Is a *self-contradictory self-referential* statement false?

Question

Fitch concludes in his paper "A Goedelized formulation of the prediction paradox" that the following is a self-contradictory self-referential statement:

P: The prisoner will be hanged next week and its date will not be deducible the night before using this statement as an axiom.

Let's assume that this statement is false, no matter what the hanging day is. A judge has said this statement to two prisoners, and has chosen Monday and Tuesday as the hanging days.

Prisoner 1 is hanged on Monday, then ~P implies that it's deducible from P that the hanging day is Monday.

Prisoner 2 is hanged on Tuesday, then ~P implies that it's deducible from P that the hanging day is Tuesday.

It's a contradiction. Where's the fault?

Answer 1

We often use "self-contradictory" to mean simply "contradictory".

In this case: yes, a contradictory statement is always false.

If with "self-contradictory" we assume some form of "self-reference", we have to consider that self-reference is a thorny issue:

In the context of language, self-reference is used to denote a statement that refers to itself or its own referent. The most famous example of a self-referential sentence is the liar sentence: “This sentence is not true.”

Thus, if with "self-contradictory" we mean the paradigmatic Liar-example :

"This sentence is not true",

the answer is that both assumptions about its truth-value lead to contradiction.