This is the fifth installment of my blog series "Mapping the Fine-Tuning Argument". For an introduction to what this series is about, see the index here. It is well-worth reading the first two posts listed there before jumping into this one.
UPDATE: I read a series of criticisms of physicist Victor Stenger which reprimanded some of Stenger's criticisms of the argument (which I referenced in my series). Click here to read the first part of those criticisms. Anyway, I believe some of these criticisms of Stenger are valid, not least because Stenger himself seemed to implicitly agree with me when I emailed him about it (in the email Stenger said that his upcoming book The Fallacy of Fine-Tuning would update his criticisms of the argument).
Let us return to premise A-2 in the fine-tuning argument:
"Conceptually changing some constants from their observed values (independently) would make the universe uninhabitable for life as we know it. NOTE: What I mean by changing 'independently' is when someone changes the constant value in their equation without changing the value(s) of any other constants."
The methodology used by many proponents of the fine-tuning argument is to take one constant value and alter its value in the equations while not changing any of the other constant values in the equations. Here's a hypothetical (and simple) example: Let's say that we have five forces (which I will refer to as A, B, C, D, and E). Let's also say that we observe that in our universe the value of each constant is 42. Now, let's say that a scientist comes along and tells us that when he changes force A's value from 42 to 43 (while in his equations keeping the observed value of 42 for forces B, C, D, and E) it makes the universe unfit for life. He observes that changing the force's value to any number between 1 and 100 (while using the observed value of 42 for forces B-E in his equations) makes the universe unfit for life. Would the scientist be correct in asserting that the value of force A is 'fine-tuned' for life and was unlikely to come about by chance?
No. The correct procedure that the scientist should follow, if he is trying to determine what the odds are against a life friendly universe coming about chance are, is this: he should allow the values of all the forces to vary at the same time in his equations. For example, he should randomly plug in different values for the 5 forces, so that his equations would look something like this:
Hypothetical Universe #1
A=23 B=61 C=70 D=99 E=44
Hypothetical Universe #2
A=70 B=5 C=49 D=2 E=28
Hypothetical Universe #3
A=6 B=90 C=51 D=8 E=80
Some scientists (like Victor Stenger) have made this point themselves and carried out studies in which they used the correct methodology I outlined above. Victor Stenger did a study in which he plugged random values into six different physical constants that are responsible for star formation*. He found that nearly 20% of the hypothetical universes in his study were life-friendly. This is still somewhat improbable, but nonetheless this is valuable because it really cuts the odds down to size. Often design proponents will try and argue that the odds against a life friendly universe are less than one in a billion billion billion billion billion (no exaggeration). But in Stenger's study, the odds turn out to be more like one in five. Other studies have come to similar conclusions.
Of course, until studies are carried out with all of the different constants claimed to be necessary to life, we won't be able to claim that they will turn out just as those studies have. Nor will proponents of the fine-tuning argument be able to claim that other studies will not turn out like the ones above, at least not until the studies are done and we know for sure. A state of ignorance is not evidence for either side.
Nontheless, these studies are important for the reasons stated above: they really cut the fine-tuning argument down to size by making a life-friendly universe much, much more probable than was expected.
Notes and References
* Life-friendliness is assumed to depend on star formation because star formation is necessary for forming heavy elements and basically for having chemistry in the universe, which I think are reasonable assumptions about what is necessary for life.
 See Stenger's webpage on the subject, or chapter 5 of God: The Failed Hypothesis.
 For example, See:
A. Aguire, “Cold Big Bang Cosmology as a counterexample to several anthropic arguments”, Phys. Rev. D 64, Issue 8, (2001): 1-13.
Fred C. Adams, "Stars In Other Universes: Stellar structure with different fundamental constants" Journal of Cosmology and Astroparticle Physics, Issue 08, pp.1-29 (2008).
This article in New Scientist gives a good run-down of what the paper is about.