You are absolutely correct. I haven’t thought this through. Thank you for the lesson.
Edit: I did take the lesson that I should think more before making such a claim, however, I wanted to point out that your sentence poses no problem and was not the point.
this p. is false is contradictory
this p. is condradictory/ambigous is false
The conjunction of contradictory and false is contradictory so you have a unique solution.
This is also what intuition tells us since the proposition cannot be true and cannot be false and that would be contradictory.
I don’t understand your solution. If the proposition is contradictory, then it’s true—just look at what it says.
Or maybe I don’t understand how we are supposed to assign truth values to disjunctions (“either/or”) in your system: can a disjunction still be contradictory if one of its clauses is true? And surely if X is contradictory, then the clause “X is contradictory” must be true… or is it?
You are absolutely correct. I haven’t thought this through. Thank you for the lesson.
Edit: I did take the lesson that I should think more before making such a claim, however, I wanted to point out that your sentence poses no problem and was not the point.
this p. is false is contradictory this p. is condradictory/ambigous is false The conjunction of contradictory and false is contradictory so you have a unique solution. This is also what intuition tells us since the proposition cannot be true and cannot be false and that would be contradictory.
I don’t understand your solution. If the proposition is contradictory, then it’s true—just look at what it says.
Or maybe I don’t understand how we are supposed to assign truth values to disjunctions (“either/or”) in your system: can a disjunction still be contradictory if one of its clauses is true? And surely if X is contradictory, then the clause “X is contradictory” must be true… or is it?
Ok, I get it now. So, I was wrong on that too. Thank you.