External Conditions of Thought
The idea of the singular proposition is that propositions can contain particulars as well as universals as their constituents. If I think that that bird is pretty, my thought’s content contains both a particular bird and the general property of being pretty. Thus a singular thought has conditions of identity and existence that depend on objective particulars—birds, cities, planets, other people, etc. No such particular, then no such thought; and thoughts are distinct in virtue of the distinct particulars they contain. It is not often remarked that the same thing is true of the properties that constitute the other half of the proposition (so to speak): they too supply the identity and existence conditions of the thought (or the meaning of the corresponding sentence). The property also sits inside the proposition, alongside its partner, the particular. Propositions offer hospitality to both sorts of entity.
Given this general picture, we can formulate a kind of transcendental argument for the existence of particulars, as follows. If we accept that singular thoughts exist, then the world must contain the particulars that form them—both those particulars in particular and also particulars as a category. That is, there is no possible world in which singular thoughts exist and particulars don’t. The particulars don’t have to be material objects or events but could also be mental particulars; so the transcendental argument doesn’t disprove idealism. What is required is just that some particulars exist—specifically those that form the singular propositions that constitute the content of singular thoughts (and meanings). We know, then, that the world cannot consist solely of universals. That would not follow if propositions were invariably general as to content; then those propositions could exist in the absence of particulars. If description theories of reference were true, perhaps accompanied by Russell’s analysis of descriptions, then the existence of particulars would not be a precondition for the existence of propositional contents; so the world could be void of particulars and those thoughts would still be available to be thought. This is a straight consequence of the theory of singular propositions: singular thought is impossible in the absence of particulars, so if there are singular thoughts there are particulars. The theory of thought thus implies a certain kind of metaphysics—one that accepts particulars as real. And it is certainly an interesting point that thought should be capable of having such metaphysical consequences. I might put it by saying that the distinctness of thoughts depends upon the distinctness of the particulars they concern.
Interesting, but perhaps not startling. More startling, however, is the analogous thesis in respect of universals: that there is a similar transcendental argument proving that universals exist. For thoughts also have general content, carried by concepts corresponding to properties, and this content depends for its existence on the existence of the properties it concerns. Without those properties general thoughts would not be possible. Just as the mind cannot from within its own resources generate singular thoughts—it needs the contribution of objective particulars—so the mind cannot from within its own resources generate general concepts—it needs the contribution of objective universals. Since the proposition contains properties, it depends on properties for its existence; but then there are no thoughts in a world without universals. Thus a certain type of metaphysics is implied: reality must contain universals, in addition to particulars, which serve to make thought possible. It is hard to see how these universals could be creatures of the mind, inventions of some sort, because invention depends upon thought, and hence presupposes the existence of general propositional content. Nor could properties reduce to sets of particulars, on pain of making thoughts about properties into thoughts about sets. I don’t have all these particular things in mind when I think that a certain bird is pretty; I simply have the property of being pretty in mind.  So we need to countenance a robust ontology of general properties (universals) given the nature of thought: no universals, no thoughts. Thus we can deduce ontology from psychology, world from mind.
The root reason for this dependence lies in an essential feature of universals: their ability to bring things together. They allow for similarity among diverse particulars. If particulars spread universals around, by giving them multiple instantiations, then universals round particulars up, by determining their similarities. So the following thesis sounds plausible: General concepts need objective universals in order to provide the groupings that general thought delivers. The mind could not manufacture the groupings that record similarities without the aid of objective universals that constitute these similarities. Picture the mind trying to find similarities among particulars without appeal to the objective basis of similarities—it would flounder in the dark. No, it needs to latch onto the external objective grounds of similarity, viz. universals. You can’t think about the class of square things without representing the objective property of being square (or if you do you will need some other subsuming concept). So the basis of mental classification is grasp of the objective respects of similarity, i.e. properties or universals. The mind can’t just make this stuff up itself—it needs outside help. It needs objective universals as much as (or more than) it needs objective particulars. That is, singular propositions really do contain particular objects and general properties of them—and this presupposes a certain kind of ontology. You can’t separate semantics from metaphysics, meaning from reality, thinking from being. In this respect, there is no logical gulf between the subjective and the objective, the inner and outer. Metaphysics shapes psychology. The external world of objects and properties is the foundation of the internal world of individual concepts and general concepts. It is not possible to hold the world of thought constant while varying what reality contains in the way of ontological categories. This is the most general lesson of what has come to be called “externalism”. There cannot be a thinking mind without an objective world to mirror. 
 This raises the question of whether direct reference theory applies to thoughts explicitly about sets: can propositions contain sets of particulars as well as particulars? That would seem to involve overpopulating the content of thought with all the members of a given set. The alternative would be to suppose that thoughts about sets have descriptive content, as in “the set consisting of all F’s”: here the thought would contain a general concept applicable to a given set and not the set itself as a particular object.
 According to traditional “Fregean” thinking, there is no overlap between thought (meaning) and reality, since propositions do not contain anything that belongs to the world of reference (particulars and their properties). But according to direct reference theory propositions contain worldly entities, so there is an overlap between world and mind: the constituents of the one are also constituents of the other. Thus it is that we can deduce ontology from psychology (and vice versa).