This volume documents a lively exchange between five philosophers of mathematics. It also introduces a new voice in one central debate in the philosophy of mathematics. Non-realism, i.e., the view supported by Hugly and Sayward in their monograph, is an original position distinct from the widely known realism and anti-realism. Non-realism is characterized by the rejection of a central assumption shared by many realists and anti-realists, i.e., the assumption that mathematical statements purport to refer to objects. The defense of their main argument for the thesis that arithmetic lacks...

Prior's view on intensionality and truth is based on the principle that sentences never name, that what sentences say cannot be otherwise signified, that a sentence says what it says whatever the type of its occurrence, and that sentential quantification is neither eliminable, substitutional, nor referential. The text defends each of these principles.