Some friends were playing a game where you say 1 truth and 1 lie about yourself, and the others have to guess which is which.
Just for fun, I was wondering if there was a reasonable way to give 2 statements about myself (1 assumed to be truth, and the other a lie) that would generate a Liar's Paradox (i.e. assigning a truth value either way leads to a paradox).
Obviously, I could make the statements:
1.) Statement 2 is False.
2.) Statement 1 is True.
and that would cleanly get me the Liar's paradox, but each of those are "meta" statements (statements that explicitly refer to the other statement). But what I want are more "reasonable" statements (preferably that could be about myself) that would lead to such a paradox. Statements like "I own all 50 state coins", or "I've never eaten waffles", etc..
Since realty is logically consistent (to the best of our knowledge), it is not possible to obtain truly paradoxical statements that are purely factual (without changing our fundamental understanding of the world). However, as you noted we can get such statements using meta references.
However, it is still possible to satisfy the intent of your question.
One solution can be to make factual statements about the kind of statements you make.
Example:
Statement 1: I have not told any lies in this game
Statement 2: I never speak the truth
The statements are fine by themselves if spoken from third person point of view ("Person A hasn't told any lies in this game" and "Person A never speaks the truth" are individually non-paradoxical statements") but cause a paradox if spoken by the same person.
Assume that statement 1 is true. Then statement 2 is a lie since you have spoken a true statement.
If statement 2 is true, then it is again a contradiction.
The trick is to make meta statements without making explicit references to the statements ;)
Note that statement 2 is actually sufficient by itself here. It is equivalent to the famous self-contradictory statement "This sentence is false".
So, strictly you could say: