"In 1936 Tarski proved a fundamental theorem of logic:
the *undefinability of truth*. Roughly speaking, this says there's no
consistent way to extend arithmetic so that it talks about 'truth' for
statements about arithmetic. Why not? Because if we /could/, we could
cook up a statement that says "I am not true." This would lead to a
contradiction, the Liar Paradox: if this sentence is true then it's not,
and if it's not then it is.
This is why the concept of 'truth' plays a limited role in most modern
work on logic... surprising as that might seem to novices! ..."
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