By properties which are asserted of a concept I naturally do not mean the characteristics which make up the concept. These latter are properties of things which fall under the concept, not of the concept. Thus “rectangular” is not a property of the concept “rectangular triangle”; but the proposition that there exists no rectangular equilateral rectilinear triangle does state a property of the concept “rectangular equilateral rectilinear triangle”; it assigns to it the number nought.
In this respect existence is analogous to number. Affirmation of existence is in fact nothing but denial of the number nought. Because existence is a property of concepts the ontological argument for the existence of God breaks down. But oneness* is not a component characteristic of the concept “God” any more than existence is. Oneness cannot be used in the definition of this concept any more than the solidity of a house, or its commodiousness or desirability, can be used in building it along with the beams, bricks and mortar.
G.W. Frege, The Foundations of Arithmetic, trans. J.L. Austin (Northwestern University Press: 1950) pp. 64-65 – emphasis mine.
- [*] Here Frege simply means “the character of being single or unique, called by theologians ‘unity'” (p. 65).