Select the option that can be used as a one-word substitute for the given…

Concept: A one-word substitute is the single noun whose dictionary sense covers an entire defining phrase. English forms most such person-nouns with the suffix -ist, which names the holder of a doctrine or attitude, while the root standing before it carries the doctrine itself. The reliable method is therefore to strip the defining phrase down to its core idea and then match that idea to a root, rather than judging by the general mood a word gives off.

Application: The defining phrase here is "believes that no principles or beliefs have any meaning". Its core idea is a denial: principles and beliefs are held to carry no meaning or value at all. The Latin root nihil means "nothing"; nihilism is the doctrine that nothing has inherent meaning or value, and the person who holds that doctrine is a nihilist. Cambridge Dictionary defines a nihilist almost in the words of this phrase, so nihilist is the required one-word substitute.

Contrast with the near-miss words:

• Optimist (Latin optimus, "best") names an expectation about how events will turn out, and says nothing about whether principles carry meaning.

• Idealist (from ideal) names a commitment to high principles and standards, which affirms their meaning instead of denying it.

• Fatalist (Latin fatum, "fate") names the belief that events are settled in advance; what such a person denies is human control over outcomes, not the meaning of principles.

Cross-check: Reverse the test to confirm the fit: ask which of these four words a dictionary would define using the phrase "rejects all principles and beliefs as meaningless". Only the root nihil ("nothing") carries that sense, so nihilist is the answer.