Eventually, the modern tradition becomes very suspicious the idea that there can be a similarity between the contents of the mind and characteristics of things in the external world. First, we have Locke denying the possibility of the similarity thesis for secondary qualities like red and sweet, and then we have others, like Berkeley and Reid, denying the possibility of the similarity thesis for primary qualities, like triangularity. In the case of primary qualities, it just seems absurd to think that the mind should hold something like a triangle.
This denial of the possibility of the similarity thesis seems to me to be a massive failure of the philosophical imagination, and a neglect of a sympathy to the history of philosophy. The allegation of the absurdity of thinking that triangularity should be present in the mind and in the world seems to come from thinking that the only way triangularity can be present in an entity is by the entity’s having triangularity. But why should having be the only possible relation by which triangularity could be present in a thing?
Here are some ways in which a property could be in a thing without the thing having the property.
Let S be the set of the polygonality properties. Thus, the members of S are triangularity, quadrilaterality, etc. Triangularity is then in S qua member of S, but S is not a triangle—it does not have triangularity.
On divine simplicity, God is identical with his divinity. But God can be present in Francis without Francis having God’s divinity—i.e., without Francis being divine.
Suppose that I have a wood triangle in a steel box. The triangle’s triangularity is in the triangle, and the triangle is in the box, so the triangularity is in the box.
Say that my fingernail is pointy. The properties of a thing are parts of a thing. So, the fingernail has its pointiness as a part. But the fingernail is a part of me, and parthood is transitive. So the pointiness of the fingernail is a part of me. But I am not pointy, even though I have a pointiness in me.
There is nothing absurd, then, about there being triangularity in the mind without the mind being itself triangular.
Moreover, having triangularity in the mind is not even a necessary condition for there to be a relevant similarity between the mind and a wooden triangle outside of me. It could be that the triangularity in the triangle is not a simple entity, but is composed of two components, T and P, where the P component is common (either as type or as token) between all properties, and the T component distinguishes triangularity from other properties. Thus, squareness might consist of S and P, and redness might consist of R and P. Well, then, we can suppose that when I think of or perceive a triangle as a triangle, then T comes to be in my mind without P doing so. Perhaps T comes to be “elementally” present in my mind, or perhaps it comes to be compounded with something else. (Here is a Thomistic version: triangularity has an essence T and a natural esse P; when present in the mind, the essence is there, but instead comes to have a different thing from the natural esse, say an intentional esse.) In either case, we have something importantly in common between the mind and the triangle qua triangular, namely T, without having triangularity in the mind, but only a component of triangularity.
There is no paucity of options. Indeed, we have an embarrassment of riches—many, many ways of making the similarity thesis true.
