Nick Bostrom
Approved
by the examiners:
Professor
Elliott Sober and Professor Peter Milne
On
July 3rd, 2000
Copyright
Email:
nick@nickbostrom.com
Personal
homepage: http://www.nickbostrom.com
This
work is available at: http://www.anthropic-principle.com
This thesis develops a theory of how to reason when our evidence has been subjected to observational selection effects. It has applications in cosmology, evolutionary biology, thermodynamics and the problem of time’s arrow, game theoretic problems with imperfect recall, the philosophical evaluation of the many-worlds and many-minds interpretations of quantum mechanics and David Lewis’ modal realism, and even for traffic planning.
After refuting several popular doctrines about the implications of cosmological fine-tuning, we present an informal model of the observational selection effects involved. Next, we evaluate attempts that have been made to codify the correct way of reasoning about such effects – in the form of so-called "anthropic principles" – and find them wanting. A new principle is proposed to replace them, the Self-Sampling Assumption (SSA).
A series of thought experiments are presented showing that SSA should be used in a wide range of contexts. We also show that SSA gives better methodological guidance than rival principles in a number of scientific fields. We then explain how SSA can lead to the infamous Doomsday argument. Identifying what additional assumptions are required to derive this consequence, we suggest alternative conclusions. We refute several objections against the Doomsday argument and show that SSA does not give rise to paradoxical "observer-relative chances" as has been alleged. However, we discover new consequences of SSA that are more counterintuitive than the Doomsday argument.
Using these results, we construct a version of SSA that avoids the paradoxes and does not lead to the Doomsday argument but caters to legitimate methodological needs. This modified principle is used as the basis for the first mathematically explicit theory of reasoning under observational selection effects. This observation theory resolves the range of conundrums associated with anthropic reasoning and provides a general framework for evaluating theories about the large-scale structure of the world and the distribution of observers within it.
ABSTRACT..........................................................................................................................
2
CONTENT...........................................................................................................................
3
ACKNOWLEDGEMENTS..................................................................................................
6
CHAPTER
1: INTRODUCTION..........................................................................................
8
CHAPTER
2: FINE-TUNING ARGUMENTS IN COSMOLOGY....................................
15
Does fine-tuning need
explaining?.................................................................................
17
Ian Hacking and the
Inverse Gambler’s Fallacy.............................................................
20
Robert White and Phil
Dowe’s analysis.........................................................................
23
Surprising vs. unsurprising
improbable events................................................................
27
Observational selection
effects......................................................................................
38
Conclusions.................................................................................................................
46
CHAPTER
3: OBSERVATIONAL SELECTION EFFECTS AND THE ANTHROPIC PRINCIPLE 48
The anthropic principle
as expressing an observational selection effect...........................
48
Anthropic hodgepodge.................................................................................................
52
Inadequacy of earlier
formulations.................................................................................
57
The Self-Sampling Assumption.....................................................................................
61
CHAPTER
4: WHY ACCEPT THE SELF-SAMPLING ASSUMPTION?........................
64
Prison..........................................................................................................................
64
Emeralds......................................................................................................................
67
Two Batches................................................................................................................
68
God’s Coin Toss..........................................................................................................
69
The reference class
problem.........................................................................................
74
The sampling density....................................................................................................
78
SSA in cosmology........................................................................................................
82
SSA in thermodynamics,
and time’s arrow....................................................................
84
SSA in evolutionary
biology..........................................................................................
87
SSA and traffic planning...............................................................................................
92
Summary.....................................................................................................................
93
CHAPTER
5: THE DOOMSDAY ARGUMENT................................................................
96
Introduction.................................................................................................................
96
Doomsday à la Gott.....................................................................................................
97
The incorrectness of
Gott’s argument..........................................................................
100
Doomsday à la Leslie.................................................................................................
102
The assumptions used
in DA, and the Old evidence problem.......................................
105
Leslie on the problem
with the reference class.............................................................
114
Alternative conclusions
of the Doomsday argument.....................................................
118
CHAPTER
6: SOME ATTEMPTED REFUTATIONS OF THE DOOMSDAY ARGUMENT
120
Objection One...........................................................................................................
120
Objection Two...........................................................................................................
122
Objection Three.........................................................................................................
126
Objection Four..........................................................................................................
127
Objection Five...........................................................................................................
130
The Self-Indication
Assumption..................................................................................
131
CHAPTER
7: OBSERVER-RELATIVE CHANCES IN ANTHROPIC REASONING?.. 135
Leslie’s argument and
why it fails................................................................................
135
Observer-relative chances:
another try........................................................................
140
Discussion..................................................................................................................
141
Conclusion.................................................................................................................
146
Appendix...................................................................................................................
146
CHAPTER
8: PARADOXES OF THE SELF-SAMPLING ASSUMPTION....................
151
Four gedanken wherein
SSA yields counterintuitive results..........................................
151
Discussion of Experiment
#2.......................................................................................
154
Discussion of Experiment
#4.......................................................................................
162
Conclusion.................................................................................................................
165
Appendix: A SuperNewcomb
problem.......................................................................
166
CHAPTER
9: A THEORY OF OBSERVATIONAL SELECTION EFFECTS.................
168
Criteria......................................................................................................................
169
The outlines of a solution............................................................................................
170
Formalizing the theory:
Equation SSSA-R...................................................................
173
Non-triviality of the
reference class.............................................................................
175
SSA and SSSA as special
cases of SSSA-R..............................................................
182
SSSA-R applied to cosmological
fine-tuning...............................................................
184
How the observation
theory based on SSSA-R measures up against desiderata........... 191
REFERENCES................................................................................................................. 194
I am indebted to more people than I can name. I am grateful to what I think must be literally hundreds of persons, for discussing these issues with me or emailing me thoughtful comments, questions and criticisms. I want to apologize to those who have asked me questions that I have not always had time to give the detailed answers they deserved. Maybe this text will provide a few answers – and hopefully provoke many new questions. Thank you all (you know who you are) for your constant stimulus and feedback!
There are some people that I want to mention explicitly though. First, I would like to thank my supervisors, Colin Howson and Craig Callender for their continuous trust and support, and for guiding me through the process.
The following people deserve my sincerest gratitude for their invaluable input in the project: Dennis Dieks, Jacques Mallah, William Eckhardt, Adam Elga, Roger White, Kevin Korb, Jonathan Oliver, Pierre Cruse, Mark Greenberg, Saar Wilf, Wei Dai, Robin Hanson, Paul Franceschi, Hal Finney, Max Tegmark, Jeremy Butterfield, Jean-Michel Delhotel, Richard Swinburne, J-P Delahaye, Bill Jefferys, and to Daniel Hill (who showed how easily breakfasts can extend into lunches when the right quality of philosophical conversation is on the table). I am grateful to my dear friend David Pearce for persuading me to go on-line from the beginning and for helping me in many practical ways. (I will continue to make my working-papers on this subject and other relevant resources available at anthropic-principle.com.) Special thanks are due to Nancy Cartwright, who went out her way to help get me a viva in time to meet a nearly impossible deadline. Thank you, Nancy!
I am grateful in a superlative way to John Leslie for being helpful and encouraging, for his patience in explaining his views to me when I was new to the field.
My warm thanks also go to my friend Milan Cirkovic, who steadfastly collaborated with me on an article (on which two paragraphs of chapter 3 are based) from Belgrade while under bombardment during the war between NATO and Serbia.
I am grateful to several anonymous referees of Mind and Erkenntnis for helpful comments that improved the articles that underlie chapters 6 and 7. I am grateful for audience comments following various presentations of parts of this thesis, particularly from participants at the London School of Advanced Study conference on the Doomsday argument (London, Nov. 6, 1998), which led to improvements of chapter 8. I thank the John Templeton Foundation for a research grant.
Finally, I would like to thank my friends and family who have supported me. I thank Vassiliki Kambourelli for her unique inspiration and kind assistance during the late stages.
I dedicate this work to my father – med ett varmt, varmt, varmt tack!
Anthropic reasoning is a philosophical gold mine. Few philosophical subject matters are as rich in important empirical implications, touch on as many fascinating scientific questions, or contain such generous quantities of conceptual and methodological confusion that needs to be sorted out.
Anthropic principles are used by contemporary cosmologists to derive observational predictions from theories like stochastic inflation which entail the existence of an ensemble of universes. Anthropic coincidences are used by some theists to argue for the existence of a Creator. Others point to anthropic reasoning as providing a counterargument to the cosmological argument for God’s existence. Anthropic constraints have been used to predict how many critical steps there were in the evolution of intelligent life on Earth. The Doomsday argument, using a form of anthropic reasoning, purports to show that the risk that the human species will go extinct fairly soon has been greatly underestimated. One main objection against the many-worlds interpretation of quantum physics draws its force from an implicit appeal to an anthropic principle, as does a common objection against Boltzmann's attempt to explain time’s arrow. There are also applications to game theoretic problems involving imperfect recall and even to traffic planning.
The anthropic principle has to do with observational selection effects. A simple example of a selection effect is if you try to catch fish with a net that doesn’t catch fish shorter than 20 cm. If you use such a net to catch a hundred fish and they all turn out to be 20 cm or longer, then obviously you are not entitled to take this as evidence that the minimum length of fish in the lake is about 20 cm.
In 1936, The Literary Digest took a phone poll to predict the outcome of the presidential election. Alf Landon was found to be the most popular candidate among those consulted, and so it was predicted that he would win. The prediction, however, failed to take account of an important selection effect owing to the fact that many people did not have telephones at that time. Especially the poor tended to lack telephones and this group also tended to support the rival candidate, Franklin Delano Roosevelt. Roosevelt won a landslide victory. A methodologically more sophisticated approach would either have interviewed a more representative sample set from the population or at least factored in known selection effects.
Or to take yet another example, suppose you’re a venture capitalist wanting to know what is the average growth rate for companies in the first year after they were founded. You wouldn’t get a very reliable estimate by extrapolating from the data about a hundred companies selected randomly from the Yellow pages in the phone book. It is not uncommon for new companies to fold within a few years, and those who do are much less likely to be listed in the Yellow pages. The companies you find there are typically several years old and can be expected to have performed substantially above average in their first year.
In these three examples, a selection effect is introduced by the fact that the instrument you use to collect data (a fishing net, a phone poll, the Yellow pages) samples only from a proper subset of the class of entities you are interested in. No different in principle are selection effects introduced not by limitations of some measurement device but by the fact that all observations require the existence of an appropriately positioned observer. The data we have are filtered not only by limitations in our instrumentation but also by the prerequisite that somebody is there to "have" the data yielded by the instruments (and to build the instruments in the first place).
For instance, we find that intelligent life evolved on Earth. It would be a mistake to infer from this that life is likely to evolve on most Earth-like planets. For however small the proportion of all planets that evolved intelligent life, we will find ourselves on a planet that did. (Or we will trace our origin to a planet where intelligent life evolved, in case we are born in a space colony.) The data point – that intelligent life evolved on our planet – is predicted equally by the hypothesis that intelligent life is very improbable even on Earth-like planets and by the hypothesis that intelligent life is probable on Earth-like planets. This data point therefore does not distinguish between the two hypotheses, provided that on both hypotheses intelligent life would have evolved somewhere. (On the other hand, if the "intelligent-life-is-improbable" hypothesis asserted that intelligent life was so improbable that is was unlikely to have evolved anywhere in the whole of cosmos, then the datum that intelligent life evolved on Earth would count against it. For this hypothesis would not have predicted our observation. In fact, it would have predicted that there would have been no observations at all.)
We don’t have to travel for long on the even path of common sense before entering a territory where observational selection effects give rise to difficult and controversial issues. Already in the preceding paragraph we came across a point which is contested. We understood the explanandum – that intelligent life evolved on our planet – in a non-rigid sense. Some authors, however, argue that the explanandum should be, why did intelligent life evolve on this planet (where "this planet" is used as a rigid designator), and that the hypothesis that intelligent life is quite probable on Earth-like planets would indeed give a higher probability to this explanandum (White 1999, Hacking 1987, Dowe 1998). I will show in chapter 2 that this is not the right way to understand the problem.
Notice also that the impermissibility of inferring from the fact that intelligent life evolved on Earth that intelligent life probably evolved on a large fraction of all Earth-like planets does not hinge on the evidence in this example consistings of only one data point. Imagine that we had telepathic abilities and could communicate directly with all other intelligent life that exists in cosmos. Suppose we ask all the aliens, did intelligent life evolve on their planets too? Obviously they would all say: Yes, it did. But equally obvious, this would still not give us any reason to think that intelligent life develops easily. We only asked about the planets where life did in fact evolve (since those planets would be the only ones which would be "theirs" to some alien), and we get no information whatever by hearing the aliens confirming that life evolved on those planets. An observational selection effect vitiates any attempt to gain information by this procedure about how unlikely intelligent life is to evolve. Other considerations would have to be brought to bear if we want to estimate that. (If all the aliens also reported that theirs was some Earth-like planet, this would suggest that intelligent life is unlikely to develop on planets that are not Earth-like – for otherwise some aliens would likely have developed on non-Earth like planets. But it does not tell us whether the evolution of intelligent life on an Earth-like planet is likely or not.)
One important application and perhaps the earliest one, of anthropic reasoning is to provide a possible (not necessarily the only) explanation of why the universe appears fine-tuned for intelligent life in the sense that if any of various physical constants or initial conditions had been even very slightly different then life as we know it would not have existed. The basic idea behind the possible explanation which uses anthropic reasoning is that the totality of spacetime might be very huge and may contain regions in which the values of fundamental constants and other conditions differ in many ways. (We might also have independent grounds for thinking that that is true.) If this is the case, then we should not be amazed to find that in our own region physical constants and conditions appear "fine-tuned". Owing to an obvious observational selection effect, only such fine-tuned regions are observed. Observing a fine-tuned region is precisely what we should expect if this theory is true, and so it can potentially account for available data in a very neat and simple way, without having to assume that conditions just happened to be "right" through some immensely lucky – and arguably a priori extremely improbable – cosmic coincidence. It also provides an alternative to the hypothesis that our universe was deliberately designed with the intention that it be life-containing.
Some skeptics doubt the meaningfulness of or need for an explanation of the apparent fine-tuning of our universe. We examine the skeptical arguments in chapter 2 and consider the counterarguments offered by proponents of anthropic explanations of fine-tuning. This leads us into a discussion of the distinction between surprising and unsurprising improbable events, and of what makes a fact cry out for explanation. We find that the anthropic theorizers’ replies fail to meet the skeptics’ challenge. However the intuitions of the former are often correct, and by digging deeper we vindicate those intuitions. This involves constructing an informal model of how observational selection effects operate in the context of cosmological fine-tuning. This model is used to draw a number of additional conclusions about the relative strength of support that various kinds of cosmological theories get from fine-tuning.
While the term "anthropic principle" is less than three decades old, the basic idea of observational selection effects as an important methodological constraint goes back much further. For example, some of the core elements in Kant’s philosophy about how the world of our experience is conditioned on the forms of our sensory and intellectual faculties are not completely unrelated to modern ideas of observational selection effects, although there are fundamental differences. Certainly in Hume’s Dialogues Concerning Natural Religion, one can find early expressions of some ideas of anthropic selection effects. However, it is only quite recently, starting with the works of Brandon Carter (and with some earlier intimations by R. H. Dicke) that the more sophisticated and intricate applications of anthropic reasoning are beginning to be discovered. Many of the most important ideas in this field date back only about a decade or less, philosophers and physicists deserving about equal shares of the credit.
Chapter 3 discusses some of the many attempts that have been made to codify the modus operandi of anthropic reasoning, often in the form of an "anthropic principle". All of them are to various degrees flawed or inadequate.
In this area confusion reigns supreme. Over twenty anthropic principles have been formulated and many of them have been defined several times over – in nonequivalent ways – by different authors. Some reject anthropic reasoning out of hand as representing an obsolete and irrational form of anthropocentrism. Some hold that anthropic inferences rest on elementary mistakes in probability calculus. Some maintain that at least some of the anthropic principles are tautological and therefore indisputable. Tautological principles have been dismissed by some as empty and thus of no interest or ability to do explanatory work. Others have insisted that like some results in mathematics, though analytically true, anthropic principles can nonetheless be interesting and illuminating. Others still purport to derive empirical predictions from these same principles and regard them as testable hypotheses.
One meta-level reason for thinking that there is something to anthropic reasoning is that it is used and taken seriously by a range of leading physicists and cosmologists. It would be surprising if this bunch of hardheaded scientists were just blowing so much hot air. I hope show that if one peels away extraneous principles, misconceptions, various fallacies and misdescriptions, one can indeed find at the core a set of interesting and useful insights.
It is interesting that so many different and opposing things have been marshaled under the ‘anthropic’ banner. Partly this is due to the philosophical opaqueness of its early formulations and to unfortunate terminological choices. Partly it is due to muddled thinking combined with the well-known capacity of probability theory to generate results that are counterintuitive to some people. But in part it is also due to genuine difficulties intrinsic to this kind of reasoning, some of which are still unresolved. One advantage of having a theory of anthropic reasoning is that we shall be able identify which of its applications uses problematic assumptions and to explicitly state what those assumptions are. But although much useful philosophical analysis of anthropic reasoning has already been done, constructing a theory of observational selection effects cannot be done by merely assembling what is already there. Many of the arguments and principles needed do not yet exist and will have to be invented here as we go along. Also, a number of erroneous doctrines found in the literature need be refuted and corrected.
Chapter 3 ends by proposing what I dub the "Self-Sampling Assumption" as a preliminary formulation (to be revised in chapter 9) of what I take to be the correct basic principle for anthropic reasoning. The content of the Self-Sampling Assumption is unpacked and gradually clarified throughout subsequent chapters.
Chapter 4 gives reasons for accepting the Self-Sampling Assumption. The arguments are of two types. The first type takes the form of thought experiments designed to establish, for a wide range of situations, that it is rational to reason in accordance with the Self-Sampling Assumption. The second type argues that a methodological principle is needed to enable us to derive probabilistic observational consequences from current cosmological theories. I show that while it current rivals fail do this, the Self-Sampling Assumption provides a simple and plausible methodology which coincides with scientific practice and intuitive judgements of what counts as evidence for or against cosmological theories. Support for the Self-Sampling Assumption is also garnered from its useful application in a number of other fields, including evolutionary biology, thermodynamics and even such a mundane activity as traffic planning.
Chapter 5 shows how the Self-Sampling Assumption, when combined with certain other premises, leads to the notorious Doomsday argument. Two different versions of this argument are identified, one of which (the one originated by Richard Gott) is showed to be flawed. The other version, which is due to Brandon Carter and John Leslie, is stronger but nonetheless inconclusive. We identify the critical assumptions that are needed, in addition to the Self-Sampling Assumption, to derive the intended conclusion.
Chapter 6 refutes six recent objections against the Doomsday argument and in the process of doing so throws light on some related issues. Whether the Doomsday argument is sound or not, it shouldn’t be dismissed for the wrong reasons. This is especially important because when the force of the Doomsday argument is appreciated, it gives us valuable clues as to a more satisfactory theory of observational selection effects.
Chapter 7 starts by examining a claim by John Leslie that anthropic reasoning leads to paradoxical observer-relative chances in some types of situations. I show that Leslie’s argument is fallacious. A different type of situation in then described where anthropic reasoning does lead to chances that are observer-relative in an interesting but not paradoxical sense.
While chapters 5-7 to some extent give reassuring messages about the Self-Sampling Assumption as originally formulated, chapter 8 discovers some truly paradoxical apparent consequences of an unrestricted use of that assumption. Among these apparent consequences are that it gives us reason to believe in backward causation, paranormal causation (e.g. psychokinesis) and that it gives advice which seems radically foolish. A careful analysis reveals that the worst of these prima facie consequences are merely apparent. Nonetheless, the fact remains that in some thought experiments the unrestricted use of the Self-Sampling Assumption gives counterintuitive results.
Chapter 9 reexamines the arguments for the Self-Sampling Assumption given in chapter 5 and argues for a modified and relativized version that performs the same useful functions as the original formulation while avoiding the counterintuitive consequences discussed in chapter 8. Taken together with the results from the preceding chapters, this establishes a general framework for modeling reasoning in situations involving conditionalization on information having an indexical component or when our evidence has been subjected to observational selection effects. The relevant probabilistic relation between such evidence and arbitrary hypotheses is given a formal expression in an equation (SSSA-R) and constraints are put in place on a key parameter.
Many valuable specific results and ideas relating to anthropic reasoning have been obtained by various investigators and are used as building blocks here together with many novel ones. This thesis, however, is the first systematic attempt to construct a general and formally explicit theory of reasoning under observational selection effects. It is hoped that it will advance our understanding of the foundational issues in this field and that it will move us closer to being able to tackle those "anthropic problems" – both scientific and philosophical – that still remain mysterious.
The aspect of anthropic reasoning that has received most attention from philosophers is the application in cosmology to explain the apparent fine-tuning of our universe. "Fine-tuning" refers to the supposed fact that there is a set of cosmological parameters or fundamental physical constants which are such that had they been very slightly different then the universe would have been void of intelligent life. For example, in the classical big bang model, the early expansion speed seems fine-tuned. Had it been very slightly greater, the universe would have expanded too rapidly and no galaxies would have formed; there would only have been a very low density hydrogen gas getting more and more dispersed over time. In such a universe, presumably, life could not evolve. Had the early expansion speed been very slightly less, then the universe would have recollapsed within a fraction of a second, and again there would have been no life. Our universe, having just the right conditions for life, appears to be balancing on a knife’s edge (Leslie 1989). A number of other parameters seem fine-tuned in the same sense – e.g. the ratio of the electron mass to the proton mass, the magnitudes of force strengths, the smoothness of the early universe, the neutron-proton mass difference, even the metric signature of spacetime (Tegmark 1997).
Some philosophers and physicists take fine-tuning to be an explanandum that cries out for an explanans. Two possible explanations are usually envisioned: the design hypothesis and the ensemble hypothesis. Although these explanations are compatible, they tend to be viewed as competing: if we knew that one of them were correct, there would be less temptation to think that the other obtained.
The design hypothesis is that our universe is the result of purposeful design. The "agent" doing the designing need not be a theistic "God", although of course that is one of the archetypal version of the design hypothesis. Other universe-designers have been considered in this context. For example, John Leslie (