I vaguely remember such a thing as the Liar’s Paradox. Someone says: I (always) lie. If that’s a lie, he spoke the truth. But he lied. Paradox!
Suddenly, I thought that’s nonsense. There is no paradox here. I looked in Wikipedia because often, that is very complete about such things.
And yes, Wikipedia has collected ideas about this paradox from the great over the years, centuries, and millennia. It quotes a number of very smart people who hold that there is no paradox. But, I lack the time and patience (and maybe intelligence or at least English skills) to grasp that quickly.
Time to share my simple idea.
1. That was a lie. Then, that’s clear. He lied and admitted it.
2. But, if he said he lied, he spoke the truth? No, he didn’t. He lied that he lied. That is fully compatible with the lying in the first possibility.
There are such people. Even when they are truthful, they ‘lie.’ But that’s another issue. They lie by default. Then, their sporadic truths confuse too.
Full disclosure: I don’t do well with liars.