Propositions and States of Affairs - III

My last two posts have been on the topic of the nature and relations of propositions ("props") and states of affairs ("sofas"), respectively. I've been lingering on the topic for two reasons. One is that I've recently become aware of a challenge by Richard Fumerton to my working theory on the topic. Another is that this is one of those topics that as soon as I get it clear in my mind, the fog starts settling in again. I'm hoping that I can meet Fumerton's challenges and clear away my mental fog for good through these posts.

In my last post, I discussed the problem that, on the one hand, props seem to be 'additudinally neutral' since they can serve as objects of various so-called 'propositional attitudes' like "knows that", "believes that", "doubts that", etc. On the other hand, as truth-bearers, props seem to be distinctively assertoric in nature, and thus not additudinally neutral. How do we reconcile this?

Here's a thought that derives from Arthur Prior's tense logic. Prior was a 'presentist', namely, he held that the only time at which anything exists is now - the past is no more, the future is not yet. In conjunction with this, he held that a reference to the present is implicated in all assertions. (For a extended defense of this claim, see Quentin Smith's Language and Time.) Accordingly, in his tense logic he treated the past and future tenses as operators on a core present-tensed prop. Thus,

WILL(p) = It will be the case that p = It will be the case that (it IS the case that p)
WAS(p) = It has been the case that p = It has been the case that (is IS the case that p)

Moreover, the present tense is taken to be basic and irreducible. Thus,

IS(IS(p)) = IS(p) = p

Given that props are fundamentally assertoric, we can parallel this with the notion of truth. Thus,

It is true that p = p
It is true that it is true that p = p
Etc.

In other words, all propositions by their very nature advance a truth claim, they are assertoric. If this is right, then just like Prior takes the past and future tenses being operators on a core present-tensed prop, so we can take the other propositional attitudes to be operators on a core assertoric prop. Thus,

DOUBTS(S,p) = S doubts that p = S doubts that p is true

So the paradox mentioned above in the second paragraph seems resolvable. We can, it seems, affirm that props are inherently assertoric, not attitidinally neutral, by taking the so-called 'propositional attitudes' to be operators.

So far so good, but there may still be a need for an attitudinally neutral object of thought. After all, we can contemplate both unrealized possibilities ("suppose I inherit a million dollars ...") and impossibilities (e.g., "suppose there is a square-circle ...") without positing either their existence or non-existence. Here's where I think abstract states-of-affairs ("sofas") come in. I can contemplate there being a square-circle, a moment's reflection on which will convince me of its impossibility, at which point I'll be prepared to endorse the prop "It is not the case that there is a square circle." But before the assertion comes the neutral contemplation.

One issue I've got to think more about, however, is the relation between abstract sofas and concrete sofas, between the idea of my inheriting a million dollars and its actually happening. In what sense, if any, are both properly thought of as species of the same genus, namely, sofas?