|Entailment: material relationship between statements, unlike the formal implication. I.e. the content of the partial statements is relevant for the truth value of the composed statement. See also conditional, implication paradox.|
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Relational Theory/Bigelow/Pargetter. Can deal well with distinctions of differences.
Question: Can it cope well with similarities? E.g., what is mass at all?
Problem: We need a relation between a common property and many relations to it. There are many implications (entailments) that have not been explained yet.
Solution: Property 2nd level shared by all massive things. E.g. "to stand in mass relations".
Entailment/N.B.: this common (property 2nd level) explains the many relations of the entailment between massive objects and the common property of massiveness.
Problem/Bigelow/Pargetter: our relational theory is still incomplete.
Problem: to explain to what extent some mass relations are more similar than others.
Relations/Common/Bigelow/Pargetter: also the relations have a common: a property of 2nd stage.
Structural universals/Bigelow/Pargetter: we need them here without modalities. For this reason, we consider once again e.g. methane:
We are dealing with a complex pattern of entailments. When a molecule instances methane, it necessarily follows that there are parts of it that instantiate the other universals of hydrogen, etc.
Problem: with such a rich pattern of entailments, modal circles threaten. The partial relation is certainly not sufficient. We learn two lessons from David Lewis:
Mereology/Lewis: is not sufficient in this case.
(1) If a structural universal is composed only in a mereological manner, then methane would only be a mereological sum of hydrogen, carbon, and bond. That gives us our pattern of entailments.
Entailment/Lewis/Bigelow: one must not assume it between entities, when one assumes that nothing in the structure of these entities explains why these entailments should exist.
Problem/Lewis/Bigelow/Pargetter: to get to our pattern of entailments, we have to accept some kind of magic.
Entailments/Quantities/Bigelow/Pargetter: We have a similar complex pattern of entailments in the sets, (e.g. an object with a specified determinate mass) must also have a determinable mass, while everything with a determinable mass must have a certain determinate mass. Solution: 3 levels.
Definition entailment/Bigelow/Pargetter: A class A of sentences entails a sentence a iff. the sentence a is true in every possible world, in which all elements of class A are true.
If a is entailed by class A, then a is true in every possible world of a particular class C (of possible worlds)
Relevance: the relevant class of possible worlds is specified by the set A of sentences.
C. is the class of possible worlds in which all the sentences of A are true.
If A entails a, this means that a is true in every possible world in C.
Relative necessity: what is necessary here is necessary relative to A and relative to C.
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990