New Post: Faith, Decision Making and Probability III: Bayes' Theorem and the Anthropic Principle

Hello all.   New post on Catholic Stand: "Faith, Decision Making and Probability III: <br>Bayes' Theorem and the Anthropic Principle."  I  derive Bayes' Theorem and discuss two examples of how it is used to incorporate new knowledge into modifying probability as a measure of belief:  the Monty Hall problem (the three doors with a prize and goats), and a medical test for a rare disease.

New Post: "Are We Special--The Anthropic Principle"

Hello all!   A new post, "Are We Special, The Anthropic Principle," on the Magis Center for Faith and Reason website.  It's taken from Essay 4 of my web-book, "Truth Cannot Contradict Truth"

New Post: "Are We Special? The Anthropic Principle

Hello all.  A new post, "Are We Special? The Anthropic Principle." is finally published.  I talk about those unlikely conditions and events in cosmology,  planetary science, physics, chemistry and molecular biology that enable carbon-based life (and thus, us) to exist in this universe.  Read, Comment, Critique!

New Post: "Is there a Probability for the Universe...?"

Hello all.  Spring has sprung and summer is almost here!  A new post on Catholic Stand: "Is there a Probability for the Universe? New Thoughts about the Anthropic Coincidences" I discuss the anthropic coincidences, those unlikely features in cosmology, physics and chemistry that are required for the existence of carbon-based life in this universe.  Since ordinary (frequentist) interpretations of probability aren't appropriate in assessing these, I present a different interpretation of probability--Bayesian, based on measure of belief.

New Post: "God's Gift to Molecular Biology: the Hydrogen Bond"

Hello all.   Here's a new post on the Magis Center for Faith and Reason: "God's Gift to Molecular Biology: the Hydrogen Bond."   It's about DNA and how the hydrogen bond enables it to do its thing.

New Post: "The Theology of Water" on Magis Center for Faith and Reason.

Hello all--another new post (actually a rewrite of an earlier one on this blog): "The Theology of Water" on the Magis Center for Faith and Reason web site.

Are We Special? New Thoughts about the Anthropic Principle

William Blake, Europe--A Prophecy
from Wikimedia Commons

“Scientists are slowly waking up to an inconvenient truth - the universe looks suspiciously like a fix. The issue concerns the very laws of nature themselves. For 40 years, physicists and cosmologists have been quietly collecting examples of all too convenient "coincidences" and special features in the underlying laws of the universe that seem to be necessary in order for life, and hence conscious beings, to exist. Change any one of them and the consequences would be lethal. Paul Davies, winner of the 1995 Templeton Prize

"It is a strange fact, incidentally, that religious apologists love the anthropic principle. For some reason that makes no sense at all, they think it supports their case. Precisely the opposite is true. The anthropic principle, like natural selection, is an alternative to the design hypothesis. It provides a rational, design-free explanation for the fact that we find ourselves in a situation propitious to our existence.”  Richard Dawkins, The God Delusion

INTRODUCTION 

You see in the quotes above two different views of the Anthropic Principle, that our universe is finely tuned to support carbon-based life; it's known in several versions ranging in acronym form from Weak Anthropic Principle (WAP), to Strong Anthropic Principle (SAP), to Christian Anthropic Principle (CAP), to Completely Ridiculous Anthropic Principle (you do the acronym).

My interest has been awakened again by conversations (via email) with an author who believes that the Anthropic Principle, as exemplified in a series of physical events and values for constants--the anthropic coincidences--strongly and quantitatively (via probability arguments)  supports the proposition of a creating God.

I also believe that these anthropic coincidences help us to believe in God, but I do not believe that probability arguments, as they have been used heretofore, are valid.     Rather, I take the point of view of the psalmist  in Psalm 19:

"The heavens declare the glory of God; and the firmament sheweth his handywork.  Day unto day uttereth speech, and night unto night sheweth knowledge.  There is no speech nor language, where their voice is not heard." KJV

THE ANTHROPIC COINCIDENCES AND FINE-TUNING

These anthropic coincidences have been discussed in two other posts on this blog:   Philosophic Issues in Cosmology 6, The Theology of Water.   I'll summarize the arguments presented in these posts;  if you, the reader, are not familiar with the ins and outs of the anthropic principle, I urge you to read these posts and the references contained therein.

I'll not go through an exhaustive list--that's done in references given in the linked posts; rather they can be categorized as follows:

• Features of the universe--e.g. space dimensionality 3; the mass/energy content of the initial universe that enabled expansion but not immediate collapse; uniformity in very early universe;  size;
• Finely tuned values for fundamental physical parameters--e.g. the mass difference between proton and neutrons that enables stability for nuclear processes; the carbon-12 excited state energy that by resonance enhances the probability of carbon-12 nucleus formation from a rare collision of three He nuclei;
• Nature of physical laws--e.g ratio of electromagnetic force to gravitational force; inverse cube force law for gravity; quantum mechanical laws that enable chemical bonding and (see below) the special properties of water;
• "Accidental" geo-astronomical features--e.g. tilt of the earth's axis enabling life-friendly climate, unusually large moon shielding earth from asteroid and meteor collision.

It must be emphasized that there are many more instances of such fine tuning--parameters for which the values have to lie between narrow limits to enable a life-supporting universe, and many more examples of geo-astronomical and chemical features.    Ellis, in the reference linked above, specifies general conditions that must obtain for a universe to contain life as we know it.

IS THERE A PROBABILITY FOR THE UNIVERSE?  

Some Christian apologists use the anthropic coincidences as an argument for the existence of God by citing the very low probability for their occurrence; all these happening would not occur by chance.   A major objection to this procedure, which Ellis points out, is that the universe is a single datum--probability arguments are generally applied to samples from larger collections for which we have information about variability.

For example, if you've examined 20,000 crates of oranges and found 100 crates containing bad oranges, you'd be justified in putting a probability of  100/20,000 or .005 in finding a bad orange in the next crate.   But if you've only come across one crate of oranges, then it's speculation to put a probability on finding a bad orange.  (But see below.)

Another error one finds is that some apologists list a string of fine tuning examples (call them a,b,c,d...x),  and then use the argument that P(a,b,c,d...x) = P(a) P(b) P(c)P(d)...P(x).    They say that the probability of the total set is the product of the probabilities for each member  of the set.

This would be true if the events were independent, in other words if what happened for one event did not depend on what happened for another.* Such independence will not necessarily hold.   Consider, for example, the properties of

Model of Ice Structure, red: oxygen; white, hydrogen
Dashed lines represent hydrogen bonds
From Wikimedia Commons

water that are life-friendly:

• thermodynamic--high freezing and boiling points, high specific heat, etc.;
• physical --surface tension, low specific gravity of ice, maximum density of liquid water at 4 deg C.   

These properties all depend on the very unusual capacity of protons in a H2O molecule to form strong hydrogen bonds to oxygen atoms in other H2O molecules.   And that hydrogen bonding capability arises from quantum mechanics and the physical nature of electrostatic attraction.    So it is one feature, not many, for which a probability should entered. .    And how do you assess the probability of quantum mechanics giving rise to hydrogen-bonding?

PROBABILITY AS A MEASURE OF BELIEF

"But is it probable that probability brings certainty?" Blaise Pascal, Pensees 496

I'm going to try a different approach, using probability as a measure of belief. (I apologize to those professional statisticians and mathematicians who will certainly be offended by my presumption.)   The approach is my take on Richard Jeffrey's Subjective Probability.

Let's start with a different definition of probability, based on strength of belief.   Consider the following examples for betting on a horse race.   You overhear a trainer telling a pal that "the next race is fixed for Trump's Nag to win, with odds of 9/1".    You bet $10,  expecting to win $90.    The defined probability, working from the odds ratio, is  1/(9+1) = 0.10.    The probability of losing your bet is then 1- 0.10 = 0.90.    The expectation value is 0 = 0.10 x 90 + 0.90 x(-10).

The next step is to consider conditional probability, that is how the probability of an event depends on a linked event.   Let A represent the event that the stock price rises to $100.   Let B represent the event that information about the possible rise of the stock is given.    Then the conditional probability is denoted as p(A|B), the probability of event A given that event B occurs.   Note that there is no causal relation implied here--it's only a matter of evidence.

Now to the meat of the matter.   Let F represent the event of fine-tuning for the universe;  G, that God exists;  N, that God does not exist (or that "Naturalism= materialism" accounts for everything).    Then

• p(G| F )  is a probability, a degree of belief, that F --> G, i.e. fine-tuning is evidence for the existence of God;  
• p(N | F)  is a probability that fine-tuning implies that God does not exist;  
• p(F | G) is the probability that if God exists then He can fine-tune the universe;  
• p(F | N) is the probability that a fine-tuned universe would occur in the absence of God;  
• p(G) is the probability--the degree of belief--that God exists;
• p(N)  is the probability--the degree of belief--that God does not exist.

Then straightforward manipulation gives (see note **) yields

 P(G | F)) = [ P(G) ] [ P(F | G) ]

 P(N | F)      [ P(N) ] [ P(F | N)]               

       1                2             3

Term 1 is a likelihood ratio for belief that fine-tuning implies the existence of God to belief that fine-tuning  implies no God;  term 2 is a likelihood ratio for belief in God to belief in no God (naturalism);   term 3 is a likelihood ratio for belief that God, if He exists, would create a fine-tuned universe to support life to belief that naturalism/materialism would yield a fine-tuned universe.

Now certainly term 3 is a number much greater than 1, even if the exact value is indeterminate.   The value for term 2 will depend on the individual--for a Christian martyr, it would be a huge number;    for Richard Dawkins or Lawrence Kraus it would be a very small number.

Here's the point: the value you impute to term 1, the likelihood ratio for belief that a fine-tuned universe is evidence for the existence of God, will be greater than  1 if you are not a hard core atheist.    If you're agnostic--it's a 50/50 proposition that God exists--then certainly fine tuning should convince you that God exists.   If you're an extreme atheist, then term 2 could become small enough to swamp term 3, even if the latter is very large.

So the upshot is that if you do believe in God or if you're an agnostic, fine tuning can be evidence for God's creating hand.   If you're an atheist--this will not be sufficient evidence.   And we come again to Grace given by the Holy Spirit as the mechanism for faith.
  

NOTES

 * Further, if you do this with a large number of events, it will certainly not lead to useful information.   Consider a series of 50 independent events, each of which has a probability of 0.9.   Then the probability for all the events happening together is 0.9 ^ 50 = .0052. which is small, even though the probability for the events individually is large.

**Consider p(A and B), the probability that both A and B occur (or that both A and B are true propositions).   Then a form of Bayes' theorem is  that
p(A and B) = p(A | B) p(B) = p (B | A) p(A);  
whence p(A | B) = [p(A)/p(B)] [ p( B | A) ]

Philosophic Issues in Cosmology 8: Foundational Propositions and Conclusions

“One question in science is not  ' is this hypothetical model true' but "is this model better than the alternatives'...If we believe dogmatically in a particular view, then no amount of contradictory data will convince us otherwise...” John Skilling, “Foundations and Algorithms” in Bayesian Methods in Cosmology

This is the eighth post summarizing Issues in the Philosophy of Cosmology by George F.R.  Ellis.   A complete list of the issues and theses he presents is given in the Appendix below*.    Before addressing the philosophic issues themselves, some preliminary remarks are in order.

•  First, because of space limitations, the summary has been selective; a number of technical issues have not been discussed; if a reader is interested in these, I'd recommend the original article, via the web link given above. 
• Second, contrary to some comments on these posts, neither Ellis nor I are making any arguments for theism or anti-atheism in the post proper; philosophic alternatives are presented, and if a reader draws theological conclusion from these alternatives, that's up to him/her.* 
• Third, no values for evidential probability (in the post on Anthropic Coincidences) have been presented; indeed, Ellis argues (and I agree) that inferring an evidential probability for one datum (our universe) is not a valid procedure. 
• Fourth, the general focus of the article, and my emphasis in these posts, is on what can science say about cosmology and what philosophic assumptions underlie such scientific conclusions.

SCIENTIFIC CRITERIA

Ellis gives as an important criteria for a scientific theory that it be empirically testable.  My position may be even stronger than that of Ellis: if a theory cannot be confirmed by quantitative measurements then it is not in my view (and that of Fr. Stanley Jaki), science, but something else—mathematical metaphysics?

• What can be confirmed by measurement is limited by the time, distance and physics horizons mentioned in the first post. 
• Using electromagnetic radiation we cannot see further back in time than when radiation decoupled from matter, about 380,000 years after the origin. 
• We cannot see further in space than given by the distance horizon, the distance at which space will be expanding at faster than the speed of light. 
• We cannot duplicate the tremendous energies present in the initial, quantum stages of the beginning of the universe (these energies are orders of magnitude greater than even the huge energies that will be available in the SLAC Hadron supper collider), so we cannot test projected theories of particle creation. 

What can be measured are inferred consequences of various theories: what the cosmic background radiation (CBR) shows about homogeneity, isotropy, fluctuations, the cosmological constant (lambda, representing expansion pressure), etc. Recent examples are the report of Gurzadyan and Penrose of rings in the CBR representing cataclysmic events pre-Big Bang  and B-mode measurements  of the CBR from which are inferred gravitational waves in the early universe and thus inflation.   One may disagree with the aspects of the theory, but the tie-in with measured data is commendable.

THESES FOR PHILOSOPHIC ISSUES 

Ellis gives a series of theses for his position on philosophic issues and these are presented as an appendix, to give a complete summary. The theses in Issue F, “The explicit philosophic basis”, will be presented in detail. As a preliminary and review, here are theses pertinent to the science of cosmology (NOTE: the theses are taken directly from the article even though no quotation marks are present):

• THESIS A1: The universe itself cannot be subjected to physical experimentation. We cannot re-run the universe with the same or altered conditions to see what would happen if they were different , so we cannot carry out scientific experiments on the universe itself.
• THESIS A2: The universe cannot be observationally compared with other universes.  We cannot compare the universe with any similar object, nor can we test our hypotheses about it by observations determining statistical properties of a known class of physically existing universes.
• THESIS B3: Establishing a Robertson-Walker geometry for the universe relies on plausible philosophic assumptions. The deduction of spatial homogeneity follows not directly from astronomical data but because we add to the observations a philosophical principle that is plausible but untestable.

(In Thesis B3, Ellis refers to the notion that the universe is isotropic and homogeneous (on a large scale). From our vantage point, we can see that the CBR (cosmic background radiation) yields this result; but to show that the inference is valid for the universe as a whole, we would need to make the same observation from at least two other (far removed) vantage points. However, if the Copernican Principle is invoked that we do not occupy a special place in the universe (this is the philosophic principle Ellis refers to in Thesis B3), then what see is equivalent to what would be seen from other positions, and the homogeneity and isotropy is demonstrated.)

• THESIS B6: Observational horizons limit our ability to observationally determine the very large scale geometry of the universe.  We can only see back to the time of decoupling of matter and radiation and so have no direct information about earlier times; and unless we live in a 'small universe', most of the matter in the universe is hidden behind the visual horizon. Conjectures as to its geometry on larger scales cannot be observationally tested. The situation is completely different in the small universe case: then we can see everything there is in the universe, including our own galaxy at earlier times! (emphasis and exclamation point added)
• THESIS C1: The Physics Horizon limits our knowledge of physics relevant to the very early universe. We cannot experimentally test much of the physics that is important in the very early universe because we cannot attain the required energies in accelerators on Earth. We have to extrapolate from known physics to the unknown and then test the implications; to do this, we assume some specific features of known lower energy physics are the true key to how things are at higher energies. We cannot experimentally test if we have got it right. 
• THESIS C2: The unknown nature of the inflation means inflationary universe proposals are incomplete. The promise of inflationary theory in terms of relating cosmology to particle physics has not been realized. This will only be the case when the nature of the inflaton (the particle representing the scalar force causing inflation)has been pinned down to a specific field that experiment confirms or particle physics requires to exist.
• THESIS D2: Testable physics cannot explain the initial state and hence specific nature of the universe. (emphasis added)

Ellis expands on Thesis D2 as follows:

"A choice between different contingent possibilities has somehow occurred; the fundamental issue is what underlies this choice. Why does the universe have one specific form rather than another, when other forms consistent with physical laws seem perfectly possible? The reason underlying the choice between different contingent possibilities for the universe (why one occurred rather than another) cannot be explained scientifically. It is an issue to be examined through philosophy or metaphysics." (emphasis added).

This last proposition is, I believe, the most important of those Ellis sets forth.

• THESIS E1: Physical laws may depend on the nature of the universe.

Ellis is saying here that the fundamental constants (e.g. the fine-structure constant, the gravitational constant may vary in time and space). It is a philosophical assumption that they remain constant. (Note: one recent finding, which is controversial, suggests that there is an asymmetric variation through space [and time] in the fine-structure constant.)

PHILOSOPHIC CRITERIA FOR SCIENTIFIC THEORIES

• THESIS F1: Philosophic choices necessarily underlie cosmological theory.Unavoidable metaphysical issues inevitably arise, in both observational and physical cosmology. Philosophical choices are needed in order to shape the theory.
•  THESIS F2: Criteria of satisfactoriness for theories cannot be scientifically chosen or validated. Criteria of satisfactoriness are necessary for choosing good cosmological theories; these criteria have to be chosen on the basis of philosophical considerations. They should include criteria for satisfactory structure of the theory, intrinsic explanatory power, and observational and experimental support.   These criteria are listed below:

1. Satisfactory structure:  a) internal consistency, b) simplicity (Ockham's razor), and c) aesthetic appeal ('beauty' or 'elegance')

2. Intrinsic explanatory power: a) logical tightness, b) scope of the theory—the ability to unify otherwise separate phenomena, and c) probability of the theory or model with respect to some well-defined measure.

3. Extrinsic explanatory power, or relatedness: a) connectedness to the rest of science, b) extendability providing a basis for further development;

4. Observational and experimental support, in terms of a) testability: the ability to make quantitative as well as qualitative predictions that can be tested; and b) confirmation: the extent to which the theory is supported by such tests as have been made.” (emphasis added)

The last criterion in my view (and that of many other scientists and philosophers of science) is critical. If a theory cannot in principle be confirmed quantitatively it is not science, but belongs to other disciplines.

• THESIS F3: Conflicts will inevitably arise in applying criteria for satisfactory cosmological theories. Philosophical criteria for satisfactory cosmological theories will in general come into conflict with each other, so that one will have to choose between them to some degree; this choice will shape the resulting theory.

Ellis elaborates on this last thesis:

“The thrust of much recent development has been away from observational tests towards strongly theoretical based proposals, indeed sometimes almost discounting observational tests. (emphasis added) At present this is being corrected by a healthy move to detailed observational analysis of the proposed theories, marking a maturity of the subject.”

• THESIS F4: The physical reason for believing in inflation is its explanatory power as regards structure growth in the universe. ... This theory has been vindicated spectacularly through observations of the CBR and matter power spectra. It is this explanatory power that makes it so acceptable to physicists, even though the underlying physics is neither well-defined nor tested, and its major large-scale observational predictions are untestable. (emphasis added).

Expanding on Thesis F4, Ellis adds:

“Inflation provides a causal model that brings a wider range of phenomena into what can be explained by cosmology (Criterion 2b), rather than just assuming the initial data had a specific restricted form. Explaining flatness (omega0 approximately 1, as predicted by inflation) and homogeneity reinforces the case, even though these are philosophical rather than physical problems (they [the initial restricted conditions] do not contradict any physical law; things could just have been that way). However claims on the basis of this model as to what happens very far outside the visual horizon (as in the chaotic inflationary theory) results from prioritizing theory over the possibility of observational and experimental testing. It will never be possible to prove these claims are correct.” (emphasis added)

Ellis asks, “how much should we try to explain” with cosmology? What should the scope of cosmology include?

• THESIS F5:Cosmological theory can have a wide or narrow scope of enquiry. The scope we envisage for our cosmological theory shapes the questions we seek to answer. The cosmological philosophical base becomes more or less dominant in shaping our theory according to the degree that we pursue a theory with more or less ambitious explanatory aims in terms of all of physics, geometry and underlying fundamental causation.

Elaborating on this point, Ellis says

“...The study of expansion of the universe and structure formation from nucleosynthesis to the present day is essential and well-informed. The philosophical stance adapted is minimal and highly plausible. The understanding of physical processes at earlier times, back to quantum gravity, is less well-founded. The philosophical stance is more significant and more debatable. Developments in the quantum gravity era are highly speculative, the philosophical position adapted is dominant because experimental and observational limits on the theory are lacking.” (emphasis added)....the basic underlying cosmological questions are

1. Why do the laws of physics have the form they do? Issues arise such as what makes particular laws work? for example, what governs the behaviour of a proton, the pull of gravity?...
2. Why do boundary conditions have the form they do?
3. Why do laws of physics at all exist? This relates to unsolved issues concerning the nature of the laws of physics: are they descriptive or prescriptive? ...Is the nature of matter really mathematically based in some sense, or does it just happen that its behaviour can be described in a mathematical way?
4. Why does anything exist? This profound existential question is a mystery whatever approach we take.
5. Why does the universe allow the existence of intelligent life? This of somewhat different character than the others and largely rests on them but is important enough to generate considerable debate in its own right. (Note: this question is that related to the Anthropic Principle--#6 in this series.)
 The status of all these questions is philosophical rather than scientific, for they cannot be resolved purely scientifically. How many of them—if any—should we consider in our construction of and assessments of cosmological theories?”

The next important question Ellis considers is how well does science, particularly cosmology, represent reality.

“It follows...that there are limits to what the scientific method can achieve in explanatory terms. We need to respect these limits and acknowledge clearly when arguments and conclusions are based on some philosophical stance rather than on purely testable scientific argument. If we acknowledge this and make that stance explicit , then the bases for different viewpoints are clear and alternatives can be argued rationally.”

• THESIS F6: Reality is not fully reflected in either observations or theoretical models. Problems arise from confusion of epistemology (the theory of knowledge) with ontology (the nature of existence) existence is not always manifest clearly in the available evidence. The theories and models of reality we use as our basis for understanding are necessarily partial and incomplete reflections of the true nature of reality, helpful in many ways but also inevitably misleading in others. They should not be confused with reality itself!”

“It may be suggested that arguments ignoring the need for experimental/observational verification of theories ultimately arise because these theories are being confused with reality, or at least are being taken as completely reliable total representation of reality. (emphasis added)   This occurs in

• "... confusing computer simulations of reality with reality itself, when they can in fact represent only a highly simplified and stylized version of what actually is."
• "...confusing the laws of physics themselves with their abstract mathematical representation (if indeed they [the laws] are ontologically real)
• ... confusing a construction of the human mind (“Laws of Physics”) with the reliable behaviour of ponderable matter...
• ...confusing theoretically based outcomes of models with proven observational results (e.g. claiming the universe necessarily has flat special sections (omega0 =1) and so this can be taken for granted, when the value of omega0 can and should be observationally determined precisely because this then tests that prediction.)”

Another  important question Ellis addresses is whether infinities are physically realizable or mathematical constructs. He agrees with the renowned 20th century mathematician David Hilbert that infinity is not a real quantity:

“Our principal result is that the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought . . . The role that remains for the infinite to play is solely that of an idea .. . which transcends all experience and which completes the concrete as a totality . . .” (quote is from Hilbert).

Since one can never count an infinite number of objects, the claim that the universe is infinite or that there are an infinite number of universes in a multiverse can never be tested or confirmed.

• THESIS I2: The often claimed physical existence of infinities is questionable. The claimed existence of physically realized infinities in cosmology or multiverses raises problematic issues. One can suggest they are unphysical; in any case such claims are certainly unverifiable.

Ellis concludes that there is much uncertainty in what one can infer from cosmology, and those inferences one draws are based on the philosophical basis one uses. More importantly, the stance one takes should be related to the totality of man's existence in the universe.

“Firstly, even in order to understand just the material world, it can be claimed that one needs to consider forms of existence other than the material only — for example a Platonic world of mathematics and a mental world, both of which can be claimed to exist and be causally effective in terms of affecting the material world. Our understanding of local causation will be incomplete unless we take them into account.

 Secondly, in examining these issues one needs to take into account data about the natures of our existence that come from our daily lives and the broad historical experience of humanity (our experiences of ethics and aesthetics, for example), as well as those discoveries attained by the scientific method. Many writings claim there is no purpose in the universe: it is all just a conglomerate of particles proceeding at a fundamental level in a purposeless and meaningless algorithmic way. But I would reply, the very fact that those writers engage in such discourse undermines their own contention; they ignore the evidence provided by their own actions. There is certainly meaning in the universe to this degree: the fact they take the trouble to write such contentions is proof that they consider it meaningful to argue about such issues; and this quality of existence has emerged out of the nature of the physical universe.... Indeed the human mind is causally effective in the real physical world precisely through many activities motivated by meanings perceived by the human mind. Any attempt to relate physics and cosmology to ultimate issues must take such real world experience seriously, otherwise it will simply be ignoring a large body of undeniable data. This data does not resolve the ultimate issues, but does indicate dimensions of existence that indeed do occur.”

With respect to the significance of cosmology, Ellis concludes

• THESIS OF UNCERTAINTY: Ultimate uncertainty is a key aspect of cosmology.Scientific exploration can tell us much about the universe, but not about its ultimate nature, or even much about some if its major geometrical and physical characteristics. Some of this uncertainty may be resolved, but much will remain. Cosmological theory should acknowledge this uncertainty.

Some final thoughts of my own:

• First, Ellis's review of the philosophical issues underlying cosmology is a most useful antidote to more grandiose presentations that ignore considerations of epistemology and metaphysics. Although in this article he touches only lightly on the place of man in the cosmos, he has also written a short book, “Before the Beginning-Cosmology Explained”, that addresses this question and theological considerations more fully. The book also gives a much simpler (ground up from basic physics) summary of the science in cosmology than that in the article.
• Second, much of the reasoning used to justify various cosmological models and theories is abductive , that is, to say that theory/model is "true" because it is the best (most elegant) explanation for the phenomena.   That type of reasoning has been criticized by philosophers of science, e.g. Bas van Fraassen, William Stoeger, Nancy Cartwright.    There are historical examples to show that the best explanation (at the time) is not necessarily true--e.g. phlogiston, disproved by Count Rumford's cannon-boring experiments, the ether, disproved by the Michelson-Morley experiments.     Unfortunately (or maybe fortunately), as Ellis emphasizes, we can't experiment on the cosmos.

APPENDIX

SUMMARY TABLE OF ISSUES AND THESES
Issue A: The uniqueness of the universe

• Thesis A1: The universe itself cannot be subjected to physical experimentation
• Thesis A2: The universe cannot be observationally compared with other universes
• Thesis A3: The concept of ‘Laws of Physics’ that apply to only one object is questionable
• Thesis A4: The concept of probability is problematic in the context of existence of only one object

Issue B: The large scale of the Universe in space and time

• Thesis B1: Astronomical observations are confined to the past null cone, and fade with distance
• Thesis B2: ‘Geological’ type observations can probe the region near our past world line in the very distant past
• Thesis B3: Establishing a Robertson-Walker geometry relies on plausible philosophical assumptions
• Thesis B4: Interpreting cosmological observations depends on astrophysical understanding
• Thesis B5: A key test for cosmology is that the age of the universe must be greater than the ages of stars
• Thesis B6: Horizons limit our ability to observationally determine the very large scale geometry of the universe
• Thesis B7: We have made great progress towards observational completeness

Issue C: The unbound energies in the early universe

• Thesis C1: The Physics Horizon limits our knowledge of physics relevant to the very early universe
• Thesis C2: The unknown nature of the inflaton means inflationary universe proposals are incomplete

Issue D: Explaining the universe — the question of origins

• Thesis D1: An initial singularity may or may not have occurred
• Thesis D2: Testable physics cannot explain the initial state and hence specific nature of the universe
• Thesis D3: The initial state of the universe may have been special or general

Issue E: The Universe as the background for existence

• Thesis E1: Physical laws may depend on the nature of the universe
• Thesis E2: We cannot take the nature of the laws of physics for granted
• Thesis E3: Physical novelty emerges in the expanding universe

Issue F: The explicit philosophical basis

• Thesis F1: Philosophical choices necessarily underly cosmological theory
• Thesis F2: Criteria for choice between theories cannot be scientifically chosen or validated
• Thesis F3: Conflicts will inevitably arise in applying criteria for satisfactory theories
• Thesis F4: The physical reason for believing in inflation is its explanatory power re structure growth.
• Thesis F5: Cosmological theory can have a wide or narrow scope of enquiry
• Thesis F6: Reality is not fully reflected in either observations or theoretical models

Issue G: The Anthropic question: fine tuning for life

• Thesis G1: Life is possible because both the laws of physics and initial conditions have a very special nature
• Thesis G2: Metaphysical uncertainty remains about ultimate causation in cosmology

Issue H: The possible existence of multiverses

• Thesis H1: The Multiverse proposal is unprovable by observation or experiment
• Thesis H2: Probability-based arguments cannot demonstrate the existence of multiverses
• Thesis H3: Multiverses are a philosophical rather than scientific proposal
• Thesis H4: The underlying physics paradigm of cosmology could be extended to include biological insights

Issue I: The natures of existence

Thesis I1: We do not understand the dominant dynamical matter components of the universe at early or late times
Thesis I2: The often claimed physical existence of infinities is questionable
Thesis I3: A deep issue underlying the nature of cosmology is the nature of the laws of physics.

Thesis of Uncertainty: Ultimate uncertainty is one of the key aspects of cosmology.

Thaaaat's all folks.    Comments  welcomed.

*To forestall invidious comments, I'll have to modify this:  Post 4, "Creatio ex Nihilo...."had a theistic bias, and of course, the quotations above posts and my bio indicate my own theistic foundations.

Philosophic Issues in Cosmology 6: Are we special?--the Anthropic Coincidences

“Scientists are slowly waking up to an inconvenient truth - the universe looks suspiciously like a fix. The issue concerns the very laws of nature themselves. For 40 years, physicists and cosmologists have been quietly collecting examples of all too convenient "coincidences" and special features in the underlying laws of the universe that seem to be necessary in order for life, and hence conscious beings, to exist."  Paul Davies.

" The argument (the Anthropic Principle) can be used to explain why the conditions happen to be just right for the existence of (intelligent) life on the earth at the present time. For if they were not just right, then we should not have found ourselves to be here now, but somewhere else, at some other appropriate time."  Roger Penrose.

"One doesn't show that something doesn't require explanation by pointing out that it is a condition of one's existence. If I ask for an explanation of the fact that the air pressure in the transcontinental jet is close to that at sea level, it is no answer to point out that if it weren't, I'd be dead.” Thomas Nagel, Mind and Cosmos.

 "A common sense interpretation of the facts suggests that a super-intellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature.   The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question."  Fred Hoyle

This is the 6th in a series of posts summarizing an article by George F.R. Ellis  on Philosophic Issues in Cosmology.

The 10,000 dials and 10,000 monkeys analogy
         The presence of organic life in the universe (namely us) requires a series of unlikely happenings and restricted values for physical laws and constants.   This “fine-tuning” (as it's been called) has been likened to a room full of 10,000 dials, each of which has to be set to a precise setting in order to achieve action; 10,000 monkeys are let into the room and each adjusts a dial and, lo, action occurs.   The set of coincidences was termed “The Anthropic Principle” by Brandon Carter in 1973, when he introduced it in a conference to oppose the “Copernican Principle”, that man has no special place in the universe.

References
The Anthropic Principle has been discussed extensively in books and articles.   There is a concise summary by Robert Koons in his philosophy lectures , giving various interpretations, with arguments for and against each.  (I'll summarize some of these below.) A good collection of articles with different (and opposing views) of the Anthropic Principle is given in God and Design  (ed. Neil Manson).   There are many versions of the Anthropic Principle ranging from the Weak Anthropic Principle, WAP, which tautologically observes that if the universe weren't fit for us to be here we would wouldn't be here discussing the principle  (see the Penrose quote above), through the Strong Anthropic Principle, SAP, that the universe has been fine-tuned for intelligent life (us), on up to the Completely Ridiculous Anthropic Principle (by Martin Gardner—you complete the acronym).

Can unlikelihood be quantified?
In assessing the improbable nature of the anthropic coincidences, some authors assign a specific  probability to the value of some particular physical constant.  Such assignment is not always justified,  because probability considerations are ill defined, in the usual sense of evidential probability.   For example, theoretical calculations have shown that if the strong nuclear force were 2 % higher or 2 % lower, then the elements as we know them would not have been formed.  This does not mean that the probability of having the strong nuclear force at an anthropic value is 4%.  In order to give a probability for this range, the population distribution of the parameters for the strong nuclear force would have to be known.  Moreover, there is a difficulty in using probability in an after-the-fact, rather than a predictive sense.  The way to use probabilities in assessing the anthropic coincidences is via Bayesian probability techniques, with well-defined prior assumptions, and to use the resulting Bayesian probability as a measure of belief.

Ellis's interpretation
Ellis, in his presentation of the anthropic coincidences, focuses on the special nature of physical laws that allow for the presence of life, rather than on their improbability:

“One of the most profound issues in cosmology is the Anthropic question...why does the Universe has the very special nature required in order that life can exist? The point is that a great deal of “fine tuning” is required in order that life be possible.  There are many relationships embedded in physical laws that are not explained by physics, but are required for life to be possible;  in particular various fundamental constants are highly constrained in their values if life as we know it is to exist...What requires explanation is why the laws of physics are such as to allow this complex functionality (life) to work.  ...We can conceive of universes where the laws of physics (and so of chemistry) were different than in ours.  Almost any change in these laws will prevent life as we know it from functioning.”

Ellis posits as a first requirement for the laws of physics “the kind of regularities that can underlie the existence of life”:   laws that are not based on symmetry and variational principles are unlikely to produce the kind of complexity that would be required for life. He also sets up general conditions that allow for organic life and cosmological boundary/initial conditions.    In this respect he cites the following as necessary:

• “Quantization that stabilizes matter and allows chemistry to exist through the Pauli exclusion principle;

• The number D of large spatial dimensions must be just 3 for complexity to exist.

• The seeds in the early universe for fluctuations (quantum fluctuations) that will later grow into galaxies must be of the right size that structures form without collapsing into black holes...

• The size of the universe and its age must be large enough...we need a sufficiently old universe for second generation stars to come into existence and then for planets to have a stable life for long enough that evolution could lead to the emergence of intelligent life.  Thus the universe must be at about 15 billion years old for life to exist.

• There must be non-interference with local systems.  The concept of locality is fundamental, allowing local systems to function effectively independently of the detailed structure of the rest of the Universe.  We need the universe and the galaxies in it to be largely empty, and gravitational waves and tidal forces to be weak enough, so that local systems can function in a largely isolated way.

• The existence of the arrow of time, and of laws like the second law of thermodynamics, are probably necessary for evolution and for consciousness.  This depends on boundary conditions at the beginning and end of the Universe.

• Presumably the emergence of a classical era out of a quantum state is required.   The very early universe would be a domain where quantum physics would dominate leading to complete uncertainty and an inability to predict the consequence of any initial situation; we need this to evolve to a state where classical physics leads to the properties of regularity and predictability that allow order to emerge.

• The fact that the night sky is dark...is a consequence of the expansion of the universe together with the photon (light particle) to baryon (mass particle) ratio.  This feature is a necessary condition for the existence of life:  the biosphere on Earth functions by disposing of waste energy to the heat sink of the dark night sky.  Thus one way of explaining why the sky is observed to be dark at night is that if this were not so, we would not be here to observe it. 

• Physical conditions on planets must be a in a quasi-equilibrium state for long enough to allow the delicate balances that enable our existence, through the very slow process of evolution, to be fulfilled.” (see the Theology of Water.)

There are a number of other constraints, limited values for forces—gravity, electromagnetic, weak nuclear, strong nuclear—and fundamental constants, including that for particle masses and number of particles that are needed for life to evolve.  In summary, Ellis puts the Anthropic Principle as the following:

     “Life is possible because both the laws of physics and the boundary conditions for the universe have a very special nature.  only particular laws of physics, and particular initial conditions in the Universe, allow the existence of intelligent life of the kind we know.  No evolutionary process whatever is possible for any kind of life if these laws and conditions do not have this restricted form.”

Robert Koons summarizes some general objections to invoking the Anthropic Principle for carbon-based life "well isn't that special" (as the Church Lady might say):

1. The problem of "old evidence";
2. Laws of nature don't need to be explained;
3. We had to be here in any event (see Penrose's quote above);
4. Exotic life might exist;
5. The Copernican Principle--rejection of anthropocentricity is fundamental to science;
6. We're only one among many universes (see below).

Objection 1 can be countered by the argument that such evidence is used frequently in science when direct experiments can't be done--witness the General Relativity explanation of the advance in the perihelion of Mercury.
Objection 2 would do away with all interpretations of theory, quantum mechanics, and the philosophy of science.
Objection 3 is countered as in Thomas Nagel's quote above; as information seeking life form we need explanations.
Objection 4 is invalid--we're talking about conditions for carbon-based life; science-fiction can explore and has explored conditions for exotic life.
Objection 5--the Anthropic Principle was introduced to rebut the Copernican Principle.
Objection 6--the multiverse proposition is not itself proven.

The philosophic/metaphysical context for these Anthropic conditions that Ellis sets forth will be given in the final post for this summary.   It should be noted that one interpretation of the anthropic coincidences is the theory that infinitely many universes with potentially different physical laws and constants exist and so it is not unlikely that in all these one universe with appropriate conditions for life would be present.    The analogy is like that of having a lottery ticket with the numbers 1 1  1  1  1 be the winner.   That combination of numbers looks improbable, but since there are a whole host of numbers from 00000  to 99999, it is no less probable than any other number.    This brings up the notion of a multiverse, which will be discussed in the next post.