Thursday, December 24, 2020

An Objection to the Eternal Society Paradox

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The Eternal Society Paradox is one in which an eternal society with the abilities of ordinary human beings in each year of its existence uses its modest abilities to create a logical contradiction, thereby casting doubt on the metaphysical possibility of an infinite past. If the past is finite, this in turn can be used as part of an argument for the universe having a transcendent personal cause. Somebody wrote an article that among other things critiqued the Eternal Society Paradox argument against an infinite past…sort of. The original link is here but in case something disastrous happens, the archived link is here.


Roughly (in the paper the Eternal Society Paradox was published), an Eternal Society is a society that has existed for a beginningless, infinite duration of time and has the abilities of ordinary human beings in each year of its existence; e.g. in each year people in the society can flip coins, write books, sing songs, and pass on information possessed in the current year to the next year. Because of the society’s extremely modest abilities, it seems like an Eternal Society would be possible if an infinite past were possible (note that by “possible” in this article I’ll be referring to metaphysical possibility, as opposed to e.g. physical possibility).

Now imagine the Eternal Society has the following Annual Coin Flipping Tradition: each year they flip a coin. If the coin comes up heads and they never did a particular chant before, then they do the chant; otherwise they do not do the chant for that year.

The coin flips are probabilistically independent events, so any particular infinite permutation of coin flips is equally unlikely but also equally possible. Consider scenario S1 in which the coin came up heads for the first time last year for the Eternal Society practicing the aforementioned Annual Coin Flipping Tradition. The Eternal Society gets together to do the chant for the first time. This seems like it would be possible if an infinite past were possible (an eternal society with the ability of ordinary humans, by which I mean the society has the ability of ordinary humans in each year of its existence, could surely do something like this), but this scenario is provably not possible.

Again, the coin flips are probabilistically independent events, so if scenario S1 were possible, then another scenario, that we can call scenario S2, would be possible: the coin came up heads each year of the infinite past for the Eternal Society engaging in the Annual Coin Flipping Tradition. If the coin came up heads each year, did the Eternal Society ever do the chant? They would have had to have done the chant some year, because they would have done the chant last year if they hadn’t done it yet (since the coin came up heads last year). And yet any year you point to, there is a prior year in which they would have done the chant if they had not done the chant before. So they had to have done the chant (since the coin came up heads last year), yet they could not have done the chant (there is no year they could have done it), and so this scenario creates a logical contradiction.

Although scenario S1 is not directly self-contradictory, scenario S1 is impossible because it implies the possibility of a logical contradiction. The Eternal Society argument against an infinite past goes like this:
  1. If an infinite past were possible, an Eternal Society would be possible.
  2. If an Eternal Society were possible, then scenario S1 would be possible.
  3. If S1 would be possible, then S2 would be possible.
  4. S2 is not possible.
  5. Therefore, an infinite past is not possible.
The Eternal Society Paradox Argument Against an Infinite Past is a deductively valid argument—the conclusion (line 5) follows logically and inescapably from the premises (lines 1-4). A sound argument is a valid argument with all true premises, so the only way the argument can fail to be sound is with a false premise.

One could deny premise (1) particularly since that seems to be the most vulnerable premise, but as the Eternal Society Paradox paper says, “Surely there is something metaphysically suspicious about an infinite past if an eternal society with the abilities of ordinary humans can actualize a logical contradiction.” The idea that an infinite past is possible but an Eternal Society is not possible strikes me as overly ad hoc due to the Eternal Society’s extremely modest abilities (the abilities of ordinary humans in each year of its existence).

The Rebuttal

When using the phrase “Eternal Society Paradox” the author seems to have in mind specifically scenario S2. From the article:
…the solution [to the paradox] is straightforward: The Eternal Society Paradox is presupposing a logical contradiction.
How is this a solution? The fact that the Eternal Society Paradox (in scenario S2) entails a logical contradiction is part of the point; it’s not a solution to simply to concede part of the claim.
It presupposes a first and a last element to a supposedly infinite series, so the Eternal Society Paradox commits the First-and-Last Fallacy.
Simply calling something a fallacy doesn’t make it so. The “first-and-last fallacy” is described as follows:
The First-and-Last Fallacy occurs if and only if a person envisions a supposedly infinite series as having both a first and a last element.
I didn’t envision it, and neither did scenario S2. Indeed, part of the reason there’s a contradiction is that the scenario (if anything) envisions that there is no first element.

Another problem with the objection is that the Eternal Society Paradox Argument is logically valid, so if the argument is unsound, which premise is false? This objection doesn’t actually attack any premise of the argument! This sort of objection is actually a red herring (for more on red herrings, see my red herring video).


When considering an objection against a logically valid argument, consider whether the objection attacks the truth or justification of any premise of the argument; if it doesn’t, it might be a red herring. The magic of logic is such that if the premises of a logically valid argument are true, then the conclusion follows inescapably regardless of what else might be true.