I was trying to frame the argument in terms of what seems to be accepted scientific (hitch-hiker level) terminology, and at the same time stay off my usual “hobby-horse” about infinity.
To me the logic ends up at one extra big infinity is offset by lots of small infinities ... not sure I like this sort of maths.
I’m glad you don’t like it. If it makes any sense at all, it is only in terms of mathematical infinities, which are simply bookkeeping conveniences.
Let’s try to dispense with infinities, at least for the time. A black hole exists in time; it has a beginning and, as far as we know, an end. It is finite. Nothing finite can become infinite, so the most we can say about the centre of a black hole is that its curvature is able to increase “infinitely”. This brings us back to the distinction between infinite and boundless.
In the interests of taking one step at a time, can we agree on what we mean when we talk of something becoming infinite? Would this be the same as what we mean if we say that something goes to infinity?
My response to those questions would be that the first is meaningless, and the second refers to boundlessness.
