In Defense of Relations


Edward N. Zalta


forthcoming, dialectica (special issue: The Metaphysics of Relational States), Jan Plate (ed.).


Two recent arguments draw startling and puzzling conclusions about relations and 2nd-order logic (2OL). The first argument concludes that 2nd-order quantifiers can't be interpreted as ranging over relations. This conclusion is puzzling because it calls into question the traditional understanding of 2OL as a formalism for quantifying over relations. The second argument, which concludes that unwelcome consequences arise if relations and relatedness are analyzed rather than taken as primitive, utilizes premises that imply that 2OL faces the very same consequences. This is puzzling because relations and predication are taken as primitive in 2OL, and so the latter should be immune to the problems raised for the analysis of relations. I consider these two arguments in light of a precise theory of relations. In particular, I show that object theory (Zalta 1983, 1988), which is an extension of 2OL, provides systematic existence and identity conditions for relations, properties, and states of affairs that forestall the two arguments.

[Author's preprint available online in PDF]