This comes really close to the ‘This statement is false’-discussion in Gödel-Escher-Bach. On itself, this statement is circular (if it were true, it would become false and vice versa), but when combined with another true/false statement, the full statement is not always circular:
If in “This sentence is false, or I am single”, the “I am single” part is false, then the truth-value of the full statement reduces to that of ‘This sentence is false’ and becomes circular. If ‘I am single’ is true, the whole statement is true independent of the first part, and so the statement is not circular (with ‘this sentence is false’ being true).
I guess the following happens in the Australia example: the Satan-worshipers must always say (full) statements which are false, so they can never set the truth-value of ‘this sentence is false’ to true. This way they are excluded from making “This sentence is false, or …”-type statements.
This comes really close to the ‘This statement is false’-discussion in Gödel-Escher-Bach. On itself, this statement is circular (if it were true, it would become false and vice versa), but when combined with another true/false statement, the full statement is not always circular:
If in “This sentence is false, or I am single”, the “I am single” part is false, then the truth-value of the full statement reduces to that of ‘This sentence is false’ and becomes circular. If ‘I am single’ is true, the whole statement is true independent of the first part, and so the statement is not circular (with ‘this sentence is false’ being true).
I guess the following happens in the Australia example: the Satan-worshipers must always say (full) statements which are false, so they can never set the truth-value of ‘this sentence is false’ to true. This way they are excluded from making “This sentence is false, or …”-type statements.