McTaggart's P1 (AKA his "A-series") is not exactly like Zeno's paradox. The A-series is an order of time positions entailing positions of past, present, and future. McTaggart argues that *each* time position in the A-series possesses *all* of these entailed positions. Most philosophers agree that being both past and present *at the same time* is contradictory. Responding that a time position is only past and present at *different* times won't help since those "different times" are subject to the same problem, which in turn pose the same problem, and so on.
As I see it, this is a legit infinite regress problem. It is similar to Parmenides' pointing out that Plato's forms would need forms, and those forms would need forms, and so on.
Zeno points out different infinite regression, but those have been reconciled mathematically, as you correctly point out. They are solvable, I think, because they always regress between two points. McTaggart's time regress and Parmenides' forms regressions have no end-point.
I don't yet see how The Growing Universe Theory (Board's and Tooley's theory) appropriately resolves McTaggart's A-series contentions. Saying there are no future objects poses additional problems as well. If there are no future objects, then it's unclear what we are talking about when we refer to, say, Earth in the year 2500. That "object" doesn't exist under the Growing Universe Theory. Moreover, it's unclear how to assign truth values to propositions dealing with the future and similarly unclear how to compare future to present and past.
Personally, at the moment I find the C-series and Eternalism most persuasive. The C-series (which Earman appears to adopt although I think he says otherwise) is just a fixed order of points in time, much like a mathematical permutation. McTaggart argues that that the C-series won't salvage time since "fixedness" is antithetical to "change," and change is necessary (in McTaggart's view) for time to be real. To avoid McTaggart's argument, I simply re-frame what counts as "change." Under the C-series, change can be viewed as the difference between any two points.
Eternalism seems to jive best with the C-series, *and GRT*, and appears to resolve most philosophical objections posed against the Growing Universe Theory (and Presentist Theory for that matter). Eternalism also salvages the language (but not so much the "substance") of the A-series (e.g., "past," "present," and "future") and B-series (e.g., "two days later", "a minute before"). Ironically, language can be a real barrier to accepting Eternalism, especially since our common notion of "existence" is often situated in the present, e.g., RoR "exists" but 2025 doesn't right? It's just a matter of being very careful with terms when talking inside this tricky field.
I'm still not sure how my view squares with Objectivism.
(Edited by Jordan on 4/21, 10:02am)