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Just as HI establishes the criterial properties
of identity for individuals and haecceities, so C (which contains HI)
establishes these properties for complexes: weak reflexivity (T12),
symmetry (T13), transitivity (T14), indiscernibility for identicals (T15#),16
and identity for self-identical indiscernibles (T16#).17
C thus grounds a minimal identity relation for individuals, haecceities,
and complexes.
-
T12
 wx( yz(w.X
= y.Z) w.X
= w.X)
(Identity is weakly reflexive.)
-
T13 wxyz(w.X
= y.Z
 y.Z
= w.X)
(Identity is symmetric.)
-
T14 vuwxyz(v.U
= w.X & w.X = y.Z v.U
= y.Z)
(Identity is transitive.)
-
T15# vuwxy(v.U
= w.X(v.U
emb Yw.X
emb Y))
(Identicals are indiscernible.)
-
T16# vuwx(v.U
= v.U & w.X = w.X y(v.U
emb Y
w.X emb Yv.U
= w.X))
(Self-identical indiscernibles are identical.)
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