Supplement to Supervenience

Appendix: List of Definitions

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).

Individual Supervenience
Weak Individual Supervenience
Possible-Worlds Formulation: A weakly supervenes on B iff for any possible world w and any individuals x and y in w, if x and y are B-indiscernible in w, then they are A-indiscernible in w.

Modal Operator Formulation: A weakly supervenes on B iff necessarily, if anything x has some property F in A, then there is at least one property G in B such that x has G, and everything that has G has F.

□∀xFA[Fx → ∃GB(Gx & ∀y(GyFy))]

Strong Individual Supervenience
Possible-Worlds Formulation: A strongly supervenes on B iff for any possible worlds w1 and w2 and any individuals x in w1 and y in w2, if x in w1 is B-indiscernible from y in w2, then x in w1 is A-indiscernible from y in w2.

Modal Operator Formulation: A strongly supervenes on B iff necessarily, if anything x has some property F in A, then there is at least one property G in B such x has G, and necessarily everything that has G has F.

□∀xFA[Fx → ∃GB(Gx & □∀y(GyFy))]
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-indiscernible 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*.

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Copyright © 2011 by
Brian McLaughlin <brianmc@rci.rutgers.edu>
Karen Bennett <kb383@cornell.edu>

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