Is the Universe fine-tuned for permitting life?

  • Clarifying the question

    symbols of physics constants with checkmarks

    There has been a significant amount of discussion recently in cosmology journals and conferences about the so-called “fine-tuning” of the Universe for life. To the untrained ear, this may sound as if the cosmologists are presupposing a fine-tuner. In reality, they are not. By fine-tuning, they just mean that of all the ways the constants and initial conditions of the universe could have been, few would have permitted life of any kind. (E.g. see these quotes)1 But are these cosmologists correct? Are the Universe's laws, constants, and initial conditions fine-tuned in this way to permit life?

      • Richard Dawkins ([Outspoken atheist] Biology professor at Oxford): “The anthropic principle is usually applied not to planets but to universes. Physicists have suggested that the laws and constants of physics are too good - as if the universe were set up to favour our eventual evolution. It is as though there were, say, half a dozen dials representing the major constants of physics. Each of the dials could in principle be tuned to any of a wide range of values. Almost all of these knob-twiddlings would yield a universe in which life would be impossible. Some universes would fizzle out within the first picosecond. Others would contain no elements heavier than hydrogen and helium. In yet others, matter would never condense into stars (and you need stars in order to forge the elements of chemistry and hence life). You can estimate the very low odds against the six knobs all just happening to be correctly tuned,” (Dawkins then gives his misconceived objection: “but then who fine-tuned God”) [“Why There is Almost Certainly no God” The Huffington Post (Oct 23, 2006).]
      • William Lane Craig ([Outspoken Christian apologist] Philosophy professor): “The physical laws of nature, when given mathematical expression, contain various constants or quantities, such as the gravitational constant or the density of the Universe, whose values are not mandated by the laws themselves; a universe governed by such laws might be characterized by any wide range of values for such variables. By “fine-tuning” one typically means that the actual values assumed by the constants and quantities in question are such that small deviations from those values would render the universe life-prohibiting.” [The Cambridge Companion to Atheism ed. Martin (Cambridge, 2006), 80.]
      • Martin Rees (Cosmology professor at Cambridge etc.): “These six numbers constitute a ‘recipe’ for a universe. Moreover, the outcome is sensitive to their values: if any one of them were to be ‘untuned’, there would be no stars and no life. Is this tuning just a brute fact, a coincidence? Or is it the providence of a benign Creator?” [Just Six Numbers: The Deep Forces that Shape the Universe (Basic Books, 2000), 4.]
      • Peter van Inwagen (Philosophy professor at Notre Dame): “Most [naturally possible universes] will last only a few seconds or will contain no protons or will contain no atoms or will contain only hydrogen and helium atoms or will be composed entirely of violently radioactive matter or will be devoid of stars or will contain only stars of a kind that would burn out before evolution could get started on their planets.” [Metaphysics 3rd ed. (Westview, 2008), 199.]
      • Sean Carroll ([Outspoken atheist] Theoretical Cosmologist at CalTech): “Other constants of nature, such as those that govern atomic and nuclear physics, seem natural by themselves, but would give rise to very different macroscopic phenomena if they were changed even slightly. For example, if the mass of the neutron were a bit larger (in comparison to the mass of the proton) than its actual value, hydrogen would not fuse into deuterium and conventional stars would be impossible; if the neutron mass were a bit smaller, all the hydrogen in the early universe would fuse into helium, and helium stars in the late universe would have much shorter lifetimes.” [The Blackwell Companion to Science and Christianity (Blackwell, 2012), 189-190]

  • Cosmologists agree: The Universe is fine-tuned

    • Geoff Brumfiel (Nature Magazine's Washington Correspondent): “If you believe the equations of the world’s leading cosmologists, the probability that the Universe would turn out this way [life-permitting] by chance are infinitesimal — one in a very large number.” [“Our Universe: Outrageous Fortune,” Nature, Vol 439:10-12 (Jan. 5, 2006)]1
    • Paul Davies ([Agnostic-turned-Deist] Physicist; Professor at 6 Universities [Cambridge, London etc.]): “There is now broad agreement among physicists and cosmologists that the universe is in several respects ‘fine-tuned' for life.” [“How bio-friendly is the universe?” International Journal of Astrobiology, vol. 2, no. 2 (2003): 115.]
    1. Others testifying that fine-tuning is not even disputed among cosmologists:
      • Stephen Hawking: “The laws of science, as we know them at present, contain many fundamental numbers, like the size of the electric charge of the electron and the ratio of the masses of the proton and the electron. We cannot, at the moment at least, predict the values of these numbers from theory – we have to find them by observation [i.e. they could have been different]. … The remarkable fact is that the values of these numbers seem to have been very finely adjusted to make possible the development of life. For example, if the electric charge of the electron had been only slightly different, stars either would have been unable to burn hydrogen and helium, or else they would not have exploded. ...it seems clear that there are relatively few ranges of values for the numbers that would allow the development of any form of intelligent life. Most sets of values would give rise to universes that, although they might be very beautiful, would contain no one able to wonder at that beauty. One can take this either as evidence of a divine purpose in Creation and the choice of the laws of science or as support for the strong anthropic principle.” [The Illustrated A Brief History of Time (Bantam, 1996), 160.]
      • Greg Bothun (Physics professor, Astronomy; Harvard Astrophysics Res. fellow): “However, in the past 20 years our understanding of physics and biology has noted a peculiar specialness to our Universe, a specialness with regard to the existence of intelligent life. This sends up warning signs from the Copernican Principle, the idea that no scientific theory should invoke a special place or aspect to humans. All the laws of Nature have particular constants associated with them, the gravitational constant, the speed of light, the electric charge, the mass of the electron, Planck's constant from quantum mechanics. Some are derived from physical laws (the speed of light, for example, comes from Maxwell's equations). However, for most, their values are arbitrary. The laws would still operate if the constants had different values, although the resulting interactions would be radically different. …All the above constants are critical to the formation of the basic building blocks of life. And, the range of possible values for these constants is very narrow.” [uoregon.edu lecture notes; online]
      • Paul Davies ([Agnostic-turned-Deist] Physicist; Professor at 6 Universities [Cambridge, London etc.]): “Most scientists concede that there are features of our observed universe which appear contrived or ingeniously and felicitously arranged in their relationship to the existence of biological organisms in general, and intelligent observers in particular.”[“Universes galore: Where will it all end?” in Universe or Multiverse? ed. Carr (Cambridge, 2007), 487.]
        Note: The math/details are given in various sources, especially Martin Rees Just Six Numbers: The Deep Forces that Shape the Universe (Basic Books, 2000), Paul Davies The Accidental Universe (Cambridge, 1982), John Barrow, Frank Tipler, John Wheeler The Anthropic Cosmological Principle (Oxford, 1988), and John Leslie Universes (Routledge, 1966).

  • Relevance to the God Question

    One of the main reasons fine-tuning is interesting is because it is very plausibly good evidence for theism. In light of fine-tuning, the likelihood that the universe would permit life is suddenly seen to be very surprising to the atheist (i.e. improbable on the hypothesis of atheism). On theism, however, the universe's being life-permitting is not nearly so unlikely--that's very much the kind of thing God would bring about. Consider thoughts from various thinkers on this subject:

    That our Universe allows life is suddenly surprising for atheists

    • Philip Ball (Physicist, 10+ years editor for Nature): “Our universe is so unlikely that we must be missing something… the incomprehensibility of our situation even drives Susskind's team to ponder whether an ‘unknown agent intervened in the evolution [of the Universe] for reasons of its own’…” [“Is Physics Watching Over Us?” Nature, Science Update, 2002.] (Ball here is referring to Dyson, F., Kleban, M. & Susskind, L. Disturbing implications of a cosmological constant. (2002).)
    • Brad Lemley (Senior correspondent for The Washington Post and Discover Magazine): “The universe is unlikely. Very unlikely. Deeply, shockingly unlikely.” [“Why Is There Life?” Discover (November 2002)]
    • David D. Deutsch: “If anyone claims not to be surprised by the special features that the universe has, he is hiding his head in the sand. These special features are surprising and unlikely.”
    • Steven Weinberg (Outspoken atheist, Nobel laureate in high energy physics): “…how surprising it is that the laws of nature and the initial conditions of the universe should allow for the existence of beings who could observe it. Life as we know it would be impossible if any one of several physical quantities had slightly different values.” [“Life in the Universe" Scientific American (Oct. 1994)”] (cited by Bruce Waltke)]
    • William Lane Craig (Philosophy professor at Talbot): “Scientists originally thought that whatever the initial conditions of the universe were, eventually the universe would evolve the complex life forms we see today. But during the last forty years or so, scientists have been stunned by the discovery of how complex and sensitive a balance of initial conditions must be given in the Big Bang in order for the universe to permit the origin and evolution of intelligent life in the cosmos.” [“What is the Relation between Science and Religion” online at ReasonableFaith.org]
    • Paul Davies (Agnostic turned deist, physics professor at Cambridge, etc.): “The really amazing thing is not that life on Earth is balanced on a knife-edge, but that the entire universe is balanced on a knife-edge, and would be total chaos if any of the natural 'constants' were off even slightly. You see… even if you dismiss man as a chance happening, the fact remains that the universe seems unreasonably suited to the existence of life -- almost contrived -- you might say a 'put-up job'.… Taken together they provide impressive evidence that life as we know it depends very sensitively on the form of the laws of physics, and on some seemingly fortuitous accidents in the actual values that nature has chosen for various particle masses, force strengths, and so on. If we could play God, and select values for these natural quantities at whim by twiddling a set of knobs, we would find that almost all knob settings would render the universe uninhabitable. Some knobs would have to be fine-tuned to enormous precision if life is to flourish in the universe” [“The Unreasonable Effectiveness of Science”, in John Marks Templeton, Evidence of Purpose (Continuum, 1996) 46.]
    • Charles Townes (Physics professor, Nobel Prize winner): “This is a very special universe: it's remarkable that it came out just this way. … the laws of gravity and nuclear laws and magnetic theory, quantum mechanics, and so on have to be just the way they are for us to be here.” [UC Berkeley NewsCenter (June 17, 2005). Online]

    That our Universe allows life is not surprising for theists

    • Alexander Vilenkin (Physics professor at Tufts, Director of Institute of Cosmology): “These and many other examples show that our presence in the universe depends on a precarious balance between different tendencies--a balance that would be destroyed if the constants of nature were to deviate significantly from their present values. What are we to make of this…? Is it a sign of a Creator…?” [Many Worlds in One (Hill and Wang, 2007), 132.]
    • Paul Davies (Agnostic turned deist, physics professor at Cambridge, etc.): “The delicate fine-tuning in the values of the constants, necessary so that the various different branches of physics can dovetail so felicitously, might be attributed to God. It is hard to resist the impression that the present structure of the universe, apparently so sensitive to minor alterations in the numbers, has been rather carefully thought out.” [God and the New Physics (Simon & Schuster, 1983), 189.]
    • Freeman Dyson (Mathematician, physicist, famed contributor to quantum mechanics & solid-state physics): “The more I examine the universe and the details of its architecture, the more evidence I find that the universe in some sense must have known we were coming.” [Disturbing the Universe (Harper & Row, 1979), 250.]
    • John Polkinghorne (Cambridge particle physicist): “The laws of nature were just exactly finely-tuned to allow that to happen, it couldn’t happen in just any old world. That’s a very striking fact about the world, and again, you can ask yourself 'is that a happy accident, or is the sign of some divine purpose behind the very fruitful history of the universe, that’s turned a ball of energy into the home of saints and mathematicians'.” [Interview with Robert Wright: Online]
    • Frank Tipler (Cosmologist, mathematical physics professor): “When I began my career as a cosmologist some twenty years ago, I was a convinced atheist. I never in my wildest dreams imagined that one day I would be writing a book purporting to show that the central claims of Judeo-Christian theology are in fact true, that these claims are straightforward deductions of the laws of physics as we now understand them. I have been forced into these conclusions by the inexorable logic of my own special branch of physics.” [The Physics Of Immortality (Doubleday, 1994), Preface.]
    • Fred Hoyle (Former atheist “greatly shaken” by fine-tuning; influential astrophysicist): “A common sense interpretation of the facts suggests that a superintellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question.” [“The Universe: Past and Present Reflections” Annual Review of Astronomy and Astrophysics (1982): 20:16.]
    • Arno Penzias (Nobel Prize in Physics): “Astronomy leads us to a unique event, a universe which was created out of nothing, one with the very delicate balance needed to provide exactly the conditions required to permit life, and one which has an underlying (one might say ‘supernatural’) plan.” [Cosmos, Bios, and Theos: Scientists Reflect on Science, God, and the Origins of the Universe, Life, and Homo Sapiens, eds. Margenau and Varghese (Open Court, 1992), 83.]
    • George Greenstein (Astronomy professor at Amherst): “It was not for some time that I was able to place my finger on the source of my discomfort. It arises, I understand now, because the contention that we owe our existence to a stupendous series of coincidences strikes a responsive chord. That contention is far too close for comfort to notions such as: We are the center of the universe. God loves mankind more than all other creatures. The cosmos is watching over us. The universe has a plan; we are essential to that plan.” [“The Symbiotic Universe: Life and Mind in the Cosmos” (William Morrow & Co, 1988), 25-26.]
“Yes, after all…

  • Constants of physics are fine-tuned

    Various constants of physics are fine-tuned for permitting life.

    This page analyzes five examples:

    • The cosmological constant
    • [The strength of gravity]
    • The strong and electromagnetic force]
    • The weak force]
    • [The proton-neutron mass difference]
    1. “‘To say a constant of physics is fine-tuned is to say that its life-permitting range of values is minuscule relative to the comparison range of possible values which are ‘epistemically illuminated,’ i.e. the range for which we can determine whether the value is life-permitting or not.'” 2.1. Robin Collins discusses these in detail, along with carbon production in stars, in his “The Evidence for Fine-Tuning,” in God and Design: The Teleological Argument and Modern Science, ed. Manson, (Routledge, 2003), 178-199. He devotes five dense pages to covering the cosmological constant in “The Teleological Argument: An Exploration of the Fine-Tuning of the Universe” in The Blackwell Companion to Natural Theology eds. Craig and Moreland (Blackwell, 2009), 215-220.] Collins's forthcoming “The Well-Tempered Universe” will be the definitive source on all things fine-tuning.

  • Initial conditions of the Universe are fine-tuned

    Various initial conditions of physics are fine-tuned for permitting life:

    This article analyzes five examples:

    • [Initial mass-density of the Universe]
    • [Initial distribution of mass-energy]
    • [Big bang “explosion” strength]
    • [Strength of density perturbations yielding star formation]
    • [Density-ratio of radiation to normal matter]
    • [More]

  • Laws of physics are fine-tuned

    Various laws of physics are fine-tuned for permitting life:

    A forthcoming page will analyze these five examples:

    • Gravity1
    • Strong nuclear force
    • …[Electromagnetic force
    • Bohr’s quantization rule
    • …Pauli exclusion principle
    1. Note: Or something relevantly similar to gravity (i.e. a universal attractive force). This same proviso applies to all the examples.
“No, after all…

  • “Changes just yield other forms of life”

    A weird disproportional creature with eyes and wings and a segmented body.

    The Universe is only fine-tuned for permitting life as we know it.1 (Supposing otherwise is a kind of “carbon chauvinism.”)2

    By way of response, however, the Universe has to be fine-tuned in several respects in order to permit any kind of life (and certainly intelligent life). Some tamperings prevent chemistry itself, or leave one with a universe consisting of only the lightest elements (hydrogen and helium).3, 4

    1. For examples of individuals raising this objection to fine-tuning:

      • Douglas Adams (on “puddle thinking”): “This is rather as if you imagine a puddle waking up one morning and thinking, ‘This is an interesting world I find myself in--an interesting hole I find myself in--fits me rather neatly, doesn’t it? In fact it fits me staggeringly well, must have been made to have me in it!’ This is such a powerful idea that as the sun rises in the sky and the air heats up and as, gradually, the puddle gets smaller and smaller, it’s still frantically hanging on to the notion that everything’s going to be alright, because this world was meant to have him in it, was built to have him in it; so the moment he disappears catches him rather by surprise.” [Speech at Digital Biota, Cambridge (1998).]
      • Victor Stenger: “life as we know it would not exist if any one of several of the constants of physics were just slightly different, [we] cannot prove that some other form of life is feasible with a different set of constants. Anyone who insists that our form of life is the only one conceivable is making a claim based on no evidence and no theory.” [Has Science Found God? (Prometheus, 2003), 156.]
      • Sean Carroll: “As skeptical as I am about the ability of physicists to accurately predict gross features of a universe in which the laws of nature are different, I am all the more skeptical of the ability or biologists (or anyone else) to describe the conditions under which intelligence may or may not arise. (Cellular automata, the simple discrete systems popularized by Wolfram and others (Stephen Wolfram, A New Kind of Science (Champaign, IL: Wolfram Media, 2002)., provide an excellent example of how extreme complexity can arise out of fundamentally very simple behaviors.)" [“Why (Almost All) Cosmologists are Atheists” (2003) online at infidels.org ]
      • Michael Ikeda and Bill Jefferys: “Indeed, virtually nothing is known about the possibility of life in universes that are very different from ours. It could well be that most universes could support life, even if it is of a type that is completely unfamiliar to us. To assert that only universes very like our own could support life goes well beyond anything that we know today.” [“The Anthropic Principle Does not Support Supernaturalism” (2004) online at talkreason.org]

    2. A popular alternative put forward is silicon-based life (the next element in carbon's group in the periodic table), but even this seems implausible: “Only two of the natural atoms, carbon and silicon, are known to serve as the back-bones of molecules sufficiently large to carry biological information… [but] unlike silicon [Carbon] can readily engage in the formation of chemical bonds with many other atoms, thereby allowing for the chemical versatility required to conduct the reactions of biological metabolism… [moreover] large silicon molecules are monotonous… [moreover] the electronic properties of carbon, unlike silicon, readily allow the formation of double or even triple bonds with other atoms." [Norman R. Pace “The universal nature of biochemistry” Proceedings of the National Academy of Sciences 98 (2001): 808.] As noted in a Scientific American article by Alexander Jenkins and Gilad Perez, Silicon-based life is very dubious; "no silicon-based molecules of any significant degree of complexity are known to exist.” [Online]
    3. See:

      • Stephen Hawking: “Of course, there might be other forms of intelligent life,… Nevertheless, it seems clear that there are relatively few ranges of values for the numbers that would allow the development of any form of intelligent life. Most sets of values would give rise to universes that, although they might be very beautiful, would contain no one able to wonder at that beauty.” [A Brief History of Time (Bantam, 1988), 125.]

    4. Bradley Monton speculates briefly about a brain made of hydrogen atoms (Seeking God in Science (Broadfview, 2009) 83.), but the following judgment seems soberer:

      Graham Oppy (Athest philosophy professor at Monash University): “in a universe in which there is nothing but hydrogen, there plainly won't be life as we know it, and moreover, it seems plausible to suppose that there won't be any other kind of life either.” [Arguing about Gods (Cambridge, 2009) 201.]

  • “The constants can't be different (T.O.E.)”

    Some theory of everything fixes the constants etc. such that there are no free parameters (e.g. M-theory, where it is perhaps naturally impossible for them to be different than what they are).

    So what if that was true? That would just push the improbability up to another level, like the proverbial ruck in the carpet. If the values of the constants are necessary for a given law, that raises the question of why a law like that exists. I.e why should the law be such that it can only produce a fine-tuned system when there are many other possible laws that could exist instead that are not likely to produce a fine-tuned system. To illustrate, imagine some Grand Unified Theory resulted in Jesus uniquely walking on water and resurrecting after his crucifixion. Far from explaining away the evidence, this would obviously just kick the problem upstairs to the superlaw itself.

    • Bernard Carr and Martin Rees (Astrophysicists, professors): “…even if all apparently anthropic coincidences could be explained [in terms of some grand unified theory], it would still be remarkable that the relationships dictated by physical theory happened also to be those propitious for life” [“The Anthropic Cosmological Principle and the Structure of the Physical World” Nature 278 (1979): 612.].

  • 99% of the Universe is hostile to life

    Over 99% of the Universe’s area is uninhabitable.1

    Consider two arguments:

    • Virtually all of its locations do not contain breathable air.
    • Virtually all of its locations are too hot/cold for us to live in.

    This is relevant because if 99% of the Universe is hostile to life (unaided by technology), then the Universe is not very fine-tuned for life.

    But so what if it is 99% hostile?…

    • Our universe is still 100% life-permitting (our physics 100% allows for life).2
    • If this is evidence against theism, it’s off topic.3
    1. This is a commonly proposed counter-argument. For example:
      • Neil deGrasse Tyson: “Most places in the universe will kill life instantly - instantly! People say, ‘Oh, the forces of nature are just right for life.’ Excuse me. Just look at the volume of the universe where you can't live. You will die instantly.” [“STUPID Design” Beyond Belief conference (2006)]
    2. The physics of this universe still obviously permits life (or else how are you reading this), and 99.99% of other possible universes don’t. The % of locations where we could live without technology is irrelevant; as long as the universe permits life in any location (which it does) and that “permitting” depends on fine-tuning (i.e. where changing the constants etc. would likely result in a universe that would not permit life anywhere in it.)
    3. Someone might point to the fact we cannot live in 99% of the universe, and say this is unlikely if God exists. The argument insists that, if God exists, God would surely design the universe such that most of it is habitable. (Think of a house designer who designs a house with only 1% of livable space.) By way of response, however, “space” can have more purpose than just livability. So as long as there is more than enough space to live in (which there is), there is no reason to expect all space to be habitable. An omnipotent God's resources are limited not with respect to how much space He creates. So, if space can have any other value aside from habitation, then extra uninhabitable space it is not at all surprising on theism. Sure enough, space plausibly has aesthetic value, worship-inducing value, and an abundance of scientific value in terms of being required for a simple Big Bang universe which through generations of stars is ultimately able to a life-friendly planet. (This is plausibly the most elegant way to bring about a life-permitting planet and many argue that alternative methods would in large part frustrate the possibility of historical cosmology.)

  • “New knowledge will eliminate fine-tuning”

    The ostensible fine-tuning in the Universe will wash away with new knowledge.1 And if it goes away with know knowledge, then it will ultimately end up false that the universe is fine-tuned for life.

    By way of response, however, physicists do not seem to think the fine-tuning will wash away, especially not all of it (any more than we think that all the evidences for an old Earth, or for plate tectonics, will wash away). For example,

    • John Leslie (Non-theist philosopher of science, professor at Guelph): “In a book of mine, Universes (1989), I made a long list of such claims about fine-tuning. …What is impressive, I suggest, is not any particular one of the claims about fine-tuning, but the large number of claims that seem plausible, and the consequent implausibility of thinking that every single claim is erroneous.” [“The Meaning of Design” in God and Design Ed. Manson (Routledge, 2003), 56.] (e.g. “clues heaped upon clues can constitute weighty evidence despite doubts about each element in the pile” [Universes (Routledge, 1989), 300.])

  • One can't normalize across an infinite range

    If there are an infinity of possible values any given constant could take, then the idea of a life-permitting range being "improbable" becomes incoherent.

    After all, the probabiltiy of landing in the life-permitting range would always be 1 over infinity, which can be interpreted as either zero or undefined. Either way, it's a problem. It being undefined is a problem because then the fine-tuning argument from probability would go out the window; we literally can't say it is both undefined and improbable that a life-permitting universe would exist. And it can't be zero, because that is counterintuitive and moreover all instances of fine-tuning would then be equally improbable regardless of scientific discoveries, which is supposed to be the vital new datum giving rise to the fine-tuning argument.

    This matters because, truly, there are an infinite range of possibe values any given constant could take. The whole argument thereby becomes incoherent.

    But no,

    • So-called “countable additivity” (i.e. “finite additivity” applied to the infinite) is false, at least for epistemic probability (which is the kind of probability this argument relies on).1

    But so what?

    • The range is not infinite.2
    1. Many mathematicians have pointed out problems with countable additivity.
      • Robin Collins: “This latter principle, however, has been very controversial for almost every type of probability, with many purported counterexamples to it. Consider, for example, the following situation. Suppose that what you firmly believe to be an angel of God tells you that the universe is infinite in extent and that there are a countably infinite number of other planets with civilizations on each planet. Finally, the “angel” tells you that within a billion miles of one and only one of those planets is a golden ball 1 mile in diameter and that it has delivered the identical message to one person on each of those planets. Finally, you decide on the following arbitrary numbering system to identify the planets: you label Earth 1, the planet that is closest to Earth 2, the planet that is next farther out 3, and so forth. Since within current Big Bang cosmology an infinite universe would have no center, there is nothing special about Earth’s location that could figure into one’s probability calculation. Accordingly, it seems obvious that, given that you fully believe the “angel”, for every planet k your confidence that the golden ball is within a billion miles of k should be zero. Yet this probability distribution violates countable additivity. One cannot argue that the scenario I proposed is in any way self-contradictory, unless one wants to argue that an infinite universe is self-contradictory.... [moreover] in some cases it would be irrational to remain agnostic. For example, it would be irrational for a billionaire who received the aforementioned message to spend millions, or even hundreds, of dollars in search of the golden planet, even if it were entirely rational for him to believe what the “angel” told him; it would even be irrational for him to hope to discover the planet. This is radically different than cases where people are legitimately agnostic, such as perhaps about the existence of extraterrestrials or the existence of God; for example, it seems rationally permitted at least to hope for and seek evidence for the existence of extraterrestrials or God. The implausibility of being agnostic in the ‘golden planet case’ is further brought out when one considers that if the billionaire were told that the universe was finite with exactly 10^10,000 planets with civilizations, clearly he should be near certain that the golden planet is not near Earth. But, clearly, if the billionaire is told that there are even more planets – infinitely many – the billionaire should be at least as confident that the planet is not near Earth; and, certainly, it should not become more rational for him to search for it than in the 10^10,000 planets case, as it would if he should switch to being agnostic.” [The Teleological Argument," in The Blackwell Companion to Natural Theology (Blackwell, 2019), 250.]
    2. Luke Barnes: "Firstly, if one agrees with the usefulness of the Little Question—that we should try to address