Philosophy Lexicon of Arguments

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I 147
Singular Term/Field: since an expression does not denote, it does not prevent it from being a real singular term. - e.g. "the number 4"/Field: does not denote any object. - But even with real singular terms, the question is whether the corresponding theorem is true. - The fact that a predicate has no extension does not prevent it from being a sortal: E.g. Homer E.g. "natural number". - FregeVsField: no singular term can stand for a concept. - (Wright pro Frege).
I 148
Sortal/Wright: syntactically, you cannot create statements of identity that contain a sortal like "well-being" (from "the well-being of children").
I 149
Singular: E.g. "2" in "2 + 3 = 5" - different: "there are two apples in the room": no singular term, but part of a quantifier - analyzed: numeric functor "the number of" plus singular term "three".
I 150
If "the direction of c1 = direction of c2" - logically equivalent: "c1 and c2 are parallel" - then expressions like "the direction of" cannot function semantically as a singular term. - If syntactically and semantically singular term, then they are without ontological commitment to other entities than lines. (no direction(s)).
Singular term/Field: we reject a singular term like e.g. "87" - solution: quantifier E87: "there are exactly 87" - quantifiers are not singular terms.
III 22
"87" does not appear as a name but as part of an operator.

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

> Counter arguments against Field
> Counter arguments in relation to Singular Terms

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Ed. Martin Schulz, access date 2017-05-27