|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._____________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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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 theBanach-Tarski theorem is not believed by all the people who believe the axioms of set theory.
Sentence meaning/Lewis: is fine-graine.d
Belief/Lewis: what one believes, is coarse-grained. - Punch line: so the conviction is always the same: with and without Banach-Tarski theorem.
FieldVsStalnaker: sets of possible worlds are too coarse-grained to distinguish beliefs. - E.g. set theory with and without Banach-Tarski theorem are the same._____________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.
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980