The Liar's paradox
- Speakpigeon
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The Liar's paradox
This sentence is false. As the explanation of the paradox goes, if the sentence is false, then it is true since it says it is false. But if it is true, then it is false since it says it is false. Hence the paradox.
If you think this is a paradox, please explain briefly how you solve the paradox, if you think you do.
Second, if you think it is not a paradox, please explain briefly why.
Finally, do you think it should be possible to prove there is in fact no paradox.
Thank you to stick to the point and refrain from personal attacks.
EB
If you think this is a paradox, please explain briefly how you solve the paradox, if you think you do.
Second, if you think it is not a paradox, please explain briefly why.
Finally, do you think it should be possible to prove there is in fact no paradox.
Thank you to stick to the point and refrain from personal attacks.
EB
Re: The Liar's paradox
The answer is that the sentence is true/false/neutral all at the same time.Speakpigeon wrote: ↑Wed Feb 06, 2019 3:39 pm This sentence is false. As the explanation of the paradox goes, if the sentence is false, then it is true since it says it is false. But if it is true, then it is false since it says it is false. Hence the paradox.
If you think this is a paradox, please explain briefly how you solve the paradox, if you think you do.
Second, if you think it is not a paradox, please explain briefly why.
Finally, do you think it should be possible to prove there is in fact no paradox.
Thank you to stick to the point and refrain from personal attacks.
EB
Paradox leads to never ending paradox, thus necessitating all paradoxes as the meaning to further paradoxes as a solution in themselves.
Re: The Liar's paradox
Bertrand Russel himself agreed that the problem with the paradox is self-reference.
Tarski's undefindability theorem tells us that truth-predicate satisfying convention-T for the sentences of a given language cannot be defined within that language. The problem cannot be resolved without a meta-language.
Meta-languages lead to recursion and Chomsky ultimately formalised the problem: https://en.wikipedia.org/wiki/Chomsky_hierarchy
Self-reference is recursion. Recursion is computation. T
In the computational realm we default to Type Theory so the sentence "This sentence is false" is a proposition. Lets call it X.
Every proposition can be determined as decidable, undecidable or unknown (Turing's halting problem).
For you to determine on the truth-value of X first you need to define the meta-language's grammar/semantics in which you evaluate the truth-value of propositions.
If you want an intro to type theory see this: https://www.heidelberg-laureate-forum.o ... TkzR_qDckM
Tarski's undefindability theorem tells us that truth-predicate satisfying convention-T for the sentences of a given language cannot be defined within that language. The problem cannot be resolved without a meta-language.
Meta-languages lead to recursion and Chomsky ultimately formalised the problem: https://en.wikipedia.org/wiki/Chomsky_hierarchy
Self-reference is recursion. Recursion is computation. T
In the computational realm we default to Type Theory so the sentence "This sentence is false" is a proposition. Lets call it X.
Every proposition can be determined as decidable, undecidable or unknown (Turing's halting problem).
For you to determine on the truth-value of X first you need to define the meta-language's grammar/semantics in which you evaluate the truth-value of propositions.
If you want an intro to type theory see this: https://www.heidelberg-laureate-forum.o ... TkzR_qDckM
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Re: The Liar's paradox
The sentence is neither true or false because while it is gramatically correct it makes no sense logically
The reason is because it lacks a referent which would determine what it was true or false in relation to
The reason is because it lacks a referent which would determine what it was true or false in relation to
Re: The Liar's paradox
In which grammar?
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Re: The Liar's paradox
Despite having no referent it is still true according to the rules of descriptive grammar
Re: The Liar's paradox
I am not sure how to parse this.surreptitious57 wrote: ↑Thu Feb 07, 2019 8:18 am
Despite having no referent it is still true according to the rules of descriptive grammar
Rules describe the grammar of any particular language.
We say that the set of rules R determine the grammar for language L.
Or maybe even language L is determined by the rules outlined in R.
The rules are not prescriptive, but it begs a question. If you aren't adhering to the rules in R are you speaking language L?
Second (back to Tarski's undefinability theorem) a self-descriptive grammar is a paradoxical notion.
In order to be able to describe, then you are necessarily being prescriptive about semantics.
Example: The sky is green.
Grammatically valid. Semantically false.
Last edited by Logik on Thu Feb 07, 2019 1:16 pm, edited 4 times in total.
- Speakpigeon
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Re: The Liar's paradox
OK, sounds right to me.surreptitious57 wrote: ↑Thu Feb 07, 2019 7:59 am The sentence is neither true or false because while it is gramatically correct it makes no sense logically
As I understand the idea of the paradox, although the grammar of it isn't enough of itself to suggest as much, the sentence is referring to itself. If so, it doesn't lack a referent.surreptitious57 wrote: ↑Thu Feb 07, 2019 7:59 amThe reason is because it lacks a referent which would determine what it was true or false in relation to
EB
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Re: The Liar's paradox
Are unsound syllogisms grammatically wrong because they are factually wrong as wellLogic wrote:
Rules describe the grammar of any particular language
No they are not as the validity of a sentence does not extend to how true or false it is
So the sky is green is a grammatically correct sentence even though it is actually false
Re: The Liar's paradox
We've missed each other.surreptitious57 wrote: ↑Thu Feb 07, 2019 2:51 pm Are unsound syllogisms grammatically wrong because they are factually wrong as well
The 'Sky is green' is not factually wrong. It's semantically 'wrong'.
I mean the same thing when I say 'The sky is green' as you mean when you say 'The sky is blue'.
So re-writing your question: Are unsound syllogisms grammatically wrong because they are semantically wrong as well?
And you will find the answer in the definition of decidability.
https://en.wikipedia.org/wiki/Decidability_(logic)
Each logical system comes with both a syntactic component, which among other things determines the notion of provability, and a semantic component, which determines the notion of logical validity.
Semantics determine validity.
Grammar determines provability e.g soundness.
You can then ask the question: Can an invalid argument be sound?
Yes! The sky is green.
Classical logicians got EVERYTHING backwards.
Last edited by Logik on Thu Feb 07, 2019 3:12 pm, edited 1 time in total.
Re: The Liar's paradox
A green sky is false to both perception and inference.surreptitious57 wrote: ↑Thu Feb 07, 2019 2:51 pm So the sky is green is a grammatically correct sentence even though it is actually false
Sky is Sky
Blue is Blue
Sky is not Blue
After eliminating the inference of equality that tags along with “to be,” playing golf under a blue sky means that when I look up I see blue, when I look down I see green, when I look all around I see an organized kaleidoscope of kolor that familiarity arranges into order.
Re: The Liar's paradox
Bullshit.Walker wrote: ↑Thu Feb 07, 2019 3:11 pmA green sky is false to both perception and inference.surreptitious57 wrote: ↑Thu Feb 07, 2019 2:51 pm So the sky is green is a grammatically correct sentence even though it is actually false
Sky is Sky
Blue is Blue
Sky is not Blue
After eliminating the inference of equality that tags along with “to be,” playing golf under a blue sky means that when I look up I see blue, when I look down I see green, when I look all around I see an organized kaleidoscope of kolor that familiarity arranges into order.
That which you call 'blue' I have DECIDED to call 'green'.
Semantic difference.
Last edited by Logik on Thu Feb 07, 2019 3:13 pm, edited 1 time in total.
Re: The Liar's paradox
different word is different word
Furthermore, x is x.
Furthermore, x is x.
Last edited by Walker on Thu Feb 07, 2019 3:14 pm, edited 1 time in total.
Re: The Liar's paradox
Same meaning is same meaning. It's called a synonym.
That's not a grammatically coorrect proposition in type theory.
Last edited by Logik on Thu Feb 07, 2019 3:17 pm, edited 2 times in total.
Re: The Liar's paradox
x is x
y is y
x is not y
y is y
x is not y