More on facts

This meditation is inspired by the Maverick's  The Problems of Order and Unity and Their Difference, an investigation into the structure of facts.

Bill's thought seems to run along the following problematic lines:

1. Relational facts such as the cat is on the mat have the form aRb where R denotes a dyadic relation and a and b denote objects.
2. Facts are complexes.
3. If two complexes differ then they differ in a constituent.
4. If R is antisymmetric then aRb and bRa denote distinct facts.
5. The constituents of both aRb and bRa are just R, a, and b.
6. How then do they differ?

In Bill's words:

So what, if anything, is the ontological ground of the difference between aRb and bRa when R is either asymmetrical or nonsymmetrical? This, I take it, the problem of order, or, in the jargon of Gustav Bergmann, the problem of providing an 'assay' of order. It may be that no assay is possible. It may be that the difference is a brute difference. But that cannot be assumed at the outset.

Let me start by admitting that I find the style of 'ontological analysis' that Bill goes in for rather alien and hard to engage with.   It presents a smooth, hard, exterior that offers no obvious points of entry.  Having said that, this post has been in draft for some time now, and as I'm laid low with the flu this weekend, perhaps this is a good moment to polish it off.

Bill gets into difficulties here, I think, because although he uses 'fact' to mean 'extra-linguistic state of affairs', his analysis above fails to get outside the world of language.  It would be more appropriate as an analysis of '(dyadic relational) factual statement' than as an analysis of what some such statement asserts.  However, at (5) he discards the one aspect of statements,  the spatial or temporal ordering of the words within them, that supports the distinction between statements aRb and bRa, to which he is committed.  Trouble ensues.

Bill has said several times that facts must have 'propositional structure'.   If facts were just shadows cast on the world by statements then this must be right.  But I am sufficiently a realist to think that there is more to it than this.  On the basis of this example alone I'm tempted by the counter-assertion that 'facts must have object-like structure'.   We have to suppose that there are higher-order objects built from ordinary objects.  Thus an on object consists of two objects, one in the above role and one in the below role.  To say that that the cat is on the mat is claim the existence of an on with the cat in above role and mat in below role.