Actually, no.
If there are no events one hour before, that does not mean there is a first event in the infinite sequence I showed. Because if there was, we will always be able to find an antecedent, which contradicts it being the first. Therefore, no first element can exist, on pure logical grounds.
There has to be a first event/cause in the infinite sequence or it does not begin.
If there is a first event/cause in that sequence, the next has to be a finite time after it and so the hour does not have an infinite number of cause/events.
If there is always an antecedent then that would have happened before the start of the hour, thus adding to infinity, which is not possible.
This is actually a direct consequence of rational numbers not being well ordered. A bounded below set of rational numbers does not necessarily have a first element. For instance, all fractional numbers bigger than zero, do not have a first element. It is not the same with integer numbers. A bounded below set of integers has always a first element.
Yes I suppose, and it is a direct consequence of mathematics which work on paper but cannot, for practical considerations, work in real life. (in this case the practical consideration is that there had to have been a first cause/event).
So, my model would work. The only argument that would defeat it is if we postulate a minimum non zero duration of time, and no time interval can be shorter than that. In other words, discrete time. Because in that case every infinite sequence would entail infinite past time. But, again, there is no reason to postulate that when there is no available physical knowledge about that. And if a first causist speculates about a first cause trying to fill a gap, I am equally free to speculate to fill the gap with a process without first cause. Both explanations would be at the same logical and evidential level.
I think the thing is that even with no minimum length of gap there always needs to be a first event/cause, whether there is or is not any "time" before the hour.
If there is a first (which there has to be) the whole thing breaks down because with finite intervals there would be less than an infinite number of event/causes.
I think your problem here is that you have a prejudice towards a first cause to explain things. As if there was some metaphysical law that requires explaining everything in terms of a first cause. But that would just beg the question by assuming a first cause as the sole mean to explain things. And at the end of the day, my model also explain things. In fact, it explains all of them in terms of their antecedent, since all of them have an antecedent that explains them. So, why do you need more than that?
Ciao
- viole
As I explained, there has to have been a first in the series (and that first event/cause would be right on the start of the hour) and the antecedent would be before that first. And after the first the intervals are always finite so it would be impossible to fit an infinite number into the hour.
This is a problem with theoretical mathematics, it can seem to be logical when looked at from one angle and then not logical from another angle.
From my pov the problem is yours. Maybe you want to keep looking at the mathematics theory and not the practical considerations.