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.
Author Item Excerpt Meta data
Field, Hartry
Books on Amazon
Fine-grained/ coarse-grained 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.

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

H. Field
Science without numbers Princeton New Jersey 1980

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Ed. Martin Schulz, access date 2017-04-24