As Asay says in the essay:
Alternatively, [the thesis is that] there is no property of truth—even in the “merely abundant” or deflated sense of ‘property’.
This opens the door to a variety of corollary definitions:
- Truth-value nihilism: Frege held that truth is not a property of sentences/propositions but is an object to which sentences can refer; when this reference is secured is when we say that sentences are true. A nihilist about truth-values/truth-objects can deny this; but then a truth-value nihilist need not be a truth-property nihilist.
- Truth-predicate nihilism: we might also call this truth-relation nihilism, taking relations as polyadic predicates. Having a naive truth-predicate/truth-property allows the liar paradox to be constructed. If for all sentences S, it is a fact that not(S and not S), i.e. if the law of noncontradiction is assumed, a theory that allows us to construct an otherwise inescapable contradiction is a disproven theory. So the theory of a naive truth-predicate is disproven; so there is no naive truth-predicate.X
- Obtaining-states-of-affairs nihilism: the obtainment relation in the theory of states-of-affairs (SoA's) is not identical to the truth relation in the theory of sentences/propositions. Although SoA's are not always indicated by expressions like, "Mary's being a neuroscientist," or, "John's having of some breakfast," etc., these are typical such markers. Whereas we can say, "This sentence is not true," we can't say, "This SoA's not being true," since gerundive nominals are not truth-apt. "This SoA's not obtaining," perhaps does not generate a paradox, or if it does, demonstrating how is different enough from constructing the liar paradox that the obtainment relation is not the same as the truth relation. So it would be possible to affirm or deny the obtainment relation independent on one's affirmation or denial of the truth relation.
So one might be an alethic nihilist in any one or two of those senses, or even all three. It does seem as if threefold alethic nihilism would be tantamount to a self-refuting position or a change-of-subject. Generally, it is less that abstract definitions of concepts are, or fail to be, factually correct, but the issue is more how the concepts are used and if our use of them is an efficient way to approach our communication goals. I would like to add that Asay's paper as posted is in draft form, and I'm not entirely sure if it has been actually published yet: this link does indicate a late 2021 publication date, but maybe that's for a different version of the essay? Another paper by two other authors and exploring this territory, however, was published in 2017, which means plenty of time for alethic nihilists to have responded. Perhaps this pro-nihilism(!) essay from 2023 includes responses to either of the preceding texts.
XOne could zigzag off the changing-the-subject objection, here, and say that the way the truth-predicate is used in the construction of the liar sentence is itself already a change-of-subject, i.e. there is a world of difference between the way the phrase "is true" is used in, "It is true that snow is white," and, "It is true that this sentence isn't true." This would undermine one of the motivations for alethic nihilism from the outside.