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Finite/finiteness/1st order logic with identity/Field: a statement about finiteness cannot 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._____________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