Actual Infinity in Reality?

[polymath257]

Not adding any layer on top of what is clearly an implication of the B-theory of time. Maybe it's the word "illusion" that puts you off, but if you want "causality" to still be implied by the B-theory of time, you do have to redefine the word to mean something that doesn't indicate the flow of time or actual change or actual motion. Fresh fruit does not cause rotten fruit in the sense that it morphs into it; the "antecedent" fresh fruit is still there and the "consequent" rotten fruit is there as well (just in different time moments). Baby horses do not actually eventually morph into adult horses; the baby horse still exists along with the adult version of it. And the key reason we have this one perceived direction happening in this one particular local universe is because of the increase of entropy from one state of this universe to the next, with entropy being at its lowest in the moment closest to the supposed "Big Bang singularity". But otherwise, as far as the laws of physics themselves are concerned, there is no direction of time. And even then, direction does not mean temporal causation anyway; both "cause" and "effect" simultaneously and eternally exist.

Your example is a potential infinite set -- not an actual infinite. Two very different things. This distinction is important for this whole discussion.

No, it isn't. The elements have always been in such a set. How many times do you need to be told this?

I'm going to push back very slightly here. Even in general relativity, which regards spacetime as a single manifold and time does not flow (so B theory is closest), there is a notion of causality.  There are constraints on how things can be at different time slices. So, we will find the rotten apple time slice after that of the fresh apple and not before (in terms of the time coordinate). We find higher entropy states at later time slices than lower entropy states, etc.

Time is still all 'out there'. It does not 'flow' in the sense of the A theory. But there are still patterns between the time slices and we call *those* patterns causality.


And yes, the set N={1,2,3,4,5....} is an actual infinity. We can say exactly which things are in it and which are not without using a 'counting process'. For example, Graham's number is in this set even though there is no physical way to count up to that number.

https://en.wikipedia.org/wiki/Graham%27s_number

I am curious if Steve thinks it is possible for Graham's number of objects to exist in our universe.