Philosophy Lexicon of Arguments

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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.

Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

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I 57
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.
I 58
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.
I 83
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.
I 84
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.
I 86
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.
I 224
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.

Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.

Big I
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990

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Ed. Martin Schulz, access date 2017-10-19