In Defense of the Fine-Tuning Argument

First, some background.

The teleological argument, otherwise known as the argument from design, is one of the many "proofs" of the existence of God. Simply put, it says that when we look around the universe, we see things (galaxies, solar system, human bodies, etc.) that are products of design which could not have come about by chance. This design implies a designer, who could only be God.

Recently, the teleological argument has taken on a new form, interesting and powerful because it is based on physics and astronomy. Hugh Ross, founder of Reasons to Believe, is the main proponent of this relatively new argument, which is presented in Design and the Anthropic Principle and Evidence for Design of the Cosmos . To summarize, the argument goes as follows:

There are many fundamental parameters in physics which determines what kind of a universe this is. Examples include the Plank's constant, the mass and charge of the electron, the gravitational force constant, the speed of light, and many others. It turns out that if some of these numbers are slightly different than their actual values, our universe would not be able to support life. It is virtually impossible that the universe came to have these correct parameters for life by chance, because so many of these numbers must all lie in such a small range of values. So it appears that the constants of the universe were fine-tuned for life. The being who did this fine-tuning must be God; without such a being, there would be virtually no chance that life could exist.

Of course, many nontheists believe this fine-tuning argument to be flawed, and they try to disprove it. One such attempt comes from Michael Ikeda and Bill Jefferys, in an article called The Anthropic Principle Does Not Support Supernaturalism . They claim to have shown that the fine tuning argument is wrong. It is my purpose here to refute their claim.

Notations and assumptions for Ikeda and Jefferys's article

Before we go into the actual content of Ikeda and Jefferys's article, it would be good to become comfortable with the notations used there. These are explained in their article, but for the sake of completeness and clarity I will reproduce them here.

First, we introduce some statements, which can either be true or false.
L: The universe contains life. This is obviously true for our universe.
F: The universe is 'life-friendly'. By 'life-friendly', we mean that the universe has a set of physical parameters and laws which allow life to exist, as explained by Ross. Both sides of the debate (Ross, and Ikeda and Jefferys) agree that F is true.
N: The universe is governed solely by naturalistic law. The negation of N, ~N, would say that the universe is governed at least in part by some supernatural law or entity. This is what we would like to find out.

Secondly, we introduce some probability notations.
P(A) = The probability that statement A is true.
P(~A) = The probability that not A is true. That is, the probability that A is false.
P(A&B;) = The probability that A and B are both true.
P(A|B) = The probability that A is true, given that B is true. P(A|B) is defined to be P(A&B;)/P(B).

To familiarize oneself with the notation, it is useful to note how valid mathematical statements would be written in this notation. All of the following statements are valid for any A and B, and they will be used in the remainder of my article.
0 < P(A) < 1
P(A) + P(~A) = 1
P(A|B) + P(~A|B) = 1
P(A&B;) + P(~A&B;) = P(B)

Lastly, we want to state common starting assumptions and see how recurring ideas would be written in this probability notation.
We assume L to be true for our universe. Our universe does indeed contain life.
We assume F to be true for our universe. This is confirmed by observation, and both sides of the argument agree on this assumption.
We assume the weak anthropic principle. In their article, Ikeda and Jefferys formulate this principle as follows; life cannot exist in a universe that is governed solely by naturalistic law unless that universe is 'life-friendly'. This statement is generally accepted. Ikeda and Jefferys assume its truth in their article, and Ross would probably agree with it, even though it is not necessary for the fine tuning argument. Ikeda and Jefferys formulate this as P(F|N&L;) = 1, but I prefer the more direct expression P(N&~F&L;) = 0. It is trivial to show that the two statements are equivalent.
Ross's assertion that the universe is extremely fine-tuned would be written as P(F|N) << 1.
What we are trying to find is whether N is true for our universe, given that our universe contains life and is 'life-friendly'. That is, we are trying to find the value of P(N|F&L;)

Summary of the content of Ikeda and Jefferys's article

These are the main points of The Anthropic Principle Does Not Support Supernaturalism by Ikeda and Jefferys:

  • The fine-tuning argument can be written in the language of probability theory as follows: P(F|N) << 1, therefore P(N|F) << 1. This is wrong for two reasons. First, it is not a valid operation to simply switch the two arguments in P(A|B). In general one cannot infer anything about P(A|B) by knowing P(B|A). Second, P(N|F) is meaningless for determining the likelihood of N in our universe, since it does not take L into account. We must take into account all things known to be true about our universe, both F and N. Therefore, P(N|F&L;), not P(N|F), is the relevant probability.
  • Using the weak anthropic principle, it can be shown mathematically that P(N|F&L;) > P(N|L). This is the "main theorem". This expression says that the observing F cannot decrease the probability that N is true. In fact, it may increase it. So the more finely tuned the universe is, the more likely that supernaturalism is wrong.

Ikeda and Jefferys also mention some other arguments in passing. While these are not their main points, Ikeda and Jefferys claim that these are valid arguments against the fine-tuning argument, so I will cover them in my discussion. They are summarized below:

  • There may be many, possibly infinitely many other universes, each with different physical laws. If there are enough universes, it is not surprising that one of them is 'life-friendly'.
  • We do not know enough about other kinds of life, or the laws of physics, to truly assert that P(F|N) << 1. There may be other possible forms of life entirely different from what we know, which may exist for other kinds of universes. Or it may be that if we learn enough about the universe, some deep law of physics (e.g. the Theory of Everything) dictates that only a universe like ours is possible.
  • Many proponents of design assert ~F (e.g. Behe), and claim that this leads to ~N. But others assert F (e.g. Ross), and claim that this leads to ~N. In other words, people who argue for design conclude ~N, whether or not F is true. These two classes of arguments can't be both true.

There is more content in Ikeda and Jefferys article, but they mostly rest on the main points mentioned above. Since refuting the main points is sufficient to discredit the parts that rely on them, I will not deal with the remainder of their article.

Refutation of the main points

Ikeda and Jefferys start out with the incorrect formulation of the fine-tuning argument. To my knowledge, there has been no attempt by Ross or others to formulate the fine-tuning argument via probability theory, and certainly nobody has claimed "P(F|N) << 1, therefore P(N|F) << 1". Ikeda and Jefferys commits a classic straw man fallacy: They construct a flawed formulation of the fine-tuning argument, discredit this flawed version, then claim that they won the debate.

The correct formulation of the fine-tuning argument in probability theory would be as follows:

  1. P(N|F&L;) = P(N&F;&L;)/P(F&L;)
    By definition.
  2. P(F&L;)= P(~N&F;&L;) + P(N&F;&L;)
    By expanding P(F&L;). ("Expanding" is covered in the 'notations' section.)
  3. P(N|F&L;) = P(N&F;&L;) / {P(~N&F;&L;) + P(N&F;&L;)}
    From (1) and (2).
  4. P(F|N) << 1
    The fine-tuning assertion.
  5. P(F&N;)/P(N) << 1
    Substituting in the definition of P(F|N).
  6. P(F&N;) << P(N) < 1
    By multiplying both sides by P(N), which is between 0 and 1.
  7. P(L&F;&N;) + P(~L&F;&N;) << 1
    By expanding P(F&N;).
  8. P(L&F;&N;) << 1 - P(~L&F;&N;) < 1
    By subtracting P(~L&F;&N;), which is between 0 and 1, from both sides.
  9. P(N|F&L;) << 1, unless P(~N&F;&L;) << 1
    From (3) and (8). (8) says that the numerator P(N&F;&L;) << 1, so the expression in (3) is << 1, unless the other term in the denominator, P(~N&F;&L;), is as small as or smaller than P(N&F;&L;). In other words, P(N|F&L;) << 1 unless P(~N&F;&L;) << 1.
This formulation of the fine-tuning argument takes into account both F and L, and addresses the correct probability, P(N|F&L;). It does not rely on asserting "P(F|N) << 1, therefore P(N|F) << 1", nor does it make any other such mistakes. In fact, it does not even rely on the weak anthropic principle. (Ross only mentions the anthropic principle to deal with the errors of participatory and the final anthropic principle. Ikeda and Jefferys incorrectly imply that the weak anthropic principle is part of the fine-tuning argument) Basically, this correct version of the fine-tuning argument shows that the theistic position (~N&F;&L;) is true. The only way to not come to this conclusion is to start with an a priori assumption of P(~N&F;&L;) << 1. In other words, the only way to hold on to naturalism is by assuming that theism is virtually impossible to begin with.

Concerning the "main theorem", I do not question the mathematical expression itself. Ikeda and Jefferys used sound mathematics and probability theory to arrive at the expression P(N|F&L;) > P(N|L), and it is a valid expression. However, they err in their interpretation of that expression.

Apparently, Ikeda and Jefferys believe that disregarding the fine-tuning argument, the probability of N being true in our universe is P(N|L). They would further say that the fine-tuning argument asserts F, therefore the correct probability is P(N|F&L;) if the fine-tuning argument is true. They then look at the expression P(N|F&L;) > P(N|L), and say that if fine-tuning is true, it would make N more likely to be true(or at least would not make it less likely) than if fine-tuning is false. This interpretation makes two distinct errors.

First, it incorrectly attributes significance to P(N|L). In reality, P(N|L) is irrelevant to our universe for the same reason that P(N|F) is irrelevant. Ikeda and Jefferys (correctly) state that P(N|F) is meaningless because it does not take L into account. Likewise, P(N|L) is meaningless because it does not take F into account. In fact, the probability of N being true for our universe, even if we disregard the fine-tuning argument, is still P(N|F&L;), not P(N|L). P(N|F&L;) will be the correct probability to consider as long as we acknowledge that F and L are both true for our universe.

So, if the fine-tuning argument doesn't change the probability to be considered from P(N|L) to P(N|F&L;), then what does it do? This is the where the second error of the above interpretation comes up. The fine-tuning argument does not assert F, as Ikeda and Jefferys believe. We have always known that F is true for our universe, with or without the fine-tuning argument. What the fine-tuning argument does assert is that P(F|N) << 1, and this is what allows us to come to the conclusion that P(N|F&L;) << 1 (unless, of course, P(~N&F;&L;) << 1).

Then, what is the correct interpretation of the "main theorem"? First we should identify the significance of P(N|L). P(N|L) is the probability of N being true given that L is true, when there is no condition on F. In other words, in some imaginary universe where there is life but nothing is known about F, P(N|L) would be the probability of naturalism in that universe. Or, even in our universe, if in the future we somehow come to the conclusion that F cannot be determined, then the relevant probability to consider would become P(N|L). Now, we have already shown that P(N|F&L;) << 1, and the "main theorem" says that P(N|L) < P(N|F&L;). In other words, in a hypothetical imaginary universe or a hypothetical future described above, the probability of N being true would be even less than (or be equal to) it is here. So the "main theorem" does not apply to our universe, but in the hypothetical cases where it would apply, it would actually support theism.

Refutation of the peripheral points

Much more can be said about refuting these arguments than what I am going to write. However, since they were not the central issue of Ikeda and Jefferys's article, I will limit my comments to be comparable in volume to what was written in their article.

Concerning the idea that there may be other universes: This is simply unscientific. There is no evidence of other universes, and such evidence is in fact in principle impossible. What is fundamentally untestable cannot be scientific. If someone is willing to stake their reputation as an experimental physicist, and publish in a scientific journal claiming that he has irrefutable experimental evidence for other universes, then this "other universes" theory can be considered as a scientific argument. But until then it must remain merely a philosophical possibility. As such it cannot touch the claims of Ross and the fine-tuning argument, which is that science supports Christian theism. Even as a philosophical possibility it runs into difficulties. It has all the hallmarks of a desperation tactic, escaping to a position that cannot be verified in order to avoid an obvious and unpleasant conclusion.

Concerning the idea that the fine-tuning argument will become moot if we knew more about life or physics: In their article Ikeda and Jefferys display disdain for the "god of the gaps". In general, everybody, including the theist, does. A god of the gaps is a kind of deity who only gets the credit for unexplained phenomena, whose existence is eventually rendered useless as more things are explained by other agents. But this idea of "well, if we understood more about physics or other life forms, we would see how it's not impossible that we're here..." is the same concept as this god of the gaps. The nontheists who assert this idea has turned the Theory of Everything into some monstrous kind of "physics of the gaps". They cannot explain the existence of life, so they attribute its existance to some undiscovered aspect of nature, ignoring the compelling explanation provided by the theists. As surely as the "god of the gaps" is an unsound idea, this "physics of the gaps" or "science of the gaps" is equally unsound. It is especially disturbing when it is the scientist who advocates this "science of the gaps".

Concerning the idea that the proponents of the design arguments assert both F and ~F: This is an extension of Ikeda and Jefferys's previously mentioned error of mistaking the fine-tuning assertion to be "F", when it is actually "P(F|N) << 1". In the language of probability theory, Ross is asserting P(F|N) << 1, but he is misunderstood as asserting F. Likewise, Behe asserts P(~F|N) = 1, but he is misunderstood as asserting ~F. These mistakes lead the nontheists to claim that the proponents of design are saying F and ~F, which are incompatible. Actually, their error is not unforgivable. Ross tends to emphasize how amazing it is that F is true, given that P(F|N) << 1. So it might be easy to develop the misconception that his main point is F. Behe claims P(~F|N) = 1, which turns into ~F for those who have N as their preconception. Of course, in reality, Behe's claim is simply a stronger version of Ross's, since P(~F|N) = 1 is equivalent to P(F|N) = 0, which is just the absolute form of P(F|N) << 1.

Now that much has been heard...

The conclusion of matter is that the main thrust of Ikeda and Jefferys's article is flawed. The fine-tuning argument, when it is translated properly into probability theory, is solidly backed up by the mathematics. Their "main theorem" is irrelevant in our current universe, and will actually strengthen theism more than the fine-tuning argument if it is ever discovered that F may not be true. Other objections, which are mentioned as an aside, against the fine-tuning argument have been answered.

The fine-tuning argument emerges as a part of the powerful collection of evidences which support the existence of God. It is backed up by physics, astronomy, the Bible, and now, probability theory.

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