Purely logical truths can be distinguished from values--moral obligations, aesthetic standards, and existential meaning--due to the self-verifying, necessary nature of the former and the fact that the latter pertains to something more than the existence of logical truths. If objective values exist, the truth of logic is a metaphysical prerequisite, or else it could not be true that any values at all are binding or obligatory; however, it does not follow from the existence or truth of logic that there is any set of obligations dictating how people should behave. Not even the total nonexistence of objective values could erase logical truths. Somehow, some people have equated nihilism with an idea that goes beyond this.
Nihilism, if true, would not and cannot mean that there is no such thing as reality. It could not mean that nothing is true or that nothing exists! Nihilism merely entails that nothing, not even truth itself, has any meaning in the sense of existential significance. If it contained a denial of the existence of objective truth, or things that are true regardless of perception or awareness, it would be false by default, as objective truth is self-evidently necessary. To deny the objective truth of logic is to stand on the very thing being denied, and thus any idea that does so is inherently contradictory and therefore false.
Truth is still true; logic still governs all things, and logical truths could not have been any other way. Nihilism might be true, as proving logical facts is not the same as proving that objective values exist, even if the nonexistence of objective meaning is utterly unprovable--and incapable of being disproven as well. If nihilism is true, then nothing other than values are affected. Everything other than values would remain exactly the same as it otherwise would be. Thus, only a fool would try to twist the concept of nihilism into something like relativism with regards to values or anything else, as some do.
There are people who understand the difference between nihilism and metaphysical relativism or anti-realism, and there are people who use the terms interchangeably, as if a nihilist is someone who believes that nothing at all exists (not even something self-evident like one's own consciousness that must be used in the rejection) or that nothing at all is true (which means nihilism could not be true). Logical truths, one's consciousness, and other demonstrable things exist even if there is no actual significance to any of them in the sense of existential meaning. Every idea about values conforms to reality or does not, but certain other things are true regardless.
All claims about values are objectively true or false, as even moral nihilism simply means that all claims that something is obligatory or meaningful are false. Truths about values are only a subset of truth either way. If objective values do not exist, logical truths about the nonexistence of objective values would still hold, and the notion of objective values would not contain an inherent contradiction if personal perceptions are not the focus of the idea. The inherent truth of logical axioms and sound deductions renders all ideologies that contradict them false, with nihilism not contradicting the few self-proving truths that define reality, yet also having no evidence in its favor at all. Nihilism is thus ultimately a matter of unverifiable and unfalsifiable speculation.
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