The "anthropic principle" (scare quotes very much deliberate) has been the source of a huge amount of confusion over the years. This is due to many things.
The first is the failure of its originator Brandon Carter to explain it in a fully idiot-proof manner. Next, the unfortunate fact that his followers John Barrow and Frank Tipler wrote a book containing no less than four different Principles -- WAP, SAP, PAP and FAP. (Check pipelinks, please.) Later authors added to the mess by inventing new Principles and redefining the old Principles in different ways.
Then, the fact that logical thinking on questions involving probability and scientific evidence is tricky and easy to get confused about -- even for cosmologists. Last and worst, the desire (conscious or unconscious) of many people to invert an argument that debunks the apparent evidence for Intelligent Design, and to replace it with its exact opposite, an argument in favour of some sort of Supreme Being organizing the Universe. So in the end, out of two people discussing "the anthropic principle", one may believe that it obviates the necessity for God to exist, the other may believe the exact opposite.
Brandon Carter himself is still living and working in Paris and apparently regrets he ever invented the phrase.
About the SAP, PAP and FAP (and other sundry versions) I will have little to say, since I don't really understand them. The SAP is apparently an argument that any Universe must of necessity be set up so that it is conducive to, and actually contains, intelligent life. Now I can easily imagine a Universe which doesn't contain intelligent life: not a pleasant prospect, but not logically inconsistent. So I don't see the argument.
The PAP is apparently an argument that only an intelligent observer can collapse the wavefunction of the Universe, so that out of the quantum superposition of hugely many alternative universes only those that contain observers actually come into being. This seems to involve a massive violation of causality, since the observers only come into being billions of years after the Big Bang yet they're supposed to determine what happened at the Bang itself. But quantum mechanics is pretty strange altogether -- if the "collapse of the wavefunction" violates causality on a small scale, why not on a large scale?
The thing is, despite the Einstein-Podolsky-Rosen paradox, what we see as wavefunction collapse doesn't allow the future to influence the past. It should be possible to describe quantum mechanical measurements using interactions that travel at or below the speed of light, so that the probability of a particular state being obtained doesn't depend on events in the far future. So PAP, for me, is a strange misinterpretation of QM. However, since I don't fully understand quantum measurement myself, I'll put it down as 'undecided'.
The FAP is the strangest: it bears some relation to the Omega Point of Teilhard de Chardin. Based on some rather speculative ideas in cosmology and black hole physics, it tries to show that the final state of the Universe will be a point not only of infinite density and temperature, but also of infinite intelligence, knowledge and potency. Martin Gardner called it the Completely Ridiculous Anthropic Principle; but Gardner was notoriously rude about Weltanschauungen that differed from his own. Without going into details I believe that the argument has a lot of holes in it, however appealing one may find the conclusion that we're all destined to meet again at the Omega Point where we'll be infinitely powerful, etc. etc.
Towards science: Anthropic reasoning
Next in the buildup to WAP, what I regard as the only useful Principle, is the concept of "anthropic reasoning". This is simply using the existence of "life as we know it" to deduce facts about physics, cosmology, etc. The existence of intelligent or human life is treated as one data point among many. For instance, the particle physicist Maurice Goldhaber joked that we know 'in our bones' that the proton lifetime is greater than about 1016 years, since otherwise the radiation produced by proton decay inside our bodies would be lethal.
(In fact experiments have shown that the lifetime is many orders of magnitude greater.)
This type of reasoning tends not to be very powerful. One exception is Fred Hoyle's celebrated deduction that a certain resonance of the carbon nucleus exists. He was studying stellar nucleosynthesis, the production of heavy elements in the cores of stars, and found there was no way that carbon could be created unless this energy level existed. Since there is lots of carbon about (we consist of several percent carbon) he predicted the existence of the resonance, which was then found experimentally. But this isn't specifically anthropic reasoning: Hoyle could have looked at his pencil lead instead.
Coincidences, fine-tuning, and the apparent need for a Designer
The tale of the carbon resonance brings us almost to the point of the Weak Anthropic Principle, which finds its motivation in the so-called "anthropic coincidences". Before Hoyle's work, no-one in nuclear physics suspected there would be a resonance at that particular energy. The physics which leads to the resonance energy is a (still somewhat obscure) mixture of different effects, depending on many dimensionless constants such as the fine structure constant, the ratio of quark masses to the proton mass, etc. Now if these fundamental physics constants took values slightly different from those measured today, the resonance would not be in the right place and carbon would not be formed in significant amounts. The change required is a small fraction of a percent. Without carbon, the long chain molecules known as organic compounds could not exist and it appears very unlikely that complex biology could occur. So we have a very fine-tuned value of this resonance energy which is just right for carbon-based life to come into existence.
The carbon resonance is perhaps the most spectacular apparent coincidence, but many others have been noted. In Big Bang nucleosynthesis, the amount of helium formed depends on a balance between the weak nuclear force, Newton's constant (the strength of gravity) and the masses of the electron, proton and neutron. Basically the lifetime of a free neutron (about 10 minutes) is incredibly similar to the time in which nuclear reactions can occur in the early Universe (The First Three Minutes). Without this coincidence, the universe would have started out as virtually pure hydrogen or helium rather than a 75-25 mixture. With no hydrogen, there would be no organic chemistry and stellar evolution would be markedly different. Without helium, stellar evolution would again be different, although it becomes harder to argue that life could not exist.
Then we can bring in the strong nuclear force, which is controlled by the ratios of the quark masses and the proton mass. If the force had been a few percent weaker, deuterium could not form (either at the Big Bang or later) and there would be nothing but hydrogen around. A bit stronger, and all the hydrogen would fuse into diprotons (bound states of two protons) which would presumably also preclude the formation of heavier nuclei.
One can go on piling up requirements: the requirement that stars don't burn out in a few million years, that heavy nuclei be stable but not so stable that everything fuses into one vast stable nucleus, that it should be possible to make stable complex atoms, etc. etc. and it becomes downright spooky. The underlying physical constants seem to have been dialed up with an exquisitely sensitive eye to the emergence of life. To some people this means that there must be some sort of Supreme Being taking care of it all. After all, what are the odds against the required tiny region of parameter space being picked out just by chance?
The existence of these apparent coincidences centering on the presence of life is sometimes incorrectly referred to as "the anthropic principle". In fact, the Principle is what one needs to interpret such fine-tunings in a meaningful way.
At last -- the Weak Anthropic Principle
The WAP is an attempt to deal with what is known as an 'observation selection effect' or selection bias. Selection effects are well known in statistics: the simplest example is if one hires a polling organization to find out what percentage of people own telephones. The problem is, the organization uses phone polling, so you get the false and useless result of 100%. An American magazine that predicted the 1936 Presidental Election would go to Alf Landon actually went out of business after losing so much credibility: all because they assumed that the people responding to their opinion poll were a representative sample of the voting population.
More subtle effects occur in astronomy: if you're doing a survey of galaxy spectra and luminosities you need to take account of the fact that your telescope can only detect light in a certain range of frequencies and down to a certain minimum intensity. We can caricature the effect of selection bias as follows: the likelihood of observing a particular situation is zero if that situation happens to be incompatible with your observing apparatus.
This may seem obvious, but when applied to the existence of intelligent life it strongly modifies our view of the "anthropic coincidences". The Weak Anthropic Principle can be stated as follows: the probability of observing a certain set of values of physical constants is zero if those values are incompatible with a form of life capable of doing the observing. Conversely, the probability of observing a set of values that do lead to intelligent life is 1. (Say it again, with emphasis on "observing".) Those arguing for intelligent design emphasize that only an astonishingly tiny corner of parameter space is suitable for life. Applying the WAP, we should not be astonished that we are in the tiny corner of parameter space where life is possible.
More generally, the WAP must be used to interpret cosmological models (such as inflation) if they have free parameters that can take a range of values. If the possibility of existence of intelligent life is strongly dependent on the parameters, then your prediction of what values will be observed will be strongly skewed towards the region where life is allowed.
Does the WAP actually explain anything?
Round 1 to the WAP: Paul Dirac gets knocked out
The WAP effectively disposes of the argument that a Creator must have set up the Universe in order to produce us, i.e. human life, or that the apparent coincidences leading to the emergence of life require a mystical explanation. The anthropic principle was in fact also used before Brandon Carter's coining in R. H. Dicke's debunking of the Dirac large numbers hypothesis. This deserves a node of its own, but here goes: in 1937 Dirac pointed out that a certain combination of physics constants h-bar/Gcmπ was rather close to the age of the Universe (about 10 billion years). Equivalently, the ratio of the gravitational force to the electrostatic force between two electrons (about 10-40) was close to the ratio of the time for light to cross a hydrogen atom to the age of the Universe (about 10-40). Dirac took this coincidence as a sign that the physical constants should be varying over time to maintain the relationship as the Universe aged. However Dicke later pointed out that because of the physics that determines the lifetime of stars, you expect an average star to burn out after about a time h-bar/Gcmπ. Combine this with the fact that elements heavier than H, He and Li can only be produced in stellar cores and supernovae and you quickly find that life on planets (which are just condensed stardust) is only possible when the age of the Universe is a few times the typical stellar lifetime. It was inevitable that we would observe that the combination of constants Dirac took was close to the age of the Universe: the Dirac "coincidence" wasn't one.
Round 2: WAP takes a hit in the GUT and stubs its TOE
However, WAP is somewhat unsatisfying if we try to apply it as a scientific theory, to explain more of the experimentally observed features of the world. In particular it doesn't explain why those features come about in terms of more fundamental entities. For example an "anthropic" answer to the question "Why is the ratio of the electron mass to the proton mass observed to be 1/1836?" is "Because any other value could not be compatible with intelligent life". This is not very enlightening, and maybe not even correct.
Physicists are working on scenarios in which these masses are explained as a consequence of a unified theory which would also explain why there is an electron and a proton in the first place. Such a theory might have such a symmetrical structure that it would be impossible for the mass ratio to come out any other way. This sort of explanation, in terms of an underlying structure or set of equations, is what provides scientists with the feeling that Progress Has Been Made. But if there really is only one possible Theory Of Everything, then it makes no sense to think about constants potentially taking different values. Although God is out of the picture, since there is no choice to be made, anthropic selection is also out of the picture, since there is nothing to select between. Then the coincidences really look very puzzling indeed, since there is no reason why the unique unified theory should have the property of allowing intelligent life to emerge.
Round 3: WAP goes on the ropes
However, string theory suggests that rather than a single possible set of values, there are many -- hugely many -- possible configurations. This is known as the vacuum selection problem. Effectively there are many solutions within a single theory, with continuous or discrete transitions between different solutions. Hence there is a large range of different possible outcomes and one can imagine a Universe with many different (very large) domains, inside each of which there is a different set of physical constants. In fact, independently of string theory, the scenario of eternal inflation described by Andrei Linde could lead to such a Universe. Roughly, eternal inflation predicts that most of the Universe is made up of very rapidly expanding regions, with occasional domains that stop inflating and settle down into slowly-evolving regions like the one we inhabit. Each non-inflationary domain can have different values of the physical constants. These scenarios arise fairly naturally from existing theories and are favourable grounds for the Principle to operate on.
Round 4: Aliens invade the pitch -- WAP appears seriously wounded
But there is another major difficulty with applying the Principle. We are required to know when "intelligent life" will emerge, given particular values of constants. But we don't really know how and why life on Earth got started, nor how and why intelligent thought arose. We know that a tiny change in constants would rule out life as we know it, but other forms of life are not inconceivable: "silicon-based life forms" for example, or Fred Hoyle's "The Black Cloud" which is a sentient configuration of charged bits of dust that floats around in space for millennia. We have no way of ruling out the possibility that one of these might be able to ask the question "Why are the physical constants as they are?". (In an appropriate language, of course.)
Freeman Dyson, in another context (asking whether life can survive in an Universe that continues to expand and cool), took the minimum requirement for life to be the ability to process information. Certainly, if we need our lifeform to be asking scientific questions, it must have this. But this throws the door wide open to forms of life that are nothing like humanity, and correspondingly weakens any predictive power the WAP might have. In Stephen Wolfram's A New Kind of Science, he describes how a one-dimensional cellular automaton can act as a universal computer: in other words, can process as much information as you can throw at it. Maybe the WAP doesn't even exclude a universe with one spatial dimension made up of little black and white cells.
This line of thought appears to conflict with the original reasoning that our form of life is extremely fine-tuned. If the requirement for intelligent life is so unexacting, it is surely no surprise that we are in a universe that contains it. Or at least, a much smaller surprise, since the Universe still has to be fairly big and long-lived for any sort of life to get going. The problem of calculating when intelligent life will and will not arise is a severe one and undermines both the assertion that the constants are fine-tuned for life and the anthropic interpretation of the fine-tuning.
Does the WAP require Many-Worlds or many worlds?
Some people assert that the application of WAP requires us to believe the Many-Worlds interpretation of QM: the idea that every time a quantum measurement can give more than one result the Universe splits into two or more universes in each of which a different result occurs. However, this is a misunderstanding. In fact we don't need to think about QM at all to formulate the WAP, since it's just an effect of statistical bias. Also, the Many-Worlds interpretation doesn't necessarily lead to universes with different physical constants.
More seriously, the question is whether WAP can be applied if the other values of constants that are allowed in the underlying theory don't actually occur in some domain of the Universe (or multiverse). That is, if the theory allows many different values, but there is only one Universe with exactly one set of values. Most people would say no, the fact that this unique Universe lands up in the (presumably) small region where life is allowed becomes an amazing coincidence again and requires further explanation.
I would disagree. If only one set of values actually occurs, then of course the chance of getting any particular tiny region in the space of possible values is very small. So it is an amazing coincidence that we get just the values that we do. But the fact that these coincide with the values that allow intelligent life is no surprise -- since the probability of observing any other set of values is zero -- and doesn't require any further explanation. It's no contradiction to think of probability despite there being only one trial: think of a roulette wheel which is only spun once.
Suppose a man is telling you how he was threatened with death by a mad gambling-obsessed criminal mastermind, how he would be executed unless he could predict the number that would come up. You're not that surprised when he tells you that he guessed right.
Luckily, due to the nature of quantum mechanics, arguments on this point are probably irrelevant: any possible alternative Universes likely do exist in some way. They could be connected to our region on a very large scale, or they could be accessible by quantum tunneling creating false vacuum bubbles; in any event, since they are solutions of the underlying theory, they are present as fluctuations about the solution we see. Hopefully, the exact degree of existence of the other solutions does not greatly influence the validity of WAP.
www.anthropic-principle.com (an excellent site)
www.starcourse.org/discussion/anthropic.html and links therein
prola.aps.org/abstract/RMP/v61/i1/p1_1 (paper by Steven Weinberg, access resticted)