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Minimal
Classical
Identity |
The minimal classical system P+ is obtained by adding
P10 to the postulates of P.
-
P10
 x y(y
ex X)
-
(Every haecceity is exemplified.)
Theorems of P+ include:
-
T42 x(x
= x)
-
(Every particular is self-identical.)
-
T43# xy(z(x
emb Z
 y
emb Z) x
= y)
-
(Indiscernible particulars are identical.)
-
T44 xy(x
= y)
-
(Every particular is classical.)
-
T45 xywz(x.Y
= w.Z)
-
(Some complex is classical.)
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Strongly
Classical
Identity |
The strongly classical system P++ is obtained by
adding P10* to the postulates of P.
-
P10* xy(y
ex X)
-
(Some haecceity is such that every individual exemplifies it.)
Theorems of P++ include:
-
T47 xy(x.Y
= x.Y)
-
(Every complex is self-identical.)
-
T29# wxyz(v(w.X
emb Vy.Z
emb V)w.X
= y.Z)
-
(Indiscernible complexes are identical.)
-
T46 xywz(x.Y
= w.Z)
(Every complex is classical.)
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Weakly
Classical
Identity |
The weakly classical system P+- is obtained by adding
P10*' to the postulates of P+.
-
P10*' ¬xy(y
ex X)
-
(No haecceity is such that every individual exemplifies it.)
Theorems of P+- include:
-
T47' ¬xy(x.Y
= x.Y)
-
(Not every complex is self-identical.)
-
T29'# ¬wxyz(v(w.X
emb Vy.Z
emb V)w.X
= y.Z)
-
(Not all indiscernible complexes are identical.)
-
T46' ¬xywz(x.Y
= w.Z)
(Not every complex is classical.)
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