Beyond Substitution—An Antipositionalist's Guide to Subtraction—

ABSTRACT Existing accounts of relations do not properly account for variably polyadic relations: they fail to capture the relationship between completions of the same relation by different numbers of relata. This paper develops a fully general account of such relations by adding an operation of subtraction to the antipositionalist theory of relations pioneered by Fine in “Neutral Relations”. Along the way we rebut a common argument against antipositionalism; defend some strong principles about the behavior of occurrences of objects; and speculatively propose some principles about the structure of variably polyadic relations.