  With Zalta’s interpretation in mind, we can understand the above passage from Mally as follows. According to Mally, a group of properties determines a conceptual object and thereby ensures that there is such an object. E.g., the property of being triangular (alone) determines the conceptual object we might identify as the triangle. This object is conceptual because it is not the case that it is a specific triangle in the ordinary sense of the verb ‘to be’ (understood as a copula). Mally would say the triangle does not instantiate the property of being triangular. But since every object is complete with respect to instantiation, the triangle instantiates the property of being non-triangular. Indeed, this latter property is implied by the property of being a conceptual object. Or, to put it in a different way: the property of being triangular is excluded by the property of being a conceptual object—conceptual objects have no shape at all. (For the concept of inclusion (Einschließung), see Mally 1912: 4 ff.) This results in the claim that the triangle is non-triangular, which is perfectly understandable if we understand ‘is’ in the sense of ‘instantiates’. Additionally, Mally offers us an algebra of properties that ensures that for each given property F there is an property non-F, i.e., its negation, which behaves in the usual manner (see Mally 1912: 14 ff.). For example, he implicitly assumes that instantiating non-F is materially equivalent to not instantiating F: