One of the possibilities being considered in the Prosblogion discussion of degrees of being is a parallel with 'being true to degree d'. I'm wary of this sort of approach. Here's why.
'Degree of truth' is a bit ambiguous. We can either mean degree (properly speaking), or grade, or simply be using 'degree' to indicate a percentage. None of these three are exactly the same.
If we mean degree, proper, we are measuring truth value on an arbitrary scale that is continuous. If we mean grade, we are measuring truth value on an arbitrary scale that has discrete gradations. Saying the scale is arbitrary doesn't mean that we aren't accurately identifying something; for instance, temperature scales and the Mohs scale (measuring mineral hardness) are arbitrary. What is arbitrary is the assignment of units (in the case of degree) or levels (in the case of grade); what is non-arbitrary is the relative ranking of the things being measured.
If we are talking about degrees of truth in these terms, we are simply ranking truths according to some standard of priority. I think it makes a lot of sense to think of degrees of being in these terms. (Indeed, I think we naturally tend to do so.) In this sense we are ranking ways of being. And, indeed, I think this is the proper way to understand the claim by Jonathan Edwards that started the claim off; it is the standard way to understand traditional claims of degrees of being.
If, however, we are thinking of 'degree' as a percentage, I think we run into problems. A percentage requires that there be an interval from 0 to 1, i.e., an empty point (0%) and a full point (100%). In the case of truth value one can set truth to 1 and false to 0; but this means that the only point that will be in a strict sense true is 1. If we do this with being, and talk about percentages of existence as such, then only 1 will exist in a strict sense. But this will mean that only the very top of the scale will actually exist; everything else will just sort of exist. Or, more strictly: only the top scale will have existence 100%; everything else will have existence to a lesser degree, which is to say, strictly speaking they will not exist.
Contrast this with the former ways of doing it. On these ways every single thing that in any way exists can be considered to exist, simply speaking; but the ways of existing admit of some sort of ranking. Not so on the latter; on the latter, we are talking about things that somehow exist to a lesser degree than existence properly speaking, whatever that would be. And we would need to be able to determine precisely what full existence would be. The problem with this is that existence have to have a determinate quantity, in the strict sense of the term; i.e., there would have to be not merely more or less with regard to existence, not merely that one can use a quantitative scale to clarify that more or less (as we do with mineral hardness) or determine precise relationships between states (as we do with temperature), but an actually determinate, in-principle quantity of an existence-stuff. (The only alternative to this I can see would be for there to be an actually determinate, in-principle quantity of a non-existence stuff, which makes even less sense.) It would take quite an argument, I think, to support this; existence, as such, is not a quantitatively determinate stuff. This problem does not arise at all on the former approach.
One is virtually nonsense; there is, perhaps a way sense can be made of it, but it would take a lot of doing, if it's genuinely possible to do so. The other is very easy, and makes a great deal of sense, since we actually do think this way. However, even in this case, the temptation remains of trying to make the matter wholly one of formal relationships, as if the scale of being were a logical scale like a scale of truth value (which is not the same as a scale of truth; a truth value scale is a purely formal scale logically characterizing a particular set of formal relationships, and only has to do with truth at all by stipulation). If we do this, however, we are talking about something very, very different from any traditional account of degrees of being. It's not even clear what we're talking about.
So, as I said, I'm wary of this sort of approach; it's perhaps usable, but I think it has many potential pitfalls that would have to be avoided.
