I was delighted to hear from John Cramer today. He was on the physics faculty at Wheaton College when I was a Freshman and Sophomore and I hadn't had communication with him since then. He is now emeritus professor of physics at Oglethorpe U in Atlanta.

John offered the following critique of multiverse theories and he gave me permission to post it. I will give all of you time to think it over and comment if you wish. In a day or two I'll submit my response to him and his response to me and perhaps we can keep the conversation going.

**Thesis:** Multiverse theories do not explain the fine tuning of our universe.

**Defense:**

1) Suppose at first that our universe, U_{0}, has only one finely tuned constant, κ. That is, the value of κ in U_{0 }lies in a small range of values, R, that permit intelligent life to exist in U_{0}.

2) Suppose also that U_{0} is only one of many extant universes, U_{i}, in which the values of κ_{i} can range over all real numbers. That is, a multiverse exists.

3) Since the universes of the multiverse are countable, their cardinality is the countable infinity, א_{0}.

4) The upper bound of κ_{i} values in any multiverse is no less than the cardinality of real numbers, א_{1}.

5) As Cantor showed long ago, א_{1 }>> א_{0}.

6) Therefore, a multiverse can never contain all possible values of κ_{i}.

**Discussion: **

Multiverse theories contain, as a standard feature, the implicit assumption that values of κ will be randomly selected from all possible real values and distributed among the universes. The U_{0} value of κ “must” somehow appear in one of the universes. This is an unwarranted belief. The probability that a multiverse contains U_{0} is not 1 but zero (א_{0}/א_{1}, with apologies to mathematical purists).

True enough, א_{0} universes may contain as many as א_{0} values of κ, but it is crucial to specify which values. The set of all integers is a countable infinity but it has א_{0} gaps (ranges like 0 to 1, etc.) in it, each with א_{1} missing values of κ. All multiverse theories necessarily have such gaps. Therefore, to explain the fine tuning of κ, a multiverse theory must be able to show that R is a likely range of values of κ in some universe (which will then be presumed to be U_{0}). Thus, even a countable infinity of universes cannot, by itself, explain the fine tuning of κ.

Additionally, there are many more than one “fine tuned” quantities in U_{0}. Consequently, it is incumbent on proponents of multiverse explanations to show that their choice of multiverse actually generates values of *each* κ in its proper R and that at least one of the universes of the multiverse has all κ values in the proper U_{0} ranges. Although I do not know this cannot be done, I very much doubt it can. Anyone undertaking such a project is to be commended; advancing a serious multiverse theory will be a prodigious undertaking. In fact, multiverse theories need to be theories of everything.

Randall D. Isaac says...Posted Monday, September 9, 2019Your argument is a bit different and I appreciate the chance of commenting on it. First, I should admit that I am somewhat partial to the idea of multiverses. While I know that some people advocate multiverses to solve the fine tuning challenge and related metaphysical ideas, that is not at all my motivation nor that of the primary proponents. They see it as a consequence of the mathematics that describe our own inflationary universe. What kind of infinity of universes that would entail, if any, isn’t clear.

As for explaining the fine tuning, perhaps you have gathered from some of my submissions to PSCF that I don’t really see that an explanation of this type is in order. In particular, the genre of arguments to which I think your argument belongs is one that I find problematic. Unless I misunderstand it, this genre is one of doing an a posteriori probability argument. Trying to determine retrospectively the probability that something unique happened is fraught with danger. An analogy would be to deal a deck of cards and then in retrospect calculate the probability that this precise sequence of dealing the cards had occurred. The answer is essentially zero but it did happen. With universes we are dealing with much bigger numbers but the principle is the same.

In the case of our universe, I still maintain that we have no idea whether an infinite number of values of κ exist or even if that parameter exists. Maybe only a finite number of possibilities exist. Maybe only 1. True, we can plug different values into mathematical equations but none may be realizable. And we don’t know if that value is tunable.

Therefore I am not convinced that there is a fine tuning problem to solve. Let alone be solved by a multiverse. As I wrote in my letter to the editor, last December 2018 issue, and to which Walter has not yet replied, I believe the very question “Why is our universe fine-tuned for life?” is an improper question. It presupposes that life was envisioned ten billion years before it occurred and that the universe is fine tunable and that fine tuning is possible. To claim that God is the answer is therefore a tautology. Rather, a more proper question would be to phrase it as “Why is life fine-tuned for our universe?” Then the chronology works well, retrocausation is not at stake, and the answer is clear—evolution does the trick very well.