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Someone named Paul has a YouTube channel called Paulogia
and he posted a video titled
Puddle Parable and FineTuning (Capturing Christianity Response) responding to a
Capturing Christianity’s Puddle Analogy video.
For those who don’t know,
finetuning refers to the observation that certain parameters of our universe (certain physical constants and quantities) are “finetuned” in the sense that if any of these parameters were altered even slightly, the universe would be lifeprohibiting rather than lifepermitting, and physical life would not have evolved. So why is the universe lifepermitting rather than lifeprohibiting? The cosmic finetuning being the result of design seems to be a good and straightforward explanation. Cosmic finetuning is taken as evidence for the universe having been designed, and this constitutes the finetuning argument.
The details of the finetuning argument vary upon its application, but the type of argument Cameron gives in his video (at around
1:34 to 1:58) is structured thusly:
 The probability that our universe would be lifepermitting given naturalism is very, very low.
 The probability that our universe would be lifepermitting given theism is not very, very low.
 Therefore, the fact that our universe is lifepermitting provides evidence for Theism over Naturalism.
The puddle analogy is where the water in the puddle notices that the hole he is in happens to fit him perfectly, and thinks the hole must be designed for him. This analogy is then used as an objection against the finetuning argument. How exactly? Well, it depends on how it’s applied. Cameron’s video criticizes the analogy for being too ambiguous because he can think of at least five interpretations, but I wouldn’t say that’s the puddle story’s fault exactly. The puddle story has multiple applications and criticism should be laid at the feet of the particular application in question. Still, one application is that just as the water can fit whatever hole it’s in, life could have evolved in pretty much whatever the universe happened to be. This application of the puddle analogy essentially denies finetuning, but this objection isn’t terribly plausible. To quote the nonChristian educational source PBS Space Time at around
14:20 to 15:26:
Many people had the following objection: they say that the universe isn’t really finetuned for life or for observers because there could be many types of observer very different to ourselves that could potentially exist if the fundamental constants were different. Well, actually, fine tuning arguments for the fundamental constants [being finetuned for life] for the most part take that into account. We can probably assume that for an intelligent observer to emerge in any universe, that universe must be capable of forming complex structures—whether or not it looks like life as we know it. So the universe needs to last a reasonable amount of time, have stable regions, and energy sources for those structures to form, and have some building blocks—whether or not they look like atoms as we know them. Much of the parameter space that the constants of nature could have taken eliminate one or more of these factors. So while there may be many small parts of that parameter space where observers can arise, most of it—and hence most universes—should be devoid of observers.
Cameron responds to the finetuning denial application of the puddle analogy (albeit not with PBS Space Time) as well as others. Cameron’s video and Paulogia’s response are both fairly lengthy, clocking in at about half an hour each. So I won’t be responding to everything, but I will respond to some of the more salient points that Paulogia made.
In
23:20 to 23:57 Paulogia says we don’t know whether the probability distribution of a particular finetuned parameter is equal across the range, but this isn’t a very effective objection. The type of probability distribution that would presumably help naturalism here is if there’s a giant spike of probability over the extremely narrow lifepermitting range, but this would require the probability distribution
itself to be finetuned for that extremely narrow lifepermitting range! The finetuning for life would merely be pushed back a step and the problem wouldn’t be solved at all.
In
24:06 to 24:44 he raises the possibility that the lifepermitting value is the way it is by necessity. The problem is that this necessity of physics would
itself be finetuned to be within that extremely narrow lifepermitting range, and it’s just as easy to conceive a physical necessity that lands somewhere on the far more enormous area of lifeprohibiting universes. As with the finetuned probability distribution, this seems like pushing the finetuning problem back a step and doesn’t really solve the problem.
Alternatively, perhaps Paulogia believes the necessity is not only one of physics but of some deeper metaphysical principle. My finetuned meteor shower scenario of a previous blog post once again helps to illustrate the problem. To recap, suppose a meteor shower clearly spelled out on the moon, “There is a cosmic designer; I supernaturally finetuned certain parameters of this universe so that this message would appear.” Now suppose we do find such finetuned parameters (certain physical constants and quantities) 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 finetuned 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 finetuned physical necessities happen to be the way they are in the absence of a cosmic designer, because this finetuning 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, not to mention severely ad hoc. A cosmic designer would seem to be the best explanation of the finetuned meteor shower text. But if we’re to be rationally consistent, we must apply the same logic for the finetuning in our universe: the parameters don’t seem to be
metaphysically necessary, and if one is putting forth the metaphysical necessity of a finetuned lifepermitting universe with no argument to back it up, it looks like an ad hoc and inferior alternative explanation to design, just as it would in the finetuned meteor shower scenario.
Paulogia makes some errors in reasoning in which some probability theory will be helpful. So here’s a little probability symbolization to get us started;
Pr(A) =  The probability of A being true; e.g. Pr(A) = 0.5 means “The probability of A being true is 50%.” 
Pr(AB) =  The probability of A being true given that B is true. For example: Pr(I am wetIt is raining) = 0.8 This means “The probability that I am wet given that it is raining is 80%.” 
To recap a bit from my
article on Bayes’ theorem, here’s one version of the theorem:
On the normal conception of evidence, evidence E is evidence for hypothesis H if P(HE) > P(H), i.e. evidence E making H more likely than without that evidence. Pr(HE) is called the
posterior probability of H, and Pr(H) is the
prior probability of H (as in “prior to taking E into account”). Notice that, all other factors being constant, the higher P(EH) is, the greater P(HE) is and thus the greater evidential force evidence E is for hypothesis H.
 N = Naturalism is true.
 L = The universe is lifepermitting.
 T = Theism is true.
The structure of Cameron’s finetuning argument is basically this:
 The P(LN) is very, very low.
 The P(LT) is not very, very low.
 (Such that P(LT) > P(LN).)
 Therefore, L provides evidence for T over N.
Thanks to the magic of math, the structure of this argument is logically valid, i.e. it’s impossible to have true premises and a false conclusion (more on this later). Note how T is in both 2 and 3 here. That’ll be important to remember in a little bit.
At around
27:27 to 27:55 Paulogia parodies Cameron’s argument with this.
 The probability that I will roll a 3 on a 6sided dice under naturalism is 16.6%.
 The probability that I will roll a 3, given an allpowerful god who wants me to roll a 3 is 100%.
 [Conclusion:] the fact that I rolled a 3 provides evidence for Theism over Naturalism.
Using these two symbols:
 G = An allpowerful god who wanted outcome X to occur existed. (The outcome in this case being the die coming up 3.)
 O = The outcome X occurred.
The structure is this:
 The P(ON) is 16.6%.
 The P(OG) is 100%.
 Therefore, O provides evidence for T over N.
After Paulogia describes his parody, he adds “That doesn’t seem right.” In a way he’s correct, because this parody fails to match the structure of Cameron’s argument; note how T is in both 2 and 3 in Cameron’s argument but T is present only in 3 in Paulogia’s parody. Paulogia’s parody is logically and mathematically invalid, unlike Cameron’s argument. We can fix the parody by using this structure:
 The P(ON) is 16.6%.
 The P(OG) is 100%.
 Note that P(OG) > P(ON).
 Therefore, O provides evidence for G over N.
The structure now sufficiently mirrors Cameron’s finetuning argument, but as a result the conclusion follows from the premises; assuming of course that our conception of “evidence” is such that a fact making something more likely would constitute evidence for that fact. We can say that O is evidence for G over N if the ratio of P(GO) to P(NO) is greater than the ratio of P(G) to P(N). Or put another way, O is evidence for G over N if this is true:
Now note the following equation, which is sometimes called the
odds form of Bayes’ theorem:
Notice that the odds form of Bayes’ theorem entails that if P(OG) > P(ON), then O is evidence for G over N. In other words:
If P(OG) > P(ON), then 


> 

Since P(OG) > P(ON), O is evidence for G over N, even if Paulogia thinks otherwise. It may be extremely weak and negligible evidence, but it is technically evidence nonetheless. The conclusion, “O provides evidence for G over N” follows logically from the premises, and the argument is logically valid. The same math applies to Cameron’s actual argument:
If P(LT) > P(LN), then 


> 

If P(LT) > P(LN) then L is evidence for T over N, and Cameron’s argument is logically valid. That said, the conclusion of Cameron’s argument is quite modest; it doesn’t specify how
much evidential support L brings, and the atheist could theoretically concede that Cameron’s argument is sound (valid + true premises) while also believing that L’s evidential force for theism over naturalism is small. How much evidence L brings will depend on the values in the odds form of Bayes’ theorem (P(LT), P(LN), etc.). I’ll comment more on that later.
Paulogia’s second parody is at around
28:01 to 28:24. In its original form it is this:
 The probability that I will win Lotto 6/49 with one ticket under naturalism is 1 in 14 million.
 The probability that I will win Lotto 6/49 with one ticket, given an allpowerful god who wants me to win Lotto 6/49 is 100%.
 [Conclusion:] Me winning Lotto 6/49 provides evidence for Theism over Naturalism.
As before, Paulogia’s parody fails to mirror Cameron’s actual argument due to a mathematically invalid structure, with this time O being the outcome of winning the 6/49 lottery:
 The P(ON) is 1 in 14 million.
 The P(OG) is 100%.
 Therefore, O provides evidence for T over N.
Unlike Cameron’s actual argument, the conclusion can be false even with the premises true. How? The probability of
God wanted specific person S to within the lottery given that God exists seems
extremely small (assuming God cares at all about who wins the lottery and has a specific random person he wants to win, the prior probability of God wanting
that specific person to win the lottery is extremely small). As such, the probability that you will win the lottery given that God exists is actually extremely small, so even though P(OG) is very high, P(OT) is very small, and if P(OT) is as small as (or smaller than) P(ON), winning the 6/49 lottery won’t be evidence for T at all and 3 would be false even with 1 and 2 being true. This parody fails as a critique of Cameron’s argument however because the parody fails to match the structure of Cameron’s actual argument. Cameron’s argument is logically valid, whereas this parody argument is logically invalid. The same problem occurs with the parody immediately following the winningthelottery one at around
28:24 to 28:39 in which premise 1 is him
not winning the lottery, premise 2 is an allpowerful god wanting him to not win the lottery, and the conclusion is that him not winning the lottery is “evidence for Theism over Naturalism”; the conclusion doesn’t follow from the premises, unlike Cameron’s argument. The parody’s math is wrong.
Suppose though we repair the winningthelottery parody argument so that it more closely fits the basic structure of Cameron’s argument as follows:
 The P(ON) is 1 in 14 million.
 The P(OG) is 100%.
 Therefore, O provides evidence for G over N.
As with the repaired parody of the die coming up 3, it is indeed evidence for the theistic hypothesis. Still, in both the rollinga3 and winningthelottery cases the putative evidence doesn’t seem like very
strong evidence. Why is the evidential force so negligible? Take the lottery case. The prior probability of
an allpowerful god who wants me to win Lotto 6/49 is extremely small (since the probability of the deity wanting
that specific person to win seems extremely low, and then there is the probability of the deity caring who wins the lottery!). So even though P(OT) is low, and G is specified in a way that cranks up P(OG) to be 1, it does so at the price of plummeting P(G) to a vanishingly small value. It’s possible for P(EH) to be very high and yet P(HE) still be very small when P(H) has an extremely low probability to begin with (recall Bayes’ theorem), e.g. when H is an allpowerful deity wanting a specific person to win the lottery, H has an extremely small prior probability and thus P(HE) ends up being very small.
Contrast all that with cosmic finetuning, letting
F represent
The universe is finetuned for life. While God wanting a specific random person to win the lottery given that God exists seems extremely small, does the probability of
God wanted a universe with life given that God exists seem extremely small? It does not. So as long as the prior probability of theism simpliciter isn’t too low and P(FT) isn’t too low, cosmicfinetuning can potentially be very strong evidence for theism.
To illustrate, suppose that the God of our conception has only a mild interest in creating a universe with life and a mild interest of creating a physical universe just right for life such that this is true:
Suppose also that the following values obtain (note that the P(FN) value below is taken from one possible value that Paulogia raised from something Cameron said in his original video, though of course Paulogia raised the necessity and probability distribution objections):
Now plug in those above values into the odds form of Bayes’ theorem:
If you do the math, P(TF)/P(NF) comes out
overwhelmingly in favor of theism over naturalism even if we gave the aforementioned implausibly low values for P(FT) and P(T). I’m not saying the above values are accurate or even close to accurate, but I used those numbers to illustrate the following point. If the following are true:
P(FN) = extremelysuperduperultramega low 
Then the result is that finetuning is going to be very strong evidence for theism over naturalism.
What amazed me about Paulogia’s response, and the responses of some internet atheists, is how they deliver remarkably bad objections to the finetuning argument. A much better objection is the multiverse hypothesis in which there’s a massive ensemble of universes with varying parameters such that at least one of them is lifepermitting, thereby affecting the value of P(FN). To be fair, this response does have its problems (there are a number of obstacles in making this a better explanation than design) but it’s certainly a lot better than pushing the finetuning back a step, or just getting math wrong.