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I'm trying to reduce Nagarjuna's concept of self to logic. However, I'm new to logic and not an expert in Tibetean Buddhism. Is this a close fit?

∃x (S ∃¬x)

I'm reading it as:

If "S" represents the concept of having a permanent, unchanging self (similar to Nagarjuna's anatman), then the statement could be seen as a way to say: "There exists something that lacks a permanent self, because the existence of a permanent self is negated."

But another candidate is:

∃x (S ∃x)

Where I reinterpret "S" as "lacks a permanent, unchanging self," and existence refers to a temporary phenomenon, it could be seen as loosely capturing the idea of impermanent selves arising from causes and conditions.

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    Your formula is ungrammatical for several reasons. Negation cannot be applied to variables, only to predicates, different quantifiers apply to different variables, not the same one, and quantified variables go inside predicates written after the quantifier. "There exists something that lacks a permanent self" might be ∃x ¬ S(x), where S(x) is "x has a permanent self".
    – Conifold
    Commented May 21 at 19:59

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Cogito ...

If Sx = x has an enduring self then,

All things lack an enduring self = ∀x(¬Sx)

Equivalent to,

There is no thing that has an enduring self = ¬∃x(Sx)

Sabbe dhamma anatta

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