Thoughts on The Fine-Tuning Argument

Yesterday, Paul Gould from Southwestern Baptist Theological Seminary presented a very interesting talk titled, “Cultural Apologetics: Renewing the Christian Voice, Conscience, and Imagination in a Disenchanted World.” In it, he argued for two important claims:

  1. The world is fine-tuned for human life, and
  2. The world is fine-tuned for human flourishing.

The argument from fine-tuning is particularly fascinating in that, as Paul rightly pointed out, everyone agrees on the data, just not on what the data shows. As I continued to think about the presentation while driving home, I realized that I can’t even agree with myself on what the data shows.

The Argument

The physics may be complicated, but the idea behind the argument is simple. Take a factor like the initial strength of the explosion at the Big Bang. Had the strength of that explosion differed by as little as one part in 1,060, the universe would have either collapsed back on itself, because the explosion was not strong enough to overcome the strength of gravity, or it would have expanded too fast for stars to form. So, had the force of that explosion been even slightly different, life would never have had a chance to form.

That factor is just one of many. By some estimates there are over 100 factors, and had any one of them been just slightly different, life would have been impossible. It is difficult to conceptualize the degree of tolerance here. An accuracy of 1 in 1,060 has been compared to firing a bullet and hitting a one-inch target twenty billion light years away on the other side of the observable universe. That’s just for one factor, the probability of all of the factors having the precise values that they do must be incredibly low.

So far, that’s nothing controversial. The universe appears to be fine-tuned for life. The controversial move is the inference from apparent fine-tuning to the probability of a fine-tuner. The intuition is that, considering the very many different ways the universe could have been, it is very unlikely that we would have ended up with this world if there were no creator. On the other hand, if there were a creator, it is very likely that a world capable of sustaining life would be created. Now, it becomes a Bayesian problem. Let L be a life sustaining universe and D be the existence of a designer, the probability of a designer given that the universe sustains life is

\Pr(D \vert L) = \frac{\Pr(D) \times \Pr(L \vert D)}{\neg L}

The probability that there is not a designer, given a life sustaining universe is

\Pr(\neg D \vert L) = \frac{\Pr(\neg D) \times \Pr(L \vert \neg D)}{\neg L}

Since the denominators are the same, \Pr(D\vert L) > \Pr(\neg D \vert L) if and only \Pr(D) \times \Pr(L \vert D) >\Pr(\neg D) \times \Pr(L \vert \neg D). Now, all we need to know is the prior probability of God existing, and we knew the probability of a life-sustaining universe on the assumption that there is a God. Easier said than done, as they say.

Instead, maybe we should rethink the strategy. If I knew how each additional factor affected the probability, then I might be able to assess how low the prior probability of D must be in order for the evidence to not raise \Pr(D\vert L) over 0.5. To do this, we can use the odds version of Bayes’ theorem: the odds of D given L is equal to the prior odds of D times the likelihood ratio:

O (D \vert L) = O(D) \times \frac{\Pr (L \vert D)}{\Pr (L \vert \neg D}

Now, let’s take that \frac{1}{1,060} tolerance from above, but let’s change it to \frac{1}{1,0001}. This does two things. First, it favors atheism some, but, more importantly for me, it makes the math much easier, because it makes the likelihood ratio a nice round number:

\frac{\Pr (L \vert D)}{\Pr (L \vert \neg D} = \frac{\frac{1,000}{1,001}}{\frac{1}{1,001}} = \frac{1,000}{1}

That means that with each new factor, the odds of the the universe being intentionally fine-tuned increase by a factor of 1,000. With 100 factors, the odds of theism are equal to the prior odds times 1 \times 10^{300}. This means that, in order for it to be less likely that God exists, given apparent fine-tuning, the prior odds of God existing must be less than \frac{1}{10^{300}}.

Now, I admit that I don’t know if all the factors have the same odds. I just know that some of them have been estimated to be higher than the value that I used. So, let’s just lower the odds by a power of 100. That is, now the degree of tolerance for each factor is a mere 1 in 10. If so, then the prior odds of God existing would still have to be lower than 1 in 1,000 before it would be unlikely that theism were true.

Next time, I’ll consider some objections and responses.

Prayer for the Fifth Sunday of Epiphany

Lord Jesus,

When the disciples heard your voice,
they left everything they had
to follow you.

Examine our hearts, Lord,
and show us those things that
we also need to abandon,
those remnants of an earthly kingdom
That have no place in the Kingdom of God:

The need to win,

The need to get our way,

Our feelings of superiority
to our brothers and sisters,

Our tendency to seek our own will,
and to call it yours.

We have muffled your voice
in the frenzied noise
Of modern life;

Lest we hear,
and, like the disciples,
be compelled to follow.

Yet in those occasional
moments of stillness,
we find that you still call.

We pray to God
that we can still hear.

Amen

Arguments in HTML

This post is not about arguments that occur on the internet, but about how to display philosophical/logical arguments in standard form on the internet. To put an argument in standard form:

  1. Write each premise on a separate, numbered line,
  2. Draw a line underneath the last premise, and
  3. Write the conclusion underneath the line.

It’s easy enough to produce an ordered list in HTML, but then the conclusion is numbered, which makes it look like another premise. This can be fixed with a trick in CSS, just add something like this to your stylesheet:

.list-arg li:last-child {
list-style: none
}

The HTML in the document looks like this:

<ol class="list-arg">
1. First premise
2. <u>Second premise</u>
3. Conclusion
</ol>

As I was writing this post, I realized that I couldn’t add custom CSS to this WordPress.com blog without upgrading at a significant cost.

I spent two days toying with moving back to a static site or to the Ghost blogging platform. As I was experimenting with a self-hosted Ghost blog, it struck me that this might be incredibly easy to do in Markdown with something like this:

1. First premise
2. <u>Second premise</u>  
Conclusion

The thought was that putting two spaces after the last premise would signal a line break and remove the paragraph formatting. This worked nice in the Markdown previewer that I use on my computer, but WordPress produced this:

  1. First premise
  2. <u>Second premise</u>
    Conclusion

The indention was perfect, but no underlining. So, I went back to experimenting with HTML. Maybe I could take all of the list markers out and put the numbers in myself, with a "therefore" symbol for the conclusion.

<ol style="list-style:none;">
<li>1. First premise</li>
<li>2. <u>Second premise</u></li>
<li>&there4; Conclusion</li>
</ol>

That produced this:

  1. 1. First premise
  2. 2. Second premise
  3. ∴ Conclusion

Finally, I wondered if I could insert the list-style attribute in the final list item:

<ol>
 	<li>First premise</li>
 	<li><u>Second premise</u></li>
 	<li style="list-style:none;">Conclusion</li>
</ol>

That gave me this, which was what I was after in the first place. It turns out that I really didn’t need to add anything to CSS at all.

  1. First premise
  2. Second premise
  3. Conclusion

Sometimes, the last premise is significantly shorter than the others, and the underline doesn’t look quite right. For example,

  1. P ⊃ Q
  2. P
  3. Q

That can be fixed with some non-breaking spaces. It looks ugly, but does take care of the problem.

<ol>
<li>P ⊃ Q</li>
<li><u>P        </u></li>
<li style="list-style:none;">Q</li>
</ol>

That produces

  1. P ⊃ Q
  2. P        
  3. Q

Now, in writing this, I discovered that the new editor can’t handle footnotes. It turns out that there is always something.