An Objection to the Eternal Society Paradox

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Intro

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. Jimmy Akin wrote an article that among other things critiqued the Eternal Society Paradox argument against an infinite past. The original link is here but in case something disastrous happens, the archived link is here.

Background

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 (ACFT):

For each year y in the beginningless, infinite past: the society flips a coin, and they do the chant if and only if these two conditions are met: (a) the coin comes up heads; (b) they never did the chant in a year prior to y.

Less technically but somewhat more roughly: ACFT is where every year they flip a coin and they do a chant in that year if and only if (a) the coin comes up heads; and (b) they never did the chant in a prior year. Even more crudely put: 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.

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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? At first blush at least, this objection doesn’t actually attack any premise of the argument! My conclusion was initially that this objection is a red herring (for more on red herrings, see my red herring video). But see the update below:

Update

After personal communication with the author in 2023-07-31-MO I discovered I hadn’t quite correctly understood his objection. While at the time it wasn’t clear to me which premise he was attacking, it seems he was attacking the premise that says scenario S2 is impossible. Although proof of its logical impossibility can be proven via symbolic logic, we won’t need to go into something so complex here. Here was Akin’s understanding of the Annual Coin-Flipping Tradition that I’ll label ACFT*:

The society flips a coin each year of the infinite past. If the coin comes up heads, then they do the chant if and only if it’s the first time the coin comes up heads.

The objection goes as follows: scenario S2 is the conjunction of ACFT* and the coin coming up heads each year. Since there is no first year the coin came up heads, they never do the chant. There is no self-contradiction with ACFT* and the coin coming up heads each year; the society just never does the chant in any year. Therefore, S2 is not self-contradictory and premise (4) is false. To think that in S2 they had to do the chant assumes that there was a first year the coin came up heads (as well as a “last time” the coin came up heads, since there is a present year); hence a “First and Last Fallacy.”

The problem is that ACFT* is not synonymous with ACFT. To see this I’ll use a reductio ad absurdum argument, which assumes the opposite of what we want to prove (the reductio assumption) and show that it leads to an absurdity (such as a self-contradiction). Recall that ACFT says that the society does the chant when these two conditions are met: (a) the coin comes up heads; and (b) they have not done the chant in a prior year. Assume for reductio that when following ACFT the society never did the chant in any year and the coin comes up heads each year. Now consider last year: are both conditions (a) and (b) met?

• Condition (a) is met, since the coin came up heads last year.
• Condition (b) is also met since they never did the chant in a prior year. (Since they never did the chant in any year.)

So on AFCT they would have done the chant last year since both conditions are met, which contradicts the original assumption that they never did the chant in any year. Thus it is logically impossible for them to have never done the chant if the coin came up heads each year and they followed AFCT. It also follows that ACFT and ACFT* are not equivalent; when the coin comes up heads each year, the society never doing the chant is possible on ACFT* but logically impossible on ACFT (since last year, both conditions (a) and (b) would have been met and they would have done the chant last year).

Somewhat more formally, the reductio argument goes as follows, where the premise (6) is true by definition of the ACFT:

6. If ACFT is true, then for any year y, the society does the chant in year y when (a) the coin comes up heads in year y; and (b) they did not do the chant prior to y. (Follows from the definition of ACFT)

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7. In scenario S2, ACFT is true, the coin came up heads each year, and they never did the chant in any year. (Reductio assumption; we’ll show that this leads to an absurdity.)
8. Last year, the coin came up heads (follows from 7) and thus condition (a) is met.
9. Last year, they never did the chant in a prior year (follows from 7) and thus condition (b) is met.
10. Last year, conditions (a) and (b) are met. (Follows from 8 and 9.)
11. If conditions (a) and (b) are met last year, then they did the chant last year. (Follows from 6.)
12. They did the chant last year. (Follows from 10 and 11.)
13. They did not do the chant last year. (Follows from 7.)
14. They did the chant last year and they did not do the chant last year. (Follows from 12 and 13.)
15. Therefore, (7) is false. (Follows from reductio and 14.)

We know that scenario S2 includes ACFT and that the coin came up heads each year, so the part of (7) that must be false is the idea that they never did the chant in any year.

Conclusion

This illustrates an important lesson in spotting straw men; sometimes statements that might initially appear to be synonymous are actually subtly different, and sometimes that subtle difference matters when evaluating objections. When evaluating an objection, consider how that objection fares against the position as it was originally stated. In the case of the Eternal Society never having done the chant in scenario S2, when we apply ACFT’s conditions (a) and (b) to last year we see that they would have done the chant last year, whereas on ACFT* they would not have done the chant. I can understand why one might think that ACFT and ACFT* are synonymous, but that wasn’t quite true; they were strongly similar but subtly different, and that subtle difference made all the difference in the world.

The Eternal Society Paradox Argument: Symbolic Logic Approaches

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Introduction

In August 2020 the Maverick Christian YouTube channel featured an interview on the Eternal Society paradox, something I’ve also talked about in article explaining why the past cannot be infinite. Here I’m going to dive into a symbolic logic approach to arguing for the premises of the Eternal Society paradox argument. This article is for logic nerds and less layperson-friendly than most of my other blog articles. I will, however, have at least rough English translations of symbolic logic for each of the premises right underneath the symbolic logic language. For those enterprising individuals who aren’t familiar with symbolic logic but want to try to understand it, I’ll explain some of the symbols in the next section.

Some Symbolic Logic

Some of the logic I will use (including the various names for the rules of logic) can be found in this introductory logic page. I won’t go into the various rules of logic here but I will explain what some symbols mean. First there are symbols of basic propositional logic:

Type of connective	English	Symbolic Logic	When it’s true/false
Conjunction	p and q	p ∧ q	True if both are true; otherwise false
Disjunction	p or q	p ∨ q	False if both are false; otherwise true
Conditional	If p, then q	p → q	False if p is true and q is false; otherwise true
Biconditional	p, if and only if q	p ↔ q	True if both have the same truth-value (i.e. both are true or both are false); otherwise false
Negation	Not-p	¬p	True if p is false; false if p is true

To give an example of predicate logic, consider the following symbolization key:

B(x)		=		x is a Bachelor.
U(x)		=		x is Unmarried.

The letters B and M in these examples are predicates which say something about the element they are predicating. Sometimes parentheses aren’t used; e.g. Bx being used to mean “x is a bachelor.” The symbol; ∀ means “For All” or “For Any” such that the following basically means “All bachelors are unmarried:”

universal quantification
In English	In Symbolic Logic
For any x: [if x is B, then x is U]	∀x[B(x) → U(x)]

There’s also the existential quantifier ∃ that denotes the existence of something.

existential quantification
In English	In Symbolic Logic
There exists an x: [x is B and x is not U]	∃x[B(x) ∧ ¬U(x)]

Note that ∀x¬[Fx] = ¬∃[Fx].

In philosophy, a possible world is a complete description of the way reality is or could have been like. On possible world semantics, a proposition is possibly true if and only if it is true in at least one possible world, and a proposition is necessarily true if and only if it is true in all possible worlds.

English	Symbolic Logic	When it’s true/false
p is possible	◊p	True if p is true in at least on possible world; otherwise false
p is necessary	□p	True if p is true in all possible worlds; otherwise false
p is not possible	¬◊p	True if p is false in all on possible worlds; otherwise true

Note that ¬◊p is equivalent to □¬p. Indeed, the ◊ and □ operators can even be defined in terms of each other; e.g. one could define ◊ as “true in at least one possible world” and then define □ as this:

□p = ¬◊¬p

Eternal Society Paradox

Roughly, 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 in a prior year, 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.

As mentioned in the paper, premises (1)-(3) can be understood as material conditionals, even though there is a sense in which I think the subjunctive mood is appropriate. Some people have disputed these premises, and to argue for them I’ll use symbolic logic.

Defining the Predicates and Propositional Variables

With the domain of discourse being the years of the past, the predicates are defined as follows.

• Py = There exists a year y’ prior to year y in which the Eternal Society did the chant in year y’.
• Cy = the chant is done in year y.
• By = there exists a year before year y.
• PBy = Where y’ represents the year before y, Py’ is true (they did the chant in a year prior to y’).
• CBy = The chant is done in the year before y.
• Fy = the coin (indeterministic, probabilistically independent) is flipped in year y.
• Hy = the coin comes up heads in year y.

The propositional variables are defined as follows:

• I = the past is infinite and beginningless such that I entails ∀y[By].
• L = the flipped coin came up heads for the first time last year.
• V = ∀y[Hy].
• In English: the flipped coin came up heads every year.
• D = (I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)])
• In English: the past is infinite and for every year y: if a flipped coin came up heads in year y and the society did not do the chant in a prior year, then the society does the chant in year y, otherwise they do not do the chant in year y.
• A = ∀y[Fy] ∧ D = ∀y[Fy] ∧ (I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)])
• In English: the Eternal Society engages in the Annual Coin-Flipping Tradition.
• E = the Eternal Society (roughly, a society that has existed throughout the infinite, beginningless past and in each year, they can do what we humans can do in contemporary society, e.g. in any year they can flip coins and do chants) obtains.
• S1 = A ∧ L = ∀y[Fy] ∧ D ∧ L
• In English: Scenario S1 obtains.
• Note that it follows from this definition that S1 entails A.
• S2 = A ∧ V = ∀y[Fy] ∧ (I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) ∧ ∀y[Hy]
• In English: scenario S2 obtains (A is true and the coin comes up heads each year of the infinite past).

Argument 1: If ◊S1 then ◊S2

Where a possible world is the way the world is or could have been like, the modal operator □ is such that □P means that P is necessarily true (true in all possible worlds), and ◊P means that P is possibly true (true in at least one possible world).

Here is an argument that if Scenario S1 is possible then Scenario S2 is possible. The justification for premise (7) below is that in the Annual Coin-Flipping Tradition the coin-flips are probabilistically independent and so any particular permutation of coin clips is possible for the Annual Coin-Flipping Tradition, including a permutation where the coin came up heads each year it was flipped.

6. □(S1 → A)
• Scenario S1 entails that the Annual Coin-Flipping Tradition obtains.
7. □(A → ◊(A ∧ V))
• Necessarily: if the Annual Coin-Flipping Tradition obtains then heads coming up each year is a possible outcome.
8. □(S2 ↔ (A ∧ V))
• Necessarily: the Annual Coin-Flipping Tradition with the coin coming up heads each year obtains if and only if scenario S2 obtains. (Recall that scenario S2 is defined to be this way.

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9. ◊S1 conditional proof assumption

10. ¬◊S2 indirect proof assumption
11. □¬S2 10, equivalence
□

¬S2 10, T-reiteration S2 ↔ (A ∧ V) 8, T-reiteration ¬(A ∧ V) 12, 13, biconditional elimination
15. □¬(A ∧ V) 12-14, necessity intro
□

□¬(A ∧ V) 15, S4-reiteration ¬◊(A ∧ V) 16, equivalence A ↔ ◊(A ∧ V) 7, T-reiteration ¬A 16, 17, biconditional elimination S1 → A 6, T-reiteration ¬S1 19, 20, modus tollens
22. □¬S1 16-21 necessity intro
23. ¬◊S1 22, equivalence
24. ◊S1 ∧ ¬◊S1 9, 23, conjunction introduction
25. ◊S210-24, indirect proof

26. ◊S1 → ◊S29-25, conditional proof

Argument 2: If ◊I then ◊E, and if ◊E then ◊S1

Next is an argument for the idea that if an infinite past is possible, then an Eternal Society is possible and S1 is possible. Premises (2) and (3) can be derived rigorously from lines (27)-(35) below:

27. □(E → I)
• Necessarily: an Eternal Society existing implies the past is infinite.
28. □(I → (I ∧ ∀y[Py ∨ ¬Py]))
• Necessarily: if the past is infinite, then (the past is infinite and for any year y, either the chant was done prior to year y or it is not the case that the chant was done prior to year y).
29. □(I → (I ∧ ∀y[Fy → (Hy ∨ ¬Hy]))
• Necessarily: if the past is infinite, then (the past is infinite and for any year y, if the coin was flipped in y then either the coin landed heads in y or it is not the case that it landed heads in y.
30. {◊I ∧ □(I → (I ∧ ∀y[Py ∨ ¬Py])) ∧ □(I → (I ∧ ∀[Fy → (Hy ∨ ¬Hy]))} → ◊E
• If [the infinite past is possible and necessarily: (if the past is infinite, then for any year y either the chant was done in a prior year or it is not the case the chant was done in a prior year) and necessarily (If the past is infinite, then for any year y if the coin was flipped then either it came up heads or it didn’t in year y)] then the Eternal Society is possible.
31. ◊E → ◊(E ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)])
• If the Eternal Society is possible, then it is possible for that Eternal Society do the following in each year y: if there is a flipped coin that comes up heads and the chant was done in a prior year they do the chant, otherwise they don’t.
32. □{D ↔ (I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)])}
• Roughly, the letter D is defined as a placeholder letter to represent the following: the past is infinite and if for any year y there exists the flipped coin that comes up heads and the chant was not done in a prior year, then the chant is done in year y, otherwise the chant is not done in y.
33. □(D ∧ E → ◊(D ∧ ∀y[Fy]))
• Necessarily: if the Eternal Society exists and D is true for that society (e.g. they do the chant depending on inter alia whether the coin came up heads), then it is possible for the Eternal Society to also actually flip a coin each year with D being true (thereby engaging in the Annual Coin-Flipping Tradition).
34. ◊(D ∧ ∀y[Fy]) → ◊(D ∧ ∀y[Fy] ∧ L)
• If the Annual Coin-Flipping Tradition is possible (the probabilistically independent coin is flipped each year etc.), then it is possible for the coin to have come up heads for the first time last year.
35. □((D ∧ ∀y[Fy] ∧ L) ↔ S1)
• Roughly: S1 is defined to be the scenario in which the Annual Coin-Flipping Tradition is done and the coin comes up heads for the first time last year.

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36. ◊I conditional proof assumption

37. ◊I ∧ □(I → (I ∧ ∀y[Fy → (Hy ∨ ¬Hy])) 28, 36, conjunction introduction
38. ◊I ∧ □(I → (I ∧ ∀y[Fy → (Hy ∨ ¬Hy])) ∧ □(I → (I ∧ ∀y[Fy → (Hy ∨ ¬Hy]) 37, 29, conjunction introduction
39. ◊E 30, 38, modus ponens

40. ◊I → ◊E 36-39, conditional proof
41. □¬(D ∧ E) conditional proof assumption

□

¬(D ∧ E) 41, T-reiteration E → I 27, T-reiteration D ↔ (I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) 32, T-reiteration E ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)] indirect proof assumption E 45, conjunction elimination I 43, 46, modus tollens (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)] 45, conjunction elimination I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)] 47, 48, conjunction introduction D 44, 49, biconditional elimination D ∧ E 46, 49, conjunction introduction (D ∧ E) ∧ ¬(D ∧ E) 42, 51, conjunction introduction ¬(E ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) 45-52, indirect proof

54. □¬(E ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) 42-53, necessity intro

55. □¬(D ∧ E) → □¬(E ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) 41-54, conditional proof
56. ¬◊(D ∧ E) → ¬◊(E ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) 55, equivalence
57. ◊(E ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) → ◊(D ∧ E) 56, transposition
58. ◊E → ◊(D ∧ E) 28, 52, hypothetical syllogism
59. □¬(D ∧ ∀y[Fy]) conditional proof assumption

□

□¬(D ∧ ∀y[Fy]) 59, S4-reiteration ¬◊(D ∧ ∀y[Fy]) 60, equivalence (D ∧ E) → ◊(D ∧ ∀y[Fy]) 33, T-reiteration ¬(D ∧ E) 61, 62, modus tollens

64. □¬(D ∧ E) 65-68, necessity intro

65. □¬(D ∧ ∀y[Fy]) → □¬(D ∧ E) 59-64, conditional proof
66. ¬◊(D ∧ ∀y[Fy]) → ¬◊(D ∧ E) 65, equivalence
67. ◊(D ∧ E) → ◊(D ∧ ∀y[Fy]) 66, transposition
68. ◊E → ◊(D ∧ ∀y[Fy]) 58, 67, hypothetical syllogism
69. ◊E → ◊(D ∧ ∀y[Fy] ∧ L) 34, 68, hypothetical syllogism
70. □¬S1 conditional proof assumption

□

¬S1 70, T-reiteration (D ∧ ∀y[Fy] ∧ L) ↔ S1 35, T-reiteration ¬(D ∧ ∀y[Fy] ∧ L) 71, 72 biconditional elimination

69. □¬(D ∧ ∀y[Fy] ∧ L) 71-73, necessity intro

75. □¬S1 → □¬(D ∧ ∀y[Fy] ∧ L) 70-74, conditional proof
76. ¬◊S1 → ¬◊(D ∧ ∀y[Fy] ∧ L) 75, equivalence
77. ◊(D ∧ ∀y[Fy] ∧ L) → ◊S1 76, transposition
78. ◊E → ◊S1 69, 77 hypothetical syllogism

Line (40) matches up with premise (1) (“If an infinite past is possible, then an eternal society is possible”) and line (78) matches up with premise (2) (“If an Eternal Society were possible, then scenario S1 would be possible”).

Argument 3: ¬◊S2

Odd as it may seem, I’ve even seen some question premise (4), even though theoretically it should be an uncontroversial premise. In addition to the definition of scenario S2 applied in premise (81) I make use of several necessary truths that apply to this situation, such as the beginningless, infinite past entailing that each year has a year before it (line (79)); that where y’ is the year right before some arbitrary year y, if the chant was done in y’ then the chant was done in a year prior to y (line (84)); and that if there exists a year y where the chant was done in a year prior to y, then there exists a year in which the chant was done (line 85).

79. □(I → ∀y[By])
• The past being beginningless and infinite entails that for every y there exists a year before y.
80. □(I → (∃y[Cy] ∨ ∃y[¬Cy]))
• The past being beginningless and infinite entails that either there exists a year in which the chant is done or there exists a year in which it is not the case that the chant was done.
81. □(S2 → (∀y[Fy] ∧ I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) ∧ ∀y[Hy]))
• Roughly, scenario S2 is defined such that: the Annual Coin-Flipping Tradition in which the coin comes up heads each year. (Note that scenario S2 is in fact defined this way.)
82. □(∀y[¬Py → Cy] → ∀y[By → (¬PBy → CBy)])
• Necessarily: if (for every year y, if the chant is not done in a year prior to y then the chant is done in y) then (if there exists year y’ before y, if the chant is not done in a year prior to y’ then the chant is done in y’)
83. □(∀y[PBy → Py])
• Necessarily: for any year y if there exists a year y’ right before y and the chant was done prior to year y’ then the chant was done prior to year y.
84. □(∀y[CBy → Py])
• Necessarily: for any year y if there exists a year y’ right before y and the chant was done in y’, then the chant was done prior to year y.
85. □(∃y[Py] → ∃y[Cy])
• Necessarily: if there exists a year y in which the chant was done in a year prior to y, then there exists a year in which the chant was done.

---

□

I → ∀y[By] 79, T-reiteration I → (∃y[Cy] ∨ ∃y[¬Cy]) 80, T-reiteration S2 ↔ (∀y[Fy] ∧ I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) ∧ ∀y[Hy] 81, T-reiteration ∀y[¬Py → Cy] → ∀y[By → (¬PBy → CBy)] 82, T-reiteration ∀y[PBy → Py] 83, T-reiteration ∀y[CBy → Py] 84, T-reiteration ∃y[Py] → ∃y[Cy] 85, T-reiteration S2 indirect proof assumption (∀y[Fy] ∧ I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) ∧ ∀y[Hy] 88, 93, modus ponens ∀y[Fy] 94, conjunction elimination I 94, conjunction elimination ∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) 94, conjunction elimination ∀y[Hy] 94, conjunction elimination ((Ha ∧ ¬Pa) → Ca) ∧ (¬(Ha ∧ ¬Pa) → ¬Ca) 97, universal instantiation (Ha ∧ ¬Pa) → Ca 99, conjunction elimination ¬(Ha ∧ ¬Pa) → ¬Ca 99, conjunction elimination ∀y[(Hy ∧ ¬Py) → Cy] 100, universal generalization ∀y[¬(Hy ∧ ¬Py) → ¬Cy] 101, universal generalization ∀y[By] 86, 96, modus ponens ¬Pb conditional proof assumption Hb 98, universal instantiation Hb ∧ ¬Pb 105, 106 conjunction introduction (Hb ∧ ¬Pb) → Cb 102, universal instantiation Cb 107, 108, modus ponens ¬Pb → Cb 105-109, conditional proof ∀y[¬Py → Cy] 110, universal generalization Pc conditional proof assumption ¬¬Pc 112, double negation ¬Hc ∨ ¬¬Pc 113, disjunction addition ¬(Hc ∧ ¬Pc) 114, De Morgan’s law ¬(Hc ∧ ¬Pc) → ¬Cc 103, universal instantiation ¬Cc 115, 116, modus ponens Pc → ¬Cc 112-117, conditional proof ∀y[Py → ¬Cy] 111, universal generalization ∀y[By → (¬PBy → CBy)] 89, 111, modus ponens Bd 104, universal instantiation Bd → (¬PBd → CBd) 120, universal instantiation ¬PBd → CBd 121, 122, modus ponens CBd → Pd 91, universal instantiation PBd → Pd 90, universal instantiation ¬Pd indirect proof assumption ¬PBd 125, 125, modus tollens ¬CBd 124, 126, modus tollens ¬¬PBd 123, 128, modus tollens ¬PBd ∧ ¬¬PBd 127, 129, conjunction introduction Pd 126-130, indirect proof Pd → ¬Cd 119, universal instantiation ¬Cd 131, 132, modus ponens ∀y¬[Cy] 133, universal generalization ¬∃y[Cy] 134, quantifier negation ∃y[Cy] ∨ ∃y[¬Cy] 87, 96, modus ponens ∃y[¬Cy] 135, 136, disjunctive syllogism ¬Ce 137, existential instantiation ¬Pe → Ce 111, universal instantiation ¬¬Pe 138, 139, modus ponens Pe 140, double negation ∃y[Py] 141, existential introduction ∃y[Py] 137-142, existential instantiation ¬∃y[Py] 92, 135, modus tollens ∃y[Py] ∧ ¬∃y[Py] 143, 144, conjunction introduction ¬S2 93-145, indirect proof

147. □¬S2 86-146, necessity intro
148. ¬◊S2 147, equivalence

And there you have it; proof for ¬◊S2.

Why the Past Cannot be Infinite

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Relevance to Theism

A finite past bears relevance to the kalam cosmological argument (KCA) which goes like this:

1. Anything that begins to exist has a cause.
2. The universe begins to exist.
3. Therefore, the universe has a cause.

Further arguments are given to show that the cause of the universe is (among other things) a transcendent personal cause. If we have adequate grounds for thinking the universe has a transcendent personal cause, this gives at least some evidence for the truth of theism. I’ve justified premise (1) in my anything that begins to exist has a cause article. In this article I’ll argue for premise (2) by arguing for a finite past.

Would a finite past mean that not even God is sempiternal (i.e. having existed for a beginningless, infinite duration)? Yes it would. One idea is that God is timeless sans creation. Note that if spacetime itself began to exist and our spacetime universe had a cause, that cause would have to transcend space and time. Whether you want to call this spacetime-transcending cause supernatural or not, such a cause would have to be something beyond the physical laws as we know them today. The fact that there is some sort of (at least) de facto supernatural cause beyond space and time creating the universe would seem to make atheism less plausible.

An Infinite Traversal

Some philosophy lingo: a potential infinite is a collection that grows towards infinity without limit but never actually gets there. For example, if you started counting “one, two, three…” at a rate of one number per second and continued indefinitely, the number you’re at would grow larger and larger without limit but you’d never actually arrive at “infinity.” An actual infinite is a collection that really is infinite, such as the set of all positive whole numbers.

Traversing an actual infinite region at a finite rate seems impossible. Suppose for example there were a road that starts at a particular location and is infinitely long. Someone named Jill Walker starts at the beginning of the road and walks at a rate of one meter per second. Will she ever traverse an infinite region? She will not; the distance (and time!) she traverses is a potential infinite only. What if she were given infinite time? The problem is that traversing an actual infinite amount of time can never happen. Even if she is given unlimited time she will never traverse an actual infinite amount of time or an actual infinite distance; both will be a potential infinite only.

A similar problem occurs with a beginningless past: for a beginningless, infinite past to exist an actual infinite amount of time would need to be traversed, which is impossible, and thus we never would have arrived at the present moment. Another way to look at it: imagine if we viewed a universe with an infinite past and rewound it, traversing it at the same rate as time normally goes but backwards. Could we traverse the entirety of the infinite past? The infinite past would be impossible to completely traverse even given unlimited time. Similarly, going the other direction would be impossible because it requires an infinite traversal and we never would have arrived at the present moment (or at any moment, since any moment in the infinite past has an infinite amount of time before it).

The Eternal Society Paradox

There are also various paradoxes one can make with an infinite past, an example of which is the Eternal Society Paradox. 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 and if it comes up heads, they all get together to do a particular chant but only if they have never done the chant before. If the coin does not come up heads 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. 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. 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:

4. If an infinite past were possible, an Eternal Society would be possible.
5. If an Eternal Society were possible, then scenario S1 would be possible.
6. If S1 would be possible, then S2 would be possible.
7. S2 is not possible.
8. Therefore, an infinite past is not possible.

One could deny premise (4) 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).

Conclusion

While there is also scientific evidence favoring a finite past, philosophical arguments seem to provide a strong case for temporal finitism (the view that the past is finite). For a beginningless, infinite past to exist an actual infinite amount of time would need to be traversed, which is impossible, and thus we never would have arrived at the present moment. Moreover, the Eternal Society Paradox shows that an eternal society with the abilities of ordinary humans would have been able to create a logical contradiction, which strongly suggests that an infinite past is metaphysically impossible.

Great Cost of the Kalam?

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Introduction

Stephen Woodford has a YouTube channel called Rationality Rules and he posted a video titled Great Cost of the Kalam claiming that the kalam cosmological argument is incompatible with libertarian free will (I’ll explain what both are shortly). A popular version of the kalam cosmological argument, popularized by American philosopher William Lane Craig, goes like this:

1. Anything that begins to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.

There are other ways to word the first premise (e.g. “Whatever begins to exist has a cause of its beginning” and “Everything that begins to exist has a cause”). Libertarian freedom is the ability to choose without being determined by prior causes; e.g. when choosing between chocolate and vanilla ice cream. Determinism is roughly the view that all events are determined by prior conditions, such that given the initial conditions only one outcome is possible. For example, determinism would say that when Sally selected chocolate over vanilla ice cream, given the initial conditions there was only one selection she could make, even if the initial conditions were that both were available at the grocery store and she had sufficient currency for both.

What is a cause?

At around 2:30 to 2:38 Woodford says this.

A cause is a person or thing that gives rise to a phenomenon, action, or condition. It is a synonym of determinism.

No, it’s not. Something bringing about the existence of something else is not synonymous with deterministically causing its existence. To give a hypothetical example, suppose a ray gun has a 30% probability of creating chocolate ice cream, with the outcome being truly indeterministic (i.e. identical initial conditions can produce different outcomes). Now suppose I turn on the ray gun and chocolate ice cream appears courtesy of the ray gun. Since the ray gun did indeed bring about the existence of the ice cream (albeit indeterministically) the ray gun caused the ice cream to exist. But if it is correct to say that in this scenario the ray gun caused the ice cream to exist, then it is not the case that causality is synonymous with determinism.

To be fair though, there is one sense in which determinism and causality are related, and that has to do with the cause of an event (as in outcome 1 coming about versus outcome 2) as opposed to a cause of the existence of a thing. The difference is subtle but important. To illustrate, consider the case of two physically identical uranium-238 atoms A and B, where atom A emits an alpha particle and atom B does not. It may indeed be true that identical physical conditions can produce different outcomes, and while this would rule out the uranium atom deterministically bringing about the alpha particle, it doesn’t rule out indeterministic causation (viz. the uranium atom bringing about the alpha particle, after all it’s the uranium atom that emits it!). So let’s consider the theory that the uranium atom indeterministically causes the existence of the alpha particle. This theory would entail that the existence of the alpha particle (the existence of the thing) has a causal explanation, but this theory would also imply that there is no causal explanation for why uranium atom A emitted an alpha particle and physically identical uranium atom B did not, i.e. there wouldn’t be a causal explanation for the different outcomes between the two physically identical atoms (though there would be a “random chance” explanation for the difference), even though the existence of the alpha particle would have a causal explanation (viz. the uranium atom).[1] The “anything that begins to exist has a cause” claim says that every thing that begins to exist has a cause, but allows for the possibility of uncaused events (e.g. outcome 1 coming about versus outcome 2) in the sense described earlier.

As William Lane Craig (the American philosopher who popularized the kalam cosmological argument in the 20th century) said:

But in any case the reader needs to recall that the premise of the argument is very carefully formulated. It is: everything that begins to exist has a cause. That is deliberately formulated so as to allow for quantum indeterminacy with regard to events. This is quite consistent with admitting that there are events that occur without a cause. And so events that are, say, movements of a libertarian free will or decay of an atomic isotope or emission of a photon, we can happily admit, at least for the sake of argument, that those are uncaused events, and it wouldn't affect the truth of the premise, which concerns whether or not things can actually begin to exist without any causes.

To reiterate, kalam’s causal premise prohibits things (alpha particles, mountains, people, root beer, etc.) beginning to exist without a caused, but does not prohibit uncaused events in the sense described earlier.

Libertarian Freedom

At around 5:11 to 5:32 Woodford says:

According to libertarianism, that is according to the vast majority of theists, the will of a free agent is at least partially non-determined. Thus, by freely stating that whatever begins to exist has a cause, you have demonstrated the contrary. You have proven its falsehood. You are contradicting your statement though the very means in which you express it.

Woodford mistakenly believes that libertarian freedom implies that free acts are uncaused, but this doesn’t follow. While some variants of libertarianism require that our acts be uncaused to be free, this isn’t true for all versions of libertarianism. One libertarian view called agency theory posits agent-causation whereby an agent (person, self) causes events without being determined by prior causes. So, a free act is not uncaused; it is indeterministically caused by an agent. The existence of the agent and its ability to have free will in turn could have been caused by something else.

Conclusion

Woodford’s objection to the kalam cosmological argument for the libertarian proponent is that causality is synonymous with determinism, and the libertarian must hold to their free actions being uncaused, which would thus require the libertarian to not believe the kalam’s causal premise. Three main problems are: (1) causality is not synonymous with determinism; (2) indeterministic causation is still an option (e.g. a uranium atom indeterministically bringing about the existence of an alpha particle); (3) not all versions of libertarianism require an act be uncaused to be free (e.g. agency theory). It would seem therefore that this objection fails.

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[1] At the same time, there is a sense in which there is a cause of the event for why A emitted the particle and B did not: the cause is time and chance acting on inherent properties of matter indeterministically bringing about the two different events (the inherent properties of uranium-238 determine the probability, which is why it has a measurable half-life, as opposed to there being no consistent probability among atoms of the same kind). To some degree it boils down to semantics of what a “cause” is.

Genetically Modified Skeptic vs Arguments for God

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Introduction

Drew McCoy has a YouTube channel called Genetically Modified Skeptic and he posted a video titled The Arguments for God's Existence Tier List responding to various arguments for theism. I’ll go through them in chronological order of the video.

Pascal’s Wager

(1:38 to 3:03)

As Genetically Modified Skeptic (GMS) presents it, Pascal’s Wager is this: if you act as if God exists and God does exist, you have infinite gain in heaven and finite loss, whereas if you act as if God doesn’t exist and God doesn’t exist you have finite gain but infinite loss in hell. Summarized in a handy table:

Belief	Gain if correct	Loss if wrong
God	Infinite	Finite
No God	Finite	Infinite

Given the gain and loss data above, the rational individual would act as if God does exist. If God exists, acting as if he does exist gives you infinite gain and at worst finite loss. Whereas if you lived as if God didn’t exist, your gain was at best finite and your loss was at worst infinite. Therefore, the rational person would act as if God does exist.

GMS claims this commits the black and white fallacy, acting as if there are only two possibilites when there are actually a lot more. After all, there are many different religions with one or more gods. Which religion to pick?

I think GMS is sort of right in his objection, but the version of Pascal’s Wager he attacks isn’t really the strongest. The strongest version of Pascal’s Wager I’ve seen is that if you’re in a situation in which atheism and Christianity are the two viable options (e.g. perhaps you believe the case for the Resurrection of Jesus is strong enough to be likely if God exists) and the probabilities between the two options are roughly equal, then you should act as if God exists. Of course, this is a particularly narrow application of Pascal’s Wager, but it is arguably true that if the conditions were met then you should act as if God exist. A nontheist might not think the aforementioned conditions are met, but if so that would be a different matter than whether it would be rational to act as if God exists if the conditions were met.

The Ontological Argument

(3:06 to 4:55)

As GMS states, there are multiple forms of the Ontological Argument and GMS (tries to) address Anselm’s version of it. In Chapter 2 of Proslogion Anselm introduces the argument like this:

For it is one thing for something to exist in a person's thought and quite another for the person to think that thing exists. For when a painter thinks ahead to what he will paint, he has that picture in his thought, but he does not yet think it exists, because he has not done it yet. Once he has painted it he has it in his thought and thinks it exists because he has done it. Thus even the fool is compelled to grant that something greater than which cannot be thought exists in thought, because he understands what he hears, and whatever is understood exists in thought. And certainly that greater than which cannot be understood cannot exist only in thought, for if it exists only in thought it could also be thought of as existing in reality as well, which is greater. If, therefore, that than which greater cannot be thought exists in thought alone, then that than which greater cannot be thought turns out to be that than which something greater actually can be thought, but that is obviously impossible. Therefore something than which greater cannot be thought undoubtedly exists both in thought and in reality.

That’s a bit of a mouthful, so let’s do a bit of analysis and simplify it a bit. One popular analysis is such that Anselm considers God as that which nothing greater can be conceived, or what is often called the “greatest conceivable being” (GCB).

1. God is the greatest conceivable being (by definition); God exists in the mind and is thus conceivable.
2. Something that exists in reality is greater than that which exists only in the mind.

3. Suppose God, the greatest conceivable being (from 1), exists only in the mind and not in reality (i.e. God does not actually exist; which is the negation of what this argument attempts to prove).
4. Then there is a conceivable being that is greater (than the being in 4), namely God existing in reality (since as 2 says, something existing in reality is greater).
5. So it is conceivable for something to have been greater than God (from 4).
6. Since God is that which nothing greater is conceivable (from 1), then it is conceivable for something to be greater than that which nothing greater is conceivable (from 5).

7. Statement (6) is absurd and cannot be rationally accepted, thus the claim of (3) must be rejected and the greatest conceivable being must exist.

As it stands I think this version of the ontological argument is unsuccessful, but not for the reason GMS claims. GMS bizarrely claims that Anslem’s argument has God’s existence as a premise, but this is not a premise in Anselm’s argument. It is a premise of Anselm’s argument that God exists in the mind but that’s not the same thing as God existing simpliciter.

A more popular objection against Anselm’s argument is attacking premise (2), the notion that existence is a great-making property. One could even argue that “existence” isn’t really a property at all (the fancy philosophy way of putting it is “existence is not a predicate”). A statement like “God is omniscient” basically claims that if God exists this entity has the property of “omniscience” (I add “if God exists” because if there is no God, then there isn’t any God to have any properties). However, even trying to phrase it like “God has the property of existence” is basically saying that if God exists, he has the property of existence, in which case “has the property of existence” isn’t adding very much to saying what God is like if he exists, and so it isn’t a real property in the sense that omniscience, redness, and having a mass of eighteen kilograms are properties. Here’s a key portion of the Anselm text I quoted earlier:

And certainly that greater than which cannot be understood cannot exist only in thought, for if it exists only in thought it could also be thought of as existing in reality as well, which is greater.

Yes we can think of God existing in reality, but that wouldn’t make him exist in reality. Similarly, we can grant that God would exist if God existed, but that doesn’t mean he exists. (I think God does exist, but I don’t think this particular argument is successful; just because a view is correct doesn’t mean that every argument for that view is a good one.)

Lots more can be said about the “existence is not a predicate” objection to premise (2), and the objection isn’t universally agreed upon, but it at least attacks a real rather than an imaginary premise.

The Kalam Cosmological Argument

(4:56 to 6:55)

The kalam cosmological argument (KCA) basically goes like this:

1. Anything that begins to exist has cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.

After that, philosophers have given further arguments to try to show that the cause has some characteristics conducive for theism, e.g. the cause of the universe being nonphysical and unimaginably powerful. You can read more about that and the argument in general at this William Lane Craig article (Craig is the philosopher famous for reigniting the KCA’s popularity in the late twentieth century).

GMS’s objection is quite bizarre; he points out that the conclusion of the KCA (the universe has a cause) doesn’t by itself get you to God. That’s true, but irrelevant. The KCA syllogism doesn’t aspire to do that. The nature of the universe’s cause is left to other arguments.

The Moral Argument

(6:59 to 9:01)

The moral argument for God’s existence that GMS critiques is this:

1. If God does not exist, then objective moral values do not exist.
2. Objective moral values do exist.
3. Therefore, God exists.

Christian philosopher William Lane Craig has popularized this variety (Craig gets around, philosophically speaking, in apologetics circles). At 7:18 to 7:27 GMS essentially attacks a straw man as follows:

This argument’s first premise is unsubstantiated. It doesn’t demonstrate that the only way objective moral values can exist is if God exists.

But that is not what the first premise claims. The first premise doesn’t claim that objective moral values cannot exist if God does not exist, it claims that objective moral values do not exist if God does not exist. This is important because all one has to do to justify the first premise as probably true is to argue that it is unlikely that objective moral values exist if God does not exist. I did just that in my debate on the moral argument with Jeffery Jay Lowder of internet infidels fame, and I didn’t need to argue at all that God is necessary for objective morality to exist (though the first premise is slightly different in the debate, the general reasoning would apply). At 7:47 to 7:58 GMS attacks another straw man:

Some other moral arguments such as C.S. Lewis’s argument in Mere Christianity state that moral law has not been shown to have a natural origin so it must have come from a supernatural moral lawgiver. First of all, this is an argument from ignorance; not knowing does not excuse asserting an unsubstantiated answer. Second, evolution by natural selection is actually a pretty good explanation for why social species would behave according to practices which promote fairness, peace, and well-being among groups.

As Lewis makes clear in chapter 3 of Mere Christianity by “moral law” Lewis is not talking about descriptive patterns of behavior as GMS seems to think here, so even if evolution by natural selection did explain why our species came up with the practices it did, this is irrelevant. Lewis is talking about the “oughtness” type of morality; e.g. men ought to be unselfish. As I’ve written before, moral oughts are non-natural.

Lewis never says that the moral law must have come from a supernatural moral lawgiver simply because it has not shown to have a natural origin. After observing that we do have this inner sense of the moral law (among other things), in chapter 4 Lewis says:

All I have got to is a Something which is directing the universe, and which appears in me as a law urging me to do right and making me feel responsible and uncomfortable when I do wrong. I think we have to assume it is more like a mind than it is like anything else we know—because after all the only other thing we know is matter and you can hardly imagine a bit of matter giving instructions.

Among known stuff, Lewis believes a mind is the best explanation. Maybe you disagree with Lewis’s inference to the best explanation, but it is not the same thing as an argument from ignorance; Lewis doesn’t say “It hasn’t been shown to be a natural cause, therefore a supernatural moral lawgiver is behind it.” For one, it isn’t just that it hasn’t been shown to be a natural cause; Lewis believes we have good reason to think it’s just not the nature of inanimate matter to give instructions, whereas the same doesn’t apply so well to a mind. Whether you like or dislike this reasoning, it’s not of the form “It has not been shown that p is true, therefore p is false.”

In 8:28 to 8:55 GMS asserts that this argument has the special ability he calls “denigrate” in which the user asserts or implies that their opponent lacks morals. The problem with this alleged “special ability” is that it’s not an ability of the argument at all. Nowhere does the argument say or imply that nontheist can’t be moral. William Lane Craig, incidentally, has made it clear on repeated occasions that the moral argument doesn’t claim that atheists can’t live a good and decent life.

Argument from Personal Experience

(9:08 to 12:59)

GMS puts the argument like this:

1. My personal experiences are reliable sources of information.
2. I personally experienced [insert God claim here].
3. Therefore [the God claim] is true.

William Lane Craig has been known to often assert that God can be immediately known and experienced, but even he claims this really isn’t an argument, e.g. in the Craig-Curley debate he says this:

God can be immediately known and experienced. This isn't really an argument for God's existence; rather it's the claim that you can know God exists wholly apart from arguments simply by immediately experiencing Him…. If you're sincerely seeking God, then God will make His existence evident to you. The Bible promises, "Draw near to God and He will draw near to you" (James 4. 8). We mustn't so concentrate on the proofs that we fail to hear the inner voice of God speaking to our own heart. For those who listen, God becomes an immediate reality in their lives.

This is more of an invitation than an argument. As an argument, I agree that it sucks—at least if you’re trying to use it to convince other people. There are instances in which subjective personal experiences can trump even objective evidence for the person who has had the experiences.

Think that can’t happen? Imagine you’re on trial for a crime you know you didn’t commit because of your own personal experience of you not committing the crime, but all the objective evidence available to the court stands against you. You have no objective evidence you can give to the court to prove you are being framed, but you are still rational to believe in your own innocence. Subjective personal experience can be a powerful source of rational justification. If people really do have personal experiences of God, this can potentially be a source of rational justification for belief in God.

But as an argument to convince other people, I don’t see it being much more useful than reporting your own personal experience of being innocent before a jury who sees the objective evidence heavily stacked against you.

GMS notes that personal experiences can sometimes be delusory, which is true, but insufficient to reject our personal experiences (e.g. I’ll still trust my experience that I was alive in the twentieth century). He notes people can have conflicting personal experiences, which is again true, but still insufficient. People can look at the same set of data and disagree where the evidence points, thus having different intuitive experiences of where the evidence points, but I doubt that would make GMS reject anthropogenic climate change. That said, arguments from personal experiences like this are still not that useful to convince other people.

Teleological (Fine-Tuning) Argument

(13:03 to 16:13)

For those who don’t know, fine-tuning refers to the observation that certain parameters of our universe (certain physical constants and quantities) are “fine-tuned” in the sense that if any of these parameters were altered even slightly, the universe would be life-prohibiting rather than life-permitting, and physical life would not have evolved. So why is the universe life-permitting rather than life-prohibiting? The cosmic fine-tuning being the result of design seems to be a good and straightforward explanation. Cosmic fine-tuning is taken as evidence for the universe having been designed.

GMS makes the claim that this argument makes a false dichotomy fallacy at around 13:43 to 13:58:

First it makes use of a false dichotomy presenting pure chance and an intelligent creator as the only two possibilities when it hasn’t successfully ruled out other options. There could perhaps be some purely physical rule to the universe which demands that these constants be the way they are.

William Lane Craig however has often introduced the fine-tuning argument this way:

1. The fine-tuning is due either to physical necessity, chance, or design.
2. It is not due to physical necessity or chance.
3. Therefore, it is due to design.

Now perhaps GMS doesn’t believe that physical necessity has been successfully ruled out, but if the third possibility of physical necessity had been considered as a possibility and the argumentation against physical necessity for fine-tuning is just unsuccessful, this isn’t a case of a false dichotomy, since three possibilities were indeed considered.

Perhaps the physical constants are physically necessary in the sense that their values (represented numerically in physics) are the way they are in the universe and there’s nothing within the physical universe that can change it (it would require something supernatural to affect them). Note that physical necessity is distinct from metaphysical necessity which is the necessity of the way things could have been in a more absolute sense. If we define a possible world as a complete description of the way reality is or could have been like, some believe there are possible worlds with different physical laws, and that is at least partly why we need empirical study to see what the physical laws of our universe are actually like. In contrast, there are no possible worlds with a married bachelor.

But even if physical constants are physically necessary, we would end up with fine-tuned physical necessities and would not solve the problem or even really provide an alternative to chance.

To illustrate why, consider the following Meter Shower Scenario. Suppose a meteor shower clearly spelled out on the moon, “There is a cosmic designer; I supernaturally fine-tuned certain parameters of this universe so that this message would appear.” Now suppose we do find such fine-tuned parameters that can be expressed as numerical values, like a series of multiple dials that are set extremely precisely for the meteor shower text to appear. Suppose also that the parameters are physically necessary (the values are part of the rules of the universe, and no force purely within the universe can alter them) but the physical necessities are nonetheless fine-tuned so that if the values were altered even slightly, no meteor shower text would appear. Clearly there’s still sense in which it is incredibly unlikely that the fine-tuned physical necessities happen to be the way they are in the absence of a cosmic designer, because this fine-tuning just doesn’t seem to be metaphysically necessary. True, one could in this scenario claim that it is metaphysically necessary that we’d see such a meteor shower text, but that would seem highly implausible under the circumstances. A cosmic designer would seem to be the best explanation of the meteor shower text.

Similarly, even if the physical constants for a life-permitting universe are physically necessary, they don’t seem to be the sort of thing that is metaphysically necessary. The notion that there couldn’t have been a life-prohibiting universe to the point of a life-prohibiting universe being metaphysically impossible does not seem plausible.

GMS continues at around 13:59 to 14:12:

Second, this is an argument from ignorance because the arguer doesn’t know how such an unlikely thing could have possibly happened, they posit unsubstantiated explanation: a God, instead of saying, “I don’t know.”

First, the conclusion is “design” not “God” (though to be fair, the fact—if it is so—that the universe was designed would make atheism considerably less plausible). Second, we can see how such an unlikely thing could have happened, it’s just…unlikely (in the absence of a cosmic designer). Third, is this really an argument from ignorance? Arguments from ignorance take the form of something like “It has not been shown that p is false, therefore p is true.” Maybe somewhere somebody has argued this way in presenting the fine-tuning argument, but it’s just not an inherent part of the reasoning.

One could more charitably see the fine-tuning argument as an inference to the best explanation. To illustrate why, consider the Meteor Shower Scenario in which someone claims the fine-tuning for the meteor shower is clear evidence of design. Suppose a skeptic responded with this:

You’re saying you don’t know how such an unlikely thing could have happened, we must posit an unsubstantiated explanation: a designer, instead of saying “I don’t know.”

This rebuttal is less than convincing, in part because (1) simply saying that A is evidence for B here doesn’t by itself imply an argument from ignorance like the skeptic described above; (2) the fine-tuning being explained is the evidence for the posited “unsubstantiated” explanation of design; and (3) this response seems like a really desperate maneuver to avoid an intelligent designer of the cosmos.

Lots more could be said about the fine-tuning argument, but the objection GMS gave here is highly unsuccessful, as were many of the objections presented in the video with respect to other arguments for theism.