If you saw "Made by God" Written in The Sky...

Should it Convince you God exists?

In debates about God’s existence it is common to argue from cases where our reasoning is more certain to contested cases where our reasoning is less certain. The specific way that an argument like this is supposed to work can differ depending on the case. Sometimes it might help to establish, by analogy, that an interlocutor has good reasons to accept the argument for the contested conclusion as it is relevantly similar to an inference already accepted. An alternative way this can be effective is by showing straightforward logical inconsistency in someones reasoning, for example an interlocutor could be shown to believe straightforwardly contradictory things that they ought to revise, or to be special pleading in order to resist the conclusion in the contested case where they don’t have rational grounds for doing so.

This sort of argumentative strategy can be very powerful as it enables interlocutors to agree to certain things and proceed together to reason through some contested issue. In the case of the big, deep disagreements — the ones you’re not supposed to bring up at the family dinner table ( religion and politics ) — wouldn’t it be great if we could set some clear markers down about what would and wouldn’t count as good evidence for a particular conclusion? If we could do that, that would let disputants know what criteria they will have to satisfy in order to persuade one another; a good sign for rational disagreement where tricky and dishonest interlocutors have a tendency to shift the ground beneath the debate if things aren’t going in their favour!

In contemporary discussions about God, it is du jour to frame ones arguments in Bayesian form¹. I am working on a partitioned series addressing whether or not we should consider this a good thing at all , but leaving all that aside for now, the argumentative strategy of reasoning from clear cases where Bayesian reasoning would establish the conclusion that God exists, can be used to show a parity between hypothetical agreed upon cases of Bayesian arguments for God (BAG), and actual BAG such as fine-tuning arguments.

One such typical example of a successful BAG would be if one saw the words “Made by God” spelt out in the sky. Bayesian reasoning, combined with the observation of “Made by God” (written in the planets or stars or something) would be a striking and amazing appearance! — If anything should convince us of Gods existence, surely it would be that? And if those nasty sceptics are going to resist that, I don’t know what to say… they must be engaging in some insane and distorted motivated reasoning if they deny that even that should convince someone of Gods existence!

“Suppose that physicists uncovered the initial state of the universe, and discovered that it was arranged to spell out the words “made by God, through love,” in every language. That would be pretty damn good evidence for the existence of God. Maybe it wouldn’t get us all the way to a perfect God—depending on one’s priors—but it would clearly make some sort of design hypothesis quite reasonable to believe.

However, most of the objections to fine-tuning are equally objections to thinking that a designer exists in such a world.”²

In the first paragraph you see the parity argument. In the second, the bridge to the case of fine-tuning.

I shall henceforth call the experience of seeing “Made by God” written in the sky ™️³ for brevity.

1. Bayesian arguments for fine-tuning are similar to Bayesian arguments for ™️ in all known respects aside from the evidence being updated on.

2. (Sceptics claim) Bayesian arguments for fine-tuning have some further feature, of not favouring the inference to a Theistic Deity over and above atheistic explanations.

3. Therefore, (Sceptics should claim) Bayesian arguments for ™️ also don’t favour the inference to a Theistic Deity over and above atheistic explanations.

4. However, Sceptics do not do this in the case of Bayesian arguments for ™️ .

5. Therefore, Sceptics should not claim (2).

(1) is the analogy premise, the conjunction of (1..2) taken with the belief that arguments from analogy are valid is sufficient to warrant belief in (3). (4) is true (for some sceptics) and so, for these sceptics, there’s a kind of inconsistency, because the reasoning they apply needs to be consistent between the two cases (on pain of irrationality). There’s a problem here though, (5) is not the only logically possible commitment that follows from the premises. What (5) should be is “So, sceptics who buy 1..5 have some work to do”. Maybe they’ll reject one of 1..4, or maybe they’ll maintain their commitment to all of those and do something else, because what logically follows from 1..4 is that sceptics should either buy the Bayesian inference to God in both cases, or reject the Bayesian inference to God in both cases. — However, this is also an argument I’ve formalised as a sceptic. Maybe someone offering it would want to put it in a stronger form? Though, even in logical form with a contradiction on our hands it isn’t clear which way any given person should proceed to modify their beliefs.

To solidify the relationship between fine-tuning arguments and ™️ as varieties of BAG we shall first work through fine-tuning BAG and motivate the parity arguers reasoning.

*note: I’m using complement set notation because LaTex won’t show ‘~’ symbol for some reason! That being said, I do think the complement notation nicely captures how what’s “opposed” to Theism here isn’t really atheism insofar as its a catchall hypothesis that even includes Deism!

\(\frac{P(T|FT)}{P(T^\complement |FT)} = \frac{P(FT|T)}{P(FT|T^\complement)} \cdot \frac{P(T)}{P(T^\complement)}\)

\(\frac{P(T|FT)}{P(T ^\complement |FT)} = \frac{P(FT|T)}{P(FT|T^\complement )} \cdot \frac{P(T)}{P(T^\complement)} \gg 1\)

\(P(T|FT) = \frac{P(FT|T)P(T)}{P(FT|T)P(T) + P(FT|T^\complement)P(T^\complement)}\)

This, broadly shows how the posterior odds favour Theism. If we started off before “updating” on the evidence for fine tuning with 50/50 credence in Theism and Atheism, then our odds comparison would be 0.5/0.5 = 1. If “updating” on evidence left us in a position where our credence towards Theism was greater than towards Atheism, say 0.8/0.2 then we would have odds of 4 favouring Theism. i.e. P(T)/P(~T)=4. If we had credences that maaasssivvvely favoured one hypothesis over the other, we can express this as P(T)/P(~T)»1, i.e. the credence in P(T) is much much much much higher than in P(~T).

Many of the objections to the fine tuning argument from sceptics attack some of the inferences involved in this comparison. This is often done by arguing that the likelihood of fine tuning conditional on Theism P( FT | T ) is either very low or inscrutable, and similarly that the prior in Theism P(T) is sufficiently low that the argument either doesn’t establish a significantly higher posterior in Theism (compared to atheism) or can’t be evaluated at all. I am sympathetic to both of these complaints. It is also worth noting that these are not the only objections to fine-tuning arguments, however, if we stay on the railroads of BAG arguers set up, this is going to be where the parity dispute takes place.

This is where BAG-arguers concerns about sceptics consistency come in. Some of these considerations that purport to undermine our ability to evaluate or reduce the likelihood of P(FT | T) are not reasons that are specific to fine-tuning, but reasons that are general to any E, where we attempt to evaluate P( E | T ) — including ™️.

“… by the same logic, we couldn’t say it’s improbable that the initial conditions would spell out “made by God almighty, through love,” in every language. This objection therefore proves too much—if it was right, the argument from design would be impotent even if the initial conditions spelled out made by God. Thus, there must be something wrong with the argument.”

If these considerations sceptically undermine fine-tuning BAG then they also undermine our evaluation of P( T | ™️ ) being high, but any sane person would evaluate P( T | ™️ ) to be very high, so unless you want to be insane you better start agreeing to fine tuning arguments!

Of course, the question is never really asked in a serious, non-rhetorical manner whether we should consider P( T | ™️ ) to be high. The question “if you saw 'Made by God’ written in the stars would you believe in Theism?” is asked rhetorically. As stated earlier, we have many different ways of resolving any logical tension in our views supposing we found one, and we ought to pause and think carefully about what we actually believe before randomly accepting highly contentious theological arguments!

BAG proponents, seem to have dialogue trees of responses like this that are devastating objections to imaginary Bayesian opponents. The problem is that in order for these sorts of arguments to work, you have to make sure your interlocutor does actually believe what you say they believe. If you don’t do this, you’re just tilting at windmills with your blog posts!

\(\frac{P(T| ™️)}{P(T ^\complement | ™️)} = \frac{P( ™️|T)}{P( ™️|T ^\complement )} \cdot \frac{P(T)}{P(T ^\complement )}\)

\(\frac{P(T| ™️)}{P(T ^\complement | ™️)} = \frac{P( ™️|T)}{P( ™️|T^\complement )} \cdot \frac{P(T)}{P(T^\complement)} \gg 1\)

\(P(T| ™️) = \frac{P( ™️|T)P(T)}{P( ™️|T)P(T) + P( ™️|T^\complement)P(T^\complement)}\)

What’s doing all of the work here is the likelihood ratio comparison between how well T and ~T “predict” (statistically) “Made by God” being spelled out in the stars. And whilst we may not have an intuition about exactly what the probability of ™️ conditional on Theism is, the point is that it isnt astonishingly small (allegedly) because that’s the sort of thing God might reasonably do (wanting to communicate with people and so on). However, if we compare this to ~T, then we find that this almost never happens in ~T worlds, and so Theism comes out “on top”.

Here we encounter our first problem for the pro-BAGger. Given Im the sort of nasty sceptic who doesn’t think they can actually evaluate what God would or wouldn’t do very well, I actually have no idea what P( ™️ | T ) should be. I either cannot assign it at all, or if I do it is very very very very small because there’s a lot of things I can imagine God doing that don’t involve this. Whilst to the pro-BAGger it might seem that seeing “Made by God” written in the sky “should” convince me, particularly upon reflection, it doesn’t seem that way to me at all. Purely rationally, I don’t see a good reason why a Theistic entity would want to do that at all, ceteris paribus.

Here is where hindsight bias comes in. A pro-BAGger is not wanting us to evaluate this evidence ceteris paribus, but instead they want us to evaluate the claim in conjunction with other claims. For example, if we consider Theism knowing

• (a) that a Theistic entity would be concerned with creating physical universes with this kind of life in it,

• (b) which symbols (physical arrangements of things like planets/stars in the sky, for example) AND combinations of symbols constitute meaningful expressions in actual (relative to our history) human languages (these are contingent),

• (c) that a Theistic entity would want to communicate to us,

• (d) that a Theistic entity would want to communicate with us in a human language (not through other means i.e. epistemic opacity vis a vis divine hiddenness OR telepathy OR something else),

• (e) that a Theistic entity would want to communicate with us in a human language in this way,

• (f) that a Theistic entity is kind of like the God(s) described in the big Monothestic religions texts and is concerned with using miraculous displays to convince people…

This geometric representation is not to scale. In fact, all of the ways a disembodied perfect mind can be (i.e. all of the combinations of sentences that it would be consistent to put together) would occupy a far larger space comparatively than the green does in this diagram. The point is that if you grant this, and this, and this, and this then all of a sudden you have a plausible story on your hands, where that model of God just might do something like write out “Made by God” in the sky. If I had all of those commitments, maybe that would constitute good, convincing evidence for me. The problem is that for many of these assumptions (I do grant (b) and only (b) of these) I do not agree, and that means that Theism does not do a good job at all of predicting ™️. In fact, according to me, it’s going to be about equivalent to ~T in predicting specific claims. This is part of a broader point about problems with using inverse probabilities for grand Theories of Everything with many degrees of freedom as explanations.

And this brings us back to the point, all that’s really gone on here is a sophisticated Moorean shift. The actual interesting points are all about our ability to assign probability distributions in principled ways to what God would do— divine psychology. Speaking as a religious person (with heterodox theology) I cannot do that. Even if my interlocutors who buy BAG can, I cannot. The only thing that will help me is BAG proponents properly explaining themselves and their assignments for pure Theism in a way that doesn’t seem ad hoc and recherche that I will agree to.

Now, suppose on my way to the Gym after writing this I did see “Made by God” written in the sky. What would I actually think?

• Maybe I would come to belief in God, but NOT as a result of Bayesian inference (being so moved by the spectacle)

• Maybe I would think I had food poisoning ( I can offer a Bayesian just so story for this )

• Maybe I would think my car was poisoning me with fumes ( I can offer a Bayesian just so story for this )

• Maybe I would think there are mischievous Aliens ( I can offer a Bayesian just so story for this )

• Maybe I would think that Elon Musk was having a joke using Star Link, though I would be more inclined to think that if I saw a Swastika in the sky! ( I can offer a Bayesian just so story for this )

• Maybe I would think that NASA have some mad DARPA HAARP weapon and it’s making me see things ( I can offer a Bayesian just so story for this ) — again, insane, but still has a better priori in my estimation than God wanting to do this

A final point I want to make is that before I ever thought about God as an explanation in technical terms I would have agreed with my first bullet point (that this would convince me) and then, if I was persuaded that what I was doing when I was reasoning was a proxy for Bayes’s theorem, I would have told myself that the reason I would believe in God if I saw that must be because there is a successful Bayesian argument for it… I think I would have been mistaken in believing all these things. Of course there can be a successful Bayesian argument for anything, but I think that after reflection the Bayesian case for things like this is very very weak unless you can specify a principled distribution for what God would do; which I, apophatically, cannot.

This is where I think the rhetorical bit of this parity argument gets people. It may seem like seeing “Made by God” in the sky should convince someone, and so for anything that strikes us as convincing, we might assume that Bayesian reasoning would get us there. In the same way, it might seem like Linda the bank teller was a feminist in her college days⁴ where more careful reasoning about the nature of a paradigm such as Bayesianism should undermine that initial impression. It is reflection on the tools of probability and Theism as an explanation that has lead me to a point where I consistently think— both in the case of fine-tuning-BAG, and ™️-BAG— that my ability to assign a likelihood for Theism predicting the evidence is just inscrutable OR improbable on par with a similarly contentless explanation like “atheism” (as a catchall for any non-Theistic hypothesis).

If we stick with our first impression of what seems right, unreflectively, then maybe everything I’m saying seems insane. But, if we slow down, listen, and think for a second earnestly about what those how disagree with us actually think… we can arise at a view where even if we don’t agree we can appreciate our disputants disagreement, their justification and maybe we can even come back to the conversation more clearly understanding and articulating our own position.

1. See my series evaluating this here

2. Bentham’s Substack Article

Fine-Tuning, Made By God

3. Out of loving affection for Renes Descartes a priori argument for God https://en.wikipedia.org/wiki/Trademark_argument ]

4. https://en.wikipedia.org/wiki/Conjunction_fallacy