Philosophy Now Forum

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

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

The answer is that the sentence is true/false/neutral all at the same time.

Paradox leads to never ending paradox, thus necessitating all paradoxes as the meaning to further paradoxes as a solution in themselves.

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

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

surreptitious57 wrote: ↑Thu Feb 07, 2019 7:59 am The sentence ... is gramatically correct

In which grammar?

surreptitious57 wrote: ↑Thu Feb 07, 2019 8:18 am
Despite having no referent it is still true according to the rules of descriptive grammar

I am not sure how to parse this.

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.

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

OK, sounds right to me.

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

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.
EB

Logic wrote:
Rules describe the grammar of any particular language

Are unsound syllogisms grammatically wrong because they are factually wrong as well
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

surreptitious57 wrote: ↑Thu Feb 07, 2019 2:51 pm Are unsound syllogisms grammatically wrong because they are factually wrong as well

We've missed each other.

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.

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

A green sky is false to both perception and inference.

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.

Walker wrote: ↑Thu Feb 07, 2019 3:11 pm

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

A green sky is false to both perception and inference.

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.

Bullshit.

That which you call 'blue' I have DECIDED to call 'green'.

Semantic difference.

different word is different word

Furthermore, x is x.

Walker wrote: ↑Thu Feb 07, 2019 3:13 pm different word is different word

Same meaning is same meaning. It's called a synonym.

Walker wrote: ↑Thu Feb 07, 2019 3:13 pm Furthermore, x is x.

That's not a grammatically coorrect proposition in type theory.

x is x

y is y

x is not y