"The Tarski paradox"? Sorry, I think your memory has failed you, because there is no such thing. There is the Banach-Tarski paradox - https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox - but that's a completely unrelated result in measure theory (and it isn't really a "paradox" but an observation about how measure would break down if you were allowed to manipulate point sets arbitrarily).

The paradox you refer to is far older, the Epimenides Paradox. In its original form it's easily demolished by saying, "Most utterances that people make are neither true or false in a mathematical sense" but that wasn't the end of it.

Forbidding sentences that refer to themselves seemed like a better way to remove it, but then runs into this sentence (from Quine): '"makes a falsehood when preceded with its own quotation" makes a falsehood when preceded with its own quotation.'

Eventually, this leads to Gödel's Incompleteness Theorem.