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> Are there examples of self-contradictory statements which aren't strictly self-referential? Depends on how you define "strictly" ;-) "This statement is fals

> Are there examples of self-contradictory statements which aren't strictly self-referential? Depends on how you define "strictly" ;-) "This statement is false" is strictly self-referentially false. "All absolute statements are false" is kind of indirectly self-referentially false, because it refutes its category, not itself as a statement. "We can only trust the results pure logic, direct sense impressions, and repeatable experiments" is a statement that is not any of those categories, and so it tells you, not that it's false, but at least that you can't trust that it's true. So that's kind of indirect, first because it's using the category, and second because it's not directly saying it's false. But, depending on your definitions, none of those may get outside your bounds of "strictly"...

dredmorbius 2y ago
The difference between your two examples is that "This statement is false" is undecidable, as it's false if true and true if false. "All absolute statements are false" includes itself, but also other statements. It's more akin to the notion of "the set of all sets that do not include themselves". That is to some extent solipsistic and tautological, in that the truth of the statement is defined by the statement itself, rather than on some exogenous state of the world. Much as "non-lactating mammal" or "spineless vertebrate" would also be dependent on definitions (mammals are lactating animals, vertebrates are animals having a spinal column).