Economics Dictionary of ArgumentsHome
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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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John Bigelow on Entailment - Dictionary of Arguments
I 57 Relational Theory/Bigelow/Pargetter. Can deal well with distinctions of differences. >Relation Theory/Bigelow. Question: Can it cope well with similarities? E.g., what is mass at all? >Determinates/Determinables. 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". >Properties/Bigelow. 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. >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. >Instantiation. 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. >Parts, >Part-of-Relation, >Circular reasoning, >Regress. Mereology/Lewis: is not sufficient in this case. >Mereology, >Sufficiency. (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. >Mereological sum. 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 Def 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. >Entailment. 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. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
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> Counter arguments against Bigelow
> Counter arguments in relation to Entailment
