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Here it is, from John Galt's big speech in "Atlas Shrugged": "A is A: non-contradiction".
The thing I think people find hard to wrap their minds around is the following non-contradiction: 1.
(See also Aristotle on Non-contradiction).
Of course the law of non-contradiction produces tautologies, too.
See Aristotle's Metaphysics, Aristotle on non-contradiction, Dancy 1975, and Code 1986 for further discussion.
But by the Law of Non-contradiction we know that ~(R ∈ R ∧ ~(R ∈ R)).
(5) Therefore, Damian has to claim that the principle of non-contradiction is not universally valid.
Such hold that there are exceptions to the law of non-contradiction.
This states the Principles of Non-contradiction and of Excluded Middle.
The Eastern responses are more dialectical, whereas Westerners are guided by the principle of Non-Contradiction.
The law of non-contradiction states that a proposition and its negation cannot be both true.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com