Philosophy Lexicon of Arguments

 
Fine-grained, logic, philosophy: statements can be be more or less detailed. E.g. the fine-grained statement (x)(y)(x = y > (N(x = x) > N(x = y))) could be displayed in a coarse-grained way as A > B. For the decision of problems the coarse-grained form is often inadequate. See also decidability, possible worlds, situation semantics, possible world semantics, hyperintensionality.

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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.

 
Author Item Excerpt Meta data

 
Books on Amazon
II 34
Fine-grained/Field: E.g. sets of possible worlds are coarser than possible belief objects: eg the axioms of set theory and the Banach-Tarski theorem (BTT, strongly counter-intuitive) are logically equivalent, i.e. valid in the same worlds - but the BTT is not believed by all the people who believe the axioms of set theory - sentence meaning/Lewis: is fine grained - belief/Lewis: what one believes, is coarse - punch line: so the conviction is always the same: with and without BTT!
II 35
FieldVsStalnaker: sets of possible worlds are too coarse to distinguish beliefs - e.g. set theory with and without Banach-Tarski theorem are the same.


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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.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980


> Counter arguments against Field

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Ed. Martin Schulz, access date 2017-09-21