Ahh, I see, FJ. It’s an emotional thing. Okay.
“If a statement is true, then it is a member of the set of true statements.”
I’m fine with that.
“If a statement is false, then it implies a contradiction (as we find in a proof by contradiction).”
This is incorrect. A false statement does not imply anything. It does not imply a contradiction. There is no logical contradiction is this: “I am handsome.” Here’s why. To say that there is a contradiction confuses the technical and everyday (or extended) usages of the word “contradiction”. Logic is about statements only. While the statement “I am handsome” contradicts observation, that makes it only untrue, and not a logical contradiction, but a “contradiction” between the claim and the empirical observation. It’s not a logical contradiction. A logical contradiction is a condition that is logically impossible. It could be true that i am handsome - it just doesn’t happen to be true.
Correct, but a statement never is “in the same place” as an observation. Statements, once subject to verification, can turn out to be false, but a simple statement is never contradictory - for it would need another statement to contradict. Now, paradoxes, which a bit different, can be apparently self-contradictory, but “I am handsome” is not paradoxical. I hope we can leave paradoxes aside, as this would only cloud the waters more.
Again, I don’t think browser made a bad assumption. i think he is confounding two sense of the word “contradiction”, as I stated above.
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