The ‘God can do anything’ objection

0. Introduction

Since I had my debate with Luke Barnes, I have received quite a few questions about different objections to fine tuning, and easily the most common one is the ‘but God could do anything’ objection. The idea is like this. God could have made a world in which there was ‘corse-tuning’. In such a world, the laws of physics are such that if you varied the values of things like gravity, the entropy of the early universe, the mass of the electron, etc, you would still have circumstances in which life as we know it could survive. Why think that if God existed then we should expect to find fine tuning? Surely, fine tuning is evidence against God? I take it this is the ‘God could do anything’ objection.

Here is Hans Halvorson making pretty much this argument. Here he is making the same sort of argument again. The relevant section involves an analogy:

“Suppose that you’re captured by an alien race whose intentions are unclear, and they make you play Russian roulette. Then suppose that you win, and survive the game. If you are convinced by the fine-tuning argument, then you might be tempted to conclude that your captors wanted you to live.

But imagine that you discover the revolver had five of six chambers loaded, and you just happened to pull the trigger on the one empty chamber. The discovery of this second fact doesn’t confirm the benevolence of your captors. It disconfirms it. The most rational conclusion is that your captors were hostile, but you got lucky.

Similarly, the fine-tuning argument rests on an interesting discovery of physical cosmology that the odds were strongly stacked against life. But if God exists, then the odds didn’t have to be stacked this way. These bad odds could themselves be taken as evidence against the existence of God.”

This is an interesting argument. I think it is a good argument. However, I think it is not the slam-dunk that some people seem to think it is. It shows that in some sense, the existence of God is very very unlikely. However, it really poses no objection to the fine tuning argument as such.

In this post, I want to explain why this is the case.

  1. Doing the maths

Part of explaining the power, and limits, of this argument requires doing a bit of maths. Firstly, we need to set out the terms involved. The idea of fine tuning is that if we vary the physical parameters of the universe by a tiny amount, then the universe becomes hostile to life as we know it. Roger Penrose expresses the odds against this happening as less than one part in ten to the power ten to the power one hundred and twenty three, or: 

1 / lklk

That is a stupidly small number!

Let’s call this fact F (for Fine tuning). Let’s call the fact that the universe is hospitable to life L, and let’s call the hypothesis that God exists G. Not all cosmologists accept the fine tuning of the universe, but a lot of them do (in some sense or another at least). Regardless of whether it is true, we can agree that if it were true, then the chances of life existing, as it were by chance, are low in the following sense, and using Penrose’s numbers:

  1. P(L | F) = 1 /  lklk

(The probability that the universe would be life-permitting, given fine tuning, is stupidly low)

Let’s also say that, because God is good, and because life is good, God favours universes that are life-permitting, in the following sense:

2.   P(L | G) > P(~L | G)

(The probability that the universe would be life-permitting given that God exists is higher than the probability that the universe would not be life-permitting given that God exists)

However, if you believe in both God and fine tuning (as people like Robin Collins or Luke Barnes do), then you believe in something only a tiny bit more likely than that the universe is life permitting by pure chance. This is what the ‘God can do anything’ objection’s most interesting implication. Here is how it works.

Firstly, let’s add in the fact of fine tuning into the conditional hypothesis in 2:

3.   P(L | G & F) > P(~L | G & F)

The idea is that the proponents of fine tuning who are also theists believe both G and F to be true. F is part of their background knowledge, as it were, so we can add it in to the right side of each conditional probability. The fact of life is more likely on God and fine tuning, than no life is on God and fine tuning. Now, we can use the conditional probability formula (see it here) to express P(L | G & F) differently. The formula says:

P(A | B) = P(A & B) / P(B)

In our case, A = L and B = G & F. If we plug them in, we get:

4. P(L|G & F) = P(L & G | F) / P(G | F)

(The probability that the universe is life permitting, given God and fine tuning, equals the probability that the universe is life permitting and God exists, given fine tuning, divided by the probability that God exists given fine tuning)

We can do exactly the same thing for the other side of 3 (which just uses ~L instead of L):

5.  P(~L|G & F) = P(~L & G | F) / P(G | F)

3 says (effectively) that 4 > 5, so we can restate 3 as:

6.  P(L & G | F) / P(G | F) > P(~L & G | F) / P(G | F)

Each side of 6 has the same denominator, namely P( G | F). So we can eliminate that as follows:

7.  P(L & G | F)  > P(~L & G | F)

All we have done so far is basic algebra, and we have an inequality which says that the probability that the universe would be life permitting and that God exists, given fine tuning, is greater than that the universe would not be life permitting and that God exists, given fine tuning. This enables us to make a rather nice move here (which is where all this maths starts to become interesting). The probability that God exists given fine tuning, P(G | F) is equal to P(L & G | F) + P(~L & G | F). This is because L and ~L constitute all the possibilities for L that there are, so if we consider both of them in there, then it means we can basically just remove them from the equation. So,

8. P(G | F)P(L & G | F) + P(~L & G | F)

And we can get P(L & G | F) + P(~L & G | F) (i.e. the right side of 8) by simply adding P(L & G | F) to each side of 7, as follows:

9. P(L & G | F) + P(L & G | F)  > P(L & G | F) + P(~L & G | F)

So the right side of 8 just is the right side of 9 (which is why they are both orange). 8 says that P(G | F) equals P(L & G | F) + P(~L & G | F), and 9 says that this is less than P(L & G | F) + P(L & G | F). Because of 8, we can substitute P(G | F) for P(L & G | F) + P(~L & G | F) in 9:

9′. P(L & G | F) + P(L & G | F) > P(G | F)

We can simplify P(L & G | F) + P(L & G | F) into 2 x P(L & G | F). What this shows is that the left side of 8 is less than 2 x P(L & G | F), i.e.:

10.  2 x P(L & G | F) > P(G | F)

It is obvious that P(L & G | F) cannot be more than P(L | F) (the probability of two propositions on a hypothesis cannot be more than the probability of one of them on that same hypothesis); so P(L & G | F) ≤ P(L | F). So, because of 10, we can say that P(G | F) must be less than 2 x P(L | F). We know from Penrose what P(L | F) was; it was the stupidly small number lklk. So we can say that the probability that God exists given fine tuning is no more than twice the probability of life given fine tuning:

11.  P(G | F) ≤ 2 x lklk

This is the mathematically rigorous way of saying that fine tuning makes the existence of God very very unlikely.

2. What does this mean?

What this shows is that if you think that a) fine tuning makes life happening by chance as unlikely as lklk, and b) you think that God would favour life permitting universes, then you should also think that c) the probability that God exists is no better than twice 1 / lklk. We have effectively put an upper limit on the conditional probability of God existing given fine tuning, and that limit is twice that of life existing by chance given fine tuning (which is the number fine tuning advocates are always keen to stress is so stupidly low).

Even if we think of the very top of this limit, we can see that it is not much help. Two times 1 / lklk is not as small as one times 1 /  lklk (obviously), but because 1 / lklk is such a stupidly low number, the upper limit is also stupidly low. 2 x stupidly low is still stupidly low. In that case, we might think, fine tuning is pretty good evidence against God. This, it seems to me, is the strength of the ‘God could do anything’ objection. It makes the probability that God exists look stupidly low.

3. The ‘God could do anything’ objection and the fine tuning argument

Yet, how does this result fit into the fine tuning argument? What impact does it have? Recall, that fine tuning argument goes like this (where N is naturalism):

  1.    P(L | N & F) << 1
  2. ~(P(L | G & F) << 1)
  3. Therefore, L is evidence of G over N.

Using our numbers, we can restate the the first two premises as follows:

  1. P(L | N & F) = 1 / lklk
  2. P(L | G & F)  ≤ 2 x (1 / lklk)

We don’t know that the second probability is actually twice the first, but it could be for all we have found out. So long as it is more than the probability in the first, then we can use the likelihood principle and infer the conclusion still. So we have not cut off the argument as such.

Even given all the maths we did above, we have not established that premise 2 is false. All we did was limit how much more likely than premise 1 it could be (it is at most twice as likely). But another way of saying this is that the second premise could be twice as likely as the first, which still enables us to infer the conclusion. And this is where the weakness of the ‘God could do anything’ objection is plain to see. Even if we grant it, we really have no good objection to the fine tuning argument. It isn’t itself a reason to doubt either premise or the inference to the conclusion.

What the fine tuning argument shows is not that God exists. It is not even really just supposed to be evidence that God exists. It is evidence that supports the hypothesis that God exists over the hypothesis that naturalism is true. It is about comparing two hypotheses together and picking the one with the higher probability. This conclusion is very weak, and this means that it is very hard to argue against. Even if fine tuning is evidence that makes the existence of God very unlikely, this is not a rebuttal to the fine tuning argument because it gives us no reason to suppose that life is more likely on naturalism. We need to remember that we are comparing two hypotheses here. Indeed, the upper bound is higher than on theism, so if anything it gives us some very limited reason to think that the fine tuning argument is actually correct, and no reason to doubt it.

Acknowledgements

Luke Barnes very helpfully sent me a copy of the unpublished paper ‘A probability problem in the fine tuning argument’ by Hans Halvorson, where I got the basic outline of the maths involved in this argument. I’m also indebted to HughJidiette for helping me get my head around the maths.

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84 thoughts on “The ‘God can do anything’ objection”

  1. I have an objection to the argument, which is that I don’t accept step 1. The argument that life is really unlikely in a fine-tuned universe is based on an assumption that the parameters of the universe are selected randomly. The whole point of the fine-tuning argument is that if god exists, then the parameters are not selected randomly. So we could say that P( L | N & F ) << 1, but if we assume that P( L | F ) << 1 that's begging the question.

    My more general objection is that the argument in "doing the maths" section strikes me as dissimilar to the argument in the introduction. But I'd have to think about how I would choose to formalize it.

    You might be interested in a similar argument that I have seen around a lot, based on a paper by Ikeda and Jefferys. My two-sentence summary: if god wants life to exist, then god can just make life exist, regardless of whether the parameters of the universe are friendly to life or not. Therefore, if the parameters of the universe are fine-tuned to accommodate life, that’s actually evidence against god. I have issues with this argument but I haven’t really thought about it in a while.

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    1. “The argument that life is really unlikely in a fine-tuned universe is based on an assumption that the parameters of the universe are selected randomly. The whole point of the fine-tuning argument is that if god exists, then the parameters are not selected randomly.”

      I think that by F, Alex doesn’t mean “the universe is fine-tuned” in the sense that fine tuning has in fact been carried out, but “the universe is a fine-tuning kind of universe” in that the universe is such as to ‘require’ fine tuning in order to be life-permitting. Otherwise, P(L|F) would be 1!

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      1. @haggholm, You’re right to point out the distinction, but that’s how I was using F too.

        After thinking about the argument more, I think the Russian Roulette analogy is problematic. If the goal of the aliens is to keep you alive, then I’d expect P(0) (ie the probability that 0 out of 6 chambers are loaded) to be ~1, because that’s by far the easiest way for aliens to achieve their goal. If 5 chambers are loaded then the aliens probably have different goals. On the other hand, if it were God, then God could easily choose not only how many chambers are loaded, but also which chamber you end up using. We could say God is indifferent to how many other chambers are loaded, in which case P(0) ~ 6*P(5) or something like that.

        If I were to formalize this argument, I would start with the claim: P( F | L & G ) = P( F| L & N). Which is to say, if God may have the goal of creating life, but God is indifferent to whether this goal is achieved by way of a finely- or coarsely-tuned universe. Thus the probability of a fine-tuned-type of universe is the same as it would be in a naturalistic universe with life.

        I played around with the math a bit and I don’t think you can use this premise to refute the fine-tuning argument. So I agree with your conclusion, Alex, that the argument sounds good at first, but seems to be a dead end.

        Liked by 1 person

  2. Alex — Good post!

    I’ve been meaning to talk with you about this topic on Discord, but I never seem to be able to find time to log on there. In any case, I wanted to correct a couple things that you’ve said here concerning this 10^10^123 number. I’ve redone the calculation myself that generates this number because I am writing a paper on the topic — I can send that to you in a pdf document if you’d like. In any case, this number is absoltuely not “the probability that the universe would be life-permitting”. That’s not what Penrose meant with the calculation — in fact, Penrose’s calculation goes in precisely the opposite direction. That is, according to Penrose, that number tells us something about how improbable anthropic hypotheses are — which includes the theistic hypothesis!

    What Penrose is concerned with when he calculates that number is how probable it would be for a fluctuation to generate a universe with an entropy as low as ours. Imagine a universe filled with some sort of gas at equilibrium. The entropy of a gas is maximized at equilibrium. The gas is at equilibrium, so, if you look at things on a macroscopic scale, nothing happens. But zoom in — if you zoom in far enough, you’ll see small fluctuations away from equilibrium. That is, you’ll see regions that fluctuate, for a time, to a lower entropy configuration. In principle, if you wait long enough, you’ll see fluctuations that are arbitrarily large. Eventually, after more time elapses than has elapsed in the observable history of our universe, a fluctuation the size of our visible universe will appear.

    Now, how should we calculate the probability of a fluctuation of that size? The probability of a fluctuation is a simple function of the entropy of the fluctuation, so Penrose just needs to calculate the entropy of our universe. Unfortunately, there are a bunch of different entropies that one could calculate. The one that is typically taken to describe the entropy of those fluctuations is called the Boltzmann entropy. But the Boltzmann entropy of the visible universe is difficult to calculate. Another entropy is the Von Neumann entropy, which arises out of quantum mechanics. In the cosmological context, the Von Neumann entropy of the universe can be calculated just by adding up the number of plank area sized patches on the universe’s horizon. And that’s what Penrose calculates. Notice that Penrose has so far made two controversial assumptions: first, that the universe arose from a fluctuation and, second, that the Von Neumann entropy is the appropriate entropy to calculate.

    Let’s take for granted Penrose’s two assumptions. Why is Penrose making these calculations? Penrose is aiming to rule out a class of cosmological hypotheses in order to argue for his own (naturalistic) cosmological hypothesis (what’s called “conformal cyclic cosmology”). He’s certainly not a theist — Penrose is an atheist — and he never meant for his calculation to provide any evidence for theism; the calculation is only meant to help us theoretically decide between sets of naturalistic hypotheses.

    But the situation gets worse, because this number does not describe the degree to which our universe’s entropy is fine-tuned for life. The kinds of hypotheses that Penrose is interested in ruling out are multiverse hypotheses that explain our universe’s apparent fine-tuning as a kind of self-selection effect. That is, observers will find themselves only in those parts of the multiverse consistent with their own existence, so that observers can only find themselves in rare life-permitting universes. We call this the weak anthropic principle. But, Penrose points out, our universe does not need an entropy anywhere near as low as our universe has in order to be life permitting. To be sure, life requires a low entropy, and, on the fluctuation hypothesis, low entropies are improbable. But the entropy of our universe is so vastly lower than the entropy required for life that adding anthropic principle does essentially nothing to alter the probability that our universe would have the low entropy that it has.

    And here’s the upshot for the theist: the theistic hypothesis is a version of the anthropic principle. In contrast to the weak anthropic principle, we can define the theistic anthropic principle: that, given God’s existence and desire for morally significant, sentient creatures, we should expect to find ourselves in a life-permitting universe. Of course, on this hypothesis, we’ve left behind the idea that the universe came from a fluctuation. But we are still asking how probable it would be for God to select a universe like ours out of the possible configurations of the universe’s matter, and that will result in the same results as the fluctuaiton calculation. We can ask: does adding the theistic anthropic principle help in explaining the universe’s low initial entropy if we add that principle to our cosmological theorizing? In other words, would adding the theistic anthropic principle raise the probability that God would select a universe with an entropy as low as ours? No, it does not — God would not require an entropy as low we find to fulfill God’s purposes. God could deliver on God’s purposes if the universe’s entropy were vastly higher. (Of course, the theist could always postulate that God likes low entropy states, but that seems gratuitously ad hoc.) Let me be explicit: God could accomplish God’s purposes with such a vastly smaller entropy that the probability that God would create a universe with an entropy as low as ours remains approximately 10^-10^123.

    To be sure, there are various parameters that, from the perspective of contemporary physics, do appear to be fine-tuned for life. The cosmological constant is an important example, with quite a respectable literature. Theists should stop appealing to the universe’s entropy because, once properly understood, the universe’s entropy does nothing to help them build any sort of case for fine-tuning.

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    1. Hi Dan!

      Yes, that is interesting. I knew some of that already, although not in as much detail. I spoke with ‘skydivephil’ a while back. You should check out his YouTube channel. He has an outstanding documentary series about cosmology. He interviews Penrose about exactly this in one episode.

      Anyway, I think it doesn’t really change anything in my post. The Penrose number is just a placeholder for some stupidly small number. I don’t see that it makes any real difference if we use a different number, so long as it is very small. The point is about the ratio between the variables in the conditional probability.

      Have you gone through my maths? I haven’t double checked it, so there may be an error in there somewhere. Let me know if you find one.

      Let’s chat soon.

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      1. Hi Alex!

        I agree with you about skydivephil’s content. Fantastic channel. There was a youtube video posted on that channel years ago, responding to Craig’s appeal to physical cosmology in defending his kalam argument, but that video has since been taken down for copyright infringement. (I guess they used a couple clips from a Discovery channel documentary or something.) It’s a real shame, as it was one of my favorite videos on that subject.

        Was your discussion with skydivephil recorded? I’d love to watch it.

        I haven’t noticed any problems with your mathematics, but I also haven’t checked that carefully. The math here isn’t terribly difficult, so maybe I’ll find some time later today to go through it. The bit about Penrose’s number grabbed my attention because I’ve been working on the topic of the fine-tuning of the universe’s entropy, and the potential implications for theism, for the past year and a half.

        I think there are several things to take away from this discussion, re: Penrose’s calculation. Of course, that’s largely the topic of the paper that I’ve been working on. I won’t go into the details of that paper here. Instead, I’ll summarize two points I think are worth bearing in mind with respect to your blog post.

        The first is that theists are not always honest — or, more charitably, sufficiently knowledgeable — to report on whether any given number is fine-tuned in a sense relevant for theism. Penrose is sufficiently secular that he feels secure using God as a metaphorical device, but that’s confused a lot of theists. (Compare, for example, Einstein’s comments on a dice-playing God.)

        Second, more to the point, not all forms of fine-tuning are born equal — importantly, some forms of fine-tuning may undermine the class of hypotheses theism belongs to, or bolster the case for naturalism. I think that point is little appreciated and, while not identical to Halvorson’s argument, is a closely related sibling.

        As a bonus, here are two papers I’d recommend reading. Only the first is related to what I mention here, but both are excellent papers not widely known among philosophers. (But they should be.)

        The first is Robert Wald’s ‘The Arrow of Time and the Initial Conditions of the Universe’. Available here: https://arxiv.org/abs/gr-qc/0507094

        The second is Donoghue, J. (2007) ‘The fine-tuning problems of particle physics and
        anthropic mechanisms’, In Bernard Carr (Ed), Universe or Multiverse. Cambridge University Press. I can send you a pdf copy of this book.

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    2. Dan Linford: A few years back, Alan Guth proposed that, if we remove any upper bound on entropy (allowing it to grow to infinity), there would be no need to assume that the Universe started in a very special (low-entropy) state. In other words, any early entropy would be “low” in the sense that it would much less than a potentially infinite maximum.

      All that’s required for the “arrow of time” is that the entropy go from loweER to highER, so this scheme would preserve the “arrow of time” without requiring a very low entropy state at the start of the Universe.

      Have you heard of Alan Guth’s research on this?

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      1. I haven’t read Guth’s paper on this topic, but I am familiar with this line of argumentation. (Sean Carroll has said similar things, as did Isenkrahe in the 19th century.) I should note that while there is no maximum entropy, in the statistical interpretation of entropy, one can always define a minimum entropy, e.g., the universe could have begun in a state for which there is only one possible microstate, in which case the entropy is 0. For mathematical reasons, negative entropy is not defined, so S=0 is as low as one can go.

        Given accounts on which there is no maximum entropy for the universe, we can still compare the relative probability of beginning the universe with one entropy as opposed to another.

        I think there is a more important upshot for the notion that there is no maximum entropy for the universe. As Susskind and co-authors point out, the usual way of thinking about the universe’s entropy supposes that the univrerse is something like a gas in a box, e.g., for most of the universe’s lifetime, the universe is an equilibrium system undergoing Poincare recurrences. (Or that the calculations one would yield from treating the universe in this way yield meaningful results.) If there is no maximum entropy for the universe, this would suggest that there is no possible equilibrium state for the universe, and so Penrose’s calculations are not physically meaningful.

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    3. Alex, I love your stuff!

      What do you think of the objection that the argument fails because it contains a hidden and unjustified value judgement?

      To explain, consider the lottery example. If you win the lottery, you don’t start wondering whether somebody rigged it in your favour. After all, there’s nothing special about you. Somebody had to win, so why not you? There’s nothing that demands an explanation.

      The usual response is to offer counterexamples. Imagine, for instance, that you won the lottery every week for the rest of your life. We wouldn’t put that down to chance.

      The issue, of course, is to decide which of these examples is most like the fine-tuning. Defenders of the argument seem to presuppose that there is something special about life. But why think that? Every possible universe will have some unique feature (such as lasting for a particular amount of time and containing a specific amount of matter). For every universe, you could postulate a designer with a preference for that outcome which would raise the probability of it happening over the chance hypothesis (maybe there exists a designer with an appreciation for the aesthetic properties of hydrogen moving at great speeds); but that doesn’t mean we’d actually take those design hypotheses seriously. So why do we take the traditional god more seriously? Why do we assume that these other gods have much lower prior probabilities? Presumably because we are strongly biased in favour of the traditional god due to cultural and biological influences. As evolved beings, we take seriously the idea that life is the most valuable thing. But that’s just the kind of bias you would expect us to have! It’s our subjective point of view; it tells us nothing about the probability of the cosmos looking a certain way. We take the traditional god seriously because the culture is saturated with references to it. (If we lived in a world where sci-fi geeks were more common than religious people, we’d probably all be discussing the fine-tuning argument for computer simulators and aliens in the next universe up, and only a small number would be pointing to the possibility of a deity.) The claim that the traditional god has a much higher prior probability has no rational justification.

      So how can we identify a result which is truly special and in need of an explanation other than chance? We can only rely on empirical evidence. The reason we would assume the lottery was being rigged if you starting winning every week is that we know, on the basis of past experience, that people have a strong interest in rigging lotteries for either themselves or people they care about. We also know that humans like to play tricks on each other. But suppose that humans were very different. Suppose we had excellent evidence that humans never cheated and were always perfectly honest. In that world, it’s not clear that your winning the lottery every week would demand some explanation in terms of rigging or design.

      Notice that we have no such empirical evidence to go on when considering the nature of the universe as a whole.

      In the end, I start to wonder whether there’s anything that needs explaining here at all. The whole argument seems shot through with anthropocentric reasoning.

      It also seems to assume some sort of moral realism and the idea that life is objectively special. Now, one might respond by pointing out that the probability of moral realism being true isn’t anywhere near as low as the probability of the constants permitting life by chance, so the fine-tuning argument should still give a boost to theism even if you are an anti-realist. But that seems weird. If that works, does that mean we can suddenly start using fine-tuning to refute all kinds of positions in philosophy? If there was a person who thought they were a brain in a vat, and who therefore rejected the ‘evidence’ for fine-tuning right off the bat, it seems strange to suggest that we could respond to them by pointing out that the probability of common-sense realism being true is not nearly so low as the probabilities in the fine-tuning argument, so theism should still get a boost for them. In general, to reject one of the claims in the fine-tuning argument, I don’t have to think it’s absurdly unlikely that I’m wrong in order for my rejection of the argument to be reasonable.

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      1. Liam —

        I think you are right that the theistic version of the fine-tuning argument may require some infeliticious value judgment. However, I don’t think that resolves the fine-tuning problem generally; I think you’ve overstated your case.

        As far as physics is concerned, the issue goes as follows. We have models purporting to tell us about the space of possible configurations of our universe given various values of the physical constants. We’d like to be able to make predictions in that large space — that is, we’d like to be able to say that the universe that we observe is probable given our models. To say that a model is fine-tuned is to say that our observations are improbable given the model; so, we need a new model in which our observations would be probable.

        And, to be clear, the issue is that perturbations to our universe result in universes radically unlike ours, so that one might predict that possible universes, generally, are radically unlike ours. Small perturbations result in universes where, e.g., there are no galaxies, or the universes is subatomic, or the universe flies apart at superluminal speeds, or matter isn’t stable, etc. If those models are correct, then our universe is not one of the typical universes, so not what one would expect to observe. In other parts of science, when we observe some phenomenon that radically departs from our expectations, we have some defeasible reason to revise our models.

        Could all of this be analogous to winning a cosmic lottery, in which case it would be improper to demand that our data be probable given the model? Well, notice that, in the lottery case, so long as a large number of people enter the lottery, it’s actually fairly probable that someone or other will win the lottery. So, we shouldn’t be surprised if we can find some winner. (Though we might be somewhat surprised if *we* happen to be the winner!) Let’s suppose that instead of a large number of people entering, only one person enters. Now, it’s possible that this one person will win, but, if we are given no other information than that the person entered, we should not believe that they will win. And, importantly, we should not predict that they will win. Nonetheless, we may suppose that the person wins. We can revise our probabilities — we may suppose that we now have strong evidence that this person won the lottery and did not, e.g., cheat — so that, now, it is highly probable that the person won the lottery. But we still cannot predict (or non-trivially retrodict) that the person won; their winning was a matter of pure happenstance and luck. (Nor, in the original case, could we have predicted who in particular would win, unless we had some selection criteria — e.g., perhaps only winners are sentient, in which case, if most entrants were non-sentient, we should not be surprised to find ourselves among the winners.)

        We prefer hypotheses in science that offer explanations for the data that we observe. In the case that the universe is just a cosmic luck of the draw, physical cosmology will have come to an end as a discipline. So, at least on that pragmatic basis, we’d better hope that there is some explanation that would render our universe typical, according to some measure, in the space of possible universes.

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      2. [The following passage is from C. S. Lewis’ Miracles, 1947.]

        Probability is founded on the presumption of a resemblance between those objects of which we have had experience and those of which we have had none; and therefore it is impossible that this presumption can arise from probability.

        HUME, Treatise of Human Nature, I, iii, vi.

        The argument up to date shows that miracles are possible and that there is nothing antecedently ridiculous in the stories which say that God has sometimes performed them. This does not mean, of course, that we are committed to believing all stories of miracles. Most stories about miraculous events are probably false: if it comes to that, most stories about natural events are false. Lies, exaggerations, misunderstandings and hearsay make up perhaps more than half of all that is said and written in the world. We must therefore find a criterion whereby to judge any particular story of the miraculous. In one sense, of course, our criterion is plain. Those stories are to be accepted for which the historical evidence is sufficiently good. But then, as we saw at the outset, the answer to the question, ‘How much evidence should we require for this story?’ depends on our answer to the question, ‘How far is this story intrinsically probable?’ We must therefore find a criterion of probability.

        The ordinary procedure of the modern historian, even if he admits the possibility of miracle, is to admit no particular instance of it until every possibility of ‘natural’ explanation has been tried and failed. That is, he will accept the most improbable ‘natural’ explanations rather than say that a miracle occurred. Collective hallucination, hypnotism of unconsenting spectators, widespread instantaneous conspiracy in lying by persons not otherwise known to be liars and not likely to gain by the lie—all these are known to be very improbable events: so improbable that, except for the special purpose of excluding a miracle, they are never suggested. But they are preferred to the admission of a miracle.

        Such a procedure is, from the purely historical point of view, sheer midsummer madness unless we start by knowing that any Miracle whatever is more improbable than the most improbable natural event. Do we know this?

        We must distinguish the different kinds of improbability. Since miracles are, by definition, rarer than other events, it is obviously improbable beforehand that one will occur at any given place and time. In that sense every miracle is improbable. But that sort of improbability does not make the story that a miracle has happened incredible; for in the same sense all events whatever were once improbable. It is immensely improbable beforehand that a pebble dropped from the stratosphere over London will hit any given spot or that any one particular person will win a large lottery. But the report that the pebble has landed outside such and such a shop or that Mr So-and-So has won the lottery is not at all incredible. When you consider the immense number of meetings and fertile unions between ancestors which were necessary in order that you should be born, you perceive that it was once immensely improbable that such a person as you should come to exist: but once you are here, the report of your existence is not in the least incredible. With probability of this kind—antecedent probability of chances—we are not here concerned. Our business is with historical probability.

        Ever since Hume’s famous Essay it has been believed that historical statements about miracles are the most intrinsically improbable of all historical statements. According to Hume, probability rests on what may be called the majority vote of our past experiences. The more often a thing has been known to happen, the more probable it is that it should happen again; and the less often the less probable. Now the regularity of Nature’s course, says Hume, is supported by something better than the majority vote of past experiences: it is supported by their unanimous vote, or, as Hume says, by ‘firm and unalterable experience.’ There is, in fact, ‘uniform experience’ against Miracle; otherwise, says Hume, it would not be a Miracle. A miracle is therefore the most improbable of all events. It is always more probable that the witnesses were lying or mistaken than that a miracle occurred.

        Now of course we must agree with Hume that if there is absolutely ‘uniform experience’ against miracles, if in other words they have never happened, why then they never have. Unfortunately we know the experience against them to be uniform only if we know that all the reports of them are false. And we can know all the reports to be false only if we know already that miracles have never occurred. In fact, we are arguing in a circle.

        There is also an objection to Hume which leads us deeper into our problem. The whole idea of Probability (as Hume understands it) depends on the principle of the Uniformity of Nature. Unless Nature always goes on in the same way, the fact that a thing had happened ten million times would not make it a whit more probable that it would happen again. And how do we know the Uniformity of Nature? A moment’s thought shows that we do not know it by experience. We observe many regularities in Nature. But of course all the observations that men have made or will make while the race lasts cover only a minute fraction of the events that actually go on. Our observations would therefore be of no use unless we felt sure that Nature when we are not watching her behaves in the same way as when we are: in other words, unless we believed in the Uniformity of Nature. Experience therefore cannot prove uniformity, because uniformity has to be assumed before experience proves anything. And mere length of experience does not help matters. It is no good saying, ‘Each fresh experience confirms our belief in uniformity and therefore we reasonably expect that it will always be confirmed’; for that argument works only on the assumption that the future will resemble the past—which is simply the assumption of Uniformity under a new name. Can we say that Uniformity is at any rate very probable? Unfortunately not. We have just seen that all probabilities depend on it. Unless Nature is uniform, nothing is either probable or improbable. And clearly the assumption which you have to make before there is any such thing as probability cannot itself be probable. The odd thing is that no man knew this better than Hume. His Essay on Miracles is quite inconsistent with the more radical, and honourable, scepticism of his main work.

        The question, ‘Do miracles occur?’ and the question, ‘Is the course of Nature absolutely uniform?’ are the same question asked in two different ways. Hume, by sleight of hand, treats them as two different questions. He first answers ‘Yes,’ to the question whether Nature is absolutely uniform: and then uses this ‘Yes’ as a ground for answering, ‘No,’ to the question, ‘Do miracles occur?’ The single real question which he set out to answer is never discussed at all. He gets the answer to one form of the question by assuming the answer to another form of the same question.

        Probabilities of the kind that Hume is concerned with hold inside the framework of an assumed Uniformity of Nature. When the question of miracles is raised we are asking about the validity or perfection of the frame itself. No study of probabilities inside a given frame can ever tell us how probable it is that the frame itself can be violated. Granted a school timetable with French on Tuesday morning at ten o’clock, it is really probable that Jones, who always skimps his French preparation, will be in trouble next Tuesday, and that he was in trouble on any previous Tuesday. But what does this tell us about the probability of the timetable’s being altered? To find that out you must eavesdrop in the masters’ common-room. It is no use studying the timetable.

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      3. Charles writes (or perhaps he’s quoting from Lewis?): “Unless Nature is uniform, nothing is either probable or improbable.”

        That’s demonstrably false. Consider the sentence ‘1+1=2’. That sentence is necessarily true. Any necessarily true sentence has an intrinsic probability of 1. Therefore, that 1+1=2 is highly probable (it’s as probable as can be!) and that would be so even if Nature were not uniform.

        Why should we believe in the uniformity of nature if, as is claimed, the uniformity of nature cannot be shown from experience? A basic principle in the probability calculus concerns the fact that the probability of a conjunction is always less than or equal to the probability of either conjunct, that is, Pr(A&B)<=Pr(A). So, the probability of a conjunction has an upper bound given by the probability of the more improbable conjunct. Moreover, that upper bound is satisfied only when the probability of the conjunction is equal to the probability of the more improbable conjunct. We have that Pr(A&B)=Pr(A)Pr(B|A). This tells us what the condition is for the probability of the conjunction to be maximized — the probability of the conjunction is maximized only when Pr(B|A) = 1. In other words, the upper bound on the probability of a conjunction is given by how probable either conjunct is given the other conjunct.

        That's a lot to take in. But here's the upshot for my argument. Since the probability of a conjunction is bounded from above by how probable either conjunct is given the other conjunct, and given that similarity is simpler than difference, the implication follows that a similiar future is more probable than a different future. In other words, all else being equal, the intrinsic probability of the uniformity of nature is higher than the intrinsic probability of the contrary.

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      4. Hi Daniel, Why is math always true, irrespective of experience?  That infers an absolute and atheism cannot justify immaterial, invariant absolutes. Similarly, laws of logic are absolute. Is logic true because of experience or true irrespective of experience?  There are some laws of logic that cannot be experienced to be true. Can you experience an entity that exists and not exists at the same time and instance?  Can you examine the term, ‘All’ of a major premise of a syllogism?  Hume doesn’t think so. You are finite and limited; how can you examine ‘All’ things at the same time and instance at all locations and instances to determine that the major premise is true? 

        You have not justified uniformity.

        Regards, Charles Gillihan

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      5. Charles Gillihan
        To:Charles Gillihan
        Dec 26 at 8:02 PM
        Charles writes (or perhaps he’s quoting from Lewis?): “Unless Nature is uniform, nothing is either probable or improbable.”

        That’s demonstrably false. Consider the sentence ‘1+1=2’. That sentence is necessarily true.
        <>
        Since the probability of a conjunction is bounded from above by how probable either conjunct is given the other conjunct, and given that similarity is simpler than difference, the implication follows that a similiar [sic] future is more probable than a different future.
        <<

        It's true that nature being uniform is simpler than nature being not uniform. So one can appeal to the principle of simplicity (ceteris paribus, simpler theories are more likely to be true) to justify the uniformity of nature. One problem: what justifies this principle of simplicity working for the future? One could reason, "Well, the principle of simplicity worked well for us in the past, so it'll probably work for the future" but that would be _assuming_ the uniformity of nature, which is precisely what simplicity is supposed to be justifying!

        One could fall back on first principles; belief in the simplicity principle is properly basic and known intuitively. I think that's correct, and much the same thing could be said for our intuition of uniformity (i.e. that the future will relevantly resemble the past) since we know that intuitively as well. But one might ask how, if this intuition is not God-given, this intuition successfully delivers warrant for uniformity/simplicity. For if the only reason we have these intuitions is that unguided evolution gave us these intuitions because they worked for our ancestors in the past, we have another kind of circularity that seems to undermine warrant for uniformity.

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      6. Thanks for your reply, Charles!

        You’ve written me about mathematics, as, I think, a reply to my post above about how we might justify the uniformity of nature based on considerations from the probability calculus. That is, I argued that the simplest hypothesis is that nature is uniform so, all else being equal, we should believe nature is uniform. My argument drew upon mathematics, so you’ve replied with a set of questions about what justifies mathematics. (As well as what justifies logic.)

        Before we begin, note that we’ve changed the topic. Before we were discussing what justifies induction. I offered an explanation as to what justifies induction based on the probability calculus. In reply, you changed the topic to what justifies mathematics and logic. Perhaps you have in mind that the probability calculus cannot justify induction unless the probability calculus is justified. And the probability calculus is not justified unless mathematics and logic are justified. But that’s not true. Induction can be justified by the probability calculus even if the probability calculus is not, itself, justified. (For analogous reasons, the conclusion of an argument can be justified by the premises in the argument, even if the premises are not, themselves, justified.)

        On my view, we don’t need to offer a metaphysical explanation for an epistemic tool before we are justified in using that tool. That’s because justification is not the same thing as explanation. For example, when you see an airplane fly, you are justified in believing that the airplane is flying, even if you cannot explain either flight or vision. Therefore, even if I could not explain why mathematics is “always true”, etc, that would not have any bearing on whether I am justified in using mathematics. The reason that you are justified in believing that the airplane is flying, even when you cannot explain either flight or vision, is because it seems as though you are seeing the airplane flying and you do not have sufficient defeaters for your belief. Of course, the situation could change; you could come to find out that someone spiked your coffee with a serum that tends to cause visual hallucinations of flying airplanes. If you did come to find that out, you’d now have a defeater for your belief, and so you may have to give up your belief that you are seeing a flying airplane. But in the absence of that defeater, your belief that you are seeing a flying airplane is justified. Likewise, I am justified in my use of mathematics so long as mathematical statements seem to be true and I do not have sufficient defeaters for mathematical statements. Of course, I could come to learn of a defeater. I could come to learn that mathematics is all some kind of giant hoax perpetuated on us by Big Math and that we all buy into math because we were introduced to the propaganda of arithmetic in elementary school. But absent some kind of defeater, I am justified in my belief in the truth of mathematical statements. (And, just to be clear, I have no defeaters for mathematical truths.)

        You stated that mathematics and the laws of logic being always true, irrespective of experience, would require immaterial, invariant absolutes, and that atheism cannot “justify immaterial, invariant absolutes”. I don’t think you mean to say that atheism cannot justify immaterial, invariant absolutes; I think you mean to say that there is some tension between atheism and immaterial, invariant absolutes, so that if atheism were true, then there couldn’t be immaterial, invariant absolutes. And I think that’s what you must mean because neither atheism nor theism, in themselves, are candidates for justifications of immaterial, invariant absolutes. (Of course, there are views on which God plays some important role in an explanation of immaterial, invariant absolutes. But that’s a very specific set of claims about God and not the more general claim that God exists.)

        But why think that if atheism were true, there couldn’t be immaterial, invariant absolutes? Atheism is the position that there is no god. Atheism is not the position that there are no immaterial entities, nor the position that there are no invariant entities, nor the position that there are no absolute entities, etc. Certainly, all of these things could exist without God existing. So, there doesn’t seem to be any tension between atheism and the reality of immaterial, invariant absolutes. (Conceivably, one might confuse materialism, the position that only matter exists, with atheism. Certainly, there is a tension between materialism and immaterial entities — if materialism is true, there no immaterial entities. While all materialists are atheists, not all atheists are materialists, nor does atheism entail materialism.)

        Perhaps I’ve misinterpreted you. Perhaps instead of asking about some sort of tension between atheism and immaterial, invariant absolutes, you have in mind that atheists, in virtue of their atheism, cannot be justified in using mathematics or laws of logic. But, again, why think that something like that is true? I already offered you a story about how I am justified in using mathematics and the laws of logic — i.e., that mathematical statements and the laws of logic seem to be true and there aren’t sufficient defeaters on offer against mathematical statements or laws of logic.

        But perhaps I’ve once again misinterpreted you. Perhaps you have in mind that the arguments atheists typically endorse for their atheism have some tension with invariant, immaterial absolutes. For example, many atheists have argued for their atheism in virtue of their empiricism. Old fashioned empiricists — like Hume — thought that we acquire all of our ideas through experience. We don’t have experience of God, so, an old fashioned empiricist might argue, contrary to appearances, we don’t have any idea of God. So, the old fashioned empiricists might have argued, theology is actually void of any ideas at all and, consequently, theological statements are some sort of gibberish. The theist might reply that there is a similar tension between old fashioned empiricism and invariant, immaterial absolutes. Perhaps this is what you have in mind when you brought up that there are mathematical and logical principles that we know to be true independent of experience. But all this would suffice to show is that old fashioned empiricists had some problems explaining immaterial, invariant absolutes. I’m not an old fashioned empiricist — I don’t think we acquire all of our ideas in virtue of experience — so I don’t face this sort of problem with invariant, immaterial absolutes.

        You ask, “Can you experience an entity that exists and not exists at the same time and instance?”

        I have no idea what you have in mind here. No entity both exists and does not exist at the same time and instant. If an entity did exist and not exist, that would plainly be a contradiction. On my view, we can justifiably believe some logical principles and the principle of non-contradiction is one such principle. I don’t think we can experience entities that do not exist. (You might object that you could experience, e.g., a purple unicorn in a hallucination, yet purple unicorns don’t exist. In reply, you wouldn’t be experiencing a purple unicorn. You’d be experiencing a hallucination, and hallucinations certainly exist.) So, since we cannot experience entities that do not exist, and the principle of non-contradiction implies that there are no contradictory entities, we cannot experience contradictory entities. (Moreover, if we cannot experience entities that do not exist, then, obviously, we cannot experience entities that both exist and do not exist.)

        I’m not sure if this helps, but I think there are plenty of things that exist, that we can know exist, and which we do not experience. For example, I think that there are some scientific theories which we can know to be true. Suppose there is some theory T which I do know to be true, because T is true and I non-accidentally and justifiably believe T. My justification for believing T would consist, at least in part, in evidence that I have for T. But, in virtue of believing T, I believe much more than just those consequences of T which I can directly observe. Instead, I’m committed to all of the consequences of T, including all of the non-observable entities whose existence is entailed by T.

        You write that Hume thought we cannot examine the term ‘all’ as it appears in the major premise in syllogism. If you know of a passage where Hume examines that term, I’d be interested in reading it. As far as I’ve read — and I’ve read a lot of Hume — Hume doesn’t have a tremendous amount to say about those sorts of technical features of Aristotelian logic. In any case, whatever Hume has to say about Aristotelian logic, I’m not committed to Hume’s views about logic. Therefore, whatever Hume may or may not have said about Aristotelian logic, and however justified or unjustified Hume’s views may have been, an objection to Hume is not an objection to my own views.

        You bring up this business about our being finite and limited. You’re certainly right that we are finite and limited and that, in many cases, we cannot check all of the instances subsumed by a universalized statement. For example, consider the statement ‘all lead balls are less than 30 light years in diameter’. I’m pretty sure that this statement is true, but I haven’t measured every individual lead ball in existence. It’s logically possible that there could be a lead ball on the other side of the universe that measures 40 light years in diameter.

        So, how am I justified in my belief that all lead balls are less than 30 light years in diameter? I’m justified in this belief because I know enough astrophysics to know that the conditions for the formation of such an object are exceedingly unlikely and that such an object, if formed, would presumably be fairly unstable. How am I justified in my knowledge of astrophysics? Well, I’m justified through a variety of independent channels — including education, self-study, and all the sorts of things that I had to go through on my way to completing a bachelor’s degree in physics and graduate level course work in astrophysics. You can keep on asking how I am justified in believing the information that I acquired through various sources, further and further back, but eventually you’re going to reach epistemic rock bottom.

        When you do hit epistemic rock bottom, I’m going to reply the same way that I did above. We’re justified in thinking that nature is uniform because that’s the simplest hypothesis and we have no reason to disregard the simplest hypothesis. Moreover, I’m justified in believing what seems to be true in the absence of sufficient defeaters. Mathematical and logical principles seem to be true, we have no defeaters for those principles, so I’m justiifed in believing that they are true.

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      7. Hi Daniel. I see you wrote a rather lengthy post. I am not replying yet, but adding a few qualifiers. You inject calculus and its relation to probability.
        How do you gauge degrees of probability? Also, please tell me you don’t place Matt Dillahunty upon a precipice of sorts.

        I shall get to the entirety of your response soon.

        Grace & Peace,

        Charles

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      8. Hello again, Charles!

        No, I don’t place Matt Dillahunty on any sort of precipice. He’s said interesting things in the past. He’s also said some things I disagree with. At any rate, he’s not me, and I’m not him, nor have I mentioned him anywhere in the conversation. Certainly, the views that I express here are not views that I arrived at from him.

        You say that I “inject calculus and its relation to probability”. No, that’s not quite right. I talked about the “probability calculus”. Here, I’m using the word ‘calculus’ in a rather broad way, and not referring to the part of mathematics you might learn in a calculus class. (The word ‘calculus’ really just means something like “a system/method for doing calculations”. The part of mathematics that you learn in calculus class is actually called the differential and integral calculus.) When you see me write “probability calculus”, if you’d like, you can just read that as “probability theory”.

        How do I guage degrees of probability? That would require a fairly lengthy response, longer than replies I’ve offered you so far, because the question you asked was so broad. (If you are interested, the subdiscipline in philosophy that deals with that sort of question is called confirmation theory.) For that reason, instead of offering you some full theory of how we judge degrees of probability, I think it would be better if you ask a more specific question. For example, you might ask me how I would go about judging the probability of some specific hypothesis that you might have in mind, or you might ask me about one of the claims that I made where I was judging the probability of some statement.

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      9. Probability requires the future to be like the past, based upon the past. Circular? The Christian Theist trusts God’s omnipotence and wisdom as revealed in special revelation, the Scriptures. God as the starting point is a better inference to coherence than mysticism or the claim, ‘it just is’. The naturalism can only allow wallowing in evolutionary dogma of arbitrary change. What maintains uniformity in chemical bonding, electron covalent bonding, physical laws, or moral ‘oughts’? Does one derive an ‘ought ‘ from an ‘is’ in your worldview?

        To Cothran’s reply shortly. Just playing with words.

        Regards

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      10. Charles — Thanks, again, for another reply!

        Before I get going in my reply back to you, I want to ask which of the two you’d like to discuss:

        1. The epistemological justification of various sorts of beliefs that we have (i.e., beliefs about the uniformity of nature, the laws of logic, etc).

        2. The metaphysical explanation of the contents of those beliefs (i.e., what metaphysically explains the uniformity of nature, the laws of logic, etc).

        Those are two distinct topics, but you keep running them together in your replies.

        You say that you plan on offering a reply to something that I wrote about how we ought to speak about God. I’m not sure which article of mine you’re referring to, though I’m not sure if this is the appropriate venue to discuss that issue. I wonder what Alex thinks about our continuing to go back and forth like this.

        You wrote: “Probability requires the future to be like the past, based upon the past. Circular?”

        I think you’ve misunderstood me, or perhaps I haven’t been clear enough. On my view, probability does *not* require the future to be like the past. Instead, my view is the following. Rational agents adjust their credences in accord with the axioms of the probability calculus. All else being equal, the axioms of the probability calculus provide us with the resources to construct an argument that simpler and more coherent hypotheses are more probable than more complex and less coherent hypotheses. The hypothesis that nature is uniform is a simple and coherent hypothesis. Therefore, all else being equal, rational agents should believe that nature is uniform.

        That the future is like the past is an instance of the uniformity of nature. In other words, its a simpler and more coherent hypothesis to postulate that the future will be like the past than the hypothesis that the future will be different from the past. Therefore, just as before, all else being equal, rational agents should think that the future will be like the past.

        Notice that no where have I utilized past experience to justify probability.

        You go on to say that, “The Christian Theist trusts God’s omnipotence and wisdom as revealed in special revelation, the Scriptures. God as the starting point is a better inference to coherence than mysticism or the claim, ‘it just is’.”

        I’ll note a few things here. It’s not obvious to me that you are using the term ‘coherent’ in the same way that I am. When I say that one hypothesis is more coherent than another, I mean that the parts of the hypothesis result in a greater increase in the probability of the other parts. For example, if we have a hypothesis H that can be written as the conjunction A&B, then the coherency of H is increased as Pr(A|B) and Pr(B|A) are increased. If A and B contradict one another, then H is maximally incoherent (or minimally coherent), because in that case Pr(A|B)=Pr(B|A)=0. And H is maximally coherent in the case that Pr(A|B)=Pr(B|A)=1.

        I say that it’s not obvious to me that this is what you mean by ‘coherent’ when you say that using special revelation and God as a starting point is a “better inference to coherence” because you said nothing about the conditional probabilities of the claims involved in your starting point.

        You go on to talk about how you think “naturalism can only allow wallowing in evolutionary dogma of arbitrary change”. I’m not sure that’s true, but, in any case, that’s a claim about naturalism and not a claim about atheism. If that consequence does follow for naturalism, all that would follow is that I need to give up naturalism and not that I would have any more reason to accept theism.

        You ask what maintains the uniformity in “chemical bonding, electron covalent bonding, physical laws, or moral ‘oughts’”. The first three are really repetative; whatever it is that would explain the uniformity in physical laws would explain the uniformity in chemical bonding. And whatever explains the uniformity in chemical bonding would explain the uniformity in electron covalent bonding. The last issue — about the uniformity in moral oughts — may require a distinct explanation than the uniformity in physical laws.

        I want to remind you of something I’ve said previously. Previously, I said that I distinguish justification from metaphysical explanation. I used the example that I can be justified in believing that I see an airplane flying, even if I cannot explain either sight or how airplanes fly. Likewise, we can be justified in belieiving in the uniformity of physical laws even when we cannot offer a metaphysical explanation of those physical laws. I explained why I am justified to believe in the uniformity of natural law when I offered an argument that drew from the probability calculus. As for what metaphysically explains the uniformity of physical law, I don’t know. (Nonetheless, since I think that I have a number of good arguments against theism, I think we can rule out theistic explanations of the uniformity of physical laws.)

        Lastly, you asked, “Does one derive an ‘ought ‘ from an ‘is’ in your worldview?”

        Nope. If you’d like, we could discuss how I think moral oughts are justified, but that seems like a digression that might not be worth pursuing.

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      11. Hi Daniel,

        Sorry to combine two or more subjects. I’m at work and busy, and probably shouldn’t be typing things. I’ll continue later on with one topic. I see only two justifications to account for experience or or reality and oppositions regarding such; Theonomy or autonomy. I also see non difference between atheism, naturalism, and autonomy/existentialism. My whole quest is to see if you can justify your worldview. You said you cannot in do many words. If you are content with adapting to change with abstracts as in probability theory, then your worldview is incoherent and subject to fiat foundations as posibilities. The Christian worldview tests upon a transcendent and immanent Being with attributes described in the Bible, summarized in the historical creeds.

        Later,

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      12. Hello, again, Charles! Thanks, again, for another stimulating response.

        You wrote, “I also see non difference between atheism, naturalism, and autonomy/existentialism.”

        Atheism is the view that there is no God.

        Naturalism is the view only nature exists. (So, according to naturalism, there is nothing supernatural.)

        Atheists don’t have to be naturalists. They could be supernaturalists — for example, an atheist could believe in ghosts — or non-natural moral realists — they could believe that the Form of the Good, or some such, exists. And naturalists don’t have to be atheists; for example, a naturalist could believe that God is part of nature, in which case they believe that only nature exists even though there is a god.

        I’m not sure what you mean when you say “autonomy/existentialism”. I thought that when presuppositionalists talk about “autonomy”, they basically just mean something like “without the authority of God”. Existentialism — at least the philosophical view — is a view that has been endorsed by some theists (e.g., Kierkegaard).

        You wrote, “My whole quest is to see if you can justify your worldview. You said you cannot in do many words.”

        This is the complete opposite of what I said. I offered a justification for the beliefs that I hold about the uniformity of nature, the laws of logic, and so on, several times. I’m hoping that after you are able to sit down after work and really digest my posts, you’ll be able to see that.

        You wrote, “If you are content with adapting to change with abstracts as in probability theory, then your worldview is incoherent and subject to fiat foundations as posibilities.”

        I have no idea what you mean here. Perhaps you could explain this a bit.

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      13. Charles — You’ve objected to my use of a simplicity principle in the justification of induction. We agree that nature being uniform is a simpler hypothesis than nature being uniform. Nonetheless, you’ve objected to my move from the simplicity of the uniformity of nature to the conclusion that nature is probably uniform.

        The trouble is that you’ve mischaracterized my argument. On your reading, I could endorse what you’ve called “the principle of simplicity” (i..e, that simpler theories are more likely to be true) for one of two reasons. Either (1) the principle of simplicity could be justified through induction or (2) the principle of simplicity could be justified through some sort of faculty of intuition. (1) won’t work because, as you correctly note, if the principle of simplicity is justified through induction, then the principle of simplicity cannot offer a non-circular justification for induction. (2) won’t work, you say, because, in an evolutionary framework, there’s no reason to think that our intuitive faculty successfully tracks truth.

        Well, *my* reason for believing the principle of simplicity is not captured by either (1) or (2). Instead, I think the principle of simplicity is justified by the axioms of the probability calculus. In this case, an appropriate reply might be something like, “well, okay, but why should we adjust our beliefs in virtue of the probability calculus?” Were you to ask me something like that, I’d reply that our beliefs should be responsive to the probability calculus because of Dutch Book Arguments. I won’t go through all the technical details of how those arguments work, but I’ll give a brief synopsis of how they work. One way to ask the degree of rational belief (read: credence) I should assign to a given hypothesis is to ask how much a rational agent should bet on the truth of that hypothesis. Well, you can mathematically prove that if your betting behavior is not in alignment with the probability calculus, then a bet can always be constructed, that you would take, and which you would lose no matter what. In other words, we can mathematically show that good bets are those that follow the probability calculus. To make a long story short, rational agents adjust their credences in accord with the probability calculus. And, as I’ve argued above, the probability calculus tells us that, all else being equal, we should believe in the uniformity of nature.

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      14. Allow me to add on a bit more about how the axioms of the probability calculus justify the principle of simplicity, and how that principle justifies the uniformity of nature. One might come away from my post on this subject thinking that either the principle of simplicity or the uniformity of nature are axioms of the probability calculus, but that’s not so.

        Instead, the axioms of the probability calculus imply that Pr(A&B) <= Pr(A). And that the left hand side is maximized (that is, the two sides are equal) when Pr(A|B) = 1. This bit of mathematics has two important implications.

        First, if we consider two propositions, then the more the two propositions sit "less well" with one another (i..e., the less coherent their conjunction), the less probable their conjunction is. So, if we hypothesize that there is some sort of tension between two parts of nature, if, for example, they are very different and don't fit well together, then that hypothesis is less probable than a hypothesis on which the two parts of nature do fit well together. That's one reason the axioms of the probability calculus give us for preferring the uniformity of nature.

        Second, if we conjoin a greater number of propositions, then, other than in the special case where each proposition entails the others, the less probable the resulting conjunction will be. In other words, if we have to postulate that nature behaves in many different ways, none of which entail the others, then the resulting postulate will be intrinsically much less probable. So, all else being equal, we again have reason to think that nature is more likely uniform.

        So: the axioms of the probability calculus give us reason to prefer simpler hypotheses — in a mathematically precise sense — and that gives us reason, all else being equal, for thinking that nature is uniform.

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      15. Gah, sorry, typo.

        I wrote that the left hand side of Pr(A|B) <= Pr(A) is maximized when Pr(A|B) = 1. That's true (trivially), though not what I meant to say. I meant to say that the left hand side is maximized when Pr(B|A) = 1, since, in that case, Pr(A|B) = Pr(A).

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      16. 1.~A (The Christian God does not exist.)

        2.~A -> B (If God does not exist: then there is no intelligible experience since God is the precondition of intelligibility)

        3.~B (There is no intelligible experience)

        4.~ ~ A (It is not the case that God does not exist – Modus Tolens from 2 & 3)

        5.A (God does exist – Law of negation)

        Can you use probability calculus to prove that probability calculus is the primary criterion for truth claims?

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      17. Charles — Thanks again for another reply!

        You asked, “Can you use probability calculus to prove that probability calculus is the primary criterion for truth claims?”

        I’m not sure what you have in mind here. I did not claim that the probability calculus is the “primary criterion for truth claims” nor did I claim that all claims need to be judged on the basis of the probability calculus. Instead, I claimed that the probability calculus is a model of how rational agents asign credences to various hypotheses in light of available evidence. And the reason that I offered for thinking that is true were the Dutch Book Arguments, which concern the kind of bets that are rational for agents to make.

        There are other ways that we have for judging the truth or falsity of some claims. For example, I noted that there are some claims which we ought to believe because they seem to be true and we don’t have sufficient defeaters for them. That’s not an application of the probability calculus, but it can be used to help justify the probability calculus.

        You’ve offered an argument for the conclusion that God does exist. I don’t think you offered your argument correctly. I think the argument that you meant to offer goes as follows:

        1. If God does not exist, then there is no intelligible experience.
        2. There is intelligible experience.
        3. Therefore, God does exist (by modus tollens from 1 and 2).

        We agree on the second premise — that is, we agree that there is intelligible experience. So, our disagreement must be about the first premise. One thing to notice about the first premise is that if God necessarily exists — that is, that God’s non-existence is logically or metaphysically impossible — then the antecedent (“God does not exist”) is necessarily false. Theists typically think that God does necessarily exist. So, on the theist’s own view, the antecedent appears to be necessarily false. But all conditional statements with necessarily false antecedents are necessarily true. Thus, on the supposition that God necessarily exists, (a) the two premises are true but (b) the two premises do not establish an important connection between the intelligibility of experience and God’s existence. That’s contrary to your aims, so let’s try again.

        We could instead formulate the first premise as a counterpossible:

        1*. If God had not existed, then there wouldn’t have been intelligible experience.

        Here, to give a full analysis of (1*), we’d have to dive into all of the technical details about counterpossibles with necessarily false antecedents. Major philosophical controversies loom about how we should analyze sentences of that sort. But, to make our lives easier, let’s set those aside. Let’s instead focus on two claims that I think capture what you’d like to talk about:

        A. God’s existence entails that experience is intelligible.
        B. God’s non-existence entails that experience is not intelligible.

        And to avoid the thorny logical issues that I’ve already flagged, let’s assume that God’s existence is not logically or metaphysically necessary. That is, let’s imagine that there is at least one possible world where God does not exist; call worlds where God does not exist B-worlds. Let’s also assume that there is at least one possible world where God does exist; call the worlds where God does exist A-worlds. Now, if (A) and (B) are true, then there is intelligible experience in the A-worlds and there is no intelligible experience in the B-worlds.

        Why should I think there is no intelligible experience in the B-world? Why coudn’t there be a possible world where there is no God but there is intelligible experience? Supposing that there are some possible worlds where God does not exist, we can consider two worlds that are very nearly identical, except that one world contains God — call this world G — and the other does not — call this world N. And we can suppose that one of the worlds is identical to our own world. If God exists, then our world is identical to G. And if God does not exist, then our world is identical to N. The features of our cognitive apparatus that are typically taken to be requirements for the intelligibility of our experience — for example, the functional fit between our sensory information and our environment or our ability to slice up the manifold of experience into the categories of the understanding — do not vary between the two worlds. But (A) and (B) would tell us that there is no intelligible experience in N. That is, even though all of the facts about our minds and our environments are identical in G and N, (A) and (B) would have us believe that there is intelligible experience only in G.

        Importantly, if (A) and (B) are true, then there’s nothing about experience that makes experience intelligible; after all, we have identical experiences in N and G.

        I think this tells us that (A) and (B) are deeply implausible. Whatever theory does explain the intelligibility of our experience had better draw upon features of our minds and of our environment to do so, and had better tell us that there are features of experience in virtue of which experience is intelligible.

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      18. Hi Daniel,

        I read a rebuttal to your paper, ‘How Should We Speak of God’. I will add to Mr. Cothran’s analysis later.

        First, the syllogism I presented was a negation only.

        When you and a commonality of all people of, ‘seems to be true’, you are begging the v question that all presuppositions of experience and reality are equal. The main tenets of life are incoherent and unjustifiable in an atheistic worldview. If logic is not sourced in a transcendent and immanent being, then reason is contingent. Yet we know that can’t be. One cannot change laws of logic. Take the law of non – contradiction. A cannot be non-A at the same time and instance. If finite beings base experience upon observation or empiricism, can you observe a car in your garage and not in your garage at the same time and instance? Logic must tie to absoluteness. Syllogism like math are true irrespective of empirical verification. How do you justify train within your worldview?

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      19. Charles —

        You wrote, “First, the syllogism I presented was a negation only.”

        I don’t know what you mean here. The term ‘negation’ refers to a logical operator. There is no such thing as a negation syllogism. I think what you might mean is that you offered a reductio ad absurdum argument — that is, an argument where you assume p, show that assuming p results in a contradiction, and then conclude not-p. But, if that is what you meant to do, the argument that you offered is still incorrect.

        The argument that I offered to replace your argument is the best that I could offer in the attempt to fix your argument for you. If you are not satisfied with my correction, then you’ll need to correct the argument yourself. If you’d like, we can discuss why the argument that you offered was not structured correctly.

        You wrote, “When you and a commonality of all people of, ‘seems to be true’, you are begging the v question that all presuppositions of experience and reality are equal.”

        I’m not sure that I am — at least it’s not obvious to me how talking about what seems to me to be true assumes that all possible presuppositions are equal. In fact, I described how what seems to be true can be revised when an appropriate defeater is presented. If what seems to be true should be revised in the presence of defeaters, then not all seemings are equal — importantly, we better not hold seemings for which there are strong defeaters!

        You go on to say, “The main tenets of life are incoherent and unjustifiable in an atheistic worldview. If logic is not sourced in a transcendent and immanent being, then reason is contingent.”

        I see no reason to think that if logic is “not sourced in a transcendent and immanent being, then reason is contingent”. Logic could be necessary, absolute, and unchanging — and, therefore, non-contingent — without being grounded in a transcendent and immanent being. I said that before, but I think you must have missed it.

        You wrote, “One cannot change laws of logic. Take the law of non – contradiction. A cannot be non-A at the same time and instance.”

        We agree. I said as much before.

        You wrote, “If finite beings base experience upon observation or empiricism, can you observe a car in your garage and not in your garage at the same time and instance?”

        I’m not sure that I’ve understood you here. Usually, when people say ‘experience’, they just mean observation. And empiricism is not a basis for experience in anyone’s worldview. Instead, empiricism is a family of theories about how knowledge relates to experience. For the record, the fact that we are finite beings does not commit us to empricism.

        You wrote this funny stuff about observing a car in my garage and not in my garage at one and the same time and instance. You’re right that no one can observe a car being in my garage and not being in my garage at the same time and instance. That’s because we never observe violations of the laws of logic.

        You wrote, “Logic must tie to absoluteness.”

        Let’s suppose that’s true. What that proves is that there must be something absolute. Nothing follows about God.

        You wrote, “Syllogism like math are true irrespective of empirical verification. How do you justify train within your worldview?”

        I’m not sure what you mean by ‘train’ in this question. From context, it seems like you are probably asking me how I can justify syllogistic logic within my worldview when syllogistic logic holds independent of empirical verification. I thought I answered this before. First, I’m not the sort of old fashioned empiricist who held that all beliefs should be justified by empirical verification. So, the fact that syllogistic logic cannot be justified in virtue of empirical verification is no problem for me. Second, there are two ways that I can think of to justify basic logical rules. On the one hand, logical rules are often analytic truths, that is, they are justified by their own meaning. On the other hand, as I’ve said several times now, we are justified in our belief in basic logical rules because such rules seem to be true and there are no defeaters for those basic logical rules.

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      20. Hi Daniel,
        You mentioned that you believe, and so does Dillahunty, that logic could be absolute. Do you consider absolutes material or immaterial in essence? If immaterial, where are they and what is their source? My worldview can account for them, whether you like it or not, but how does your worldview do so? If you say, like Dillahinty, “they just are”, then the Theist can say, “God just is”. Debate over.

        One other thing and back to work here, what is your primary epistemology?

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      21. Charles — Thanks again for the stimulating conversation! You’ve raised some interesting ideas. But before I get into all of that, I want to, again, remind you of the fundamental distinction between:

        1. Offering a metaphysical explanation. For example, if you ask me for an account of the laws of logic, you are asking me to offer a metaphysical explanation of the laws of logic.

        2. Offering a justification. For example, if you are asking me to justify my belief in the laws of logic, you are asking me how I can rationally believe in the laws of logic.

        The former — offering a metaphysical explanation — has to do with metaphysics. The latter has to do with epistemology. And, again, one can successfully offer a justification for a belief without offering a metaphysical explanation for the content of that belief. To use my example from before, if I see a flying airplane, then, all else being equal, I am justified in believing that there is a flying airplane, and this is so even if I cannot explain either sight or flight. Likewise, I can be justified in using the laws of logic, just because the laws of logic seem to be true, even if I don’t have a metaphysical explanation of the laws of logic or why they seem to be true.

        You wrote, “You mentioned that you believe, and so does Dillahunty, that logic could be absolute. Do you consider absolutes material or immaterial in essence?”

        I think you are asking me whether all absolutes are material, or if all absolutes are immaterial. I see no reason to think either that all absolutes are material or that all absolutes are immaterial. Either of those two options could be true, or it could instead be true that some absolutes are material while others are immaterial.

        For the sake of our conversation, I am perfectly happy to suppose that the laws of logic are immaterial absolutes.

        You go on to ask, “If immaterial, where are they and what is their source?”

        Well, I haven’t offered a metaphysical explanation of the laws of logic. Remember, again, the distinction between offering a metaphysical explanation and offering a justification. I’ve previously offered a justification for the laws of logic, while noting that I don’t claim to have a metaphysical explanation of the laws of logic.

        But I’ve already supposed, for the purpose of our conversation, that the laws of logic are immaterial absolutes. So, we can ask, if the laws of logic are immaterial absolutes, then where are they located and what is their source? I don’t think the laws of logic have a location in space or time, nor do I think that the laws of logic ever began to exist. That is, I don’t think there was ever a time when the laws of logic were not true. So, I don’t think the laws of logic have a source or any sort of cause for their existence. The laws of logic are necessarily true, could not fail to be true, and there is no state of affairs that could count as the laws of logic being false. I think that if you ask a question like “where are the laws of logic located?” or “what brought about the laws of logic?” then you’ve fundamentally misunderstood what laws of logic are in the first place.

        You write, “how does your worldview do so [that is, account for the laws of logic]?”

        Again, there is the distinction I laid out at the beginning between offering a metaphysical explanation (that is, offering an account) and offering a justification. In my worldview, I am justified in my belief in the laws of logic for reasons I’ve already explained. My worldview is consistent with multiple different possible metaphysical explanations of the laws of logic. Part of what we do in philosophical research is to examine those different possible explanations and see how those explanations work out. I’m open to the possibility that the laws of logic are best explained by some particular theology, but none of the theological explanations that I’ve seen for the laws of logic have been terribly convincing.

        You go on to write, “If you say, like Dillahinty, ‘[the laws of logic] just are’, then the Theist can say, ‘God just is’. Debate over.”

        That’s not true. This statement comes after you asked me about the location and the source of the laws of logic. If I asked about the location and the source of God, you’d rightfully say that I misunderstood what sort of thing God is supposed to be. According to theism, God is located outside of space and time, so God does not have a location, and God does not have a cause of God’s existence, so there is no source for God. But clearly that doesn’t mean the debate is over.

        You ended your post with the question, “what is your primary epistemology?”

        I’m a phenomenological conservative. That is, I think we are justified in believing what seems to be true until sufficient defeaters are presented. I’m also a fallibilist. This means that it’s possible, in principle, that I could be wrong about all (or perhaps most) of the beliefs that I have. That is, none (or perhaps almost none) of our beliefs are infallible. I think that many of our substantive rationally held beliefs arise in virtue of our interactions with nature, but I don’t endorse the sort of tabula rasa popular among early modern empiricists. That is, we may well have some of our beliefs (or, more plausibly, belief templates) innately. And I’m certainly not a concept empiricist, like Hume or Locke. And while I used to be a coherentist about our noetic architecture, I’m no longer sure where I stand on the debate between coherentism and foundationalism.

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      22. Daniel, hello once again. Seems you conflate laws of logic with space, time, and energy. They are immaterial, invariant, and universally binding. If they have no source, then how do they exist? You can only find that the Christian God is transcendent and immanent or personal. All other deities are one or the other, but not both. Greek gods are merely glorified versions of man. Logic also being transcendent and personal as to our accommodation, it is coherent to attribute them to the mind of a similar source, namely the Christian God.

        A justification is not about their ontology, but their existence as immaterial, invariant, and universally binding upon rationality. It is not how you can rationally believe or appropriate them. Justification refers to their fitting as a tenet of one’s worldview; not a pragmatic usage of them. The airplane example is pragmatism, not justification.

        It sounds like your epistemology, ‘fallibilistic’ is more fitting in the skeptic camp.

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      23. Charles — Thanks, again, for your kind response and for continuing an interesting conversation.

        You wrote, “Seems you conflate laws of logic with space, time, and energy.”

        I’m not sure why you say that. I explicitly stated that the laws of logic do not have a location in space or time. Energy has a location in both space and time, so I’m certainly not conflating the laws of logic with energy. As far as conflating the laws of logic with space or time, I have no idea why you’d think that I’m doing that. For an explicit example, the law of non-contradiction is a law of logic. The law of non-contradiction is not space, time, or energy.

        Can you quote for me any sentence, or group of sentences, which I wrote and that lead you to think I conflate the laws of logic with space, time, and energy?

        You ask, “If they have no source, then how do they exist?”

        They necessarily exist. They exist because they cannot fail to exist. And they cannot fail to exist because there is no possible state of affairs that could count as the laws of logic being false.

        You wrote, “Logic also being transcendent and personal as to our accommodation, it is coherent to attribute them to the mind of a similar source, namely the Christian God.”

        Two questions. First, what do you mean when you say that the laws of logic are “personal”? For example, how is the law of non-contradiction “personal”? Second, why think that the laws of logic originate in the mind of the Christian God?

        You wrote, “A justification is not about their ontology, but their existence as immaterial, invariant, and universally binding upon rationality.”

        I’m sorry, but this is incorrect, in several ways. First, when we ask about the epistemic justification for a claim, we are asking about why the claim is rational to accept. So, when we ask about the epistemic justification for my belief in the laws of logic, we are asking why it is rational for me to believe in the laws of logic. We are not asking about their “existence as immaterial, invariant, and universally binding upon rationality”.

        I’ve defended phenomenological conservatism. If you are not convinced that this is a view about justification — at one point, you claim that this a view about pragmatics — you should check out the Internet Encyclopedia of Philosophy’s article on this topic, which explicitly states that this is a view about justification: https://www.iep.utm.edu/phen-con/

        Second, to say that the laws of logic exist as immaterial and invariant entities just is a claim about the ontology of the laws of logic. That is, to say that the laws of logic are immaterial and invariant entities is to make a claim about a metaphysical explanation of the laws of logic. So, you’ve once again confused the distinction between the epistemic justification of a belief and a metaphysical account for the content of that belief.

        You go on to say that a justification is “not how you can rationally believe or appropriate them”. I don’t know what you mean by “appropriate”, but an epistemic justification for my belief in the laws of logic is, by definition, about how I can rationally believe in the laws of logic. (Again, see the article that I linked above.)

        You wrote, “The airplane example is pragmatism, not justification.”

        That’s not right. Remember: the epistemic justification for a belief is whatever it is that makes the belief rational to believe. To put this another way, the epistemic justification for a belief is the grounds upon which one ought to hold that belief. In the airplane example, I see a flying airplane and form the belief that there is a flying airplane. We can ask what epistemic justification I have for believing that there is a flying airplane. The reason that I am rational in holding the belief that there is a flying airplane is that it seems to me that I am seeing a flying airplane and I have no defeater for my belief. Notice that I have justification for this belief even if I have not offered a metaphysical account either of my own vision or of the airplane’s ability to fly.

        Lastly, you wrote, “It sounds like your epistemology, ‘fallibilistic’ is more fitting in the skeptic camp.”

        What do you mean by the “skeptic camp”? Usually, at least among philosophers, skepticism is understood as a family of theories according to which we should doubt either that we have various kinds of knowledge or that various kinds of knowledge are possible to hold. For example, a moral skeptic might doubt that we have moral knowledge and an external world skeptic might doubt that we have knowledge of an external world.

        Fallibilism does not entail that we should be doubtful that we possess knowledge and is therefore not a skeptical thesis. To say that a given belief is fallible is just to admit that it’s possible we could be mistaken about that belief. I suspect that you are a fallibilist, too, and that you’d think it heretical to think otherwise. We are limited creatures. You’re not God, so there’s nothing that you could know with the sort of absolute certainty that God has in God’s beliefs. But just because you don’t have the sort of absolute certainty that God possesses does not mean that there are no beliefs about which you are as sure as you could be about anything and whose revision you’d find very unlikely. For myself, there are some core beliefs about which I am more certain than any of my other beliefs and whose revision I think exceedingly unlikely.

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      24. Dan, you wrote: “that the left hand side of Pr(A|B) <= Pr(A) is maximized when Pr(A|B) = 1. That's true (trivially), though not what I meant to say. I meant to say that the left hand side is maximized when Pr(B|A) = 1, since, in that case, Pr(A|B) = Pr(A)."

        Unless I’m misreading something, it is not true, in general, that Pr(A|B) <= Pr(A). In fact, Pr(A|B) can be 1 while Pr(A) can be much less than 1, in which case it would not be true that Pr(A|B) <= Pr(A).

        It is also not true that Pr(B|A) = 1 entails that Pr(A|B) = Pr(A). In fact Pr(B|A) = 1 entails Pr(A|B) = Pr(A)/Pr(B) which is not equal to Pr(A) in general, since Pr(B) is not 1 in general.

        Finally, it is not generally true that the left-hand side, Pr(A|B), is maximized when Pr(B|A) = 1. The statement Pr(B|A) = 1 entails that Pr(A|B) = Pr(A)/Pr(B), and this tells us nothing about how large or small Pr(A|B) is. In fact, Pr(A|B) could range from very small to all the way to 1 under the constraint Pr(B|A) = 1.

        You probably meant that if we know Pr(A) and Pr(B) (or more generally, if we know their ratio), Pr(A|B) reaches its maximum when Pr(B|A) = 1, and that maximum is their ratio, Pr(A)/Pr(B).

        Or you may have meant that Pr(A&B) <= Pr(A), and that Pr(A&B) reaches its maximum, namely Pr(A), whenever Pr(B|A) = 1, all of which is straightforwardly true, although I'm unclear as to how this is relevant to your point regarding the uniformity of nature.

        In fact, I remember being a bit puzzled about your initial statement back in August 12 regarding the uniformity of nature. I wanted to ask you about it, but never got around to it. Your conclusion that the uniformity of nature is more probable than the contrary seems quite interesting (and ambitious), but unless I'm misreading something, I didn't follow the logic of your argument.

        You wrote: “Since the probability of a conjunction is bounded from above by how probable either conjunct is given the other conjunct, and given that similarity is simpler than difference, the implication follows that a similar future is more probable than a different future. In other words, all else being equal, the intrinsic probability of the uniformity of nature is higher than the intrinsic probability of the contrary.”

        What do you mean, exactly, by the uniformity of nature? Do you mean predictability? How is it that the probability of a conjunction being less than or equal to the probability of any one of its conjuncts is relevant to similarity vs. difference, and how is that relevant to the uniformity of nature? Can you flesh that out some more?

        To me, your argument reads as follows:

        P1: The probability of a conjunction is bounded from above by the lesser of the probabilities of its individual conjuncts.

        P2: Similarity is simpler than difference.

        C1: Therefore a similar future is more probable than a different future.

        C2: Therefore the uniformity of nature is more probable than the contrary (the non-uniformity of nature?).

        P1 is straightforwardly true. P2 is unclear to me. What exactly do you mean by similarity, simpler and difference? From C1 it seems to me that you’re referring to temporally related events. Are the conjuncts in P1 referring to events occurring at different times and is the conjunction referring to a sequential occurrence of these events? Does similarity refer to predictability and difference to lack of predictability?

        In that case, would a similar future refer to a future that is predictable while a different future refers to an unpredictable (or less predictable) future? But if that is the case, why would a predictable future be more probable than a less predictable future?

        Also, are you implicitly stating that simplicity is more probable than the contrary?

        In C2 I read that the uniformity of nature is equivalent to a similar future, or that the uniformity of nature refers to nature’s predictability?

        I’m not sure if my interpretation of what you meant is correct, but even if it were, I don’t think it would follow that the probability of a temporal conjunction of events being less than or equal to the individual events’ probabilities has anything to do with predictability. In fact, such a state of affairs is consistent with a whole range of predictability, from high predictability to no predictability at all.

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      25. Miguel —

        Yes, you are right that I meant that Pr(A&B) <= Pr(A) and that this follows from Pr(A&B) = Pr(B|A)Pr(A). So my post contained multiple typos! My apologies — my presentation of the argument probably made the issue less transparent than it should have been.

        While this argument is ambitious, the argument does not originate with me. The argument originates with my dissertation advisor, Paul Draper, who has argued that (1) the uniformity of nature is a simpler and more cohesive hypothesis than the non-uniformity of nature and (2) simpler and more cohesive hypotheses are, all else being equal, more probable than more complex and less cohesive hypotheses.

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      26. Dan, in fact, let me take a crack at this problem of the uniformity of nature to see where it might lead.

        One could define the “uniformity of nature” as something akin to temporal predictability; i.e., that nature exhibits some patterns consistent with descriptive laws of some sort such that the future resembles the past in some sense. Likewise, non-uniformity (or what you refer to as “difference”) could be defined as a complete lack of predictability or temporal patterns.

        Define a state of affairs B as occurring some time after a prior state of affairs A. Under the non-uniformity hypothesis, we should see that A has no predictive power on B, or in other words:

        (1) Pr(B|A) = Pr(B) (Non-uniformity).

        Since Pr(B|A) = Pr(A&B)/Pr(A), this is equivalent to:

        (1a) Pr(A&B) – Pr(A)Pr(B) = 0 (Non-uniformity)

        which is nothing more than a statement of the statistical independence (unpredictability) of A and B, as required by the Non-uniformity hypothesis.

        On the other hand, under the “Uniformity” hypothesis, we expect the probability of the conjunction to be different from the product of the probabilities of the conjuncts (statistical dependence):

        (2) Pr(B|A) > Pr(B) or Pr(B|A) 0 (Uniformity).

        In fact, we can define the “Uniformity” as the absolute deviation from statistical independence:

        U := abs[Pr(A&B) – Pr(A)Pr(B)],

        where U ranges from 0 to 1; the larger U, the more predictability A has on B.

        So the conditions for Uniformity and Non-Uniformity are:

        (3) U = 0 (Non-Uniformity)
        (4) U > 0 (Uniformity)

        Applying the Principle of Indifference to this (a favorite among those who advance the Fine Tuning Argument in the context of the possible values of physical constants), one might be able to claim that if U is uniformly distributed between 0 and 1, then it must be vastly more probable that U lies in the interval (0,1] than exactly on the single value 0, since the interval (0,1] contains an infinity of values, whereas 0 is a single value. From this, one might conclude that it is vastly more likely that nature is uniform (predictable) than non-uniform (entirely unpredictable), without any recourse to a supernatural entity.

        Of course, at this point, one might object that all this relies on probability theory being valid in the first place, but I don’t think this derails the argument.

        (In fact, I don’t see that the Problem of Induction is a show-stopper for induction, any more than our inability to prove the axioms of first-order logic using first-order logic, should prevent us from being justified in using logic.)

        A more substantial objection might be the reliance on the Principle of Indifference (which states that, absent any knowledge of, or information about, the distribution of any quantity, one is justified in assuming a Uniform Distribution, since that is the distribution with the least amount of information). I believe that the Principle of Indifference is justified as a starting ansatz so that one can make progress in an argument, but only as long as the conclusion of said argument doesn’t rely too stringently on the distribution of the quantity in question, as it clearly does in this instance (and as it does, incidentally, in the case where the Principle of Indifference is recruited by Fine Tuning Argument proponents to reach their conclusions about vast improbabilities of the constants of nature).

        There are other ways that I can think of defining U where it can follow a known distribution and proper statistics can be done on it without reliance on the (I think problematic) Principle of Indifference.

        In any case, this is how I would sketch an approach to the uniformity of nature.

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      27. That’s interesting stuff, though I don’t think that’s how Paul would argue for the point. He denies with the principle of indifference and maintains a different set of principles for justifying what he calls the intrinsic probability of a hypothesis (what other authors call the prior probability). Let me see if I can drudge up a paper where Paul discusses the issue.

        As for what the uniformity of nature is supposed to amount to, I take it that the uniformity of nature is the thesis that the laws of physics are invariant across both space and time. If you deny the uniformity of nature, then you are postulating that there are different laws of physics in different places and at different times and there is no simple description that would unify the laws at both places. Many folks, like our pressupositionalist friend, have supposed that if nature is not uniform in that sense, then induction wouldn’t be possible.

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      28. Miguel — I managed to find a paper where Paul discusses his proposal for solving the problem of induction by appealing to the intrinsic probability of the uniformity of nature. I could send that paper to you if you’d like, but I’d rather not post the paper to the blog. (Not sure how — or if — I could post a pdf to this blog in any case.) Is there an e-mail address that I could use to send the paper to you?

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      29. Charles — I’ve read nearly everything that Bahnsen had to say on this subject. So, I’ve certainly read this paper before.

        Have you read much outside of the presuppositionalist literature on the problem of induction?

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      30. Hi Daniel, Before leaving that article by Bahnsen, why don’t you show the major errors Bahnsen applies for my sake. I am a ‘learner’ and love the antithesis.

        The answer to your question is, ‘Yes, I have read Craig and Moreland on Uniformity.’  

        Grace & Peace, Charles Gillihan P.S.  Have a happy new year!

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      31. Okay, so you’ve read Bahnsen, Craig, and Moreland on the uniformity of nature.

        Have you read what philosophers — whether theists or otherwise — have had to say about induction or the uniformity of nature outside of the philosophy of religion or theology literatures?

        As far as providing a response to Bahnsen’s article, that would consume more time than I presently have.

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      32. Daniel, Fair enough on the time issue. I have read many Theologians/philosophers from the Chalcedon Foundation, Cornelius Van Til, Abraham Kuyper, and other noteworthy writers. Here is an interesting article using ‘tid-bits’ of input from the late Dr. Cornelius Van Til from the Chalcedon Foundation on God and time.

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      33. Charles — I’ve read Van Til previously, too.

        I cannot emphasize this enough, but, if the authors you’ve mentioned do represent the scope of what you’ve read, then all of the authors you’ve read are fairly marginal and unimportant figures in intellectual history. Most philosophers have not heard of van Til, Kuyper, etc. I have heard about these figures, because I’ve read up on presuppositionalism, but these figures are not widely known nor are their ideas widely respected.

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      34. It’s not an ad hominem.

        An ad hominem is a fallacious objection to an argument that draws upon characteristics of the argument’s author in the attempt to show that the author was incorrect.

        My claim was a response to your statement that these folks were noteworthy. I made no claim as to whether these authors were right or wrong about anything that they wrote or any argument that they constructed. Even if they were right about everything that they said, it would still be the case that these are extremely marginal and not terribly well known figures, whose ideas are not well known or held in high repute.

        Perhaps the majority is wrong to hold that view. My only point is that if these are the figures that you’ve read, then you won’t have a terribly good idea of what the philosophical landscape looks like.

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      35. Daniel, Do you believe our cells die and are replaced over time?  I’d say that you will agree to this. Does this mean we are a different person if we get different and new cells?  If not, you must accept the view that our person is not our bodies per se. Is that true or false. Can you elaborate on that? Thanks, Charles

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      36. The issue that you’ve raised is an interesting one, called the problem of the persistance of personal identity. On the one hand, we think that we are the same person today as we were yesterday — that is, our personal identity persists over time. On the other hand, the materials that compose our bodies are not the same today as they were yesterday. So, it seems that we are not identical to the materials composing our bodies.

        Indeed, I don’t think we are the materials that compose our bodies.

        You might be surprised to read that. You might think that someone who does not believe in a soul would have to believe that we are identical to the material that composes our bodies.

        To explain how I could maintain that (1) I exist, (2) I am not the materials that compose my body, and (3) in the space presently occupied by my body, there is only matter (e.g., there is no soul), let’s consider an analogy. Consider a chair. Now, for the sake of argument, let’s suppose that the chair does not have a soul. (I think you may well agree to that.) And let’s suppose that, over night, a small piece is torn off the chair and replaced by another piece. Do we still have the same chair or is this a new chair? I would say that this is the same chair.

        That is, on one hand, the chair is the same chair today as it was yesterday. On the other hand, the materials that compose the chair are not the same today as they were yesterday. So, it seems that the chair is not identical to the materials composing the chair. Indeed, analogous with (1)-(3), we have: (1*) the chair exists, (2*) the chair is not the materials that compose the chair, and (3*) in the space presently occupied by the chair, there is only matter (e.g., there is no chair soul).

        There are many different theories about the persistance of personal identity. I haven’t sided with a specific theory here; all I’ve done is to show that naturalism does not commit us to some kind of naive reductionism about personal identity anymore so than any of us are committed to naive reductionism about chairs.

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      37. Dan, I emailed you on your Purdue email, so you can send me that Draper paper. I’m a big admirer of Draper’s work, BTW.

        On the persistence of identity, what identifies us (or just about any other material entity) is the pattern, not the ingredients. It’s the arrangement of matter and molecules that counts, not the molecules themselves, which are fully interchangeable. An H2O molecule is like any other and whether you exchange it with another H2O molecule inside your body, the arrangement or pattern remains the same.

        To wit, by way of a reductio: a pile of sawdust cannot carry you across the Mississippi River, but a well-crafted wooden boat can. They’re both made of exactly the same stuff. In fact if you take your boat and run it through a wood chipper, the resulting pile of sawdust would be comprised of exactly the same molecules that constituted the boat, yet the pile and the boat are not one and the same, are they?

        There are many ways to put together flour, raw eggs, and granulated sugar (neither one of which tastes very good), but very few ways that they can be arranged to make a cake (which can taste good). Again, it’s the pattern, the arrangement, that matters, not just the constituents.

        As long as the pattern/arrangement persists, it doesn’t matter if you exchange some, many, or even all molecules for identical ones. Personhood persists, not because molecules have been interchanged with the environment, but because of the continuity of pattern/arrangement.

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      38. Right, I think all of that is fairly plausible. Of course, what you still leaves much open between various different theories of the persistence of personal identity.

        I was hoping that my reply, in terms of the chair analogy, could leave the debate open, but show why a naturalist would not run into any problems. Your explanation — that our personal identity is a feature of higher level patterns, regardless of constituents, is a more explicit example of how one such naturalistic view might work out.

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  3. Very interesting post, Alex, thank you. I have a minor comment on your maths section, a strong objection to your last section, and some analysis.

    Strict Inequality

    First, I think that the math in your Doing the maths section is correct, except that your equation 11 in that section should be a strict inequality, if I’m not mistaken. In other words, P(G|F) < 2P(L|F), so that equation 11 should have a "<" instead of a " &leq;" and it should read:

    11. P(G|F) < 2Pp,

    (where I labeled the (ridiculously small) Penrose probability as Pp). Of course, this is minor and doesn’t change your findings in the maths section in any significant way.

    Objection to Your Objection Section

    However, in your ‘God could do anything’ objection section, I don’t think that equation 2 is correct and thus your objection to Premise 2 of the Fine-Tuning Argument (FTA) is not justified.

    To see this, using your equations 4 and 10 from the maths section would immediately yield the following:

    (4*) P(L|G&F)P(G|F) = P(L&G|F) (by multiplying equation 4 by P(G|F) on both sides);

    (10*) P(L&G|F) > 1/2 P(G|F) (by multiplying equation 10 By 1/2 on both sides).

    Putting (10*) into (4*) yields:

    P(L|G&F) P(G|F) > 1/2 P(G|F). Dividing both sides by P(G|F) (assuming it is not zero!), I get:

    P(L|G&F) > 1/2.

    This contradicts your 2. P(L|G&F) < 2Pp in the ‘God could do anything’ objection section, and leaves the FTA’ Premise 2 unchallenged:

    2. ~[P(L|G&F) << 1] (Premise 2. from FTA remains unchallenged).

    The problem, I believe, comes from the “God prefers L” assumption in equation 2 of the maths section,

    2. P(L|G) > P(~L|G).

    This is equivalent to saying that P(L|G) > 1/2, which in turn translates into P(L|G&F) > 1/2, via “God can do anything” since this would render F moot when conjuncting it with G in the conditional.

    “God could do anything” vs. “Divine Psychology”

    I still think that your “God could do anything” objection is generally well-motivated, but its force comes precisely from not engaging in “divine psychology” and pretending to know that “God prefers L.”

    The problem with “God could do anything” is that any hypothesis and its negation could be “justified” using this omnipotence premise, which would render the omnipotence premise incapable of discriminating between competing hypotheses. In other words:

    The “God could do anything” premise is entirely vapid as it offers no discriminating information whatsoever to discern between competing hypotheses, unless one engages in “divine psychoanalysis” and pretends to know God’s psychological states of mind such as “He prefers this,” or “He wants that.”

    Also, your analysis is all a priori, or prior to observing the universe, with the exception of knowledge of a “divine state of mind” whereby “God prefers L.” Once the universe is observed, L ceases to be a hypothesis and becomes observed fact (evidence). If one still believes that “Fine Tuning” (FT) of the universe is required to sustain L (i.e., that L would be fantastically improbable without FT), this would mean that L is actually (or overwhelmingly likely to be) physical or “physically embodied,” call this L*. But, if “God can do anything” there is no reason to expect L* over L even if we engage in “divine psychoanalysis” and conclude that, for some divine psychological reason, “God prefers L.” In fact, even on this divine penchant for L, God could have created L in any form whatsoever (not necessarily L*), and this would entail no requirement for FT, and thus FT would constitute evidence against G. Ikeda and Jefferys have formalized (a version of) this argument irrefutably using Bayes’ Rule (which is essentially a nested application of the conditional probability rule that you quoted in your maths section).

    Unless, that is, one engages in more “divine psychoanalysis,” and pretends to know that “God prefers L*” after all. This can be “justified” by engaging in yet more “divine psychoanalysis,” like “God wants His creatures to be ‘physically embodied,’ (L*) so that they have to struggle in a physical universe with all its physical and moral constraints because of the valuable ‘lessons’ that they would thus learn, etc.” Also, “God wants His creatures to be ‘physically embodied,’ so that, even though L might make Him obvious, L* would not, and the creatures would not be able to find God straightforwardly, because God wants His creatures to find Him in a circuitous way in order that they may discover the noble attribute of ‘faith,’ etc.” Or perhaps “God wants to make Himself very difficult to ‘psychoanalyze’ so that His creatures spend a great deal of time speculating about His divine ‘state of mind,’ in the hope that this will bring them closer to Him, because he really wants to bring them closer to Him, but doesn’t want to seem “easy to get,” and wants to give them a “challenge” to strive for, etc. etc. …”

    Perhaps. But what’s clear is that there seems to be no end to this ad hoc “divine psychoanalyzing” which one could tack on to “God can do anything” in order to arrive at G. One wonders why proponents of G bother to advance the FTA to begin with. If the FTA rests on “divine psychology” in the first place, why not just stick with “divine psychology” (a.k.a. Theology) all the way?

    It is ironic how “divine psychoanalysis” is quickly withdrawn and traded for God’s “inscrutability,” “mysterious ways,” and the ever-vapid “for all we know,” when “divine psychoanalysis” becomes inconvenient or self-refuting in arguments favoring ~G.

    The Malpass Gambit

    I think that the main result in your maths section is very interesting in its own right. You’ve established a tight a priori upper bound (the Malpass Bound, MB) on the Likelihood Ratio (K) of G vs. L conditioned on F and the “God prefers L” assumption:

    K = P(G|F)/P(L|F) < 2.

    This holds even while granting the “God prefers L” assertion. Now, prior to observing the universe, K can range from 0 to 2 only. If K is in the interval [0,1) it does not favor G. If it is in the interval (1,2) it favors G, and if K = 1, it favors neither. In other words, it’s a wash even under the “God prefers L” stipulation.

    Before stating the “Malpass Gambit” I need to give some background. Proponents of the FTA are fond of applying the “Principle of Indifference” when it comes to ascribing ridiculously low probabilities to (underived) physical constants. This Principle of Indifference states that the value of an unknown quantity should be presumed to be equiprobable within its range of validity (i.e., any value of the uncertain quantity in its region of validity is as probable as any other) because of our epistemic inability to prefer one value over another. In other words, it assumes equiprobable values for an uncertain quantity within some (often arbitrarily chosen) range of validity. If the range of validity of the quantity is extremely large compared to the quantity’s “life-permitting range” (also often arbitrarily chosen by FTA proponents), then the probability that the constant would lie within the life-permitting range is vanishingly small. Or so the argument goes.

    There are many problems with this, besides the arbitrariness of the intervals in question, upon which the extremely-low-probability conclusion crucially hinges. For example, even if the range of validity of an uncertain quantity is well-defined and specified ahead of time, epistemic uncertainty about the quantity does not entail certainty about the probability distribution of the quantity within its range of validity. The Principle of Indifference requires us to assign a uniform distribution (equiprobability) to the uncertain quantity because the uniform distribution entails maximal uncertainty within the range of possibilities. However, why should epistemic uncertainty entail maximal uncertainty? For example, in the 19th Century, when Maxwell unified electricity and magnetism, the speed of light (which prior to this was an underived physical constant) became uniquely determined using the electric and magnetic constants. This meant that, given those two constants, the distribution of the speed of light had a single derived value, not a uniform distribution of equiprobable values over some range, no matter what our epistemic uncertainty was prior to Maxwell’s theory.

    It is true that the Principle of Indifference is useful in some contexts, as it allows us to make progress by accepting the uniform (equiprobable) distribution as the default when there is no warrant to prefer one distribution over another. However, when the conclusions of an argument (such as the fantastically low probabilities of the physical constants proffered by FTA proponents) depend crucially on the choice of the uniform distribution (and the range of validity plus the life-permitting range), and when these conclusions would collapse under a different choice of distribution (as in the example with the speed of light), the argument’s conclusions should be considered with a great deal of suspicion. Such is the case with the FTA, or at least with its main assumption, namely the “The Fine-Tuning Problem” (“F” in your notation).

    This objection notwithstanding, if FTA proponents insist on relying on the Principle of Indifference, there’s no reason that it could not also be applied to K (the Malpass Gambit). This would mean that a priori, in other words, before knowing anything about the existence of any physical constants, their valid ranges, “life-permitting regions,” or even if the universe is life-permitting (L), we would have to assume that K would be equiprobable over the MB range, namely over the interval [0,2). In turn, this means that the G hypothesis would not be favored a priori, since under the Principle of Indifference, K is just as likely to fall in the range that does not favor G as in the range that favors G. And this is even after having granted that “God prefers L.”

    Yet another problem with relying on the Principle of Indifference to make broad conclusions about fantastically low probabilities of unknown quantities, is the strong dependence on the units or scale used to measure those quantities, which are arbitrary. For example, suppose that we take the reciprocal of the MB:

    K’ = P(L|F)/P(G|F) > 1/2.

    In this case, the likelihood of not favoring G can range anywhere over the interval (1/2, ∞), so that it has a much larger probability to fall in a range of values >> 1, which would vastly favor L over G. (See [**] below for a rebuttal of a possible objection to this.) The result can depend on the scale used to represent the quantity in question.

    To continue to flog this dead horse, consider instead the logarithm of the MB. (The Log-Likelihood Ratio is commonly used in statistical decision theory for reasons of mathematical expediency.) The MB would now read as follows:

    log(K) = log[P(G|F)/P(L|F)] < log(1/2).

    In this case, the Log-Likelihood, log(K) is valid in the interval (-∞,log(1/2)). Since log(1/2) is a negative number, the Log-Likelihood of K never even makes it to 0 (log(K) = 0 would mean indifference between G and L on F), which in turn means that G is never favored. In fact, applying the Principle of Indifference to the Log Likelihood Ratio would mean that log(K) is vastly more likely to be a very large negative number, which would vastly not favor G. (See [**] below.) So, again, the result is scale-dependent.

    There are other games that one could play with the MB to reach other numerical results (none of which would favor G, however). The point is that we should be very suspicious of the grand claims made by FTA proponents because the FTA relies on unwarranted assumptions ranging from arbitrarily using equiprobable distributions, arbitrarily selected ranges of validity, arbitrarily selected “life-permitting” ranges (when L is not even well-defined enough), and arbitrarily selected units for the underived physical constants in question. But perhaps especially because of the copious amount of ad hoc “divine psychoanalyzing” to which FTA proponents help themselves when it suits their argument.

    FTA proponents would have to grapple with either the problems inherent in the FTA assumptions, or with the Malpass Gambit before proceeding with the FTA.

    Therefore, a priori (but for the assumption that “God prefers L”), the Principle of Indifference applied to K (the Malpass Gambit) would render the G hypothesis moot, while a posteriori, after observing the universe, the Ikeda and Jefferys argument demonstrates that FT actually favors ~G. Unless, of course, one engages in ad hoc “divine psychoanalyzing,” a.k.a. Theology.

    In conclusion, I think it’s fair to say that:

    The FTA has been reduced to a theological argument, instead of an evidentiary one.

    My Brute Facts are Better than Your Brute Facts

    Finally, I watched your conversation with Luke Barnes (as well as Luke’s conversation with Sean Carroll). Luke is very likable and sharp, but it seems to me that he fails to come to terms with his own epistemological bedrock. In your conversation (and in the one with Sean), Luke–if I recall correctly–claims that, even if the physical constants could be explained (and thus no longer deemed “Fine-Tuned”), and even if physicists someday come up with a “Theory of Everything” from which those constants are derived (like the speed of light was derived from other constants in Maxwell’s theory), then that theory itself would have to have been, you guessed it: “Fine-Tuned.” By God. Therefore G.

    Mind you, if that “Theory of Everything” were found, it would be pretty much on par with the Axioms of Logic. It would just “be,” without requiring or having any explanation. This is the definition of a “Brute Fact.”

    It’s all well and good to try to find out if what we now consider a “Brute Fact” could possibly be explained so that it is no longer a “Brute Fact.” I suppose that, to explain a “Brute Fact” with another “Brute Fact” might be legitimate if the explanatory “Brute Fact” either (a) Is simpler than the explained-away “Brute Fact,” or (b) It explains other facts by making well-substantiated predictions that cannot be explained via the original, explained-away, “Brute Fact.”

    Even assuming that G is coherent (and that’s a big if, for example, what does it mean for God to “exist outside of time and space”? does “omniscience” contradict itself? could it ever be verified, etc. etc.), it certainly qualifies as a “Brute Fact,” because it has no explanation outside of itself, and, moreover, none seems forthcoming! (who created God?, how did God actually do the creating out of “the force of His will” alone? what does creation ex nihilo mean, exactly? why does God want this instead of that? etc. etc.).

    Unfortunately for FTA proponents, it doesn’t appear that G is a good candidate for an explanatory “Brute Fact” which would explain the “Brute Fact” of a naturalistic “Theory of Everything,” if such were ever found. The reasons are that: (a) It’s not simpler because, even if it were coherent, it relies on a variety of “Brute Facts” like God’s existence, and the ample assortment of miscellaneous “psychological states” and “divine motivations” that appear to be unavoidable, even under the all-encompassing “God can do anything” proposition, in order to make the FTA work. (b) It is not “explanatory” in the sense that it relies on the infinitely vapid “God can do anything” assertion, which, by virtue of its all-encompassing scope (including any hypothesis and its negation), explains nothing at all, and because it relies on a variety of ad hoc “divine psychological states” and “divine motivations” that are quickly and just as ad hoc-ly withdrawn into “inscrutability” on an as-needed basis…

    Luke Barnes is definitely no Matt Slick, and I apologize to have dared to place them in the same sentence. However, it seems to me that, ultimately, they suffer from the same “Brute Fact,” namely that:

    “My Brute Fact is better than your Brute Fact, and that is a Brute Fact!”

    -Miguel Castro

    [**] To place a uniform probability distribution on an infinite (or semi-infinite) interval is ill-defined and leads to contradictions if one insists that probabilities be well-defined (normalizable). This, of course, is the same problem that FTA proponents encounter when considering allowable ranges of non-derived physical constants. The solution that FTA proponents take is to constrain the allowable ranges to be finite instead of infinite. In the case of the K’s with different scalings considered above, we could easily (if arbitrarily) do the same. For example, we could arbitrarily use the Penrose probability, Pp (or its reciprocal), to limit the outer bounds in the scalings where K ranges out to infinite values.

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    1. Awesome comment. Thanks for checking through the maths. I did simply assume that P(L | G & F) ≤ 2 x (1 / 10 ^ 10 ^ 123) without actually running through to make sure. I thought I could trust my own intuition. What an idiot! I’m going to have to think more about your discussion of the ‘Malpass Gambit’. Really, it is the Halvorson Gambit (and shouldn’t be named after me), because he make the argument (though in an extremely quick way) in a draft paper that Luke sent me. Unfortunately, Halvorson has now withdrawn the paper from circulation (I suspect either because it is going to be published somewhere or because he is modifying the argument in some way). I deserve no credit for seeing it. I’m just trying to explain it, as I thought it was a cool result as well.

      Anyway, when I have some more time I will think more on your comments. Thanks again.

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  4. Daniel Linford: “I haven’t read Guth’s paper on this topic…” I don’t know that Guth actually has a paper on this topic yet; that was the point of my question. I know that a few years back he (informally) made mention of this topic here
    and here, for instance, and stated that an actual paper was forthcoming, but I haven’t seen that, and I was wondering if you had.

    Guth’s point, I believe, is that allowing for an infinite state space would naturally fit in with the “arrow of time,” while addressing a number of early-universe “puzzles” like special initial conditions, thermalization, (and possibly Boltzmann Brains, global Poincare recurrences, etc.). I think you’re right that this would render Penrose’s calculations largely meaningless. The real question is whether Guth can actually marry his simple “remove the box from the gas in a box” cartoon with inflation, as he hinted that he would.

    I believe that you are incorrect in stating that S = 0 is the lowest that entropy can go (due, essentially, to quantum-mechanical effects). This might be the case conceptually, but not in an actual physical system. I’m not active in this area of research, but some years back while in grad school, I gave a talk where I proposed a non-zero lower bound on the entropy of any physical system (I didn’t publish the result, so I can’t point you to a paper, or even to slides). The idea was based on a straightforward application of Hawking radiation to obtain the minimal possible increase in a black hole’s area, which corresponds to the minimum possible increase of entropy in the universe via Bekenstein’s Generalized Second Law, since the change in entropy of the universe (dSuniv) can never be less than the change in entropy of a black hole (dSbh):

    dSuniv >= dSbh > 0,

    (at least over time scales comparable to or greater than the age of the universe). This is linked to the so-far elusive quantization of gravity, etc., and may have interesting implications, but we probably won’t know what the real lower bound is until we have the theory, since Hawking radiation is likely just an approximation.

    Come to think of it, I should’ve published this little result. Let me know if you’d like to collaborate. 🙂

    Like

    1. Miguel —

      Thanks for getting back to me! The project that you have in mind certainly sounds interesting. There are papers from other authors suggesting that the universe’s entropy can go to zero (Djordje Minic worked out something like that with a graduate student), but, come to think of it, this doesn’t seem to be possible. As you know, quantum mechanics dictates the quantization of phase space. That was the basis of the old quantum theory and of the Heisenberg uncertainty principle. And the quantization of phase space would appear to suggest that a system can never occupy a single phase space point, since phase space volumes come in multiples of plank’s constant.

      Anyway, I think the idea you mentioned concerning the universe’s Bekenstein Bound, etc, sounds interesting. I have to confess that I’m not completely sure that I understand it. I would love to collaborate — especially since I’d love to have a publication in this area — but I’m not sure how much help I will be. In any case, perhaps you could write something up and e-mail it to me: dlinford@purdue.edu

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  5. I reviewed Collins’ FTA in the Blackwell Companion to Natural Theology for the Secular Web.

    https://infidels.org/library/modern/aron_lucas/natural-theology.html

    In my review I give a different version of the “God can do anything” objection, in which I argue that God wouldn’t have a need to set the constants to life permitting values because life could exist in a supernatural theistic universe *regardless* of what values the constants have. So P(life permitting value|theism) is not necessarily any greater than P(life permitting value|naturalism).

    Liked by 1 person

    1. Ron: Great review of Collins’ FTA in the Secular Web Library site. However, one can make a stronger statement than ‘P(Life-Permitting|Theism) is not necessarily any greater than P(Life-Permitting|Naturalism).” This is precisely for the reasons stated in your review, namely that “physical requirements need not constrain God.” Back in 2004 Ikeda and Jefferys formalized this here. Their claim is that any “fine tuning” is evidence for naturalism, (and against the classical theism of an omnipotent God).

      To my mind Ikeda and Jeffery’s Bayesian argument is irrefutable, and can only be dealt with by stipulating that “God wanted physically embodied life” after all, because of the lessons that this would teach His creatures, or something like that, etc. But this would ground the FTA in theology, not in cosmological evidences.

      Liked by 1 person

      1. Dan, I’m not sure if you’re referring to Ron’s link to his “Review of The Blackwell Companion to Natural Theology (2018)” (above) or to my link to Ikeda and Jeffery’s article on “The Anthropic Principle Does Not Support Supernaturalism” on http://www.talkreason.org/articles/super.cfm

        They both work for me, but you can always try searching for the titles.

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  6. I don’t think Carrier comes across very well in those blog interactions. I find his way of approaching these things unnecessarily hyperbolic and uncharitable. In all honesty, I found Barnes’ blog quite interesting, and he is definitely not an idiot. I think that much of how Carrier thinks about this could be dealt with by someone like Collins (and I think probably is if you read his academic work). But Carrier would need the ability to accept that he got something wrong first before that could ever sink in, and I really don’t know if he can do that…

    Liked by 1 person

  7. Miguel — I meant your link to the Ikeda and Jeffery paper. Your link doesn’t work for me on either my laptop or on mobile.

    Like

    1. Dan, that’s strange. It works for me, on a PC-based laptop, even after clearing my browsing history and cookies. It work on my iPhone also. It’s an old article (2004), so maybe it’s not friendly across all platforms.

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  8. God acts in accordance with His nature as described by the Bible, as in the Westminster Confession.

    By the way, who is the moderator or owner of this web site and why is he annonymous or hidden from revealing his or her name and what they do in life, etc..?

    Like

    1. I’m not anonymous, hidden or anything like that. It’s true, there is no bio on this site, but there is a link in (I think) the second or third post to a video where I am in a hangout with Matt Slick. I also linked to my podcast (https://www.youtube.com/channel/UCwbA80IQy8pfbil09XiBKfw). My name is Alex Malpass. I don’t really see the need to gush about my personal life in this blog. You can see my Academia.edu page here: https://bristol.academia.edu/AlexMalpass. I have a youtube channel which is in my name.

      Liked by 1 person

      1. Hi Alex, Just wondering, as it seemed like a really cool site and some very smart folks interacting. Not sure how I stumbled upon it. Thanks for the info at any rate. My name is listed and I live in the Memphis, TN area. Is this considered an all0in-one site with a combination of Theists and atheists or agnostics?  What is your basic worldview in regards to the Christian God? Best Regards, Charles

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  9. Daniel,

    Your chair example of adding a small piece to the entire chair being the same chair fails. It is not the exact same chair, but a percentage of the original and a very small percentage of a different one.

    Regards,

    Charles Gillihan

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    1. Charles — Thanks for your reply!

      I can see what you mean. If being the same chair means being composed of the same materials, then (obviously) it’s not the same chair.

      But I don’t think we talk this way. I am currently sitting on a couch. Throughout this past night, there was some complex process whereby some small number of atoms were exchanged between the couch and the surrounding atmosphere. Nonetheless, I regard the couch as the same couch, despite the materials of the couch having changed.

      Here’s a general claim: macroscopic objects are not identical to their microscopic parts. So, changes in the microscopic parts do not necessarily result in changes to the identities of the macroscopic objects. And if that’s true, then I — as a macroscopic object — can persist in my identity even though my microscopic parts change.

      Liked by 2 people

      1. Dan,  You raised some good points. We are in the area of induction or deduction; depending upon our starting point. True, the whole is not determined by the parts or particulars. The conundrum sets in when we have particulars passing the 50.01% mark. That makes the majority of particulars trump the previous ones. Do your cells in your body die and regenerate over time?  Are you the same person?  No, if we are looking through the lenses of materialism. Yes, if you are aware of a spiritual component to the ‘you’.  You and your body are not the same exact essence or substance. A person is composed of a spirit and a body. Spirit and ‘soul’ are used interchangeably at at times. I hold to a dualistic view that we are body and spirit; the ‘soul’ being the attributes of the spirit.  This is from a Christian worldview. If we lose the majority of our bodies to all except the ‘brain a vat’ scenario, are we still the same person?   Regards, Charles Gillihan

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      2. Charles — Thanks, again, for your reply.

        I previously called myself a “naturalist”. For a variety of reasons, I prefer that label over “materialist”, which is sometimes taken to have a different meaning. But, here, I will go along with your terminology and discuss what the materialist is committed to.

        You wrote: “The conundrum sets in when we have particulars passing the 50.01% mark. That makes the majority of particulars trump the previous ones. Do your cells in your body die and regenerate over time? Are you the same person? No, if we are looking through the lenses of materialism.”

        I take that, here, you are imagining that we replace the atoms that compose my body, one by one, until more than 50% of the original atoms have been replaced. And then you claimed that if materialism is true, then I would no longer be the same person.

        I don’t think that’s true. I said before that I didn’t want to endorse a particular theory of either personal identity or the persistence of personal identity. Instead, my aim was to simply point out that there are a variety of views in which I am not identical to my body but in which my identity persists even as you replace my atoms.

        Your argument would make sense if the materialist were committed to the view that my identity persists so long as I retain a majority of my original atoms. If the materialist endorsed that sort of view, then they would have to say that once a majority of my atoms have been replaced, I no longer exist; instead, a new counterpart has taken my place. And some materialists do say exactly that.

        But the materialist does not have to say that our identity consists of a collection of atoms. Here’s one alternative view that the materialist could take; keep in mind that this is not the only option that the materialist has available. The materialist could say that my identity consists in a function (or, perhaps, a set of functions) performed by my body. We can call this functionalism. And the functionalist will say that the same one function can be performed by different atoms. So long as the function — or set of functions — persists, I persist. So, if functionalism is true, then, even if materialism is true, you could replace all of my atoms without my ceasing to exist.

        You asked, “If we lose the majority of our bodies to all except the ‘brain a vat’ scenario, are we still the same person?”

        Again, I’m not committed to any particular account of the persistence of personal identity. Nonetheless, we can take a look at what the functionalist would say in order to examine some of the options open to the materialist.

        You’ve imagined some procedure by which we remove all of macroscopic parts except for my brain. Do I still exist even after that procedure? Well, some functionalists could say that we do continue to exist, so long as my brain keeps executing some particular set of functions. Other functionalists would say that there are parts of my body, other than my brain, which perform functions integral to my persistence. I don’t know which of these options are correct, if either is correct.

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      3. Charles Gillihan,

        None of what you say here presents a problem for “materialism” (by which I think you mean something like “anti-dualism”). However, it may well present a problem for the “Christian worldview,” as I argue below.

        On one hand, you correctly state that “the whole is not determined by the parts or particulars.” Agreed. Examples were given earlier in this comment thread about a wooden boat and a pile of sawdust obtained from running the boat through a woodchipper. The two share 100% of their “particulars” (by which I think you mean atoms or elementary constituents) yet they are nowhere near identical. Therefore, “particulars” cannot be the sole determinants of the individual identity of the boat or the sawdust pile. The same can be said about a heap of raw eggs, flour and sugar not being identical to a cake. Or a polished diamond not being the same as a lump of coal, even though they’re both made of carbon atoms, etc… As mentioned before, it’s not so much the “particulars” but the pattern or arrangement of said “particulars” that gives a “whole” its unique characteristics or identity. This much seems clear and denying it would incur the fallacy of composition or, in other words, equating the whole with its constituents.

        But then, having correctly stated that “the whole is not determined by [or identical to] the parts or particulars,” you jump to a statement about how, on materialism, a person cannot be “the same” whenever 50.01% of his/her “particulars” are changed. But “materialism” makes no commitment to this last statement, as far as I know, and I don’t believe that you’ve made a case that it does.

        Then you go on to say that “looking through the lens of materialism,” a person is not the same if the majority (50.01%) of her cells die and regenerate over time. But this would not be “looking through the lens of materialism.” This would be looking through the lens of the fallacy of composition which wrongly assumes that the whole (a person) is identical to (the majority of) its “particulars” (the body’s atoms or cells) which you agreed before is incorrect. In effect, it seems that you have stated a fallacy of composition (while previously recognizing that it is wrong) and subsequently impugned this fallacy to “materialism,” without any explanation as to why “materialism” must necessarily be committed to this fallacy. Thus, you have not argued against “materialism,” but against some cartoonish imputation of the fallacy of composition that is neither alleged by nor required of “materialism.”

        You proceed to assert, without demonstration, that there is a certain continuity to a person that cannot be captured by her constituent “particulars” because the particulars change over time, and that the only way this “personhood continuity” can arise over time is via a “spirit” or “soul,” and that this comes from “the Christian worldview.”

        But the examples above show that “particulars” are not the only determinant of identity, as in the case of the wooden boat and the pile of sawdust, but that in fact the pattern or arrangement is at least as important as the “particulars” themselves. This is not, in any way, incompatible with “materialism.” It is quite possible that the continuity of the identity of a person can come from a continuity in the pattern or arrangement of the “particulars” and not so much from the “particulars” themselves. You have not explained why this cannot be the case, on “materialism,” nor that the only option left to explain “personhood continuity” is the “soul.”

        If, for the sake of argument, we were to accept your assertion that, on “materialism,” a person is not “the same” if 50.01% of her “particulars” have been replaced, this would not represent a problem for “materialism” either, because the replacement of “particulars” doesn’t happen instantaneously, but over a period of time. Both the pattern or arrangement of “particulars” that make up the person, as well as the vast majority of the “particulars” themselves, persist from moment to moment, so there’s no disruption of, or sharp transition in, the “personhood” or individuality of a human being. “Personhood continuity” can still be maintained, even under your 50.01% threshold.

        In other words, you have not exchanged anywhere near 50.01% of your “particulars” with your environment from one minute ago, or even from one day ago, so you are the same “person” now as you were a minute ago, or as you were yesterday, because according to your 50.01% threshold, you have not yet become a different person.

        Moreover, it is not so much the “particulars” that matter, but the pattern or arrangement of those “particulars,” which has also persisted from yesterday to today, so that you are the same person today as you were yesterday under this description. There is no specific moment or specific day in which you change from one person to another, so it is not clear that any transition from one person to another has happened at all over longer periods of time. If from minute to minute or from day to day you keep the same identity as a person, there’s no reason to think that you are a different person once enough time has elapsed to change 50.01% of your “particulars,” or whatever else may have changed regarding your “particulars” over that longer period of time. No appeal to a “soul” or “spirit” is required here to achieve “personhood continuity.” All of this seems perfectly consistent with “materialism.”

        Also, the unproven concept of the “soul” or “spirit” is not unique to “the Christian worldview.” It is consistent with Hinduism, Islam, Mormonism, and a wide variety of other religions, and precedes Christianity by centuries. So, it is not exactly reasonable of you to claim the concept of the “soul” for “the Christian worldview,” even if you had provided a sound argument for its existence.

        But notice that your argument is actually inconsistent with “the Christian worldview.” Let me explain.

        According to some estimates, human beings replace almost all of the atoms in their bodies (98%) every year through breathing, ingestion and excretion. Water molecules in human bodies are entirely replaced every 16 days. Water makes up 72% of human bodies, so this would exceed your threshold of 50.01%. This means that every two weeks, or so, more than 50.01% of the “particulars” in human bodies are replaced.

        Now, all living organisms exchange “particulars” with their environment through metabolic activities. In particular, animals such as dogs, cats, etc., being smaller than humans, have a faster metabolic rate than humans and exchange atoms with their environment faster than humans do. This means that someone’s pet dog, (let’s call him Fido), would have changed more than 50.01% of its “particulars” in the last two weeks.

        According to your argument, there are two possibilities.

        Possibility 1. Fido is not the same today as the Fido of two weeks ago, because more than 50.01% of his “particulars” have changed since two weeks ago. Of course, this seems ridiculous, since this is the same Fido that, week after week, recognizes his owner and greets him at the door every day after work, week after week, has some foods that he likes and others that he dislikes, week after week, has some games that he likes to play and other games that he doesn’t, week after week, knows some tricks well but not others, etc., so it seems like he’s the same Fido today as the two-weeks-ago Fido and one-year-ago Fido. After all, we don’t see his owner renaming Fido every two weeks: “Fido 1,” “Fido 2,” “Fido 3,” etc…, do we? We don’t see his owner teach him exactly the same tricks from scratch over and over again every two weeks, because “Fido 15,” being a different dog from two weeks ago, has forgotten what “Fido 14” knew… So, it seems that Possibility 1 is absurd, and we’re left with:

        Possibility 2. Fido has a “soul”! This was the only other alternative, according to your argument, whereby Fido’s personality could persist longer than the two-week interval within which his “particulars” were changed by more than the 50.01% threshold. However, this is inconsistent with “the Christian worldview,” because Christianity does not allow for the possibility that dogs can have “souls.” Or pet birds, cats, reptiles, goldfish, hamsters, squirrels, elephants, horses, plants…

        So, your argument neither counters “materialism” nor supports “the Christian worldview.” In fact, your argument, when taken seriously, seems to run afoul of “the Christian worldview.”

        By the way, cellular regeneration is a different matter than replacement of atoms. For example, certain brain cells (neurons) are never replaced throughout a person’s lifetime. Maybe those brain cells and their arrangement are the key to “personhood continuity” after all? Unlike the “soul,” changes in those brain cells (through trauma, disease, medications, drugs, etc.) have been demonstrated to have direct impacts on human beings’ personality and behavior. Or at the very least, those brain cells have been proven to exist, unlike the “soul.”

        Cheers

        Liked by 1 person

      1. anondoc2, I’m not sure what you are talking about. Sorry.  I’m not aware of a page ‘na’.  I’ll check into it.   Charles

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      2. I don’t have a website.  Is that a requirement for rational interchange here? Regards, Charles

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      3. “I don’t have a website.”
        Ok, I’ll assume you’re right.
        “Is that a requirement for rational interchange here?”
        No, I’m just asking about the page that your name links to.
        ( http://na/ ) Just those two letters and the link is broken. That’s it.

        I get this message:
        “This site can’t be reached
        na’s server IP address could not be found.”

        Why is that?

        Like

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