The partitions of Mark-Arithmetic I, `{(),()()}/{(())}`, assert the *Call* rule `()=()()`; idempotency is the primary differentiator between logic and numerics. The mark is TRUE, while forms SHARING a space are interpreted as joined by disjunction. BOUNDING is negation.
f void t ( ) ¬A (A) A → B (A) B A ∨ B A B A ∧ B ((A)(B))
Spencer Brown's innovation was to equate `(())` with nothing at all, that is, with the contents of the dotted frame prior to drawing the first mark. This created two Boolean equivalence classes while using only one symbol. Truth is confounded with existence, a capability unique to the spatial structure of the mark. The *Cross* rule generalizes to algebra as both *Occlusion*, which terminates proofs, and *Involution*, which enforces depth parity.
CALL ()() = () CROSS (()) = void OCCLUSION (A ()) = void INVOLUTION ((A)) = A PERVASION A {A B} = A {B}
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idempotency ⇒ Idempotence: […] in the words of George Boole, who explains his figure-like law of idempotence (" x x = x ") as follows:
> The case supposed [...] is that of *absolute* identity of meaning. The law which it expresses is practically exemplified in language. To say „good, good“ in relation to any subject, though a cumbrous and useless pleonasm, is the same as to say „good“. Thus „good, good“ men, is equivalent to „good“ men. Such repetitions of words are indeed sometimes employed to heighten a quality or strengthen an affirmation. But this effect is merely secondary and conventional; it is not founded in the intrinsic relations of language and thought.