“This statement is a lie” is considered a logical paradox which should be more accurately stated as “This statement is a lie sometimes” since “This true or false statement is a lie” is an absurd inaccurate illogical statement when the meaning is accurately expressed and when accurately expressed the contradiction is revealed and is no longer hidden by a generality which the word statement is.
There is also the seeming “paradox” in science that something can exist in two places at the same time on the subatomic level. Since time is measured in finite intervals it is entirely possible for something to oscillate between two locations during that finite interval of time so it creates the illusion that it exists in two places at the same time but the reality is that it is a logical and realistic absurdity. If the time interval used to measure the phenomenon were infinitely small the oscillation between the two locations would become apparent and we would not reach the absurd conclusion that something can exist in two places at the same time.
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