (correctly) that every statement is implicitly prefixed with the phrase "it is true that...." but then in his analysis of the relevant paradox he illicitly morphs the precursor phrase to "This statement is true and..." which is what makes his characterization of the phrase as a simple contradiction "A and not A" seem plausible. The legerdemain behind that maneuver is fairly easy to detect. "It is true that" is a connective phrase; it intends to describe the subordinate clause that follows, which means that the claim to truth is an inseparable aspect of the following proposition. "this statement is true and..." conversely sets up two parallel and independent claims, and as such does not accurately model the original paradox.

Would you like to do a debate on this? (My first round would basically just consist of things I've written here). I think it would be fun.