The Cosmos is infinite and yet there are particles here-and-now

 My ever ongoing debating theist (MG) insists that if there is a past temporal infinity then it is impossible to reach the present since you have to participate in an infinite number of events before you can arrive at any current event. He introduced the analogy of "the infinite ladder" and how if you climb such a ladder you will never reach the top. However, he muddled his own analogy big time as the following series of exchanges made over many moons, and which I've cobbled together, demonstrate.

My key distinction here is that if you have a finite lifespan and you started an infinite amount of time ago, then clearly you can't reach the present. However, if you happened to be blessed with an infinite lifespan, like say an up-quark (which can neither be created nor destroyed) then there's no problem. A finite lifespan can only travel through a finite time period; an infinite lifespan is under no such restrictions.

[Note: previous to-and-fro discussions resulted in the following exchanges.]

MG - "As such, you have a series where each event is closer to a line than the previous ones, and eventually the series arrives at that line. Infinite series cannot do that. It's like having an infinite number of rungs on a ladder, but claiming to have arrived at that top just now. It is incoherent."

JP - If you were climbing a ladder with infinite rungs, why would you ever claim that you had reached the top? We've already agreed that infinity has no endpoints - no top in other words.

MG - "If you agree that you can't climb to the top of an infinite ladder, and you see someone at the top, the right conclusion is that the ladder wasn't infinite after all!!"

JP - Whoa! It's 1) incorrect to use the word "you" since "you" is a finite event, and 2) you destroyed any and all logic by saying that "you see someone at the top". Since I have said that infinity has no endpoints, it's illogical for me to state that I see someone (again a fallacy since someone is also a finite event) at the endpoint.

MG - "The ladder is the past series of events (not "moments"; "events", like the Civil War, my breakfast this morning, etc.) and it ends at the present event (me typing this sentence) because that's what "past" MEANS. I made it past all of the rungs of the PAST series of events, and am at the top (the present event). But, as you said, you cannot reach the top of an infinite ladder. Therefore the past is not infinite."

JP 1 - It is more than possible to get from an infinite past to the here-and-how if you yourself have an infinite lifespan. This is not a difficult concept.

JP 2 - Of course "you" can't since humans have a finite lifespan, but that doesn't mean it can't be done, especially if you don't actually have a finite lifespan. Now if you take an infinite time and infinite events, the two infinites cancel and you have just time and events. You can cross any number of events if you have enough time. You can cross an infinite number of events if you have an infinite amount of time. I'm just going to substitute something that doesn't have a finite lifetime (i.e. - "you") with something that does, say an up-quark. Actually never mind about the timing of your First Cause argument for the moment. Just tell me how old an up-quark actually is.

MG - "It was a current event, just like every rung on the ladder below me was once the current rung. I still can't complete a climb of infinite steps. It's logically incoherent. It defies even your definition of "infinite", and you know it."

JP - Of course YOU can't climb an infinite ladder since you are a temporally finite event. But if something (i.e. - an up-quark) is a temporally infinite 'event' then I fail to see the problem.

MG - "So, your argument is "well, I agree that you can't make it to the top of a ladder with infinite rungs, but... I guess that infinite particle MUST have done it, since it's here and it's infinite"?"

JP - The proof of the pudding is in the eating. A temporally infinite particle [like an up-quark] just happens to find itself in the here-and-now. For all I know it tunneled through a wormhole, but here it is. Now you can negate this by 'creating' the particle out of existence, thus refuting or negating the idea that a particle is invincible!

MG - "[A]nd you can't get out of that by saying "the proof is in the pudding".

JP - But the proof IS in the pudding. The Cosmos is infinite and yet there are particles here-and-now. Deal with it! Now even if there is an infinite past and an infinite future, your concept of "The Present Moment" where we find those particles has to fall somewhere on that timeline. Let's call that High Noon in New York City (NYC). There was a High Noon in NYC the day before. There will be a High Noon in NYC the day after. It's no big deal to time-travel that finite interval between High Noon the day before "The Present Moment" to High Noon the day after "The Present Moment" - a 48-hour period. The existence of an infinite past / future is irrelevant. Now keep pushing that concept back and forwards as far back and as far forward as your imagination can imagine.