Against Vallicellan facts

BV has been posting recently on constituent ontology so I have been reviewing his collection of postings on that topic.  One that caught my attention is Are Facts Perceivable? An Aporetic Pentad.  By fact Bill does not mean a true sentence or proposition, which would be my preferred usage.  Rather he means the situation or state-of-the-world that makes a proposition true.  In other words, its 'truth-maker'.  But this idea is problematic because the following pentad is inconsistent though each limb seems true.
  1. If one knows that Rab, then one knows this by seeing that Rab (or by otherwise sense-perceiving it).
  2. To see that Rab is to see a fact.
  3. To see a fact is to see all its constituents.
  4. The relation R is a constituent of the fact that Rab
  5. The relation R is not visible (or otherwise sense-perceivable).   
where Rab denotes a relational truth between two objects a and b such as the table is against the wall or the cat is on the mat.  Bill discusses several ways out.  He regards (1) and (5) as all but unassailable and considers rejecting (2), (3), and (4) in turn,  though he finds objections to each of these moves.  He concludes
Our problem seems to be insoluble. Each limb makes a very strong claim on our acceptance. But they cannot all be true.
I'm not so sure.  It seems to me that Bill's non-standard definition of 'fact', like that of Russell's barber, is simply inconsistent.  Just as there can be no Russellian barber, so there can be no Vallicellan facts.  Why is Bill's usage non-standard?  Well, if someone demands "Give me the facts!" we usually take him to be expecting sentences about some salient matter, not bits of the world.  Indeed, Bill himself falls back to this common usage when he says in defence of (2)
But if there are no facts about observable things, then it is reasonable to hold that there are no facts at all. [my italics]
Surely it is sentences and other intentional items that are about things.  Bill's facts appear to contain or consist of things.  Now, if we want a category of entities that are both visible and consist of things, then we need look no further than visible things themselves, which I take to be objects.  Why not consider the assertion that the cat is on the mat to be an existence claim for a compound object consisting of the cat and the mat in a certain spatial relation?  After all, the existence of the cat itself is equivalent to the existence of various cat parts in specified spatial relations with one another, and if so then the boundary between objects and facts is rather arbitrary.  And if we can draw this boundary anywhere it would suggest that there cannot be a separate category of facts, assuming we accept already the category of objects. 

Bill argues in this piece (and elsewhere) that truth-makers must have a proposition-like structure for which Vallicellan facts are the natural candidates.  But does this follow?  Here is a possible counter-example:  suppose there are three line segments in the plane and that each of the six end-points is coincident with exactly one of the other end-points.  This appears to be a Vallicellan fact concerning line segments.  Yet we find it easier to say there is a triangle, ie, we assert the existence of an object.  Our understanding of the concept triangle includes an understanding of the requirement for pairwise coincident line segment end-points.

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