For ease of reference, the technical definitions discussed in earlier
sections are collected in this section. ‘A’ and
‘B’ should be understood as variables ranging
over non-empty sets of properties (though the quantification is
typically implicit).
- Regional Supervenience
- Weak: A weak-regionally supervenes on
B iff for any possible world w and any space-time
regions r1 and
r2 in w, if
r1 and r2
are exactly alike in every intrinsic B-respect in w,
then they are exactly alike in every intrinsic A-respect in
w.
Strong: A strong-regionally supervenes on
B iff for any possible worlds
w1 and
w2 and any space-time regions
r1 in
w1 and spacetime region
r2 in
w2, if
r1 in
w1 is exactly like
r2 in
w2 in every intrinsic
B-respect, then r1 in
w1 is exactly like
r2 in
w2 in every intrinsic
A-respect.
- Similarity-Based Supervenience
- Weak Similarity-Based: A weakly
supervenes on B iff for any world w, and for any
x and y in w, if x and y
are not largely different with respect to B-properties, then
they are not largely different with respect to A-properties.
Strong Similarity-Based: A strongly
supervenes on B iff for any worlds
w1 and
w2, and for any x in
w1 and y in
w2, if x in
w1 is not largely different from
y in w2 with respect to
B-properties, then x in
w1 is not largely different from
y in w2 with respect to
A-properties.
- Global Supervenience
- Generic Global: A globally supervenes on
B iff for any worlds w1
and w2, if
w1 and
w2 have exactly the same world-wide
pattern of distribution of B-properties, then they have
exactly the same world-wide pattern of distribution of
A-properties.
Weak Global: A weakly globally
supervenes on B iff for any worlds
w1 and
w2, if there is a
B-preserving isomorphism between
w1 and
w2, then there is an
A-preserving isomorphism between them.
Intermediate Global: A intermediately
globally supervenes on B iff for any worlds
w1 and
w2, if there is a
B-preserving isomorphism between
w1 and
w2, then there is an
A-and-B-preserving isomorphism between
w1 and
w2.
Strong Global: A strongly globally supervenes on
B iff for any worlds w1
and w2, every B-preserving
isomorphism between w1 and
w2 is an A-preserving
isomorphism between them.
- Multiple Domain Supervenience
-
Weak Multiple Domain: A weakly supervenes on
B relative to relation R just in for any world
w and any x and y in w, if
R|x in w is B-indiscernible from
R|y in w, then x and y are
A-indiscernible in w.
Strong Multiple Domain: A strongly
supervenes on B relative to relation R just in case
for any worlds w1 and
w2, any x in
w1 and y in
w2, if R|x in
w1 is B-indiscernible from
R|y in w2,
x in w1 is
A-indiscernible from y in
w2.
Weak Coincident-Friendly: For any world w
and any x and y in w, if x in
w is B-discernible from y in w, then for
each thing x* in w to which x is
R-related, there is something y* in w to
which y is R-related, and which is
A-indiscernible from x*.
Strong Coincident-Friendly: For all x and
y, and all worlds w1 and
w2, if x in
w1 is B-indiscernible from
y in w2, then for each
thing x* in w1 to which
x is R-related, there is something y* in
w2 to which y is
R-related, and which is A-indiscernible from
x*.
∀x∀F∈A[Fx
→
∃G∈B(Gx &
∀y(Gy→Fy))]