This reminds me of an old talk some guy gave at a Humanist meeting a while ago in my town:
The concept of a triangle refers to a thing that exists.
The concept of a six-hundred-foot diamond triangle floating above the Pentagon refers to a thing that does not exist.
The concept of a five-sided triangular square does not refer to a thing that does exist.
The concept of a five-sided triangular square does not refer to a thing that does not exist.
To say, "There is no five-sided triangular square" is to state that such a concept refers to a thing (albeit a non-existent thing) when in fact "five-sided triangular square" does not refer to a thing that either exists or does not exist.
This logical format is often used by ignostics to explain why they do not identify as agnostics/atheists; they argue that the concept of God is meaningless both linguistically and conceptually, and that even denying that God exists posits a link between language and form that doesn't actually exist.
The same argument works remarkably well when it comes to the self - to say "the concept of a self refers to something that exists" is wrong but it is also technically inaccurate to say "the concept of a self refers to something that does not exist" because the Buddha made it clear that the self wasn't even a meaningful or otherwise cognitively functional concept due to anatta, anicca, and dukkha. So that's why we have a doctrine of non-self; it negates the entire concept of the self entirely, instead of saying "this is what the self is/would be, do we or do we not have it?"
At least that's my take on it.
Gain and loss, status and disgrace,
censure and praise, pleasure and pain:
these conditions among human beings are inconstant,
impermanent, subject to change.
Knowing this, the wise person, mindful,
ponders these changing conditions.
Desirable things don’t charm the mind,
undesirable ones bring no resistance.
His welcoming and rebelling are scattered,
gone to their end,
do not exist.
- Lokavipatti Sutta