Philosophy Lexicon of Arguments

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Field, Hartry
 
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Finiteness III 95
finite / 1st order logic with identity / Field: a statement about finiteness can not be identified with a sentence of 1st order logic plus identity - solution: take "There is only a finite number of" as a primitive quantifier - a theory of truth for "E-fin" of course, would have to introduce the notion of finiteness. But this is not an objection to the clarity and usability of the logic - at least the assertion "there are infinitely many grains of sand" needs no functions, quantities and numbers.

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


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Ed. Martin Schulz, access date 2017-04-25