Fine-Tuning

Some constants have bounded ranges for stable atoms, nuclei, and stars. Popular diproton, 10^120, and Penrose probability claims fail; the evidence does not identify God.

Draft:  August 2026

"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." — Fred Hoyle, 1981.  Hoyle was not a Christian and never became one.1

"There is no 'diproton disaster'." — Luke Barnes, 2015, retiring the single most quoted fine-tuning argument in Christian apologetics.  Barnes is a Christian and the argument's leading academic defender.2

"To retreat to the point where the argument rests on unargued intuitions is to deprive it of anything more than devotional significance." — Timothy McGrew, Lydia McGrew and Eric Vestrup, 2001, in the flagship journal of academic philosophy.  All three are Christians.3

Summary

The numbers in the laws of physics could have been different.  Change some of them by a little and you get a universe with no atoms heavier than hydrogen, or no stable protons, or no stars that last long enough to matter.  This is not a religious claim.  It is a large and mostly uncontroversial body of physics literature, and the people who built it are mostly not Christians.

That much is real.  Much of what apologetics does with it is not.

This article sorts every claim into three tiers, because the tiers behave very differently and almost nobody separates them:

  1. Constants and laws. True under any cosmology. If the big bang never happened, these are untouched. This is where the argument is strongest and where this article spends most of its time.
  2. The initial conditions of the hot big bang. Flatness, the horizon problem, the initial entropy, the size of the primordial ripples. These are only questions because the standard model says the universe began hot and dense and evolved under general relativity. Reject that model and most of them do not survive.
  3. The fine-tuning of the repairs. The big bang had problems. Inflation was invented to fix them. Inflation turns out to need extraordinary fine-tuning of its own. This article argues that tier three must never be used as evidence for God, and the reasoning is given in full below.

What this article concedes before it argues anything

A skeptical reader deserves the bad news first, and there is a lot of it.  Every item here is sourced in the body of the article.

  • The diproton argument is dead. For forty years the flagship example was that a slightly stronger nuclear force would bind two protons together and sterilise the universe. It was refuted in 2015 by Luke Barnes — a Christian, and the most credentialed academic defender the fine-tuning argument has. His paper's abstract says "There is no 'diproton disaster'."2 Fred Adams files the same claim under "myths and unnecessary constraints."4 Any site still running this argument straight is a decade behind.
  • "One part in 10120" is not what people think it is. That famous figure for the cosmological constant is the gap between a quantum-field-theory estimate and the measurement. It is not the width of the window that permits life. Steven Weinberg's own anthropic ceiling is of order a hundred times the observed value — roughly two orders of magnitude, not 120.5
  • Penrose's 1-in-1010123^ is not the probability of a life-permitting universe, and Penrose rejects the anthropic reading of it in print: the anthropic principle "is virtually no help to us whatever in resolving our conundrum."6
  • The electron-to-proton mass ratio is not fine-tuned. The often-quoted 1:1836 claim does not survive: the constraint is on a hierarchy, it is about five orders of magnitude wide, and it admits a second solution with the ratio inverted.7
  • Hoyle did not predict the carbon resonance because life needs carbon. His 1954 paper never mentions life. The anthropic version of the story is a documented myth, traced in detail by a historian of science in 2010.8
  • The flatness problem is disputed inside mainstream cosmology, in blunt language. One paper calls the standard argument "completely bogus"; another calls it "an illusion."910
  • The strongest technical objection to the whole argument was published by three Christians in Mind, and it kills the "the odds against this are one in 10N" form of the argument outright.3
  • The strongest theological objection was published by an orthodox Christian philosopher at Princeton.11 Luke Barnes has replied in print — twice — and the exchange is treated in full below.
  • Our universe is not the most life-friendly universe possible. Fred Adams lists six specific ways it could be improved.4

None of that is fatal.  What is left is still substantial, and the last section says exactly what it is.  But an argument that has to hide its own literature is not worth making, and a reader who finds these facts elsewhere after reading a version that concealed them has been given every reason to distrust everything else on this site.

What survives

The short version:  the fine-tuning that holds up best is the fine-tuning that has nothing to do with cosmology.  It is about whether nuclei stick together, whether atoms are stable, and whether stars can burn slowly.  Those are facts about the laws, not about a cosmic history.  Not because the cosmology-free claims have been safe from attack — the diproton and the triple-alpha percentages were both attacked with stellar modelling and both fell.  The pattern is narrower and more interesting:  when a claim about the laws falls, something about the laws replaces it — a hierarchy, a configuration, a wider but still bounded window.  When a claim about cosmic initial conditions falls, or its model is rejected, nothing is left.

That pattern is real, and it points somewhere useful.  It also happens to be exactly the material a reader who doubts the big bang can use without contradicting himself.

Everyone agrees on the data

It is worth being precise about the consensus, because apologetics routinely overstates it in one direction and skeptics understate it in the other.

The physics is not in dispute.  Luke Barnes reviewed the technical literature for Publications of the Astronomical Society of Australia in 2012 and named twenty-five scientists "of varying religious persuasions, who accept that the universe is fine-tuned for life."12  Defending that review on his blog the following year, he added that of the two-hundred-plus papers he had read, "I can only think of a handful that oppose this conclusion, and piles and piles that support it."13  Paul Davies, who is neither a theist nor an atheist, wrote in the International Journal of Astrobiology that "there is now broad agreement among physicists and cosmologists that the universe is in several respects 'fine-tuned' for life."14

What is in dispute is what it means.  Here is how the most-quoted witnesses actually sort:

Witness Position on God Accepts the fine-tuning? Their own explanation
Fred Hoyle Not a theist; proposed a cosmic superintellect Yes, emphatically A superintellect, and panspermia
Freeman Dyson Non-believing Christian Yes "Consistent with the hypothesis that mind plays an essential role" — explicitly not a proof
Stephen Hawking Atheist Yes, "very finely adjusted" Divine purpose or the strong anthropic principle; later, the multiverse
Roger Penrose Atheist Yes A new law of physics — the Weyl Curvature Hypothesis
Martin Rees Non-believer Yes; names six numbers The multiverse, explicitly not a Creator
Paul Davies Neither theist nor atheist For the building blocks A "life principle"
Alexander Vilenkin Not stated Yes Anthropic selection in a multiverse
Lee Smolin Not stated Yes, about thirty numbers Cosmological natural selection; rejects both God and the anthropic multiverse
Charles Townes Protestant; accepts evolution, rejects young-earth creationism Yes Design, including through evolution
Geraint Lewis Not a theist Yes — co-wrote the standard book on it The multiverse
Luke Barnes Christian Yes — co-wrote the same book Theism, as a rival to naturalism rather than to science

Nobody in that list disputes the data, and only two of the eleven draw a theistic conclusion from it.  ("Not stated" appears where no primary self-description exists — a discipline explained on the companion quotes page.)  That is a stronger thing to be able to say than "scientists agree the universe was designed," and it is the thing the sources will actually bear.  The disagreement is entirely downstream of the physics.

Two of them wrote a book together about it.  Geraint Lewis and Luke Barnes — an unbeliever and a Christian — co-authored A Fortunate Universe for Cambridge University Press in 2016, agreed on every number in it, and then split in the final chapter.  Lewis takes the multiverse.  Barnes takes God.  The book ends with the two of them walking off in opposite directions, which is the honest picture of this entire field.15

Why the three tiers matter

Suppose a reader doubts the big bang.  Plenty of people do, for reasons ranging from good to bad, and this site will eventually publish its own assessment of the model.  What happens to the fine-tuning argument?

The answer depends entirely on which fine-tuning you mean, and the difference is enormous.  Robin Collins already sorts the evidence into laws, constants, and initial conditions — that split is not new.  What appears to be new here is the question this article asks of the sorting:  which of these claims survives if big bang cosmology is false — and a third category the literature does not name at all, the fine-tuning of the repairs.

Tier one is about the laws themselves.  Whether a proton is stable.  Whether carbon nuclei hold together.  Whether atoms can form molecules.  These questions have the same answers in a big-bang universe, a steady-state universe, and a universe created last Thursday.  You can check them with a particle accelerator.  Nothing about them assumes a cosmic history.

One caveat, stated here rather than buried:  several of the tightest tier-one bounds are stellar — they assume stars burning steadily for hundreds of millions to billions of years.  That assumption is independent of how the universe began, but it is not independent of deep time, and a reader who rejects deep time should weight those rows accordingly.  The bounds that need nothing beyond a laboratory are the nuclear-stability ones:  whether hydrogen exists, whether heavy nuclei bind, whether atoms are stable, how many dimensions there are.

Tier two is about the state the universe started in.  "The density was within one part in 1060 of the critical value at the Planck time" is not a fact you can check in a laboratory.  It is a number computed by taking today's measurements and running the standard model backwards fourteen billion years.  Change the model and the number changes or disappears.

Tier three is about the machinery invented to fix tier two, and it is where the reasoning goes badly wrong.

Here is the trap, stated plainly.  The standard big bang model had three well-known problems in the 1970s: the universe was too flat, too uniform across regions that had never been in contact, and should have been littered with magnetic monopoles that nobody could find.  Inflation was proposed in 1981 to solve all three.16  Inflation then turned out to require its own fine-tuning — of the inflaton potential, and of the conditions needed to start inflation at all.

So the sequence runs: the model has a problem, a mechanism is invented to fix it, the fix needs improbable settings, and the improbability of the fix is then presented as evidence for God.

This article will not run that argument, and the reason should be stated carefully rather than shouted.  A defender could reply that the improbability attaches to the observations — a universe smooth across disconnected regions, flat to half a per cent — which are real whether or not inflation is the right mechanism, and that if every known naturalistic mechanism for producing them is itself improbable, a comparative design argument gets exactly what it needs.  That reply is not stupid, and this article does not claim to have refuted it.  What it claims is narrower and two-fold.  First, the improbability of an undetected field's potential function is far weaker evidence than the improbability of a measured constant, because nothing anchors it:  if the patch is unlikely, the live first conclusion is that the patch — or the model that needs it — is wrong.  Second, and specific to this site:  an argument that presupposes the standard cosmological model is not one this site may run while preparing to publish a critique of that model, and any apologist who elsewhere attacks the big bang because it needs inflation may not also bank inflation's improbability as design evidence.  Consistency costs something, and this is where it is paid.

Tier one: the constants and the laws

This is the strongest material, and it should be led with rather than buried.  It is also the material a reader who rejects the big bang can use without contradicting himself.

Lead with the hierarchies, not with the sensitivities

The most robust result in this field is not that some constant sits in a razor-thin slot.  It is that the constants are separated from each other by vast, unexplained gaps, and that those gaps are required.

Fred Adams is the right witness here.  He is an astrophysicist at Michigan who draws no design inference and has stated no religious position, and in 2019 he published the definitive quantitative survey of the whole subject — one hundred and eleven pages in Physics Reports.4  His project was largely deflationary: he went looking for how much room the parameters actually have, and mostly found more than apologists claim.  And he concluded:

Although they represent a significant problem for particle physics theories, the observed hierarchies of the fundamental parameters are a distinguishing feature of the cosmos, and extreme hierarchies are required for any universe to be viable:  The strength of gravity can vary over several orders of magnitude, but it must remain weak compared to other forces so that the universe can evolve and produce structure, and stars can function.4

Gravity is about 1036 times weaker than electromagnetism.  Adams' own analysis says that ratio must exceed roughly 1032 for any astrophysical structure at all.4  That is a real constraint, derived by a skeptic, and it does not depend on cosmology.

Adams also concludes something that cuts directly against the popular emphasis:

The limiting feature for a viable universe — including ours — is not the astrophysical engines that synthesize heavy elements and generate energy, but rather the parameters of particle physics that allow for the existence of stable nuclei.4

Particle physics binds harder than astronomy.  That is precisely the tier-one claim.

The light quark masses

The tightest of the twelve physical parameters in Adams' summary table is the down quark mass, which he confines to 0.85 decades — a factor of about seven.4  This is his own figure, from his own deflationary analysis.

Thibault Damour and John Donoghue attacked the same region with real nuclear binding calculations in 2008 and found that the sum of the up and down quark masses can rise by at most 64% before heavy nuclei fall apart entirely.17

The reason this matters is worth stating in plain terms.  If the down quark were about one MeV lighter, protons inside hydrogen atoms would capture their own electrons and turn into neutrons.  There would be no hydrogen.  No water, no hydrocarbons, no organic chemistry of any kind.  Adams — again, the skeptic — describes this as the most confining constraint he found, and notes that our universe sits close to the limit.4

None of this involves the big bang.

The Higgs vacuum expectation value

The Higgs field sets the mass of every fundamental particle.  Damour and Donoghue's window is 0.39 to 1.64 times its actual value — the upper end at 95% confidence — holding the Yukawa and gauge couplings fixed.17  Outside it you get either no heavy nuclei or no hydrogen.  A factor of four.  One honesty note:  at fixed Yukawa couplings the quark masses scale directly with the Higgs value, so this window and the +64% quark-mass bound above are one result stated in two currencies, not two independent constraints.  The parameter table below lists them as a single row.

There is a separate and much more dramatic fact about the Higgs, and the two must not be merged.  The Higgs mass-squared parameter is about 10-34 in Planck units — Agrawal and co-authors put it at "about 33 ± 1 orders of magnitude smaller than the natural scale" (equivalently, the vacuum expectation value itself sits seventeen orders of magnitude below the Planck mass).18  That is the hierarchy problem, and it is a puzzle about why quantum field theory does not do what it appears it should.  It is not a statement about what life requires.  Apologetics literature routinely quotes that 10-34 as though it were a life-permitting range.  It is not, and a physicist will catch it immediately.

There is also a quote-mine circulating on this paper that this site had in its own notes.  Agrawal, Barr, Donoghue and Seckel are usually quoted up to the point where they describe nuclei falling apart at large Higgs values.  In the small-v section of the same paper they write that they "see no reason why values of v/v₀ < 1 could not support life" — adding that in that regime they "can no longer reliably estimate the results of nucleosynthesis."18  So the constraint they establish is one-sided, the low end of the window is softer than tables imply, and part of what softens it is big bang nucleosynthesis.

Three spatial dimensions

Paul Ehrenfest showed in 1917 that in more than three spatial dimensions, planetary orbits and electron orbits are both unstable.19  In fewer than three, nothing complicated can happen — nerves cannot cross, and there is not enough room for structure.  Max Tegmark extended the argument in 1997 to cover the number of time dimensions, showing that with anything other than one, physics has no well-posed initial value problem and prediction becomes impossible.20

Tegmark states his own caveats, and this article states them too: the argument assumes the same basic form of physical law carries over to other dimensionalities, which is not obviously true.  There is also a published counterexample to half of it:  Scargill argued in 2020 that life in two spatial dimensions may not be impossible, constructing planar analogues of gravity and of neural networks.21  The instability of orbits and atoms above three dimensions has no such challenge.

The carbon resonance — told correctly

This is the best-known example in the field and the story usually told about it is false.

Here is the true version.  In 1953 Fred Hoyle argued that stars could not produce the observed abundance of carbon unless there was a previously unknown energy level in the carbon-12 nucleus, at around 7.65 MeV.  He pushed a group at Caltech to look for it.  They found it, within months, essentially where he said it would be.  It is one of the most striking successful predictions in twentieth-century astrophysics.

The configuration involved is genuinely remarkable.  Beryllium-8 is unstable — it falls apart in about 10-16 seconds — but it is unstable by only 92 keV, which is just barely long-lived enough for a third helium nucleus to arrive and make carbon.  The carbon level sits 379 keV above the three-alpha threshold.  And a nearby level in oxygen-16 sits 43 keV below the carbon-plus-helium threshold, which is why the carbon that gets made is not immediately burned to oxygen.  Three separate nuclear coincidences, arranged so that a star makes both carbon and oxygen instead of neither or only one.

One of the three cuts both ways, and honesty requires saying so.  The 92 keV is small enough to make the triple-alpha process work — and small enough that Adams counts a change of that size as one of the ways our universe could have been made more habitable, since a stable beryllium-8 would open a second carbon-making channel and remove the need for the resonance altogether.  The coincidence with no such escape is the oxygen one:  if the oxygen-16 level sat 43 keV higher, the carbon would be burned away as fast as it was made.

Now the corrections, and there are three.

Hoyle was not reasoning from life.  His 1954 paper does not mention life once.  The historian Helge Kragh traced this story in 2010 and titled his paper "An anthropic myth."8  The inference ran from the observed cosmic abundance of carbon to nuclear structure.  As Lee Smolin pointed out, the argument would work identically for an element nothing living needs — the "carbon is necessary for life" premise does no work at all.12  Barnes and Lewis concede the same point in their own book.15

The precision claims have been walked back, repeatedly, by the people who made them.  In 2000, Oberhummer, Csótó and Schlattl published in Science that a change of 0.5% in the strong force would wreck carbon or oxygen production.22  That figure is in a thousand apologetics articles.  In 2004, the same group revisited it with better stellar modelling and concluded the anthropic significance "might be of considerably less" importance than they had said.23  Almost nobody noticed.  A 2013 nuclear lattice effective-field-theory calculation put the tolerance at 2-3% in the quark masses — 0.7% on its own worst-case reading — and stated that its error bars were compatible with there being no fine-tuning at all, while adding that beyond that range "the anthropic principle appears necessary."24  A 2019 stellar-modelling study widened the allowed shift in the resonance energy to somewhere between −300 and +500 keV.25

Adams summarises the resulting position bluntly: measured against the spacing of nuclear energy levels, the chance of landing close enough to the resonance is "about 1 part in 4."4

The trend is monotonic, and it runs against the argument.  Every improvement in the stellar physics since 2000 has widened the window.  This article states that rather than quoting the year 2000 and stopping.

What survives is the configuration, not the percentage.  Even on Adams' widened window there is still a window, and the 43 keV near-miss in oxygen-16 remains striking.  The tier assignment holds on the physics:  the argument is about stellar helium burning, stars make their own helium from hydrogen, and so the argument needs no primordial helium abundance — which is why Hoyle, who rejected the big bang to the end of his life, could build it while arguing that the elements are made in stars rather than in a primordial fireball.  One honest caveat:  the published sensitivity studies all run their stellar models with big-bang-derived starting compositions, though nothing about the argument's logic requires that.4

Arguments this article does not make

A reader who watches a site retire its own best-known talking points has good reason to trust what is left.  Three retirements follow.

The diproton disaster

The claim, from Freeman Dyson in 1971 and repeated everywhere since: if the strong nuclear force were a few per cent stronger, two protons would bind into a "diproton," all the hydrogen in the universe would burn to helium in the first minutes after the big bang, and there would be no water and no long-lived stars.

Two separate groups have now taken this apart.  MacDonald and Mullan ran the big bang nucleosynthesis calculation properly in 2009 and found that hydrogen survives even with the strong force increased by close to 50%; their conclusion was that "anthropic limits on the strong force strength from BBN are indeed weak."26  Then Barnes ran the stellar half in 2015 and found that stars in a diproton-binding universe have "remarkably familiar masses, luminosities, surface temperatures and lifetimes."2  His abstract states the result in four words: "There is no 'diproton disaster'."2

Note who did this.  Barnes is a Christian and the argument's chief academic defender.  Adams independently lists it under myths.4  And the refutation was a trade, not a pure loss:  Barnes' same paper shows that in diproton-binding universes all stars burn out within millions of years unless the gravitational coupling is below about 10-30 — a tighter constraint than the one that fell.  Ours is 5.9 × 10-39.2

There is a second observation that matters more for this article than the refutation.  The argument had two halves, one in each tier, and both are gone:  MacDonald and Mullan took the big-bang half, Barnes took the stellar half.  What remains is a narrower tier point — the form that sounded strongest, Dyson's and Barrow and Tipler's "during the early stages of the Big Bang" version, was always a tier-two argument, so a reader who rejects the hot big bang never had it to lose.

What survives on this axis is the opposite bound: if the strong force were weaker, the deuteron would come apart and the first step of stellar fusion would fail.  Barnes and Lewis argued in 2017 that this is the sharpest boundary in the whole parameter space.27  Adams and Grohs disputed it the same year, arguing that stars could still work through gravitational contraction and the CNO cycle.28  Two teams, in print, disagreeing.  This article reports that rather than picking the convenient winner.

The electron-to-proton mass ratio

The claim that 1:1836 is finely tuned, usually sourced to apologetics websites, does not survive.  The real constraint is on the hierarchy — the electron must be much lighter than the proton for solids to be stable — and Tegmark showed that the relevant condition is symmetric: it "also allows replacing β by 1/β."7  Adams gives the allowed range as about five decades, with a second habitable island besides.4  The claim as usually stated is simply false.

Carter's convective-star coincidence

Brandon Carter argued in the 1970s that a coincidence between gravitational and electromagnetic couplings was needed to put stars on the convective/radiative boundary, which was thought necessary for planet formation.  Exoplanet surveys have since established that planet formation does not depend on stellar convection at all.  Adams lists it among the constraints that are simply not needed.4

The parameter table

Values, ranges, and — the column that matters for this article — whether the claim survives if the big bang is false.

Parameter Claimed range or figure What breaks outside it Tier Survives without the big bang? Source
Gravity vs electromagnetism (α/α_G) Ratio must exceed ~1032; observed 1036 No astrophysical structure of any kind 1 Yes Adams 2019
Down quark mass 0.85 decades (factor ~7) Hydrogen atoms capture their own electrons; no organic chemistry 1 Yes Adams 2019
Light quark masses / Higgs vev (one result, two currencies) m_u+m_d ≤ +64% (95% CL); equivalently 0.39 – 1.64 × the observed vev at fixed Yukawas Heavy nuclei unbound above; no hydrogen below 1 Yes Damour & Donoghue 2008
Fine-structure constant α ~4 decades total; α ≲ 1/3 Relativistic electrons; no large nuclei 1 Yes Adams 2019
Spatial dimensions Exactly 3 Orbits and atoms unstable above 3; too simple below 1 Yes Ehrenfest 1917; Tegmark 1997
Time dimensions Exactly 1 No well-posed initial value problem 1 Yes Tegmark 1997
Hoyle resonance energy −300 to +500 keV Stars make carbon or oxygen, not both 1 Yes Huang, Adams & Grohs 2019
Oxygen-16 level vs carbon + helium Sits 43 keV below threshold Carbon immediately burned to oxygen 1 Yes Hogan 200029
Strong force, upper bound (diproton) Claim refuted Nothing — stars remain stable and long-lived 2 (BBN form) No — and refuted anyway Barnes 2015
Strong force, lower bound (deuteron) −4% to −9%, model-dependent (Barnes & Lewis use 5–8%) First step of fusion fails — contested 1 Partly Barnes & Lewis 2017; disputed by Adams & Grohs 2017
Cosmological constant — the problem QFT estimate exceeds observation by 1041–10120 — a naturalness mismatch, not a life-permitting range Nothing directly; it is an unexplained mismatch 1 (calculation) / 2 (the measured value) Only the calculation Weinberg 1989
Cosmological constant — the anthropic bound ≲ of order 100× observed (Rees: 5–10×) No galaxies form 2 No Weinberg 1989; Martel, Shapiro & Weinberg 1998
Horizon / large-scale uniformity The sky at last scattering divides into thousands of causally disconnected patches at the same temperature Requires unexplained uniformity 2 No Carroll & Tam 2010
Flatness (Ω at the Planck time) 1 part in 1060 — contested within mainstream cosmology Universe recollapses or disperses 2 No Dicke & Peebles 1979; disputed by Helbig 2012, Carroll & Tam 2010
Initial entropy 1 in 1010123^ — a phase-space ratio, not a probability of life — 2 No Penrose 1989, 2006
Fluctuation amplitude Q ~10-6 to ~10-4 (Tegmark & Rees); ~10-6 to ~10-2 (Adams) No galaxies, or planets stripped from orbits 2 No — vanishes entirely Tegmark & Rees 1998; Adams 2019
Baryon-to-photon ratio η ~6 decades — 2 No — vanishes entirely Adams 2019
Inflaton potential and starting conditions ~0.1% of random potentials succeed — a model-space rate, not a life-permitting range Inflation never starts, never ends, or ruins the universe 3 No Tegmark 2005 via Barnes 2012; Carroll & Tam 2010

Two things about this table are worth saying out loud.

With one contested exception — the deuteron bound — every row that survives the loss of the big bang is about the laws themselves:  particle physics, nuclear physics, or the structure of spacetime.  Every row that vanishes is about cosmic initial conditions.  That is not a coincidence, and it is the organising fact of this whole subject.

The ranges are wider than apologetics usually admits.  Adams makes this point with a comparison the article has to answer rather than ignore:

Given that the concept of fine-tuning evokes the image of tuning the dials of a radio…  To find a particular radio station, the electronics must be accurate to about 1 part in 100…  Tuning a radio thus requires far more precision than tuning a universe.4

The reply is that Adams and Barnes are using different rulers, and neither ruler is obviously correct.  Adams measures how far a constant can move relative to its own value.  Barnes measures the life-permitting window against the theoretically available range — for a mass, everything from zero to the Planck mass.  On Adams' ruler the down quark has a factor of seven to play with, which sounds roomy.  On Barnes' ruler, the chemistry-permitting region of the up-down quark plane is a shard of order 10-40 of the available area.2

This is a genuine, unresolved methodological disagreement about how to measure.  This article says so rather than quietly choosing the flattering ruler.

Tier two: the initial conditions of the big bang

This section exists mainly to be honest about what it cannot support.

The cosmological constant

Empty space has an energy density.  Quantum field theory, applied naively, predicts a value enormously larger than what is measured.  How much larger depends entirely on where you cut the calculation off.  Cutting at the Planck scale gives the famous 120 orders of magnitude.  Weinberg himself, restricting to energies where the physics is actually tested, gives 1056;30 his 1989 review gives 41 decimal places for QCD alone.5

This mismatch is real and is genuinely one of the deepest unsolved problems in physics.  But be careful about which half of it survives without the big bang.  The quantum-field-theory calculation is tier one — it needs no cosmology.  The measured value it is compared against is not:  the cosmological constant is measured only through the expansion history — supernova distances, baryon acoustic oscillations, the microwave background — all interpreted inside the standard model.  There is no laboratory measurement of Λ.  A reader who rejects the model keeps the embarrassing calculation and loses the number it is embarrassed by.  So the mismatch, like the anthropic bound, is tier two, and this article builds on neither.

What does not survive is the popular version.  "The cosmological constant is tuned to one part in 10120 for life" is a claim Weinberg never made and never calculated.  His anthropic bound — the point past which galaxies cannot form — he states as "say, 100" times the cosmic matter density, with his careful formula giving about 400 times at a formation redshift of 4; converted to today's measured dark-energy density that is of order a hundred times the observed value, and Martin Rees puts the galaxy-precluding threshold at only 5-10 times.5  Two orders of magnitude at most, not 120.  The two famous numbers only look related because the observed value happens to sit near the anthropic ceiling.

And that bound is computed from structure formation inside an expanding universe, which makes it tier two.  Reject the model and the calculation goes with it.

There is a further complication that has developed since 2025, and it is worth stating because it cuts against everyone.  The DESI survey's second data release reported that the data prefer a dark energy whose strength changes over time rather than a fixed cosmological constant, at somewhere between 2.8 and 4.2 standard deviations depending on which supernova sample is used.31  If that holds up, then the quantity everyone has been calling finely tuned is not a constant at all, and the tuning claim would have to be restated from scratch.  It may well not hold up:  the Dark Energy Survey's own team recalibrated their supernovae — in a late-2025 preprint published in MNRAS in 2026 — and cut their headline figure from 4.2σ to 3.2σ, describing what remained as "only a weak preference."32  A 2026 review summarises the position as "a dataset-dependent indication rather than a settled discovery."33

That is worth watching for a reason beyond dark energy.  The recent history of cosmology is full of tensions that looked like new physics and turned out to be calibration.  The S₈ tension between the microwave background and gravitational lensing was reported at three standard deviations in 2021 and was widely treated as a crisis; by 2025 the same collaboration reported agreement at 0.73σ, and said plainly that the change came from better redshift calibration rather than new physics.34  Any argument that leans on a live cosmological anomaly is borrowing against a loan that is often called in.

Flatness — concede this one

The standard claim is that the density of the early universe had to be within one part in 1060 of the critical value.  It is quoted constantly.

It is also disputed inside mainstream cosmology in unusually direct language.  Phillip Helbig's 2012 paper in MNRAS calls the standard argument "completely bogus."9  Carroll and Tam, applying a natural measure on the space of solutions to Einstein's equations, conclude that "the flatness problem is an illusion."10  Evrard and Coles had argued in 1995 that it rests on an inappropriate choice of prior.  Even Barnes and Lewis concede the point in their own book: on the Hawking-Page measure, flat universes have measure 100%, and "flat universes are utterly unsurprising."15

This article does not use the flatness problem as evidence for anything.  It is the weakest item in tier two and using it is a liability.

The horizon problem — this one survives

Curiously, the same paper that demolishes the flatness problem defends the horizon problem:

the observed homogeneity of our universe does imply considerable fine-tuning; unlike the flatness problem, the horizon problem is real.10

And, from the same authors:  "Inflation by itself cannot solve the horizon problem, in the sense of making the smooth early universe a natural outcome of a wide variety of initial conditions" — though the same abstract adds that inflation "provides an appealing target for true theories of initial conditions."10

That is the best tier-two material available, and it comes with a hostile witness.  It is still tier two — a statement about the early universe in the standard model — and this article does not bank a residue of it either:  the Carroll-Tam result is itself a computation on a measure over solution space, and having declined to treat such measures as chances in answering Halvorson, the article cannot quietly collect on this one.  What survives without any measure is Penrose's qualitative point, treated under tier three:  smoothing processes use the Second Law and therefore cannot explain it.

Penrose's number

Roger Penrose estimated that the initial state of the universe was specified to a precision of one part in 1010123^.  It is the largest number in apologetics.

Three things must be said about it.

It is not a probability that the universe would support life.  It is a ratio of phase-space volumes, computed in a heuristic construction.  Penrose says so himself, and rejects the anthropic reading in his own words: the anthropic principle "is virtually no help to us whatever in resolving our conundrum."6  He was not arguing for a designer.  He was arguing for a new law of physics — the Weyl Curvature Hypothesis.

The entropy tuning is vastly more extreme than life requires, and Sean Carroll turns this into an argument against theism:

If the point of arranging the universe was to set the stage for the eventual evolution of intelligent life, why all the grandiose excess represented by the needlessly low entropy at early times and the universe's hundred billion galaxies?35

That is a serious objection and the honest reply is a theological one, not a physical one: a designed universe need only be sufficient for its purpose, not minimal.  But it is a real cost, and it is a cost that lands specifically on tier two.

It is tier two.  If the universe did not begin in a hot dense state fourteen billion years ago, the number is void.

Q and the baryon-to-photon ratio

The amplitude of the primordial density ripples, Q ≈ 10-5, has a life-permitting band of roughly 10-6 to 10-4.36  Below it no galaxies form; above it everything collapses into black holes.  The baryon-to-photon ratio has a range of about six decades.4

It is worth noting that Rees himself has since re-described this one.  In a 2018 paper with Mario Livio he gives the same band — about 10-6 to 10-4 — and adds the words "and therefore not particularly finely tuned."37  The interval did not change; his judgement of what two decades of room means did.  When the man who put Q on his own list of six declines, twenty years later, to call it fine-tuned, that belongs in the article rather than in a critic's reply.  Adams' survey widens the band further still, to roughly 10-6 to 10-2.4

Both of these vanish completely without the hot big bang.  No primordial perturbations means no Q.  No annihilation epoch means no η.  There is nothing left to be tuned.

There is also a paper that apologetics almost never engages.  Anthony Aguirre constructed a "cold big bang" in 2001 in which η, Q and Λ all differ from our values by many orders of magnitude — Λ by about seventeen — and argued that sun-like stars with planets still form.38  Anyone building a case on tier two has to answer it.

Tier three: the fine-tuning of the repairs

This section is the reason the article is organised the way it is.

Inflation was proposed by Alan Guth in 1981 to solve the horizon, flatness and monopole problems.16  Guth's paper ends by flagging a defect in his own model — old inflation had no graceful way to end:  "I am publishing this paper in the hope that it will highlight the existence of these problems and encourage others to find some way to avoid the undesirable features of the inflationary scenario."16  That specific defect was repaired within two years by "new inflation."  The sentence is still worth quoting, because it shows what inflation was from the start:  a repair, offered tentatively, by an author who said so.

Inflation has genuine observational successes and this article does not pretend otherwise.  It predicted a spectrum of primordial ripples tilted slightly away from perfectly uniform; the measured tilt is 0.9649 ± 0.0042, which is eight standard deviations from uniform.39  It predicted the fluctuations would be adiabatic and very nearly Gaussian, and they are.  It predicted a coherent pattern of peaks in the microwave background, and that pattern is there.  And it made an advance prediction about the density of the universe:  when inflation was proposed the average mass density was uncertain by a factor of three, and inflation said it should come out at the critical value.  It has since been measured to about half a per cent and it agrees.40

That last claim needs a qualification which inflation's own architects supply.  Through the 1990s the measured density looked like about a third of the critical value, in open conflict with the prediction — and the response was not to abandon inflation but to build inflationary models that accommodated the wrong answer.  Andrei Linde says so himself:  "Before the discovery of dark energy, many astronomers believed that Ω ~ 0.3.  At that time, experts in inflationary theory made many attempts to save inflation by inventing inflationary models compatible with this value of Ω."41  Two such models were published in Physical Review D in 1995.42  Viatcheslav Mukhanov puts it more bluntly still:  the flatness prediction "was first confirmed only at the end of 90th with the discovery of dark energy.  Note that the experimental data before were in strong disagreement with it."43

So the honest version is that inflation predicted flatness in 1981, the data disagreed for a decade, the framework absorbed the disagreement, and then the data changed back.  That is a real prediction with a real confirmation, and it is also a demonstration that the framework can accommodate its own refutation.  Both halves are true and a reader deserves both.

When Steinhardt and his co-authors attacked inflation in Scientific American in 2017, thirty-three physicists signed a reply — including Guth, Linde, Hawking, Weinberg, Witten, Wilczek, Rees, Susskind, Maldacena and Sean Carroll.40  Their central point is fair:  "standard inflationary models could have failed any of the empirical tests described above, but they did not."

But inflation needs six separate things to go right.  Barnes lists them: there must be an inflaton field at all; inflation must start; it must last long enough; it must end; it must reheat into ordinary matter without making monopoles; and it must leave behind the right density ripples.12  Tegmark surveyed random inflaton potentials in 2005; Barnes, reading Tegmark's figure, puts the peak success rate at about 0.1% and concludes that "even with a scalar field, inflation is far from guaranteed."44  Carroll and Tam computed the fraction of realistic cosmologies eligible for inflation at roughly one in 1066,000,000 — on the canonical measure over solutions to Einstein's equations, a measure which is itself unnormalizable, a caveat this article's own McGrew section obliges it to attach.10  Hollands and Wald put it plainly: inflationary models "create new 'fine tuning' issues with regard to the properties of the scalar field."45

So the repair costs about as much as the disease, and possibly more.

There is a deeper objection, and it is Roger Penrose's.  He argues that inflation cannot explain the smoothness of the early universe even in principle, because smoothing is an entropy-increasing process, and any such process presupposes the very low-entropy starting point that needs explaining.  His statement of it is the sharpest thing written on this subject:

All spontaneous symmetry-breaking processes and all phase transitions (these being needed for inflation) take place only by the good grace of the Second Law.  These processes do not explain the Second Law:  they use it.46

And elsewhere in the same section:  "if the thermalization is actually doing anything… then it represents a definite increasing of the entropy.  Thus, the universe would have been even more special before the thermalization than after."46

Penrose is careful, and this article will be too:  he says explicitly that his remarks "do not tell us that inflationary cosmology is wrong," only that they undercut most of the original motivations for it.46  But notice what he has done.  He has caught the repair using the thing it was hired to explain — which is your circularity worry stated at the level of thermodynamics rather than rhetoric.

Andreas Albrecht, one of inflation's co-founders, concedes the point in print:  "inflation does not predict the arrow of time.  Inflation 'passes the arrow of time buck' to the special initial conditions of the inflaton field."47  Sean Carroll and Chien-Yao Chen agree with the critique and can escape it only by giving up the assumption that the universe's evolution is reversible.48  Linde and co-authors reject the whole argument on the grounds that inflation is not entropy-preserving in the required sense.49  The dispute is live and technical, and no side has closed it.

There is a further problem.  Inflation's most direct prediction is a background of gravitational waves, measured by a number called the tensor-to-scalar ratio.  The tightest published limit is 0.032, from a 2022 combination of Planck and BICEP/Keck data; BICEP/Keck's own 2021 constraint is 0.036.50  That limit has already killed several of the simplest and best-motivated models.  Planck reported in 2013 that "monomial potential models of degree n ≥ 2 do not provide a good fit to the data," and in 2015 restated the point specifically for the quadratic potential and natural inflation.51

But it has not killed inflation, and here is the difficulty:  it is not clear what could.  The surviving models — the plateau and "α-attractor" families — have an adjustable parameter that pushes the predicted signal arbitrarily close to zero.  No finite upper limit on the tensor-to-scalar ratio can rule the paradigm out.  The major forecasting documents — the Snowmass inflation white paper, the LiteBIRD science paper, the Kamionkowski-Kovetz review of the B-mode search — state which model classes future experiments will exclude; searching them for a threshold that would falsify inflation itself turns up none.  Paul Steinhardt, one of inflation's own founders, has been making exactly this complaint for over a decade, with co-authors, in Physics Letters B and in Scientific American: that inflationary cosmology "cannot be evaluated using the scientific method" because "no experiment can ever disprove it."52

Guth, Kaiser and Nomura replied in print and the exchange is worth reading on both sides.53  But for this article's purposes the dispute settles the question:  a mechanism whose own inventors argue publicly about whether it is falsifiable is not a foundation on which to build an argument for God.

None of that is evidence for God, and this article will not use it as such.  Here is the reasoning, in full.

Fine-tuning becomes evidence for design only when the improbability attaches to something we have independent reason to think is real.  The values of the quark masses are measured.  The stability of hydrogen is observed.  If those sit in narrow windows, the narrowness is a fact about the world that wants explaining.

The inflaton field has never been detected.  Inflation is a proposal, introduced to repair a model, and its fine-tuning is a fact about the proposal, not about the world.  Citing it as evidence for God means arguing: our model needed a patch, the patch is improbable, therefore God.  But if the patch is improbable, the first thing that follows is that the patch may be wrong — and after that, that the model requiring it may be wrong.  Design does not enter anywhere.

There is a sharper way to see it, and it is a hazard rather than an accusation:  a creationist writer who attacks the big bang because it needs inflation to survive cannot also bank inflation's improbability as design evidence.  Both arguments cannot be run by the same author.  This site intends to run the first, so it drops the second — permanently.

Barnes makes a related observation that is the most intellectually honest passage in his review paper, and it cuts against the tier-two case generally:

Inflation thus represents a very special case.  Waiting inside the life-permitting range (L) is another physical parameter (p).  Aim for p and you will get L thrown in for free.  This is not true of the vast majority of fine-tuning cases.  There is no known physical scale waiting in the life-permitting range of the quark masses, fundamental force strengths or the dimensionality of spacetime.  There can be no inflation-like dynamical solution to these fine-tuning problems because dynamical processes are blind to the requirements of intelligent life.12

That is simultaneously a concession — flatness is the one case where a natural fix was available — and the strongest available argument that tier-one cases cannot be fixed the same way.

How improbable is "improbable"? The McGrew critique

The most serious technical objection to the fine-tuning argument was published in 2001 in Mind, the leading general philosophy journal in the English-speaking world.  Its three authors — Timothy McGrew, Lydia McGrew and Eric Vestrup — are all Christians.  Timothy McGrew is a specialist in probability and confirmation theory and one of the best-known Christian apologists working in analytic philosophy.  Eric Vestrup wrote a measure theory textbook for Wiley.3

They do not dispute the physics.  They grant it explicitly.  What they dispute is whether "fine-tuned" can be converted into "improbable."

The objection

Suppose the strength of gravity could, for all we know, have taken any positive value.  The life-permitting range is some finite window.  What fraction of the possible values is that?

The answer is that the question breaks, and it breaks in two distinct ways.  If probabilities must sum to one in the standard way — countable additivity — then no uniform distribution over an unbounded range exists at all, and "the fraction of possible values that permit life" has no value.  If instead you relax that requirement and use a finitely-additive uniform measure, a value exists — and it is exactly zero, for every finite window, including windows billions of orders of magnitude wider than the real one.  Either the sentence "the life-permitting range is a vanishingly small fraction of the possible range" expresses nothing, or it expresses something that would be equally true of a universe nobody would call tuned.

The coarse-tuning reductio

This is the memorable part.  If the argument worked, it would work exactly as well if the life-permitting window were enormously wider — billions of orders of magnitude wide.  The probability would still be zero, on the same reasoning.  But nobody would find a universe with a billion-order-of-magnitude margin for error surprising or in need of a designer.  So something has gone wrong with the reasoning, not merely with the numbers.

Collins has a direct reply to this reductio, and fairness requires printing it:  he argues that it proves too much in the other direction — on the McGrews' reasoning, the fine-tuning argument "gets stronger and stronger as the range grows," and then "magically, when the range becomes actually infinite," loses all force at once, which he takes to be the counterintuitive result.54  The reductio and the counter-reductio are both live; neither side has conceded.

The replies

Robin Collins proposes restricting the comparison range to an "epistemically illuminated" region — the range over which our physics can actually say anything.  Inside a bounded region, probabilities are defined again.  Collins does not concede the objection — his own sentence is that "the McGrews and others are wrong in claiming that there would be no epistemic probability if the range is infinite" — but he does concede what the repair costs: if the comparison range is genuinely infinite, "the popular presentation of the argument would have to be modified."54

Jeffrey Koperski bites the bullet: use measure theory rather than probability, accept that fine and coarse tuning come out equivalent, and argue that this is a tolerable result.55

Luke Barnes gives the strongest reply.  He argues that the objection, taken seriously, would paralyse all of theoretical physics — physicists declared the cosmological constant and the Higgs mass "unnatural" long before anyone brought God into it, using exactly this kind of reasoning about ranges.  He supplies bounds from physics itself: the Planck scale for dimensionful parameters, and 't Hooft naturalness for dimensionless ones.56

Neil Manson, surveying the debate neutrally, sides with the McGrews on the key point: a bound derived from where our theories break down is a fact about the reach of our theories, not about what was possible.57

The debate has continued past 2018.  A 2021 paper in a physics journal attempted a maximum-entropy construction of normalizable bounds and concluded that some ratios are genuinely fine-tuned while the primordial fluctuation amplitude is not; a 2022 philosophy paper argues on independent grounds that fine-tuning supports design even under indifference worries.58  Neither has settled anything, but a section that stopped at 2018 would be out of date.

The verdict

The objection wounds the argument seriously and kills one form of it outright.

What it kills: the absolute-probability version.  "The probability of a life-permitting universe by chance is 10-120, therefore chance is refuted" is dead, and every serious defender concedes it in some form.  Any presentation that quotes a raw probability without stating what range it is a fraction of is stating a quantity with no defined value.  Most popular presentations do exactly this.  This article does not.

What survives is a comparative argument: a life-permitting set of constants is more expected on design than on blind chance, given the ranges and priors that physics itself supplies.  Even that form is under attack — Jonathan Weisberg argues that a designer with unknown aims gives no more reason to expect life-permitting constants than chance does, a challenge aimed precisely at the likelihood premise, with Roger White replying in the same journal.59  Three things are true of that surviving form.  It requires a defensible finite range, and whether physics supplies one is genuinely unsettled.  It can never produce a number a reader should treat as odds against atheism, because a likelihood ratio compares two hypotheses and says nothing until you supply priors that nothing measures.  And the emotional force of the very small number — the sense of a dartboard whose edges we can see — is not licensed by the logic actually available.

Neither McGrew has retracted the objection.  What Lydia McGrew has done since is more interesting:  in 2016 she published "Four (Or So) New Fine-Tuning Arguments," proposing design arguments built to route around her own 2001 objection rather than answer it — noting that "MMV do not appear to question the proposition that the life-permitting range of the constants is narrow.  In fact, they appear willing to grant it" — MMV being her own 2001 paper, referred to in the third person.60  She builds around the objection without disowning it, and anyone claiming she recanted is overreading.

The McGrews close their 2001 paper with a warning that applies well beyond this argument:

To retreat to the point where the argument rests on unargued intuitions is to deprive it of anything more than devotional significance.3

That is a Christian philosopher's warning to Christian apologists, and it is correct.

Fine-tuning for discoverability

Robin Collins has proposed a distinct argument that deserves separate treatment, along with a distinct warning.

The idea

The multiverse explains fine-tuning by selection: in a vast ensemble of universes with different constants, observers necessarily find themselves in one of the rare habitable ones.  But that filter is keyed to exactly one property — the existence of observers.  It gives no explanation at all for any other remarkable property the universe happens to have.

Collins argues that our universe is not merely habitable but unusually well suited to having its own laws discovered, and that observer-selection cannot explain this.  Luke Barnes puts the logic in an analogy: if a factory built cars by randomly assembling parts and discarding everything that could not be driven a kilometre, you would not be surprised that your car drives.  You would be very surprised to find a working satellite navigation system in it.61

The logical core of this is correct and underappreciated.  A selection effect explains only what it selects for.

The warnings, stated first

  • The full argument has never been published. Collins' two-volume work has been in progress since 1999 and remains unfinished. The technical calculations exist as self-published drafts that Collins himself labels as not peer reviewed.
  • The philosophy literature has not refuted it. It has ignored it. The Stanford Encyclopedia of Philosophy entry on fine-tuning cites Collins repeatedly and does not mention discoverability once. Silence is not agreement.
  • The extra tuning it buys is modest. On Collins' own summary for the fine-structure constant, livability constrains α to about a factor of four, and discoverability narrows that to about a factor of 1.4. A fourfold shrink. Not 1 in 10120, and anyone implying otherwise is overselling.
  • Do not use the Higgs boson as an example. Apologetics sites cite the 125 GeV Higgs as being conveniently placed for discovery. At the 2014 forum where Collins first presented this argument, the Higgs was the lead counterexample against him, delivered from the same platform by Sean Carroll minutes later. Physics is full of things that are frustratingly hard to detect — dark matter above all.

What is worth keeping

The strongest example is the microwave background.  Its detectability depends on the baryon-to-photon ratio, and Collins argues the actual value sits near the optimum for observing it.  The cleanest example is that the large-scale smoothness of the universe is exactly what makes the equations of cosmology solvable at all — quantitative cosmology is possible because the universe is simple on large scales, and that simplicity is not entailed by the existence of observers.

Collins also deserves credit for something rare: he documents the moment he thought he had refuted his own thesis, and reports it.

One more problem, by this article's own rules:  the two best examples just given are both tier two.  The microwave background is a big-bang relic whose detectability turns on the baryon-to-photon ratio, and large-scale smoothness is the horizon problem wearing a different hat.  A reader following this article's discipline can keep only the bare logical point — a selection effect explains only what it selects for — plus Collins' fine-structure-constant example.

Verdict:  an interesting suggestion with one sound logical insight and no established empirical support, whose best examples are unavailable to this article's own framework.  It belongs here as a secondary section, clearly labelled as untested, and it should not be led with.

Objections

Each objection is stated at its strongest, then answered — or conceded.

1. Halvorson's theological objection

This is the strongest objection in this article, and it comes from an orthodox Christian philosopher at Princeton.  He first circulated it as a preprint in 2014; the published chapter is 2018.11

Hans Halvorson argues the fine-tuning argument undermines itself.  If God chose the laws of nature, then God chose laws under which life-permitting universes are astronomically rare.  Halvorson's illustration is a game of reverse Russian roulette: your captor hands you a revolver with five of six chambers loaded, you pull the trigger, and you survive.  Should you conclude the captor designed the game for your survival?  Why load five chambers?  Why not none?

Formally:  if the theist grants that God favours life-permitting universes, and grants — for the sake of argument, as Halvorson does and this article does not — that Penrose's ratio can be read as a chance, then the probability that God exists comes out vanishingly small.  The laws themselves, considered apart from which universe is actual, become strong evidence against God.

Halvorson actually makes the argument three times:  for the initial conditions of the universe, for the constants, and for the laws themselves.  The constants version needs no objective chances at all — it argues that if a flat distribution over the possible values is rational for the skeptic, it is equally rational for someone who believes God chose the values, in which case a life-permitting outcome is just as improbable given God.  His punchline for that version deserves quoting, because it is structurally the same charge this article levels at tier three:  "this sort of fine-tuning argument is not so much an argument for God's existence as it is an argument against contemporary physics."

There is a published reply, and it comes from the argument's leading defender.  Luke Barnes answered Halvorson in the European Journal for Philosophy of Science in 2018 and again in Ergo in 2019:  chances play no role in his formulation of the argument, and a measure supplied by a theory is not the same thing as an objective chance — Barnes' illustration is that a physicist running computer simulations of universes picks the initial conditions freely rather than sampling them from the theory's measure, and "God could do the same."62  Halvorson has not replied in print.

Notice what Barnes' move shows:  one can deny that the measure is an objective chance and still keep the fine-tuning probabilities as epistemic ones — Barnes does exactly that.  This article makes a stricter choice than Barnes does:  it declines to use Penrose's number as any kind of probability, and it declines to build on tier two.  That is a choice this site makes for its own reasons — chiefly its forthcoming assessment of big bang cosmology — not a price Halvorson's argument extracts.  The second escape, denying that God is especially likely to create a life-permitting universe, remains open and theologically respectable, but it abandons the premise the fine-tuning argument needs.

2. We could not have observed anything else

This is the objection every atheist philosopher raises first, and its cleanest form is Elliott Sober's.63  Arthur Eddington imagined a net that cannot catch fish under ten inches:  a haul of fifty large fish tells you nothing about the fish in the lake, because the procedure guaranteed the result.  Likewise, observers can only ever find themselves in a universe whose constants permit observers.  Given that we exist, Sober argues, the constants had to be right "regardless of whether the universe was produced by intelligent design or by chance" — so our observation cannot favour either.

The standard counter is John Leslie's firing squad:  fifty sharpshooters fire at a condemned man and all miss.  "If they hadn't all missed, I wouldn't be here to wonder about it" is true — and plainly no answer.  The survivor is rational to suspect the squad missed on purpose.64

Sober's rejoinder is a dilemma:  analysed by likelihoods, he argues, the prisoner is not entitled to his suspicion, because he is subject to the selection effect; analysed instead by probabilities, the prisoner is entitled to it, but his inference then no longer resembles the fine-tuning argument.  Whether that dilemma succeeds is one of the most contested questions in this literature — Sober's critique targets the inference, not God's existence, and he draws no atheistic conclusion from it.  The honest verdict is that the weak-anthropic point defeats lazy statements of the argument ("it's surprising we're here") and does not by itself defeat the comparative form, but the firing-squad analogy settles less than apologists assume, because its disanalogies — we know the marksmen's intentions and skill from background knowledge; we know nothing comparable about universe-generators — are exactly where the argument's remaining work lives.

3. The multiverse

If there are enough universes with enough different constants, some will be habitable, and observers necessarily find themselves in those.

This is the main naturalistic explanation and it should not be dismissed.  It is not an arbitrary invention: eternal inflation produces bubble universes as a near-unavoidable consequence, and string theory appears to permit an enormous landscape of vacuum states.  Serious physicists hold it for serious reasons.

Three replies have force.  There is no observational evidence for it, and George Ellis and Joe Silk argued in Nature that defending untestable theories damages the integrity of physics.65  A universe-generating mechanism needs its own laws, and those laws must be capable of producing life-permitting universes rather than only dead ones.  And an eternally inflating multiverse appears to be infested with Boltzmann brains — freak observers fluctuating out of equilibrium with false memories — which, if they outnumber ordinary observers, makes the theory self-undermining.  Barnes, who is sympathetic to neither extreme, considers the Boltzmann brain problem serious enough that it "might sink the whole idea," while cautioning that it does not falsify the multiverse.15

4. The inverse gambler's fallacy

Ian Hacking and Roger White argued that inferring many universes from one improbable universe is a fallacy: the roll in front of you is not evidence about how many other rolls occurred.  This cuts against the multiverse.

The honest report is that this is unresolved.  Isaacs, Hawthorne and Russell mounted a systematic defence of the multiverse inference against the fallacy charge in 2022; White's original paper also pressed the mirror-image "this universe" objection — a multiverse might explain why some universe is life-permitting but not why this one is.66  And Klaas Landsman, who endorses the fallacy charge against the multiverse, argues that the design inference fails too.  He is hostile to both sides.  This article reports the dispute rather than claiming the point.

5. The universe is not fine-tuned for life

Lawrence Krauss and Sean Carroll both press the observation that the universe is overwhelmingly lethal and empty, and that a designer aiming at life would have done it differently.

Part of this has a good answer.  The emptiness is not waste — a universe dense enough to breathe everywhere would collapse within a day.  The scale of the universe is a consequence of the time required to make heavy elements in stars, which is a physical requirement rather than an extravagance.

Part of it does not have a good answer, and that is Carroll's entropy point in section on Penrose above.  Adams presses a related version: he lists six specific ways our universe could be made more hospitable — a smaller cosmological constant, larger primordial fluctuations, more baryons, a smaller fine-structure constant, stable beryllium-8, and weaker gravity — and concludes that "in spite of its biophilic properties, our universe is not fully optimized for the emergence of life."4

The available reply is theological rather than physical.  A designed universe need not be a maximally life-producing universe, only one sufficient for its purpose.  That is a coherent position but it is not a physics result, and it should not be dressed up as one.

6. Only one variable at a time

Victor Stenger argued that fine-tuning claims come from varying a single constant while holding the others fixed, and that compensating changes can restore habitability.  His simulation, MonkeyGod, purported to show a wide range of viable universes.

The methodological point is fair and worth conceding.  The specific charge is not accurate about the literature: multi-parameter studies have been standard since the 1970s, and Barnes documents this in detail.12  Adams' 2019 survey varies many parameters at once and still finds required hierarchies.

7. Carbon chauvinism

Perhaps other chemistries support life.  Silicon is the usual candidate.

Silicon is genuinely worse: its bonds are weaker, its long chains are unstable, and its oxide is a solid rather than a gas, which makes respiration difficult.  Norman Pace's review in PNAS is the standard citation.67  Barnes adds a neat structural point: any universe that can make silicon can also make carbon, since carbon is lighter, so the silicon-life region sits inside the carbon-life region rather than beside it.

This objection does bite on marginal cases and should not be waved away entirely.  It does not rescue universes with no stable nuclei at all.

8. The constants might be necessary

Perhaps a final theory will show the constants could not have been otherwise.

Paul Davies, a theoretical physicist, considers this demonstrably wrong: he finds it easy to imagine alternative universes that are logically consistent, and there is no evidence the universe is logically necessary.  And Carr and Rees ended their founding 1979 paper with the observation that even if a deeper theory fixed all the constants, "it would still be remarkable that the relationships dictated by physical theory happened also to be those propitious for life."68

It should be noted in fairness that Carr and Rees also called the anthropic principle "entirely post hoc" in the same paper.68  Quoting the closing sentence without that is selective.

9. Who designed the designer?

Richard Dawkins argues that a designer capable of setting the constants would be more complex than what it explains, and so more in need of explanation.

The reply is that this misidentifies what kind of explanation is on offer.  A mind is not being posited as a complex arrangement of parts requiring assembly; it is being posited as a fundamental explanatory terminus, in the same way that naturalism posits fundamental laws that are not themselves explained.  Whether that is satisfying is a genuine philosophical dispute.  Dawkins is widely reported as calling fine-tuning "the best one going" among arguments for God while adding that it remains "a very, very bad argument" — but no primary source with a date and venue has been verified for that remark, so this article reports it as attributed rather than quoted.  Reporting only the first half of it would in any case be dishonest.

What this article claims, and what it does not

It does not claim that the odds against a life-permitting universe are one in some enormous number.  That claim has no defined value, and three Christian philosophers demonstrated as much in the flagship journal of their field.

It does not claim that fine-tuning proves God exists.  The surviving form of the argument is comparative: it says a life-permitting universe is more expected under design than under blind indifference.  How much that should move a reader depends on what he thought before, and nothing measures that.

It does not claim the initial conditions of the big bang as evidence, because this site is not persuaded the model is correct, and building on a foundation you intend to question later is not honest.

It emphatically does not claim that the fine-tuning required by inflation is evidence for God.  Inflation was invented to repair a model.  Its improbability is evidence that the repair is expensive, and therefore that the model may be wrong.  Using it as design evidence is a temptation this site refuses, for the reasons given in the tier-three section.

What it does claim is narrower and holds up.  The laws of physics contain roughly thirty numbers that nobody can derive.  Several of them sit in windows outside which there are no stable nuclei, no hydrogen, no chemistry, or no stars that last.  The tightest of those windows are in particle physics, not astronomy — which is the judgement of the field's leading skeptical surveyor, not of an apologist.  The vast hierarchies between the forces are required, not optional, and that too is his judgement.  None of this depends on how the universe began.

That is a smaller claim than the one usually made.  It is also one built to be checked:  every number above carries its primary source, and this draft has already been through one adversarial audit that corrected it in more than thirty places.  A smaller claim that survives checking is worth considerably more than a large one that cannot.

Two companion pages carry the working: what the physicists actually said, with each speaker's own position on God, and the literature, where every source is catalogued with what it measured and which way it cuts.

Sources


  1. 1.

    Hoyle, Fred.  “The Universe: Past and Present Reflections.”  Engineering and Science 45(2):8–12.  Nov 1981.  An essay by the astronomer Fred Hoyle arguing that astronomers' approximations are less good than most of them assume.  He tells the story of his work on interstellar dust grains, where graphite and then a graphite-and-ice mix each failed to fit the observations.  The article quotes his 1981 remark that a superintellect has monkeyed with physics, chemistry and biology. ↩

  2. 2.

    Barnes, Luke A.  “Binding the Diproton in Stars: Anthropic Limits on the Strength of Gravity.”  Journal of Cosmology and Astroparticle Physics 12:050.  2015.  A calculation of the stars that would form in a universe where the diproton, a nucleus of two protons, is bound, compared with stars like ours that burn slowly through the weak interaction.  It works through one representative case, a star with equal numbers of protons and deuterons, and finds that these strong-burning stars settle into familiar surface temperatures, luminosities and lifetimes.  The article uses it as the refutation of the diproton argument, and notes that the same paper gives a tighter limit on gravity. ↩ ↩ ↩

    1. 2a.

      Section 4 Discussion:  Stars in a diproton-binding universe have.  “remarkably familiar masses, luminosities, surface temperatures and lifetimes.” ↩

    2. 2b.

      Section 1 Introduction:  Citing Barr & Khan:  “chemistry-permitting universes are huddled in a small shard of parameter space which has area ∆m_up ∆m_down / m²_Planck ≈ 10⁻⁴⁰.” ↩

    3. 2c.

      Section Abstract and §4:  “all stars burn out in mere millions of years unless the gravitational coupling constant is extremely small, α_G < 10⁻³⁰.” ↩

  3. 3.

    McGrew, Timothy et al.  “Probabilities and the Fine-Tuning Argument: A Sceptical View.”  Mind 110(440):1027–1037.  Oct 2001.  A sceptical paper on the probabilities used in the fine-tuning argument.  The article uses it as the most serious technical objection to the argument, because it attacks the form of the argument that says the odds against this universe are one in 10^N. ↩ ↩

    1. 3a.

      Page 206:  Reprinted in Neil A. Manson, ed., God and Design: The Teleological Argument and Modern Science, pages 200–208 (Routledge, 2003).  The quoted words are on page 206 of that reprint.  “To retreat to the point where the argument rests on unargued intuitions is to deprive it of anything more than devotional significance.” ↩ ↩

  4. 4.

    Adams, Fred C.  “The Degree of Fine-Tuning in our Universe — and Others.”  Physics Reports 807:1–111.  2019.  A review of the scientific limits on the constants of physics and the cosmological parameters that a universe must fall within to form stars, planets and life.  Its author works through each parameter, finds the allowed range for each one, and concludes that viable universes exist over a range of parameter space.  The article uses it as the definitive quantitative survey of the whole subject, and as the source that shows how much room the parameters actually have. ↩ ↩

    1. 4a.

      Table 2:  Ranges of parameter values for viable universes, in decades: down quark mass 0.85; electron-proton mass ratio 5; fine structure constant 4; baryon-to-photon ratio 6; gravitational constant more than 10. ↩ ↩ ↩

    2. 4b.

      The down-quark constraint is described as the most confining found, with our universe close to the limit. ↩

    3. 4c.

      Section §10.6:  “The limiting feature for a viable universe — including ours — is not the astrophysical engines that synthesize heavy elements and generate energy, but rather the parameters of particle physics that allow for the existence of stable nuclei.” ↩

    4. 4d.

      Table 4:  The ≥ 1032 floor on α/α_G is given in Adams' Table 4, which records 36 decades observed and a minimum of 32.  Section §10.6:  “Although they represent a significant problem for particle physics theories, the observed hierarchies of the fundamental parameters are a distinguishing feature of the cosmos, and extreme hierarchies are required for any universe to be viable:  The strength of gravity can vary over several orders of magnitude, but it must remain weak compared to other forces so that the universe can evolve and produce structure, and stars can function.” ↩ ↩

    5. 4e.

      Section §10.4:  Under the heading "Is our Universe Maximally Habitable?", it lists smaller vacuum energy, larger primordial fluctuations, stable beryllium-8 and weaker gravity.  Section §10.6:  “Finally, in spite of its biophilic properties, our universe is not fully optimized for the emergence of life.” ↩ ↩

    6. 4f.

      Section §10.2, Myths and unnecessary constraints:  “In universes with stable diprotons, where nuclear reactions proceed through the strong force only, stars operate with somewhat lower central temperatures, but do not burn through their nuclear fuel in a catastrophic manner…  Another commonly invoked constraint is the requirement that some stars must be convective in order to produce planets; we now know that planet formation is independent of stellar convection.” ↩ ↩ ↩

    7. 4g.

      Section §7.4:  On the triple-alpha resonance:  “the chance of being sufficiently near resonance is about 1 part in 4.” ↩

    8. 4h.

      Section §10:  Adams' §10 summary states that.  “Big Bang Nucleosynthesis generally does not cause a universe to lose its potential habitability”.  Primordial nucleosynthesis is not where the binding constraints live. ↩

    9. 4i.

      Section §10.1:  “Given that the concept of fine-tuning evokes the image of tuning the dials of a radio, as one point of comparison we consider the tuning required to capture a radio station…  Tuning a radio thus requires far more precision than tuning a universe.” ↩

  5. 5.

    Weinberg, Steven.  “The cosmological constant problem.”  Reviews of Modern Physics 61(1):1–23.  1989.  Section V:  The anthropic requirement is.  “a vacuum energy density no larger than, say 100ρ_M,”.  The bracketed, more careful form gives 410ρ_M at z_c = 4.  His 2000 restatement gives.  “about 200 times the present mass density.”  The same 1989 review contains the QCD-only figure, cancellation.  “to about 41 decimal places.”  The 120 orders of magnitude is the theory-versus-observation mismatch, a different quantity.  Rees 2004 puts the galaxy-formation threshold at 5-10 times the observed dark energy.  A review article by the physicist Steven Weinberg on the cosmological constant problem, the mismatch between the vacuum energy that particle theory predicts and the much smaller value observed.  It sets out the history of the problem and five different approaches to solving it.  The article uses it for Weinberg's anthropic bound, the limit past which galaxies cannot form. ↩ ↩ ↩

  6. 6.

    Penrose, Roger.  “Before the Big Bang: An Outrageous New Perspective and its Implications for Particle Physics.”  Proceedings of EPAC 2006, 2759–2763.  2006.  A conference paper, THESPA01, in the proceedings of EPAC 2006 in Edinburgh, Scotland, in which Penrose sets out what he calls the basic conundrum: the Second Law of thermodynamics seems to make the universe's starting state the most special possible, and the anthropic principle does not help.  He puts a lower bound on the size of the gap at a factor above 10 raised to the power 10^123, and proposes the Weyl Curvature Hypothesis as his answer.  The article uses it because Penrose's large number is not the probability of a life-permitting universe, and he rejects the anthropic reading of it in his own words.

    1. 6a.

      Section THE BASIC CONUNDRUM:  “What about the anthropic principle?  Again, this is virtually no help to us whatever in resolving our conundrum.” ↩ ↩

  7. 7.

    Tegmark, Max.  “Is 'the theory of everything' merely the ultimate ensemble theory?”  Annals of Physics 270:1–51.  1998.  The lattice-stability constraint.  “also allows replacing β by 1/β.”  A long theoretical paper on the "ultimate ensemble theory", in which every mathematically possible world counts as physically real.  It argues that this theory, which has no free parameters, is far from clearly ruled out by observation.  The article uses it for the lattice-stability constraint on the electron-to-proton mass ratio, which allows the ratio to be inverted, so the often-quoted 1:1836 claim does not survive.  Mirror:  arXiv ↩ ↩

  8. 8.

    Kragh, Helge.  “An anthropic myth: Fred Hoyle's carbon-12 resonance level.”  Archive for History of Exact Sciences 64:721–751.  2010.  A paper whose title calls the anthropic account of Fred Hoyle's carbon-12 resonance level "an anthropic myth."  The article uses it for the point that Hoyle did not predict the carbon resonance because life needs carbon. ↩ ↩

  9. 9.

    Helbig, Phillip.  “Is there a flatness problem in classical cosmology?”  Monthly Notices of the Royal Astronomical Society 421(1):561–569.  2012.  A paper that reviews the flatness problem and works out new calculations for models that will collapse in the future.  Together with earlier results for models that expand forever, these show that the flatness problem does not exist for any Friedmann-Lemaître model.  The article uses it as a clear example of mainstream cosmologists rejecting the flatness problem.  Mirror:  arXiv

    1. 9a.

      Section 3.1 The qualitative flatness problem:  The paper describes the standard flatness argument as:  “completely bogus”. ↩ ↩

  10. 10.

    Carroll, Sean M., and Heywood Tam.  Unitary Evolution and Cosmological Fine-Tuning.  2010.  A theory paper by Sean Carroll and Heywood Tam of the California Institute of Technology.  It uses a natural measure on the solutions of Einstein's equations to test how much fine-tuning inflation removes.  It finds that the flatness problem does not exist, because almost all such universes are flat, but that the horizon problem is real, and that inflation happens in only a negligibly small fraction of cosmologies once perturbations are included.  The article cites it on both points.

    1. 10a.

      Section 5.2 Computation of the measure:  “the observed homogeneity of our universe does imply considerable fine-tuning; unlike the flatness problem, the horizon problem is real.” ↩

    2. 10b.

      Section 6 Discussion:  “the flatness problem is an illusion.” ↩ ↩

    3. 10c.

      Section 6 Discussion:  “Inflation by itself cannot solve the horizon problem.” ↩

    4. 10d.

      “the fraction of realistic cosmologies that are eligible for inflation is therefore P(inflation) ≈ 10^(−6.6×10⁷).” ↩

  11. 11.

    Halvorson, Hans.  “A Theological Critique of the Fine-Tuning Argument.”  Knowledge, Belief, and God: New Insights in Religious Epistemology, 122–135.  Oxford University Press.  Edited by Matthew A. Benton, John Hawthorne and Dani Rabinowitz.  2018.  A book chapter in which the author argues that the fine-tuning argument undermines itself.  If a life-permitting universe confirms God's existence, then the low probability of such a universe counts against God.  The article uses it as the strongest theological objection to the argument. ↩ ↩

  12. 12.

    Barnes, Luke A.  “The Fine-Tuning of the Universe for Intelligent Life.”  Publications of the Astronomical Society of Australia 29(4):529–564.  2012.  A review of the scientific literature on fine-tuning, the claim that very small changes to the laws, constants or starting conditions of physics would leave a universe unable to evolve intelligent life.  It uses Victor Stenger's The Fallacy of Fine-Tuning as its foil, since Stenger argues that all known cases can be explained without a multiverse, and it finds many of Stenger's claims highly problematic while defending no conclusion about fine-tuning itself.  The article uses it as the technical review that names the scientists who accept fine-tuning and sets out what inflation has to achieve.

    1. 12a.

      “There are a great many scientists, of varying religious persuasions, who accept that the universe is fine-tuned for life, e.g. Barrow, Carr, Carter, Davies, Dawkins, Deutsch, Ellis, Greene, Guth, Harrison, Hawking, Linde, Page, Penrose, Polkinghorne, Rees, Sandage, Smolin, Susskind, Tegmark, Tipler, Vilenkin, Weinberg, Wheeler, Wilczek.  They differ, of course, on what conclusion we should draw from this fact.” ↩

    2. 12b.

      Section §4.7:  Footnote 32, citing Smolin:  “The conclusion does not depend in any way on the first, 'anthropic' premise.  The argument would work just as well if the element in question were the inert gas neon, for which the first premise is (probably) false.” ↩

    3. 12c.

      Section §4.4.2:  The section lists the six requirements that inflation must satisfy. ↩

    4. 12d.

      Section §4.4.3:  “Inflation thus represents a very special case.  Waiting inside the life-permitting range (L) is another physical parameter (p)…  There can be no inflation-like dynamical solution to these fine-tuning problems because dynamical processes are blind to the requirements of intelligent life.” ↩

    5. 12e.

      Section §4.9 and following:  Documents that multi-parameter variation has been standard in the fine-tuning literature since the 1970s. ↩

  13. 13.

    Barnes, Luke A.  “Christmas Tripe: A Fine-Tuned Critique of Richard Carrier (Part 3).”  Letters to Nature (blog).  Dec 23, 2013.  A blog post, part 3 of a critique of Richard Carrier by Barnes.  The article cites it for Barnes's own count of the literature he had read: of more than two hundred papers, he could think of only a handful that oppose fine-tuning. ↩

  14. 14.

    Davies, Paul C. W.  “How bio-friendly is the universe?”  International Journal of Astrobiology 2(2):115–120.  2003.  An essay in an astrobiology journal that tests the claim that life is written into the laws of nature.  It argues that the universe is fine-tuned for the building blocks of life and the environments it needs, which is a necessary but by no means sufficient condition for life to start.  The article cites it for Davies's statement that there is now broad agreement that the universe is fine-tuned for life. ↩

  15. 15.

    Lewis, Geraint F., and Luke A. Barnes.  A Fortunate Universe: Life in a Finely Tuned Cosmos.  Cambridge University Press.  2016.  A book for general readers by Geraint Lewis, a professor of astrophysics, and Luke Barnes, a postdoctoral researcher, both at the Sydney Institute for Astronomy.  It surveys how the laws and constants of physics bear on life, from particles and forces to planets, stars and galaxies, and sets out the explanations that have been offered, from pure chance and a multiverse to theistic explanations.  The article uses it because its two authors agree on every number in it but divide over the conclusion in the final chapter.

    1. 15a.

      The concluding chapter, in which Barnes argues for theism and Lewis for the multiverse.  Lewis says:  “I think I still stick with the multiverse.  Ours is but one of a vast sea of universes…  we find ourselves in one of the extremely few universes that can support life.” ↩

    2. 15b.

      On Hoyle:  “Historically, this probably isn't true, and in any case life plays no part in the reasoning.” ↩

    3. 15c.

      On flatness: the Hawking-Page measure gives flat universes measure 100%.  “flat universes are utterly unsurprising.” ↩

    4. 15d.

      Barnes says:  “But those Boltzmann Brains are a worry.  A multiverse that avoids them must favour biological life forms — like us — over isolated, freak observers.  This might sink the whole idea.” ↩

  16. 16.

    Guth, Alan H.  “Inflationary universe: A possible solution to the horizon and flatness problems.”  Physical Review D 23:347–356.  1981.  A paper proposing an inflationary universe as a possible solution to the horizon and flatness problems.  The article cites it as the source of inflation and for a warning Guth wrote into the paper about the model's defects. ↩ ↩

    1. 16a.

      “In conclusion, the inflationary scenario seems like a natural and simple way to eliminate both the horizon and the flatness problems.  I am publishing this paper in the hope that it will highlight the existence of these problems and encourage others to find some way to avoid the undesirable features of the inflationary scenario.” ↩

  17. 17.

    Damour, Thibault, and John F. Donoghue.  “Constraints on the variability of quark masses from nuclear binding.”  Physical Review D 78:014014.  2008.  A theory paper by Damour and Donoghue that updates the limits nuclear binding places on the light quark masses.  They find that heavy nuclei would fall apart if the sum of the up and down quark masses rose more than 64% above its real value, at 95% confidence.  With the Yukawa couplings held fixed, the Higgs vacuum expectation value, the strength of the Higgs field, could range only from 0.39 to 1.64 times its real value.  The article cites both figures. ↩ ↩

  18. 18.

    Agrawal, Vijay et al.  “Viable range of the mass scale of the standard model.”  Physical Review D 57:5480.  1998.  A study of the range of values for the mass scale of the standard model of particle physics that is viable.  The article uses it for the size of the Higgs mass-squared parameter, which sits far below the natural scale, and for a warning that the low end of the study's range is softer than tables imply. ↩

    1. 18a.

      “we see no reason why values of v/v₀ < 1 could not support life.”  This sentence follows immediately after the passage usually quoted, and reverses the usual gloss. ↩

  19. 19.

    Ehrenfest, Paul.  “In what way does it become manifest in the fundamental laws of physics that space has three dimensions?”  Proceedings of the KNAW 20:200–209.  1917.  A paper in the Proceedings of the KNAW, with the volume dated 1917/1918, that asks in its title why physical laws show three dimensions of space.  The article cites it for Ehrenfest's 1917 demonstration that in more than three spatial dimensions, planetary and electron orbits are both unstable. ↩

  20. 20.

    Tegmark, Max.  “On the dimensionality of spacetime.”  Classical and Quantum Gravity 14:L69–L75.  1997.  A short physics paper arguing that three space dimensions and one time dimension may be the only setup that allows observers, though it says it does not rigorously prove this.  It argues that more or fewer space dimensions break atoms or gravity, and that more or fewer time dimensions break the predictability physics needs.  The article uses it for the time-dimension argument. ↩

  21. 21.

    Scargill, J. H. C.  “Existence of life in 2+1 dimensions.”  Physical Review Research 2:013217.  2020.  A 2020 physics paper whose title, "Existence of life in 2+1 dimensions," refers to a universe with two dimensions of space and one of time.  The article uses it as the published counterexample to the half of Tegmark's argument that concerns two dimensions of space. ↩

  22. 22.

    Oberhummer, H. et al.  “Stellar Production Rates of Carbon and Its Abundance in the Universe.”  Science 289:88–90.  2000.  A paper that recalculated the triple-alpha reaction, the step by which red giant stars make carbon, using a model of the carbon-12 nucleus built from twelve nucleons.  It varied the strengths of the nuclear and electromagnetic forces, and found that outside a narrow window of 0.5 and 4 percent for the strong and Coulomb forces, the stellar production of carbon or oxygen falls by factors of 30 to 1000.  The article uses it as the source of the 0.5 percent figure that apologetics repeats.  Mirror:  arXiv ↩

  23. 23.

    Schlattl, H. et al.  “Sensitivity of the C and O production on the 3-alpha rate.”  Astrophysics and Space Science 291:27–56.  2004.  They find that the anthropic significance of the triple-alpha rate.  “might be of considerably less”.  importance.  A stellar-modelling study that followed carbon and oxygen production through the lives of stars of 1.3, 5, 15 and 25 solar masses.  The same authors revise their own 2000 conclusion.  The article uses it to show that the authors of a claim repeated by apologetics writers later walked it back.  Mirror:  arXiv ↩

  24. 24.

    Epelbaum, Evgeny et al.  “Viability of Carbon-Based Life as a Function of the Light Quark Mass.”  Physical Review Letters 110:112502.  2013.  The paper states that its theoretical uncertainty.  “is also compatible with a vanishing ∂ε/∂M_π (complete lack of fine-tuning).”  A calculation by nuclear physicists, using nuclear lattice simulations built on chiral effective field theory, of how far the light quark mass can change before carbon and oxygen production in stars fails.  It finds that carbon-based life survives at least a 0.7% shift in the light quark mass in its worst case, and that shifts of 2 to 3% are unlikely to be catastrophic.  The article cites it for that 2 to 3% tolerance and the 0.7% worst case. ↩

  25. 25.

    Huang, Lillian et al.  “Sensitivity of carbon and oxygen yields to the triple-alpha resonance in massive stars.”  Astroparticle Physics 105:13–24.  2019.  A paper on how sensitive the carbon and oxygen yields of massive stars are to the triple-alpha resonance.  The article cites it in its passage on the precision claims made about carbon and oxygen production. ↩

  26. 26.

    MacDonald, J., and D. J. Mullan.  “Big bang nucleosynthesis: The strong nuclear force meets the weak anthropic principle.”  Physical Review D 80:043507.  2009.  “Anthropic limits on the strong force strength from BBN are indeed weak.”  A calculation of how the early universe would make light elements if the strong nuclear force were stronger, by J. MacDonald and D. J. Mullan of the University of Delaware.  It includes processes that earlier treatments overlooked, and it finds that substantial hydrogen survives as long as the strong force is raised by less than about 50 percent.  The article uses it as the first of two groups that took apart the claim that a stronger strong force would turn all the hydrogen into helium.  Mirror:  arXiv ↩

  27. 27.

    Barnes, Luke A., and Geraint F. Lewis.  “Producing the Deuteron in Stars: Anthropic Limits on Fundamental Constants.”  Journal of Cosmology and Astroparticle Physics (07):036.  2017.  A theoretical calculation of what happens to stars if the nuclear force is weakened enough to unbind the deuteron, the two-particle nucleus of heavy hydrogen.  It extends a published stellar model by Adams (2008) and tracks the neutrino losses that cool a ball of gas before it can ignite.  It finds that an unbound deuteron stops a gas ball from becoming a stable star, which makes it the most definitive boundary in parameter space between life-permitting and life-prohibiting universes, while a weakly bound deuteron does not seem to be catastrophic for life.  The article uses it for the claim that this is the sharpest boundary in the whole parameter space. ↩

  28. 28.

    Adams, Fred C., and Evan Grohs.  “On the Habitability of Universes without Stable Deuterium.”  Astroparticle Physics 91:90–104.  2017.  “universes with no stable deuterium are thus potentially habitable, contrary to many previous claims.”  A theoretical study of stars in universes where the strong force is weak enough that deuterium, the heavy hydrogen nucleus whose production is the first step toward heavier nuclei, is not stable.  Using analytic estimates and a stellar evolution code, it finds that such stars can still shine by gravitational contraction, can make heavy elements when massive ones explode, can make helium by a triple-nucleon reaction, and can use the CNO cycle once trace heavy elements exist, so these universes may be habitable.  The article sets it against Barnes and Lewis's 2017 claim that the deuterium boundary is the sharpest in the whole parameter space, and treats the two as a real disagreement.  Mirror:  arXiv ↩

  29. 29.

    Hogan, Craig J.  “Why the universe is just so.”  Reviews of Modern Physics 72:1149–1161.  2000.  A review of anthropic reasoning, the idea that some constants are selected from a range of possibilities because complex things such as observers must be able to exist.  It reviews several successes and failures of that reasoning, and says three of the Standard Model parameters sit in a very narrow window that gives stable nucleons and nuclei and abundant carbon.  The article cites it for one row of its table of nuclear levels, the oxygen-16 level that sits 43 keV below the carbon-plus-helium threshold.  Mirror:  arXiv ↩

  30. 30.

    Weinberg, Steven.  Living in the Multiverse.  Sep 2005.  “Quantum fluctuations in known fields at well-understood energies (say, less than 100 GeV) give a value of ρ_V larger than observationally allowed by a factor 10^56.”  The opening talk at the Trinity College, Cambridge symposium "Expectations of a Final Theory", to be published in Universe or Multiverse?, edited by B. Carr (Cambridge University Press).  It argues that the string landscape, with its many possible universes, makes anthropic reasoning, the argument that observers can only find physical values that allow observers, a new basis for physics.  The article uses it for Weinberg's account of the vacuum energy as an apparently successful example of anthropic reasoning. ↩

  31. 31.

    DESI Collaboration.  “DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints.”  Physical Review D 112:083515.  2025.  A survey paper by the DESI collaboration, which measures baryon acoustic oscillations (BAO), a regular pattern in the spacing of galaxies left by sound waves in the early universe, from more than 14 million galaxies.  The lead author is Abdul-Karim, M.  The preference for evolving dark energy over a cosmological constant is 2.8σ with the Pantheon+ supernova sample, 3.8σ with Union3, 4.2σ with DES-Y5, and 3.1σ using no supernovae at all.  The article cites it for the 2.8 to 4.2 standard deviation range. ↩

  32. 32.

    Popovic, Brodie et al.  “The Dark Energy Survey Supernova Program: A Reanalysis Of Cosmology Results And Evidence For Evolving Dark Energy With An Updated Type Ia Supernova Calibration.”  MNRAS.  2026.  “Our results hold a significance of 3.2σ, reduced from 4.2σ for DES-SN5YR…  our updated data exhibits only a weak preference for evolving dark energy.”  A reanalysis by the Dark Energy Survey collaboration of its own five-year sample of Type Ia supernovae, after an improved calibration of the supernova measurements.  It lowers the evidence that dark energy changes over time from 4.2 to 3.2 standard deviations, and calls the remaining preference weak.  The article uses it as the reason the signal from the DESI survey may not hold up. ↩

  33. 33.

    Li, Tian-Nuo et al.  “Dark Energy in the DESI Era: A Brief Review of Evidence, Beyond-ΛCDM Interpretations, and Tensions.”  Research in Astronomy and Astrophysics 26:084002.  2026.  “Taken together, the current evidence for DDE is best understood as a dataset-dependent indication rather than a settled discovery.”  An invited review of the evidence from the DESI survey that dark energy may change over time, which the review calls dynamical dark energy.  It examines how that evidence depends on the model and the datasets combined, and what other physics could produce the same effect.  The article uses it to show that the DESI result is not yet a settled discovery. ↩

  34. 34.

    Wright, Angus H. et al.  “KiDS-Legacy: Cosmological constraints from cosmic shear.”  Astronomy & Astrophysics 703:A158.  2025.  Section Abstract:  The earlier KiDS-1000 analysis had reported a 3σ tension.  “in agreement (0.73σ) with results from the Planck Legacy cosmic microwave background experiment”.  The authors attribute the change to this.  “improved redshift distribution estimation and calibration.”  A survey paper from the Kilo-Degree Survey (KiDS) that measures cosmic shear, the faint distortion of distant galaxy shapes by the mass between us and them, using the completed survey.  It finds the S8 value, a measure of how clumped matter is, in agreement with the Planck satellite's microwave background results.  The article cites it for a tension that looked like new physics and turned out to be calibration. ↩

  35. 35.

    Carroll, Sean M.  “Does the Universe Need God?”  The Blackwell Companion to Science and Christianity.  Wiley-Blackwell.  Edited by J. B. Stump and Alan G. Padgett.  2012.  A chapter in a 2012 handbook on science and Christianity.  The article quotes one question from it, about why the universe would need so much needless low entropy and so many galaxies if its purpose was life. ↩

  36. 36.

    Tegmark, Max, and Martin J. Rees.  “Why is the Cosmic Microwave Background Fluctuation Level 10⁻⁵?”  Astrophysical Journal 499:526–532.  1998.  A journal paper by Max Tegmark and Martin Rees on the size of the fluctuations in the cosmic microwave background, which the title puts at 10⁻⁵.  The article uses it for that size, Q of about 10⁻⁵, and for the band of roughly 10⁻⁶ to 10⁻⁴ that the article says permits life. ↩

  37. 37.

    Livio, Mario, and Martin J. Rees.  Fine-Tuning, Complexity, and Life in the Multiverse.  2018.  “should best be between 10-6 and 10-4, and therefore not particularly finely tuned.”  A chapter by Mario Livio of the University of Nevada, Las Vegas, and Martin Rees of the University of Cambridge.  It traces how the values of the constants decide whether stars, planets and life can form, and it argues that testing whether a multiverse exists is a scientific task.  The article uses it because Rees, who once listed the fluctuation amplitude among six fine-tuned constants, here calls it not particularly finely tuned.  Mirror:  arXiv ↩

  38. 38.

    Aguirre, Anthony.  “The cold big-bang cosmology as a counter-example to several anthropic arguments.”  Physical Review D 64:083508.  2001.  A theoretical cosmology study that builds a family of universes on the classical cold big bang model, in which some or all of the cosmological parameters differ by orders of magnitude from the standard hot big bang values.  It argues that the requirement of sun-like stars with planets does not fix these parameters, and that such universes do not preclude intelligent life in any obvious way.  The article uses it because apologetics almost never engages it, and anyone building a case on the anthropic arguments has to answer it.  Mirror:  arXiv ↩

  39. 39.

    Planck Collaboration.  “Planck 2018 results. VI. Cosmological parameters.”  Astronomy & Astrophysics 641:A6.  2020.  “n_s = 0.9649 ± 0.0042 (68 %, Planck TT,TE,EE+lowE+lensing), which is 8 σ away from scale-invariance (n_s = 1), confirming the red tilt of the spectrum at high significance in ΛCDM.”  A paper from the Planck team that reports the fitted values of the main numbers in the standard cosmological model, from its 2018 results.  The article uses it for the measured tilt of the primordial density ripples, which lies eight standard deviations from scale-invariance. ↩

  40. 40.

    Guth, Alan H. et al.  “A Cosmic Controversy.”  Scientific American.  May 10, 2017.  A reply to Ijjas, Steinhardt and Loeb, signed by thirty-three physicists including Stephen Hawking, Steven Weinberg, Edward Witten, Frank Wilczek, Martin Rees, Leonard Susskind, Juan Maldacena, Lisa Randall, Sean Carroll and Lawrence Krauss.  Ijjas, Steinhardt and Loeb's response is printed on the same page.  The article uses it for the signers' central reply, that standard inflation models could have failed the empirical tests but did not. ↩

    1. 40a.

      “The average mass density of the universe has now been measured to an accuracy of about half of a percent, and it agrees perfectly with the prediction of inflation.  (When inflation was first proposed, the average mass density was uncertain by at least a factor of three, so this is an impressive success.)”  “An important point is that standard inflationary models could have failed any of the empirical tests described above, but they did not.” ↩

  41. 41.

    Linde, Andrei.  Inflationary Cosmology after Planck 2013.  2014.  Section 11.  A review of inflationary cosmology in the light of the 2013 data from the Planck satellite, by Andrei Linde of Stanford, one of inflation's own architects.  It gives special attention to a newer class of models, the cosmological attractors.  The article uses it for Linde's own admission that inflation's theorists built models to fit a density of about 0.3 before dark energy was discovered.  Mirror:  arXiv ↩

  42. 42.

    Bucher, Martin et al.  “An open universe from inflation.”  Physical Review D 52:3314.  1995.  A 1995 paper, titled "An open universe from inflation," in Physical Review D.  A second 1995 paper in the same journal, by Andrei Linde and Arthur Mezhlumian, is "Inflation with Ω ≠ 1," Physical Review D 52 (1995): 6789.  The article uses these two papers as its 1995 examples of inflation models built to fit a density of about a third of the critical value. ↩

  43. 43.

    Mukhanov, Viatcheslav.  Quantum Cosmological Perturbations: Predictions and Observations.  2013.  A short paper by Viatcheslav Mukhanov that works out what the theory of quantum fluctuations predicts for inflation, using a model-independent description.  It finds that the spectral index should deviate from a flat one by at least 3 percent whatever the scenario, and it derives a lower bound on the gravitational waves produced.  The article cites it in its account of inflation's own theorists adjusting their models to the measured density.  Mirror:  arXiv ↩

  44. 44.

    Tegmark, Max.  “What does inflation really predict?”  Journal of Cosmology and Astroparticle Physics 04:001.  2005.  The quoted sentences are Barnes' summary of Tegmark's figure, in Barnes, PASA 29 (2012), arXiv:1112.4647:  “The success rate peaks at ∼ 0.1 percent, and drops rapidly as m_h increases or decreases away from m_Pl.  Even with a scalar field, inflation is far from guaranteed.”  A physics paper that computes the probabilities of the cosmological parameters that inflation would predict, across several classes of inflation models.  It finds that, unless the scale on which the potential varies is near the Planck scale, the only feature of the potential that matters observationally is the statistical distribution of its peaks and troughs.  The article uses it through Barnes's reading of its figure, which puts the peak success rate of inflation at about 0.1%.  Mirror:  arXiv ↩

  45. 45.

    Hollands, Stefan, and Robert M. Wald.  “An alternative to inflation.”  General Relativity and Gravitation 34:2043–2055.  2002.  “although inflationary models may alleviate the 'fine tuning' in the choice of initial conditions, the models themselves create new 'fine tuning' issues with regard to the properties of the scalar field.”  A paper by Stefan Hollands and Robert Wald of the University of Chicago.  It argues that inflation's explanations of the universe's smoothness and flatness are not satisfactory, and that non-inflationary models could produce the same spectrum of density ripples.  The article cites it as a rival to inflation.  Mirror:  arXiv ↩

  46. 46.

    Penrose, Roger.  The Road to Reality: A Complete Guide to the Laws of the Universe.  Jonathan Cape.  2004.  Section 28.5, pages 753–757:  The critique of inflation is in this section.  Section 28.8:  This section covers the Weyl Curvature Hypothesis.  A general book on the laws of physics by Roger Penrose.  The article uses its critique of cosmic inflation, which says the original reasons for inflation are weaker than they seemed.

    1. 46a.

      Section 28.5, page 757. ↩

    2. 46b.

      Section 28.5, page 755. ↩

    3. 46c.

      Section 28.5, page 753:  “my remarks do not tell us that inflationary cosmology is wrong.  They merely provide strong reasons to doubt most of the initial motivations behind the inflationary idea.”  He also grants that.  “inflationists have made some definite predictions which, in recent years, have measured up remarkably well against a number of impressive new observations.” ↩

  47. 47.

    Albrecht, Andreas.  Cosmic Inflation and the Arrow of Time.  2002.  Section 5.2 Inflation and the arrow of time:  “So while inflation does dynamically 'predict' the special initial state of the big bang phase, it does not predict the arrow of time.  Inflation 'passes the arrow of time buck' to the special initial conditions of the inflaton field.”  An essay on whether cosmic inflation can explain the arrow of time, the one-way direction in which processes such as breaking a glass run.  It starts from the point that the arrow of time comes from very unusual low-entropy starting conditions.  Albrecht is a co-author of the 1982 new-inflation paper.  The article cites it for his own concession that inflation does not predict the arrow of time. ↩

  48. 48.

    Carroll, Sean M., and Jennifer Chen.  Spontaneous Inflation and the Origin of the Arrow of Time.  2004.  “it requires much less fine-tuning to simply put the universe in some state that can evolve into our present conditions”.  A 2004 preprint in which Carroll and Chen accept the critique of inflation's account of the arrow of time.  They escape it only by questioning whether the evolution of the universe is unitary.  The article cites it for Carroll and Chen's agreement with the critique, and for their escape by giving up the assumption that the universe's evolution is reversible. ↩

  49. 49.

    Kofman, Lev et al.  “Inflationary Theory and Alternative Cosmology.”  JHEP 0210:057.  2002.  “inflationary evolution is irreversible, and the 'obvious' requirement of measure preserving evolution is not satisfied in inflationary cosmology.”  A 2002 reply by three inflation theorists to Hollands and Wald's alternative to inflation, arguing that the alternative needs density ripples to form when the hot universe's energy density was 1095 times the Planck density, where nobody can make calculations.  The authors also reject the entropy critique of inflation, saying inflationary evolution is not measure-preserving.  The article uses it for Linde and co-authors' rejection of the argument that inflation fails on the arrow of time.  Mirror:  arXiv ↩

  50. 50.

    BICEP/Keck Collaboration.  “BICEP/Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season.”  Physical Review Letters 127:151301.  2021.  The collaboration reports:  “The likelihood analysis yields the constraint r_0.05 < 0.036 at 95% confidence.”  A collaboration paper that limits primordial gravitational waves, the hypothesised ripples in spacetime left by the early universe, by combining Planck and WMAP satellite data with BICEP/Keck telescope observations.  The lead author is P. A. R. Ade.  The article cites it for the 0.036 limit on the tensor-to-scalar ratio, the number that measures how strong those waves are.  Tristram et al., Physical Review D 105 (2022): 083524, combine Planck PR4 with these data and obtain r < 0.032.  A more sensitive BICEP result is forecast but unpublished as of 2026. ↩

  51. 51.

    Planck Collaboration.  “Planck 2015 results. XX. Constraints on inflation.”  Astronomy & Astrophysics.  2015.  “These results imply that V(φ) ∝ φ² and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R² inflation.”  The 2013 statement is from Planck 2013 results XXII, arXiv:1303.5082:  “monomial potential models of degree n ≥ 2 do not provide a good fit to the data.”  A paper by the Planck team that tests the simplest models of cosmic inflation against the full Planck mission data, which include temperature and polarization measurements of the cosmic microwave background.  It sets an upper limit of 0.11 (95% confidence) on the tensor-to-scalar ratio, a measure of how strong the gravitational waves from inflation would be.  The article uses it for the finding that the quadratic potential and natural inflation are now disfavoured. ↩

  52. 52.

    Ijjas, Anna et al.  “Cosmic Inflation Theory Faces Challenges.”  Scientific American.  Feb 2017.  A magazine article by three authors arguing that cosmic inflation faces challenges.  Their earlier technical statements are "Inflationary paradigm in trouble after Planck2013," Physics Letters B 723 (2013): 261–266, arXiv:1304.2785, and "Inflationary schism after Planck2013," Physics Letters B (2014), arXiv:1402.6980.  The article uses it for Paul Steinhardt's argument, from one of inflation's own founders, that the theory's forecasts contain no threshold that would falsify it. ↩

  53. 53.

    Guth, Alan H. et al.  “Inflationary paradigm after Planck 2013.”  Physics Letters B 733:112–119.  2014.  “We argue that their conclusions rest on several problematic assumptions, and we conclude that cosmic inflation is on a stronger footing than ever before.”  A reply by three physicists, Alan Guth, David Kaiser and Yasunori Nomura, to a critique of inflation.  They argue that the critics' conclusions rest on several problematic assumptions, and they conclude that inflation stands on a stronger footing than ever before.  The article cites it because inflation's own theorists argue in print about whether the theory is falsifiable, and that dispute matters to its case.  Mirror:  arXiv ↩

  54. 54.

    Collins, Robin.  “The Teleological Argument: An Exploration of the Fine-Tuning of the Universe.”  The Blackwell Companion to Natural Theology, 202–281.  Wiley-Blackwell.  Edited by William Lane Craig and J. P. Moreland.  2009.  Page 251:  The concession on the popular presentation is on this page.  “the popular presentation of the argument would have to be modified.”  “the McGrews and others are wrong in claiming that there would be no epistemic probability if the range is infinite”.  A chapter, abridged from a book-length project, in which Collins argues that the fine-tuning of the universe for life, together with the beauty and intelligibility of the laws of nature, supports the existence of God.  The article cites it for Collins's answer to the McGrews' reductio on infinite comparison ranges, and for his concession on the popular presentation of the argument. ↩ ↩

  55. 55.

    Koperski, Jeffrey.  “Should We Care about Fine-Tuning?”  British Journal for the Philosophy of Science 56(2):303–319.  2005.  A paper that asks in its title whether we should care about fine-tuning.  The article uses it for Koperski's answer: use measure theory rather than probability, accept that fine and coarse tuning come out equivalent, and treat that as a tolerable result. ↩

  56. 56.

    Barnes, Luke A.  “Fine-tuning in the context of Bayesian theory testing.”  European Journal for Philosophy of Science 8:253–269.  2018.  A physicist's paper on how to test a theory that has free constants, using Bayesian probability, the method physicists use to compare models.  It argues that the objection that fine-tuning probabilities cannot be normalised applies to any theory with free parameters, and that physics avoids the problem by bounding some parameters at the Planck scale and not assuming that the others are spread evenly.  The article relies on it for the strongest reply to the objection that the probabilities cannot be calculated at all. ↩

  57. 57.

    Manson, Neil A.  “The Fine-Tuning Argument.”  Philosophy Compass 4(1):271–286.  2009.  A survey article by Neil A. Manson of the University of Mississippi.  It sets out the fine-tuning argument, then covers two objections: that a multiverse plus the anthropic principle explains fine-tuning, and the normalizability problem, the claim that fine-tuning is not actually improbable.  The article uses it because Manson surveys the debate neutrally and sides with the McGrews on the key point: a bound taken from where our theories break down is a fact about the reach of those theories, not about what was possible. ↩

  58. 58.

    Díaz-Pachón, Daniel Andrés et al.  “Is Cosmological Tuning Fine or Coarse?”  Journal of Cosmology and Astroparticle Physics 07:020.  2021.  A 2021 physics paper that asks whether cosmological tuning is fine or coarse.  The same footnote also cites Chris Dorst and Kevin Dorst, "Splitting the (In)Difference: Why Fine-Tuning Supports Design," Thought 11 (2022): 14–23.  The article uses these two papers to show that the debate went on after 2018. ↩

  59. 59.

    Weisberg, Jonathan.  “A note on design: what's fine-tuning got to do with it?”  Analysis 70:431–438.  2010.  A short philosophy paper in the journal Analysis, asking what the fine-tuning of the constants has to do with design.  The same journal also carries Weisberg's "The argument from divine indifference" (Analysis 72 (2012): 707–714) and a reply by White, "The argument from cosmological fine-tuning" (Analysis 71 (2011)).  The article uses it for the challenge that a designer with unknown aims gives no more reason than chance to expect life-permitting constants. ↩

  60. 60.

    McGrew, Lydia.  “Four (Or So) New Fine-Tuning Arguments.”  European Journal for Philosophy of Religion 8(2):85–106.  2016.  A 2016 paper that proposes four, or so, new fine-tuning arguments.  The article uses it because McGrew builds new arguments around her 2001 objection without retracting it. ↩

  61. 61.

    Barnes, Luke A.  “Fine-Tuning on the TV: A Review of ABC's Catalyst.”  Letters to Nature (blog).  Aug 30, 2013.  A blog post reviewing the ABC television programme Catalyst and its treatment of fine-tuning.  The article uses it for Barnes's analogy of a factory that builds cars from random parts, which shows why a working car would not surprise you but a working satellite navigation system would. ↩

  62. 62.

    Barnes, Luke A.  “A Reasonable Little Question: A Formulation of the Fine-Tuning Argument.”  Ergo 6(42).  2019.  Section 4.4:  Replies to Halvorson by name.  The fuller technical reply is in section 6.2 of Barnes's 2018 journal paper, which cites Halvorson's 2014 preprint A probability problem in the fine-tuning argument.  A philosophy paper that offers a new version of the fine-tuning argument for God's existence.  It focuses on the fundamental constants and initial conditions of the universe, and says physics itself supplies the probabilities the argument needs.  The article uses it as the published reply to the objection of Hans Halvorson. ↩

  63. 63.

    Sober, Elliott.  “The Design Argument.”  The Blackwell Guide to the Philosophy of Religion, 117–147.  Blackwell.  Edited by William E. Mann.  2004.  Pages 132–134:  The Eddington analogy and its application are on these pages.  Pages 136–138:  The firing-squad dilemma is on these pages.  A chapter by Elliott Sober in a guide to the philosophy of religion.  The article uses it for the cleanest form of the objection that observers can only find a universe that allows observers, so finding ourselves here cannot favour design. ↩

  64. 64.

    Leslie, John.  Universes.  Routledge.  1989.  Section 1.17, pages 13–15.  Page 198:  “God is real, and/or there are many and varied universes”.  A 1989 book in which Leslie gives his own version of the firing-squad example, with fifty sharpshooters.  The widely quoted "144 shots" version is Swinburne's retelling; his conclusion is disjunctive, and his "God" is an impersonal creative principle rather than the God of theism.  The article uses the firing squad as the standard reply to the claim that we should not be surprised to find a universe fit for us. ↩

  65. 65.

    Ellis, George, and Joe Silk.  “Scientific method: Defend the integrity of physics.”  Nature 516:321–323.  Dec 18, 2014.  A piece in Nature by George Ellis and Joe Silk.  The article cites it for their argument that defending untestable theories damages the integrity of physics. ↩

  66. 66.

    Isaacs, Yoaav et al.  “Multiple Universes and Self-Locating Evidence.”  Philosophical Review 131(3):241–294.  2022.  A philosophy paper that defends the multiverse inference against the charge, made by Ian Hacking and Roger White, that it rests on a fallacy.  The authors say the key issue is self-locating evidence, which is evidence about our own place in the world.  The 'this universe' objection comes from Roger White, "Fine-tuning and multiple universes," Noûs 34 (2000): 260–276.  The article uses it to report that the question is unresolved. ↩

  67. 67.

    Pace, Norman R.  “The universal nature of biochemistry.”  Proceedings of the National Academy of Sciences 98(3):805–808.  2001.  A paper on the universal nature of biochemistry.  The article uses it as the standard citation for silicon being a worse basis for life than carbon: silicon's bonds are weaker, its long chains are unstable, and its oxide is a solid rather than a gas, which makes respiration difficult. ↩

  68. 68.

    Carr, Bernard J., and Martin J. Rees.  “The anthropic principle and the structure of the physical world.”  Nature 278:605–612.  Apr 12, 1979.  A paper in Nature that the article calls the founding 1979 study of the anthropic principle. ↩

    1. 68a.

      “entirely post hoc”.  The same paper describes the anthropic principle this way.  It also notes that the principle has never made a prediction. ↩