Self Doubt: Mathematical Logic

Question

Is the assertion "This statement is false" a proposition?

Answer 1

Yes Indeed its a proposition. 

This is a Liar Paradox. Read it here. It is a very very interesting read. You will love it, I am sure. 

Comments

@rude, a proposition is a declarative sentence to which we can assign exactly one value, true or false but not both.
"This statement is false". We can't assign any value to this how this can be a proposition.
I know this is Liar's paradox.

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I also think that It is not a proposition which is given here

Here, Statement (A) is getting both True and False truth values based on hypotheses but a proposition either has true or false but not both truth values and in both cases it is getting contradiction. So, given statement does not have any truth value. So, It should not be a proposition.

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U mean liar paradox isnot a proposition

rt??

Answer 2

any assertion for which you can give answer in TRUE OR FALSE/////.... is a proposition..

for example...

1+1=3 is a proposition...coz it is false 

what is your name ?....... is not a proposition..coz u can't say..true or false abt this statement..

Is the assertion "This statement is false" is surely

a proposition....coz u can give answer in true/false

Answer 3

This is definitely Not a proposition,because its self referential and its a liar's paradox.
If u assign truth value of the statement TRUE, then its self conflicting because at the same time it says the statement is false as well as true which is not correct for a proposition as a proposition always has a single truth value.
If u assign FALSE,then u are saying the truth value of the statement is false i.e the statement is actually true,so again self-conflicting.So its not a proposition.
https://math.stackexchange.com/questions/697444/propositional-logic-dont-know-the-answer

Answer 4

Nope. Absolutely not. Here's why:

A proposition is either a true or false whether it's from my perspective or yours, it is a must TRUE or FALSE but not both. If something that is beyond this than it can be considered as into somewhat in the Fuzzy Logic zone.

Now our sentence is "This statement is false." What does this mean?

If the statement is true than the given "This statement is false" is true meaning that the given statement is false.

If the given statement is false than the statement "This statement is false" is false meaning that the given statement is true.

So we get True with false and False with True. Nothing but seems sort of a paradox.

But what is the root of this given "predicate" that is making it so much amazing.

What. Why is this a predicate? 

-> "This statement is false" is just a statement until and unless we provide it with some values. And once we provide it with the "True" or "False" values it becomes a proposition that is a "statement". 

now, what or where these "True" or "False" values being applied.

These values are being applied on the "this" part of the predicate.

"This statement is false". 

We can treat "This" as a free variable that can choose values from the given domain of {True, False}.

As seen earlier, the statement outputs True on input False and output False on input True. 

More, the given predicate is a self referencing predicate. 

Now if we take "This sentence is false" as F(x), x being the truth value we want to take then we can write predicate as not of F(F(x)).

But this is not a proposition as we can't determine a single truth value. We can't determine what F(x) is. true or false?

Therefore from the given statement "This statement is false" nothing can be concluded that is true or false but not both. Hence not a proposition.