Primary truth bearers, none of them?
Primary truth bearers are the kind of entities that are always true or false. This is in contrast to secondary truth bearers that are only sometimes true or false. It seems possible that there are no primary truth bearers but that there are two or more secondary (= non-primary) truth bearers. All the theories that I am acquainted with are theories that include a primary truth bearers be it sentences, propositions, beliefs or whatever.
Exploring the notion of primary truth bearer
This notion of primary truth bearer seems to me to warrant further investigation and clarification. I would like to find a more rigorous description than the one I gave above. What is meant by “always” in that context? It seems to me that it is best to think of it in relations to facts. There is something in relation to the fact that the Earth is spherical that is true/false. What is it? To say that there is a primary truth bearer is to say that:
For all facts, there exists a truth bearer of a certain kind in relation to that fact.
Though I am still not satisfied. This “of a certain kind” is not formalizable. I want a formalizable version. The below seems to capture the same idea and it is formalizable:
For all facts, there exists a truth bearer such that that truth bearer has the property true/false in relation to that fact and that truth bearer is of a certain kind.
The fact and truth bearer distinction
Note the distinction between facts and whatever it is that it true/false. “fact” here means things such as the spherical planet referred to by “Earth”. It is not the Earth that is true/false. Since we're assuming that there is something that is true/false, it has to be something else.
A joint sentence and proposition theory of truth bearers
It seems possible that there is not a single kind of entity that has the property true/false in relation to all facts. Perhaps a theory could be that in all relations to facts where a sentence of the right kind has been uttered, it is that sentence that is true/false and in cases where such a sentence has not been uttered it is a proposition that is true/false. What are the merits of such a theory? One thing is that it posits less objects than does a pluralistic theory which posits more than one entity being true/false in relation to a single fact. On grounds of simplicity of ontology, we should prefer the above theory. (Maybe. See the next passage.) The above theory posits exactly the name number of truth bearers as does a monist proposition theory, that is, one for each fact.
Infinities and comparisons
I'm not well versed in infinite math, but I think there is a sense in which a theory that posits more than exactly one truth bearer for each fact posits more truth bearers than a theory that posits exactly one? There is an infinite number of facts in each case. I don't know the technical answer.
Simplicity and truth bearers kinds
Is there some reason for preferring a theory that posits only a single kind of truth bearers over a theory that posits multiple kinds if the number of truth bearers is the same? Maybe. We seem to favor theories on the same grounds in other fields.