.: That Which Stands Under :.

Tuesday, September 13

Let X be: "This statement is false."
Then,
Is X true or false?

... or something else?

What is your answer?

The statement is self-referentially absurd.

By Pilgrim in Progress, at 12:32 PM
B Jay

It all depends on what "this" is modifying. If "this" is self-referential, then the statement is incoherent. If "this" refers to some other proposition, say y=the sky is green, then x would be true, e.g., this proposition [implying y] is false.

By Jeremy, at 12:44 PM
Jeremy,

Let X be: "This statement is false."

This proposition is an "identity statement," if you will.

Let us write it this way:
X = This statement is false.

The question "is X true or false" must therefore regard the content that we have assigned to X, namely, that x= this statement is false.

"This," therefore, does not refer to any other proposition.

"This" can only refer to the statement itself.

Therefore, the statement is self-referentially absurd.

By Pilgrim in Progress, at 8:27 PM