What is the solution to the liar's paradox?

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Age
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Re: What is the solution to the liar's paradox?

Post by Age »

Eodnhoj7 wrote: Tue Sep 23, 2025 1:40 am
popeye1945 wrote: Mon Sep 22, 2025 1:54 am The recognition that the liar's paradox is a self-negating premise, no matter what its premise. It is futility, a dog chasing its own tail, never to catch it.
It simultaneously self-justified as there is a simultaneous truth value as well. A paradox is superpositioned, overlayed specifically, that coexist until a transformation in perspective is achieved.
To some others, anyway, a 'paradox' is just;
A statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.

While to even some others, a 'paradox' is just;
Two seemingly opposite things that seem impossible but are actually both true.

While to even some others, a 'paradox' is just;
A seeming absurd or contradictory statement but on further reflection actually expresses a truth.

So, literally, a paradox can be a paradox of itself.

Therefore, there is no wonder why 'these people', back when this was being written, were so lost and so confused as much as they were and for as long as they were.

'They' would continually use the same words, back and forth to each other, while meaning the exact opposite of what 'the other' was meaning.

'They' would rarely, if ever, seek out and obtain actual clarification, first, before they would respond, thus causing and creating even more misunderstanding/s and conflict/s.

What one would imply another would infer the exact opposite, and what one would infer another meant the exact opposite.

And, then there were some who would speak and write words like, for example,
A paradox is super positioned, overlayed specifically, that coexist until a transformation in perspective is achieved'

Which I would sometimes wonder if 'that one' would ever wonder why absolutely no one, besides "itself", ever had a clue as to what 'it' was even on about?
Eodnhoj7
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Re: What is the solution to the liar's paradox?

Post by Eodnhoj7 »

huphuphup123 wrote: Tue Sep 23, 2025 4:18 am
Eodnhoj7 wrote: Sun Sep 21, 2025 6:34 pm
huphuphup123 wrote: Sun Sep 21, 2025 4:09 pm https://upload.wikimedia.org/wikipedia/ ... ox.svg.png

A - The statement to the right is true nature B - the statement to the left is false

if A is true B is true, but if A is false then B if false, if B is false then A is true, if A is true then B is true

What is the solution or meaning of this?
There are two answers that occur immediately to me.

The first:


In one condition the person is a liar, in another the person is not a liar. In the magnitude of all possible conditions this person is both a liar and not a liar. Each condition that occurs reveals the potentiality of said person's inmate qualities thus these qualities exist simultaneously until a specific condition occurs. The solution, and I have had discussions with AI over this that back up my stance, is that paradoxes are superpositioned logical states.



Second:


Another answer is everything the person says is a half truth, necessitating a lie, and a half lie, necessitating a truth. All assertions have gradient truth values where truth and falsity are less of a binary assertion and more of a gradient way of viewing things. The person being both a liar and truth teller points to a gradient viewpoint.



So there are two answers, both legitimate:

Paradoxes are superpositioned assertions.
Paradoxes are gradient assertions.
So you are saying that both "true and false" together is between true and false, it is a gradient between those two. But how can you have true and false together without it cancelling each other out?
Yes a gradient approach can occur.

The statement of "I am a liar" observes that the person in question both tells the truth and lies. So how does that occur?

Within a given framework of identity, lets say the time and space of a week or several years, that identity has multiple expressions within the given space. Sometimes it is a liar. Sometimes it is a truthteller.

Within the given framework these things occur simultaneously and in grades, sometimes more truth than lies are told or vice versa. These can be observes at meta-identities, identities within identities. So where an identity in the time and space of a week may be "x and y", within the meta identity "x" may only occur in one time and space and "y" within another, all of which are part of the larger time and space of a week.

So identity as grades can be akin to a meta-identity, and identity within an identity.

Now on the other hand all dualisms result in gradation by degree of the dualism itself. Take for example the following dualistic symbolic chain (if you want this in normal language just ask):

1. T
2. F
3. (T,F)
4. T(T,F)
5. F(T,F)
6. (T,F)(T,F)
7. T((T,F)(T,F))
8. F((T,F)(T,F))
9. (T,F)((T,F)(T,F))
10. Unto infinity.

Any dualism, and paradox requires a dualism by degree of differing but isomorphic expressions, results in infinite gradation of said dualism.

So the liars paradox results in different grades of true and false. This can be evidenced by true may be more than false on one set of days, vice versa, or all truths are partial truths and all lies are partial lies.


There is also another complementary way of viewing paradox:

Two opposing or various states existing at once in quantum mechanics is called superpositioning. These states existing at once are effectively indistinct potentiality. When the superposition states are observed one of the potential states is localized according to the state of the observer.

Now a paradox is similar. It is multiple values at once. The paradox is indistinct in its present state. Now when the paradox is observed one or more of the following things happens:

1. The observer chooses one of the several potential values and makes distinctions from there. You will see this in everyday life where a paradox of "this is that" is observed and people naturally takes sides. The paradox becomes a mirror of the observer in this scenario.

2. The observer adds context to the paradox. Now in a general paradox there is no context but the paradox itself and this leads to multiple states coexisting at once. Now if a paradox is given further context, by the observer(s), then a distinct value occurs.

For example the paradox of "I am a liar" had multiple values coexisting that results in the indistinct state of the paradox itself.

Now if the context of "on wednesdays" so we have "I am a liar on wednesdays" then the paradox ceases and we have a clearer and more defined assertion.

3. If opposites cancel eachother out then the paradox becomes pure logical potentiality, a logical space by which values can be projected or assigned. In these respects the paradox is empty of meaning and yet this emptiness becomes of mirror to the observer. As such it is a point by which the observers attention is transformed. You will find this method quite frequently in zen Buddhism where two opposing points, under the paradox, are observed and the cancelation causes a space of potentiality by which the observer is looking into a metaphorical mirror.




The key to all of this is context.

Context determines how the paradox unfolds to the observer.

Under one context the paradox can lead to gradation, another superpositioned logical states subject to context application, another a mirror to the observer by nature of being empty....so on and so forth.
Age
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Re: What is the solution to the liar's paradox?

Post by Age »

Eodnhoj7 wrote: Tue Sep 23, 2025 4:45 am
huphuphup123 wrote: Tue Sep 23, 2025 4:18 am
Eodnhoj7 wrote: Sun Sep 21, 2025 6:34 pm

There are two answers that occur immediately to me.

The first:


In one condition the person is a liar, in another the person is not a liar. In the magnitude of all possible conditions this person is both a liar and not a liar. Each condition that occurs reveals the potentiality of said person's inmate qualities thus these qualities exist simultaneously until a specific condition occurs. The solution, and I have had discussions with AI over this that back up my stance, is that paradoxes are superpositioned logical states.



Second:


Another answer is everything the person says is a half truth, necessitating a lie, and a half lie, necessitating a truth. All assertions have gradient truth values where truth and falsity are less of a binary assertion and more of a gradient way of viewing things. The person being both a liar and truth teller points to a gradient viewpoint.



So there are two answers, both legitimate:

Paradoxes are superpositioned assertions.
Paradoxes are gradient assertions.
So you are saying that both "true and false" together is between true and false, it is a gradient between those two. But how can you have true and false together without it cancelling each other out?
Yes a gradient approach can occur.

The statement of "I am a liar" observes that the person in question both tells the truth and lies.
No it does not.

And to prove 'this' one only has to 'look at' only 'the words', alone, here.

'I am a liar', is saying, and stating, that 'I am a liar', and absolutely nothing more, nor anything else.

Therefore, the statement, 'I am a liar', literally means that 'I am nothing else, at all'.

Which means nothing like 'your claim', here, that 'that one' does other things than just lies.

So, the rest is moot.
Eodnhoj7 wrote: Tue Sep 23, 2025 4:45 am So how does that occur?

Within a given framework of identity, lets say the time and space of a week or several years, that identity has multiple expressions within the given space. Sometimes it is a liar. Sometimes it is a truthteller.

Within the given framework these things occur simultaneously and in grades, sometimes more truth than lies are told or vice versa. These can be observes at meta-identities, identities within identities. So where an identity in the time and space of a week may be "x and y", within the meta identity "x" may only occur in one time and space and "y" within another, all of which are part of the larger time and space of a week.

So identity as grades can be akin to a meta-identity, and identity within an identity.

Now on the other hand all dualisms result in gradation by degree of the dualism itself. Take for example the following dualistic symbolic chain (if you want this in normal language just ask):

1. T
2. F
3. (T,F)
4. T(T,F)
5. F(T,F)
6. (T,F)(T,F)
7. T((T,F)(T,F))
8. F((T,F)(T,F))
9. (T,F)((T,F)(T,F))
10. Unto infinity.

Any dualism, and paradox requires a dualism by degree of differing but isomorphic expressions, results in infinite gradation of said dualism.

So the liars paradox results in different grades of true and false. This can be evidenced by true may be more than false on one set of days, vice versa, or all truths are partial truths and all lies are partial lies.


There is also another complementary way of viewing paradox:

Two opposing or various states existing at once in quantum mechanics is called superpositioning. These states existing at once are effectively indistinct potentiality. When the superposition states are observed one of the potential states is localized according to the state of the observer.

Now a paradox is similar. It is multiple values at once. The paradox is indistinct in its present state. Now when the paradox is observed one or more of the following things happens:

1. The observer chooses one of the several potential values and makes distinctions from there. You will see this in everyday life where a paradox of "this is that" is observed and people naturally takes sides. The paradox becomes a mirror of the observer in this scenario.

2. The observer adds context to the paradox. Now in a general paradox there is no context but the paradox itself and this leads to multiple states coexisting at once. Now if a paradox is given further context, by the observer(s), then a distinct value occurs.

For example the paradox of "I am a liar" had multiple values coexisting that results in the indistinct state of the paradox itself.

Now if the context of "on wednesdays" so we have "I am a liar on wednesdays" then the paradox ceases and we have a clearer and more defined assertion.

3. If opposites cancel eachother out then the paradox becomes pure logical potentiality, a logical space by which values can be projected or assigned. In these respects the paradox is empty of meaning and yet this emptiness becomes of mirror to the observer. As such it is a point by which the observers attention is transformed. You will find this method quite frequently in zen Buddhism where two opposing points, under the paradox, are observed and the cancelation causes a space of potentiality by which the observer is looking into a metaphorical mirror.




The key to all of this is context.

Context determines how the paradox unfolds to the observer.

Under one context the paradox can lead to gradation, another superpositioned logical states subject to context application, another a mirror to the observer by nature of being empty....so on and so forth.
Age
Posts: 27841
Joined: Sun Aug 05, 2018 8:17 am

Re: What is the solution to the liar's paradox?

Post by Age »

What is called 'the liar's paradox', and its supposed solution, is just more absurd nonsense, which has obviously kept some people distracted for long enough that they do not get to recognize and see the actual Truths, in Life.
huphuphup123
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Joined: Sun Aug 24, 2025 6:51 pm

Re: What is the solution to the liar's paradox?

Post by huphuphup123 »

Eodnhoj7 wrote: Tue Sep 23, 2025 4:45 am
huphuphup123 wrote: Tue Sep 23, 2025 4:18 am
Eodnhoj7 wrote: Sun Sep 21, 2025 6:34 pm

There are two answers that occur immediately to me.

The first:


In one condition the person is a liar, in another the person is not a liar. In the magnitude of all possible conditions this person is both a liar and not a liar. Each condition that occurs reveals the potentiality of said person's inmate qualities thus these qualities exist simultaneously until a specific condition occurs. The solution, and I have had discussions with AI over this that back up my stance, is that paradoxes are superpositioned logical states.



Second:


Another answer is everything the person says is a half truth, necessitating a lie, and a half lie, necessitating a truth. All assertions have gradient truth values where truth and falsity are less of a binary assertion and more of a gradient way of viewing things. The person being both a liar and truth teller points to a gradient viewpoint.



So there are two answers, both legitimate:

Paradoxes are superpositioned assertions.
Paradoxes are gradient assertions.
So you are saying that both "true and false" together is between true and false, it is a gradient between those two. But how can you have true and false together without it cancelling each other out?
Yes a gradient approach can occur.

The statement of "I am a liar" observes that the person in question both tells the truth and lies. So how does that occur?

Within a given framework of identity, lets say the time and space of a week or several years, that identity has multiple expressions within the given space. Sometimes it is a liar. Sometimes it is a truthteller.

Within the given framework these things occur simultaneously and in grades, sometimes more truth than lies are told or vice versa. These can be observes at meta-identities, identities within identities. So where an identity in the time and space of a week may be "x and y", within the meta identity "x" may only occur in one time and space and "y" within another, all of which are part of the larger time and space of a week.

So identity as grades can be akin to a meta-identity, and identity within an identity.

Now on the other hand all dualisms result in gradation by degree of the dualism itself. Take for example the following dualistic symbolic chain (if you want this in normal language just ask):
1. T
2. F
3. (T,F)
4. T(T,F)
5. F(T,F)
6. (T,F)(T,F)
7. T((T,F)(T,F))
8. F((T,F)(T,F))
9. (T,F)((T,F)(T,F))
10. Unto infinity.
in here you need to put equals and not-equals signs because the truth's and false's should either be equal or not equal. You are saying that the truth and the false are seperate things from each other, correct? but that how can you have that, how can they be seperate. Like isn't F(T,F) the same as F=F, because you are saying in the former that true=false is itself false
Magnus Anderson
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Joined: Mon Apr 20, 2015 3:26 am

Re: What is the solution to the liar's paradox?

Post by Magnus Anderson »

Eodnhoj7 wrote: Sun Sep 21, 2025 9:09 pm "I am a liar" is a propositional statement by degree of the assertion of symbols corresponding to a reality "I" and the state of reality "liar", which is a meta-reality.
"I am a liar" is a propositional statement. It has a valid reference to a portion of reality ( denoted by the symbol "I" ) and a description of it ( denoted by the symbol "liar". ) However, it is NOT a liar's paradox.

A liar's paradox would be, "This statement is false". That statement does not have a valid reference. Its reference is circular, so it's never actually resolved.
Eodnhoj7 wrote: Sun Sep 21, 2025 9:09 pm There can be paradoxical truth values when context is not properly assigned, for instance: "It is both not snowing and snowing in Minnesota" is a paradox given multiple contexts are either ignored and/or viewed simultaneously. If each portion was properly contextualized the paradox ceases.
That is an example of an illusory contradiction.
Eodnhoj7 wrote: Sun Sep 21, 2025 9:09 pm The problem of paradoxes is the assumption that truth is strictly an "either/or" assertion
That's hardly an assumption. Rather, it's a definitional truth.

Every proposition is either true or false. There is no middle ground. It follows from the way the words "proposition", "true" and "false" are defined.

The problem occurs when you generalize that to statements. Statements can be nonsensical, so they can very easily be void of truth value. A statement such as "A is B", where neither A nor B has a meaning assigned to it, has no truth value. There is no valid reference and no valid description. That's why "This statement is false" is nether true nor false. It's a statement but it's not a proposition. It's missing a valid reference.
Eodnhoj7
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Re: What is the solution to the liar's paradox?

Post by Eodnhoj7 »

huphuphup123 wrote: Tue Sep 23, 2025 7:28 pm
Eodnhoj7 wrote: Tue Sep 23, 2025 4:45 am
huphuphup123 wrote: Tue Sep 23, 2025 4:18 am

So you are saying that both "true and false" together is between true and false, it is a gradient between those two. But how can you have true and false together without it cancelling each other out?
Yes a gradient approach can occur.

The statement of "I am a liar" observes that the person in question both tells the truth and lies. So how does that occur?

Within a given framework of identity, lets say the time and space of a week or several years, that identity has multiple expressions within the given space. Sometimes it is a liar. Sometimes it is a truthteller.

Within the given framework these things occur simultaneously and in grades, sometimes more truth than lies are told or vice versa. These can be observes at meta-identities, identities within identities. So where an identity in the time and space of a week may be "x and y", within the meta identity "x" may only occur in one time and space and "y" within another, all of which are part of the larger time and space of a week.

So identity as grades can be akin to a meta-identity, and identity within an identity.

Now on the other hand all dualisms result in gradation by degree of the dualism itself. Take for example the following dualistic symbolic chain (if you want this in normal language just ask):
1. T
2. F
3. (T,F)
4. T(T,F)
5. F(T,F)
6. (T,F)(T,F)
7. T((T,F)(T,F))
8. F((T,F)(T,F))
9. (T,F)((T,F)(T,F))
10. Unto infinity.
in here you need to put equals and not-equals signs because the truth's and false's should either be equal or not equal. You are saying that the truth and the false are seperate things from each other, correct? but that how can you have that, how can they be seperate. Like isn't F(T,F) the same as F=F, because you are saying in the former that true=false is itself false
The symbol grounding is more efficient, the symbol of equality can lead to inefficiency and confusion as equality has meta-foundational nuances. Recursive notation is more efficient in expression for a sequence as this.

Here is an AI explanation, of the symbolism:

Great question! Let's unpack this step by step to understand what's going on here.

First, what is a dualism?

In philosophy, dualism typically refers to the idea that two fundamental concepts or substances are distinct yet interconnected—like mind and body, or good and evil. Think of dualism as a way to describe two opposing or contrasting ideas that exist together.

Now, what does the statement mean by "all dualisms result in gradation by degree of the dualism itself"?

This suggests that when you try to analyze or express a dualism, you can do so at different levels or degrees of complexity. The more you break down the dualism, the more nuanced or layered it becomes, potentially leading to an infinite process of refinement.

The Chain Explained
Let's look at the chain you provided:

T
F
(T, F)
T(T, F)
F(T, F)
(T, F)(T, F)
T((T, F)(T, F))
F((T, F)(T, F))
(T, F)((T, F)(T, F))
And so on, to infinity.

What's happening here?

T and F are the basic dualistic opposites—like "true" and "false."
(T, F) is a pairing or a relation between the two—think of it as a simple dualistic relationship.

Moving forward, you start building more complex expressions:

T(T, F) and F(T, F) are applying the concepts of T or F to the pair.
The expressions grow more complex as you nest these structures, like T((T, F)(T, F)), which is T applied to a pair of pairs.

This process can continue infinitely because there's always a way to nest or layer these dualisms further.
Eodnhoj7
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Re: What is the solution to the liar's paradox?

Post by Eodnhoj7 »

Magnus Anderson wrote: Tue Sep 23, 2025 10:54 pm
Eodnhoj7 wrote: Sun Sep 21, 2025 9:09 pm "I am a liar" is a propositional statement by degree of the assertion of symbols corresponding to a reality "I" and the state of reality "liar", which is a meta-reality.
"I am a liar" is a propositional statement. It has a valid reference to a portion of reality ( denoted by the symbol "I" ) and a description of it ( denoted by the symbol "liar". ) However, it is NOT a liar's paradox.

A liar's paradox would be, "This statement is false". That statement does not have a valid reference. Its reference is circular, so it's never actually resolved.
Eodnhoj7 wrote: Sun Sep 21, 2025 9:09 pm There can be paradoxical truth values when context is not properly assigned, for instance: "It is both not snowing and snowing in Minnesota" is a paradox given multiple contexts are either ignored and/or viewed simultaneously. If each portion was properly contextualized the paradox ceases.
That is an example of an illusory contradiction.
Eodnhoj7 wrote: Sun Sep 21, 2025 9:09 pm The problem of paradoxes is the assumption that truth is strictly an "either/or" assertion
That's hardly an assumption. Rather, it's a definitional truth.

Every proposition is either true or false. There is no middle ground. It follows from the way the words "proposition", "true" and "false" are defined.

The problem occurs when you generalize that to statements. Statements can be nonsensical, so they can very easily be void of truth value. A statement such as "A is B", where neither A nor B has a meaning assigned to it, has no truth value. There is no valid reference and no valid description. That's why "This statement is false" is nether true nor false. It's a statement but it's not a proposition. It's missing a valid reference.
1. "I am a liar" is a paradox given if I am a liar than I would be lying about lying or telling the truth I am lying.

2. If the statement is not circular than it is subject to infinite regress as there always requires a reference beyond what is referenced. Reference nuances occur either way.

3. All contradictions can be reduced to contextual problems, hence all contradictions can fit in the category of illusory contradiction.

4. It is an assumption as there is no justification for "definitional truth" that does not go into infinite regress or leaves a finite point which is assumed. If I asked you "what a definition truth is?" and you said "x" and I asked "what is x?" and then you said "x1" and we continued this conversation it would end at a finite point where the foundation is fundamentally assumed.

5. Not all propositions are true or false. The proposition of "The x is y" is gradient by degree of multiple expressions of x and y and multiple meta expressions of x and y. If I said "The car is red" it may be a gradient truth as there are shades of red greater or less than other as well as other colors on the car...thus the degree of truth is gradational (or it is mostly true the car is red). Given any category of things there are subcategories that act as grades, meta-categories you can say.

Fuzzy logics observe this in logic as well as the numerical fractions in mathematics. Not every thing can be limit it "either/or" without committing to overgeneralization.

6. "A is B" has a truth value of correspondence. Valid reference is nonsensical if assumed as fixed as you are requiring an observer at that point and subjectivity is involved. Saying "Car is red" leaves an innumerable number of cars and reds that can be observed where "car" and "red" are effectively variables like "A" and "B".



Truth is subject to distinction for truth is a distinction.
Magnus Anderson
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Re: What is the solution to the liar's paradox?

Post by Magnus Anderson »

1.

"I am a liar" is not a paradox even if the word "liar" means "a person who always lies".

If the word "liar" means "a person who lies a lot", then it might even be true.

If it means "a person who always lies", then it's necessarily false. You might be a huge liar but you're not an absolute liar. Absolute liars never speak truth.

3.
Eodnhoj7 wrote: Tue Sep 23, 2025 11:48 pm All contradictions can be reduced to contextual problems, hence all contradictions can fit in the category of illusory contradiction.
That's not quite true.

A natural number is either odd or it is even. It can't be both. "A natural number that is both odd and even" would thus be a real contradiction.

5.
Eodnhoj7 wrote: Tue Sep 23, 2025 11:48 pm Not all propositions are true or false. The proposition of "The x is y" is gradient by degree of multiple expressions of x and y and multiple meta expressions of x and y.
I think you're confusing propositions with statements and closed statements with open ones.

Propositions are non-linguistic entities.

Statements are their linguistic representations ( but only propositional ones. )

There's a difference between a closed statement and an open one.

An open statement is a statement that has at least one free variable. This gives it the possibility of being "sometimes true and sometimes false". An example is "X is blue" where "X" is a free variable ranging over every conceivable physical object. If X refers to the sky, the statement is true. If it refers to an apple, it is false.

Not every statement is an open statement. In fact, most statements aren't.
Eodnhoj7 wrote: Tue Sep 23, 2025 11:48 pm If I said "The car is red" it may be a gradient truth as there are shades of red greater or less than other as well as other colors on the car...thus the degree of truth is gradational (or it is mostly true the car is red).
It's a lot simpler than that. When we speak of the color of an object, such as a car, we're speaking of its average color -- or something to that effect. Regardless of how it's computed, we're speaking of a single color.

"This car is red" does not literally mean "It's all red". And if it did, then the logical consequence would be that no car is red. Again, no need for gradation.

Whether we're going to classify truth values using a binary scheme or an infinitary one is a matter of choice guided by need. It has nothing to do with what's true.
Eodnhoj7 wrote: Tue Sep 23, 2025 11:48 pm Fuzzy logics observe this in logic as well as the numerical fractions in mathematics. Not every thing can be limit it "either/or" without committing to overgeneralization.
Fuzzy logic, like other systems of logic, do not show that the binary classification of truth values is false. They do not even show it's useless.
Eodnhoj7
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Re: What is the solution to the liar's paradox?

Post by Eodnhoj7 »

Magnus Anderson wrote: Wed Sep 24, 2025 2:03 am 1.

"I am a liar" is not a paradox even if the word "liar" means "a person who always lies".

If the word "liar" means "a person who lies a lot", then it might even be true.

If it means "a person who always lies", then it's necessarily false. You might be a huge liar but you're not an absolute liar. Absolute liars never speak truth.

3.
Eodnhoj7 wrote: Tue Sep 23, 2025 11:48 pm All contradictions can be reduced to contextual problems, hence all contradictions can fit in the category of illusory contradiction.
That's not quite true.

A natural number is either odd or it is even. It can't be both. "A natural number that is both odd and even" would thus be a real contradiction.

5.
Eodnhoj7 wrote: Tue Sep 23, 2025 11:48 pm Not all propositions are true or false. The proposition of "The x is y" is gradient by degree of multiple expressions of x and y and multiple meta expressions of x and y.
I think you're confusing propositions with statements and closed statements with open ones.

Propositions are non-linguistic entities.

Statements are their linguistic representations ( but only propositional ones. )

There's a difference between a closed statement and an open one.

An open statement is a statement that has at least one free variable. This gives it the possibility of being "sometimes true and sometimes false". An example is "X is blue" where "X" is a free variable ranging over every conceivable physical object. If X refers to the sky, the statement is true. If it refers to an apple, it is false.

Not every statement is an open statement. In fact, most statements aren't.
Eodnhoj7 wrote: Tue Sep 23, 2025 11:48 pm If I said "The car is red" it may be a gradient truth as there are shades of red greater or less than other as well as other colors on the car...thus the degree of truth is gradational (or it is mostly true the car is red).
It's a lot simpler than that. When we speak of the color of an object, such as a car, we're speaking of its average color -- or something to that effect. Regardless of how it's computed, we're speaking of a single color.

"This car is red" does not literally mean "It's all red". And if it did, then the logical consequence would be that no car is red. Again, no need for gradation.

Whether we're going to classify truth values using a binary scheme or an infinitary one is a matter of choice guided by need. It has nothing to do with what's true.
Eodnhoj7 wrote: Tue Sep 23, 2025 11:48 pm Fuzzy logics observe this in logic as well as the numerical fractions in mathematics. Not every thing can be limit it "either/or" without committing to overgeneralization.
Fuzzy logic, like other systems of logic, do not show that the binary classification of truth values is false. They do not even show it's useless.
1. And that is the point...context determines paradox.

2. Explain your line of reasoning where me stating that "all contradictions resort to illusory contradiction" leads to talking about how natural numbers do not contradict when I am referring to contradictions specifically.

3. If propositions are non-linguistic entities than you cannot derive logical laws around them, such a propositional logic, given that logic is inherently tied to language by means of words and symbols. Reflection is not always equivlanence thus propositional statements are not necessarily accurate, provide me an example of a proposition without using language. As a matter of fact provide for me a propositional portion of reality that is fixed and is not open ended by means of change.

The nature that statements occur through further statements necessitates an absence of a fixed state in one respect. Dually a fixed statement, that ceases regress, always begins with an assumption. The paradoxical nature of statements is not avoided.

4. The "car is red paradox" is solved if you contextualize the meaning as not literal. The paradox exists because of context. Given there are grades of red there are grades of truth value corresponding to redness as one car is a "truer red" than another.

5. If need guides choice than truth is secondary.

6. I never claimed the binary system is false, I claim things cannot be limited to a binary state only. I am not arguing that the laws of excluded middle doesn't exist, I am arguing that limiting things to the law of excluded middle is an illusion.
Magnus Anderson
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Re: What is the solution to the liar's paradox?

Post by Magnus Anderson »

Eodnhoj7 wrote: Wed Sep 24, 2025 4:56 am 1. And that is the point...context determines paradox.
But you said that "I am an absolute liar" is a paradox and I said that it is not.

"This is statement is false" is paradoxical because if it's true then it's also false and if it's false then it's also true.

The statement "I am an absolute liar", on the other hand, is just false.
Eodnhoj7
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Re: What is the solution to the liar's paradox?

Post by Eodnhoj7 »

Magnus Anderson wrote: Thu Sep 25, 2025 3:46 pm
Eodnhoj7 wrote: Wed Sep 24, 2025 4:56 am 1. And that is the point...context determines paradox.
But you said that "I am an absolute liar" is a paradox and I said that it is not.

"This is statement is false" is paradoxical because if it's true then it's also false and if it's false then it's also true.

The statement "I am an absolute liar", on the other hand, is just false.

No I did not.

Here is what I said in point 1 prior to my recent response.


"1. "I am a liar" is a paradox given if I am a liar than I would be lying about lying or telling the truth I am lying."

You see paradoxes are contextual problems, and as contextual problems cease to be problems when we observe them, in quantum terms, as 'superpositioned contexts' .

You are right about illusionary contradictions, but I do not think you are aware how deeply correct you actually are. You solved the problem without knowing it.


Paradoxes are a problem in the context of a strict linear context. Change the context to Non-Linear and they cease to be problems and become opportunities to perceive more deeply.
Hudjefa
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Re: What is the solution to the liar's paradox?

Post by Hudjefa »

The statement to the right is true. The statement to the left is false.
The sentences above are not statements.
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