Presentism again

Bill has been posting once more this month on presentism.  His latest takes to task those who would see 'exists' and 'is present' as synonymous. 

One misunderstanding floated in the Facebook Medieval Logic forum is that presentism in the current analytic philosophy of time is the thesis that 'exists' and 'is present' are synonyms.

Well, according to the SEP some discussion of this view, known as Existence Presentism, has appeared in the literature.

But Bill argues against any synonymity.  First, he says that 'exists' applies to God and to abstract objects well enough, but 'is present' does not.  These things are 'out of time'.  I reply that if these things don't present themselves they hardly stand out (ex+sistere) either.  But let's concentrate on concrete objects. Bill goes on,

Now suppose there are no timeless entities and that everything is 'in time.' It would still not be the case that 'exists' and 'is present' have the same meaning or sense. The following questions make sense and are substantive in the sense that they do not have trivial answers:

Is everything that exists present? Or are there things that exist that are not present?

But the following questions have trivial answers:

Is everything present present? Or are there present things that are not present?

The answer to the first question in the second pair is a tautology and thus trivially true. The answer to the second is a contradiction and thus trivially false.

Since the first two questions are substantive, 'exists' and 'is present' are not synonyms.

Perhaps we should grant this. But if not synonymous then at least co-extensive. Here is an analogy: In the world of plane geometry, 'triangle' and 'trilateral' are co-extensive.  Every triangle is a trilateral and vice versa.  And I suspect that if one were to give a really sharp definition of 'triangle' one would have to bring in trilaterality, and vice versa.  The reason for the co-extensiveness is that the two terms focus on different aspects that all figures in an easily understood class must possess.  Something similar may be happening with our understanding of 'exists' and 'is present'.  Bill's question, Are there things that exist that are not present? may be like asking, Are there triangles that aren't trilateral? Here is a suggestion:  just as the concepts 'triangle' and 'trilateral' can be arithmetised, that is, explained in terms of sets of pairs of real numbers, can we so arithmetise 'exists' and 'is present' (at least for concrete objects)?  We might arrive at a kind of four-dimensionalist picture in which the lives of objects are tube-like regions in  space-time.  The location, orientation, and shape of each object at a given moment is given by a cross-section perpendicular to the time axis [this needs a diagram].  What we mean by 'exists' and 'is present' can be explained in the terms of this model.  Of course, the model could be taken to support an eternalistic understanding of 'tenseless existence' too.  One can 'see' the finite tube-like regions that correspond to objects.  But these four-dimensional sets of points aren't the objects themselves, they are more like biographies of objects.  They contain all the geometric information that is to be known of objects over their lifetimes.

Perhaps also we could use such a model to tease out what the eternalist means by 'tenseless existence' or 'existence without presence'  We could ask if the model gives an adequate history of matter.  If it doesn't, what does it omit or where does it go wrong?  If it does, the eternalist ought to be able to explain what he means in the terms of the model.  That would be illuminating.