Becoming

A-theorists talk of something called "becoming" which they say B-theorists have no room for. I don't really understand what this is. I am inclined to say that

1. x becomes F if and only if there is a time at which x is non-F and a later time at which x is F.

If so, then there is becoming—-indeed, objective becoming—-on the B-theory. Now, I think most A-theorists will agree that (1) is a necessary truth. So where's the disagreement on becoming?

Maybe, the disagreement lies in this. Although (1) is a necessary truth, nonetheless becoming is something more than just being non-F and later being F. This "something more" is necessarily there whenever something is earlier non-F and later F, but it is nonetheless something extra. (Just as God's knowing that the sky is blue is something more than just the sky being blue, but that "something more" is always there whenever the sky is blue, since God knows that the sky is blue necessarily if and only if the sky is blue.) But I really don't know what this "something more" is. I feel here like van Inwagen on substitutional quantification.

Well, that's not quite right. For it may be that (1) isn't exactly right. Suppose x has gappy existence. It exists from morning until noon and then from dinner until midnight. From morning until noon x is non-F and from dinner until midnight x is F. Does x become F? I could imagine someone saying "No" (and indeed a colleague did say just that). If not, then (1) may not be right.

Maybe one thinks gappy existence is impossible. (But why not? It seems no harder than being a spatially scattered individual, and if we're made of precisely located particles, which sure seems comprehensible, we're that.) But then consider this case. At every time that (in some unit system) is an irrational number, x is non-F and at every time that is a rational number, x is F. Then x satisfies (1). But does x ever become F? If so, when? At any time at which it is F, it also was F at an infinite number of earlier but arbitrarily close times. (This argument requires time to be a continuum, which I fear it's not.)

So one might question (1), though I am happy to bite the bullet in both cases. Maybe one should insist that to become F, you need to be non-F over an interval of times and be F over a succeeding interval of times, or something like that. But such modifications are neutral between the A- and B-theories.

Perhaps, though, the A-theorist's insistence on becoming is not so much about objects becoming a certain way, as about truths changing. The B-theorist is committed to propositions not changing in truth value. Many (but not all) A-theorists think propositions change in truth value. Thus,

2. There is becoming if and only if there is a proposition p that is true at one time and not true at another.

The B-theorist will then reject that there is becoming in this way. But notice that no it no longer seems appropriate to speak, as some A-theorists do, of doing justice to our "experience of becoming." For while we may experience the sky turning from blue to purple, we do not experience, except in a very theory-dependent way, the proposition <The sky is blue> turning from true to false. That's a change (though presumably a Cambridge one) in a Platonic entity.