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1 a : a viewpoint that traditional values and beliefs are unfounded and that existence is senseless and useless b : a doctrine that denies any objective ground of truth and especially of moral truths
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To practice nihilism is to deny the possibility of discovering absolute truth.
In this context, the denial of absolute truth is your attempt to characterize "left" versus "right" as "apples versus oranges", by way of your claim that anyone who doesn't entertain both leanings is wanting. This is a form of nihilism.
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I'm still not sure how, looking at the definitions of nihilism, what it has to do with anything.
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See sig...
Put more simply:
Usd identifies as right wing.
His basis for denying the "objectivity" of the left-leaning is that they claim to be objective yet refuse to consider his position as equally valid. In reality, his views are simply wrong, and have been considered and rejected by those people.
Hence, to cop out of that rejection, he denies that any viewpoint can be objectively determined to be incorrect. In reality, of course, it is possible to determine that some ideas are correct and some ideas are incorrect - the opposite of nihilism - which is why those who claim to be "objective" in rejecting the viewpoint are not being hypocritical.