I skimmed over Barnes' restatement of Ikeda & Jeffries argument. I didn't see anything new from the original. I'll skip to Barnes' own argument.

I'll briefly restate his variable definitions, without his digressions on evolution. One problem that Barnes' has in his argument is that he's not crystal clear in his definitions of random variables. Barnes uses the terminology "this universe" without being super-explicit that this universe was randomly selected. There are only two serious problems in his definitions, which I'll get to in a minute.

- $L$: A randomly selected universe contains life
- $X$: The physics of a randomly selected universe is sufficient for the existence of life
- $I$: The causes of the physics of a randomly selected universe were indifferent to whether those physics were sufficient for the existence of life. The complement, $I^C$ (Barnes' $\ov I$, which doesn't render well), is that the causes of the physics of a randomly selected intentionally created life.

The problems come in Barnes' definitions of $N$ and $F$. Barnes defines $N$ as "the natural phenomena of this universe are the causal products of the physics of this universe." It is unclear whether or not this is a random variable. However, Barnes conditions

*everything*on $N$. Therefore, if $N$ is not a random variable, it is just a truth of all universes; if $N$ is a random variable, we can just take our sample space to be $N$.

Note that Barnes correctly states that $P(X|LN)=1$; since we're looking only at the sample space where $N$ is 1, the equivalent is $P(X|L)=1$.

The second, somewhat more serious problem, is his definition of $F$: "in the set of possible physics, the subset that permit the existence (evolution) of life is very small. In other words, the physics of a particular universe must be fine-tuned if that universe is to support the existence (evolution) of life." This does not look

*at all*like a random variable. Instead, it looks like a scalar probability: $f=P(X|I)$. As a scalar, both advocates and critics of the FTA stipulate (

*arguendo*) that $f<<1$. I don't think these quibbles seriously affect his argument, but clearing them up simplifies everything considerably.

(However, Barnes does assert that "IJ’s 'N' slightly misses the point. The question is whether physics is fine-tuned and what we can conclude from this, not whether there are any exceptions to the laws of nature." This is an overstatement. Ikeda and Jeffries might miss

*Barnes'*point, but I think they directly tackle points made by others, especially the non-empty set of theists who assert the possibility of "miracles.")

I think I can skip over Barnes' restatement of Ikeda and Jeffries, and just accept that Barnes is making a different argument from the one that Ikeda and Jeffries make.

Barnes then wants to investigate the ratio:

$$R≡{P(I|LXFN)}/{P(I^C|LXFN)}$$

Given that Barnes $F$ does not seem like a random variable and $N$ defines our sample space, we can simplify:

$$R≡{P(I|LX)}/{P(I^C|LX)}$$

But by Ikeda and Jeffries' extension to Bayes theorem:

$$P(I|LX)={P(X|IL)P(I|L)}/{P(X|L)}=P(I|L) \text " given that " P(X|L)=1$$

$$P(I^C|LX)={P(X|I^CL)P(I^C|L)}/{P(X|L)}=P(I^C|L)$$

By Bayes Theorem again,

$$P(I|L)={P(L|I)P(I)}/{P(L)} \text " and " P(I^C|L)={P(I^C|L)P(I^C)}/{P(L)}$$

Therefore (simplifying):

$$R={P(L|I)P(I)}/{P(L|I^C)P(I^C)}$$

Given that we stipulate $P(L|I^C)=1$,

$$R=P(L|I){P(I)}/{P(I^C)}$$

Again, even if we we stipulate $P(L|I)<P(X|I)<<1$, then $R<1$ iff $P(L|I)<{P(I^C)}/{P(I)}$, which is the point I made in my previous post.

Let's look again at his original argument. Barnes' does fine until he reaches his first problem between iii) and iv):

$$\text "iii) " P(L|IFN)<<P(L|I^CFN) \text " thus, iv) " {P(I|LXFN)}/{P(I^C|LXFN}<<{P(I|N)}/{P(I^C|N)}$$

This conclusion is more or less true, but it is poorly stated. As I noted in my previous post, it is already admitted that $P(I^C|X)>P(I^C)$ and $P(I|X)<P(I)$,

*regardless*of the magnitude of $f=P(X|I)$, so long as $f<1$, and the smaller $f$ is, the more it "swings" the relative probabilities. However, Barnes' use of << in iv) is unwarranted; without knowing the magnitude of ${P(I)}/{P(I^C)}$, we don't know know if ${P(I|LXFN)}/{P(I^C|LXFN}$ is

*a lot less than*${P(I)}/{P(I^C)}$. But it is less than, again which is already admitted.

Essentially, as I wrote in my previous post, Barnes post is just an overcomplicated version of this post; he's added nothing new.

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