Logic versus Science.
There are three rules of the logic of internal consistency:
- Identity, 2) Non Contradiction, and 3) Excluded Middle.
Unfortunately, these rules refer to binary truth (identity) wherein all statements are true or false. But that presumption is false. All statements are true, false, or undecidable (null, meaningless, or unknown). But since undecidable statements cannot be used as premises in syllogism or deduction, they must be *treated* as false.
So in deductive logic we treat undecidable statements as false, even if they are merely unknown.
We use internally consistent, deductive truth in the discipline (science) of measurement that we call mathematics,
We use internally consistent deductive truth in the interpretation of Justificationary language: Law and Scripture (logic). We refer to collections of these proofs of internal consistency as axiomatic systems. They refer to ideals.
But in science, all operational statements are either false, surviving(not false: theoretical), or unknown(untested, or untestable). We refer to collections of these statements as theoretic systems (models not proofs), They refer to reality, not ideals.
So, whereas you can compose the liar’s paradox in ideal axiomatic language, you cannot do so in scientific language since a person would only compose the liar’s paradox as an accident, a trick or deception, and therefore we fault the speaker not the speech.