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Definition Positive Fact/Chalmers: A positive fact in world W is one that applies in every possible world that contains W as a real part, correspondingly a positive property in W is one that is instantiated in every world containing W as a real part. (Chalmers I 363: Containment of possible worlds.)
On the other hand:
Negative facts always imply negative existence statements, which cannot be evaluated locally on their part.
We will restrict ourselves to positive facts and properties when considering supervenience.
Negative Facts/Chalmers: Facts that involve negative existence statements are not logically determined by any localizable facts. Even facts about conscious experience cannot help here. ((Chalmers I 369 Negative facts and logical supervenience ...+...).
Solution/Chalmers: we must introduce a second-level fact which, according to the enumeration of the microphysical, phenomenal, indexical, etc. facts says:
"This is all." All the negative facts follow from the fact of the second level together with all the basic single facts.
Reductive explanation: negative facts are not a serious problem for reductionist explanations.
2nd level fact/Chalmers: there will be probably a statement "that is all" for every possible world and such a fact is never included in the single facts. It merely expresses the finite nature of our world or of any other world. It is a simple way to deal with negative and universally quantified facts. (> Universal quantification, > Lists, inside/outside, > totality).
Facts/World/Chalmers: Facts about the world are exhausted by
1. Physical single facts
2. Facts about conscious experience
3. Natural laws
4. A fact of the 2nd level, which means "This is all."
5. An indexical fact about my localization.
The Conscious Mind Oxford New York 1996
Constructing the World Oxford 2014