# propositional logic

Question

Why

“This statement is true” is proposition while “This statement is false” is liar paradox?

Aren’t both statements supposed to be liar paradox ?

Answer 1

If you assume  “This statement is true”  as TRUE ,  then there is no contradiction to this , it is true only,

but if you assume “This statement is false”  as TRUE ,  but this statement is actually false , so here is a contradiction.

 

you can refer → https://www.quora.com/The-liars-paradox-is-usually-resolved-by-saying-the-statement-is-neither-true-nor-false-but-what-about-the-statement-this-sentence-is-not-true-How-do-we-resolve-this-form-of-the-paradox

Comments

And what about assuming “This statement is true” as false?

---

Aditi Thakur

I think its the same .(reverse of this)

Answer 2

Statement : Statement is false.

 

Assuming Statement = True, then Statement is false.

Assuming  Statement = False, then Statement is true.

 

Hence its a paradox.

Comments

Do we need to prove the contradiction for all the possible assumptions or for just one is enough to be called a paradox?

---

As paradox is a situation or statement with two or more parts that seem strange or impossible together so,

Either of them should be enough as one case is enough to prove that it has contradicted.