 But maybe there is not much to explain here. Maybe reality does not have anything like a structure that mirrors the form of our thoughts, at least not understood a certain way. One might hold that the truth of the thought “John smokes” does not require a world split up into objects and properties, it only requires a smoking John. And all that is required for that is a world that contains John, but not also another thing, the property of smoking. Thus a structural match would be less demanding, only requiring a match between objects and object directed thought, but no further match. Such a view would be broadly nominalistic about properties, and it is rather controversial. 