Anthropic arguments in multiverse cosmology and string theory rely on the
weak anthropic principle (WAP). We show that the principle, though ultimately a
tautology, is nevertheless ambiguous. It can be reformulated in one of two
unambiguous ways, which we refer to as WAP_1 and WAP_2. We show that WAP_2, the
version most commonly used in anthropic reasoning, makes no physical
predictions unless supplemented by a further assumption of "typicality", and we
argue that this assumption is both misguided and unjustified. WAP_1, however,
requires no such supplementation; it directly implies that any theory that
assigns a non-zero probability to our universe predicts that we will observe
our universe with probability one. We argue, therefore, that WAP_1 is
preferable, and note that it has the benefit of avoiding the inductive
overreach characteristic of much anthropic reasoning.Comment: 7 pages. Expanded discussion of selection effects and some minor
  clarifications, as publishe

Aguirre A

Bostrom N

Bousso R

Carter B Longair M

Freivogel B

Kachru S

Rees M

Smolin L

Steven Weinstein

Susskind L

Vilenkin A

English

arXiv

Anthropic arguments in multiverse cosmology and string theory rely on the weak anthropic principle (WAP). We show that the principle, though ultimately a tautology, is nevertheless ambiguous. It can be reformulated in one of two unambiguous ways, which we refer to as WAP_1 and WAP_2. We show that WAP_2, the version most commonly used in anthropic reasoning, makes no physical predictions unless supplemented by a further assumption of "typicality", and we argue that this assumption is both misguided and unjustified. WAP_1, however, requires no such supplementation; it directly implies that any theory that assigns a non-zero probability to our universe predicts that we will observe our universe with probability one. We argue, therefore, that WAP_1 is preferable, and note that it has the benefit of avoiding the inductive overreach characteristic of much anthropic reasoning

Weinstein, Steven

Name not available

arXiv:hep-th/0508006 v1   1 Aug 2005Anthropic reasoning in multiverse cosmology and string theory∗Steven Weinstein†Perimeter Institute for Theoretical Physics, 31 Caroline St, Waterloo, ON N2L 2Y5 CanadaDept. of Philosophy, University of Waterloo, Waterloo, ON N2L 3G1 CanadaDept. of Physics, University of Waterloo, Waterloo, ON N2L 3G1 CanadaJuly 31, 2005AbstractAnthropic arguments in multiverse cosmology and string theory rely on the weak an-thropic principle (WAP). We show that the principle, though ultimately a tautology, isnevertheless ambiguous. It can be reformulated in one of two unambiguous ways, whichwe refer to as WAP1 and WAP2. We show that WAP2, the version most commonly usedin anthropic reasoning, makes no physical predictions unless supplemented by a furtherassumption of “typicality”, and we argue that this assumption is both misguided and un-justified. WAP1, however, requires no such supplementation; it directly implies that anytheory that assigns a non-zero probability to our universe predicts that we will observeour universe with probability one. We argue, therefore, that WAP1 is preferable, and notethat it has the benefit of avoiding the inductive overreach characteristic of much anthropicreasoning.1 IntroductionOver the last twenty years or so, inflationary cosmologists have been toying with theoreticalmodels that postulate the existence of a multiverse, a set of quasi-universes (henceforth “uni-verses”) which are more-or-less causally disjoint [1],[2]. String theorists, who once hoped topredict a unique supersymmetric extension to the standard model, now find themselves con-templating a similar scenario, with perhaps 10500 or more metastable low-energy vacua (the“landscape”) realized via inflationary mechanisms as essentially distinct universes [3],[4],[5],[6].The vast majority of the universes in these scenarios look nothing like our universe, the valuesof the fundamental physical parameters (e.g., the cosmological constant) differing markedlyfrom the values we observe.A significant number of physicists have understood this situation — in particular, the factthat universes like ours are atypical — to be problematic because, it is felt, it reveals a lackof explanatory or predictive power. Others seem more concerned with our inability to eitherconfirm or falsify such theories. It is in addressing these concerns that anthropic reasoningenters the picture.∗Thanks to Rob Caldwell, Jim Peebles, and Lee Smolin for helpful discussions and comments on an earlierdraft.†Email: sw@uwaterloo.ca1Anthropic reasoning is reasoning based on the use of the (weak) anthropic principle, artic-ulated by Carter asWAP: “What we can expect to observe must be restricted by the conditions nec-essary for our presence as observers.” ([7], p. 291).This seems unobjectionable; in fact, it is a tautology. As such, one wonders how it can do anyexplanatory or methodological work, much less be the object of heated disagreement. We willargue that the anthropic principle, as stated by Carter, contains what Bohr might have calledan “essential ambiguity”, and that the problematic aspects of anthropic reasoning stem fromthe use of a form of the principle which requires recourse to an additional and unsupportedassumption of “typicality” in order to make contact with observation. Though the crucialimportance of the “principle of mediocrity” which encodes the assumption of typicality isunderstood by some, its connection to a particular form of the WAP and its status as adistinct and unargued-for assumption seems not to be well understood.2 Anthropic arguments2.1 GeneralThe general strategy of an anthropic argument is as follows. Begin with some mulitiversehypothesis, a hypothesis which gives:• a set of possible universes parametrized by the values taken by the cosmological constant,the dark matter density, and other physical parameters, and• a probability distribution describing the relative frequency of occurrence for these uni-verses in the (generally infinite) ensemble.Now, in accordance with WAP, restrict attention to the subset of universes that support theexistence of observers, since these are the only universes we could hope to observe, and considerthe distribution of the parameters over this “anthropic” subset. These are the universes it ispossible to observe, and so the predictions for what we can expect to observe should be basedon this subset.Given the restriction to the anthropic subset, one has a new probability distribution foreach parameter reflecting the relative frequency with which the various values of the parameteroccur in the anthropic subset. If the parameters take on a continuous set of values, or even alarge but finite number, the probability of any particular value will be absurdly small, so thatno particular outcome is to be expected. What, then, does anthropic reasoning predict?It is here that one must introduce an assumption of typicality, such as Vilenkin’s “principleof mediocrity,” which he describes as “the assumption that we are typical among the observersin the universe.” He elaborates,Quantitatively, this can be expressed as the expectation that we should find our-selves, say, within the 95% range of the distribution. This can be regarded as aprediction at a 95% confidence level. ([8], p. 2)2Equipped with this further assumption, one can infer that the observed values of the parameterswill lie within the 95% range.1 In short, if we assume we are typical (i.e., if we apply theprinciple of mediocrity), we get a range of predicted outcomes which is a proper subset of theanthropic subset.From here, the anthropic reasoner will generally conclude that the observation of an (an-thropically) typical value by us means that the theory has successfully explained the value(since we are a generic prediction of the theory). Furthermore, she will judge that the obser-vation of a typical value offers inductive support to the theory.Similarly, observation of an atypical value is judged to constitute a disconfirmation, evenfalsification, of the theory [9],[10]. However, from a logical standpoint, all that has been shownby a failure to observe an anthropically typical value is that the conjunction of the theoryand the principle of mediocrity is inadequate. One might just as well impugn the principle ofmediocrity rather than the theory. The following example brings this out.2.2 Example: The GoogolverseConsider a multiverse theory which postulates the existence of a “Googolverse”, an infiniteensemble made up of 10100 (a googol) different sorts of universe, where “different sorts” meansthat the universes are characterized by different values of one or more physical parameters.The postulated theory also provides a probability distribution over the parameters, so that onecan talk about “typical” and “atypical” values. Suppose, finally, that the values we observeare atypical, lying outside the 95% confidence interval. In such a situation, we might turn tothe anthropic principle in order to assess the theory.Upon doing an anthropic analysis of this multiverse, let us suppose we discover that 105 ofthe 10100 universes support observers. In accordance with the anthropic principle, we reasonthat these are the only universes we could possibly observe, and we go on to ask whether whatwe observe — the value of the cosmological constant, the electron mass, and so on — is typicalof this observer-supporting, “anthropic” subset. In other words, would a generic observerexpect to see something like what we see? The anthropic reasoner says that if the answer isno, then our theory should be regarded as an explanatory failure, and our observation of theatypical values should count against acceptance of the theory.So far, so good... perhaps. But suppose we analyze the observer-supporting subset further,and discover that there are really only two general sorts of observers, Humans and Aliens (thereader is encouraged to envision insect-like creatures akin to those portrayed in the film Alien),and that Aliens are by far the dominant form of life in the observer-supporting subset. In fact,we discover that only 17 of the 105 sorts of universes support the existence of Humans (Aliensare far more adaptable, apparently), and that these account for only 0.1% (i.e., 100) of theuniverses in the observer-supporting subset. Statistical analysis reveals that of this Human-accommodating subset of 17 universes, the values we observe in our universe, one of the 17,are entirely typical.In short, we come out looking like an atypical member of the Googolverse, an atypicalmember of the observer-supporting subset, and a typical member of the Human-supportingsubset. Most anthropic reasoning seeks typicality (or “mediocrity”) amongst the broadest1But note that the notion of typicality, of lying within some confidence interval, is not well-defined for allprobability distributions. For example, a flat distribution has no “typical” values. What, for example, is atypical outcome of the roll of a fair die?3possible subset of observers, judging that “it is prudent to condition probabilities, not on adetailed description of ‘us’, but on the weakest condition consistent with ‘us’ that plausiblyprovides useful results.” ([11], p. 5). Thus most anthropic reasoners would presumably con-clude that the observed values are not explained by the Googolverse hypothesis, and a fortiorithat these values do not support the hypothesis. On the other hand, the typical member of thesmall subset of the human race who is not completely flummoxed by the idea of a multiversemight well disagree, noting that the Googolverse hypothesis succeeds very well in explainingwhat we observe, since we are Humans, not Aliens.3 The Essential AmbiguityThe Googolverse example is of course a caricature, but it highlights the way in which theparticular choice of a reference class can make an enormous difference to the outcome of ananthropic argument. It does so via the additional requirement of typicality with respect tothe reference class of observers.2 Given the seemingly uncontroversial nature of the WAP, itis surprising that its application can be so contentious. In this section, we will see that this isa result of an ambiguity in the principle itself.Consider once again the Weak Anthropic Principle, “What we can expect to observe mustbe restricted by the conditions necessary for our presence as observers.” How are we to under-stand the phrase “our presence as observers”? Are we to understand it as talking about ourpresence, or the presence of observers, in general. The difference is pivotal.Given that we are observers, the conditions necessary for our presence as observers are nodifferent from the conditions necessary for our presence, and we might reformulate the WAPaccordingly:WAP1: “What we can expect to observe must be restricted by the conditionsnecessary for our presence.”This is an uncontroversial claim, since “we” can only observe the properties of worlds thatallow our presence. So for example, we cannot observe a world or a universe in which we failedto evolve, even if that universe has earth-like planets and other DNA-based life forms.3Clearly, most proponents of anthropic reasoning understand Carter’s principle in a differentway, interpreting WAP as,WAP2: “What we can expect to observe must be restricted by the conditionsnecessary for the presence of observers.”Application of WAP2 requires one to establish what “observers” are, and then to identify theconditions necessary for their presence. The constraint is much looser than the constraintimposed by WAP1, in that it admits universes which do not contain “us”, do not containhuman beings at all. Furthermore, although WAP2 tells us that what we can expect to observeis restricted by the conditions necessary for observers, it does not tell us anything about thelikelihood of our observing particular conditions, even though it does instruct us to calculatethe probability distribution of the parameters over the sub-ensemble of universes that support2See [12] and [13] for further discussion of the problem of the reference class.3Interpreting the weak anthropic principle in this way more or less implies the “top-down” approach of [14].4the existence of observers. In order to extract concrete predictions from WAP2, it must besupplemented by the principle of mediocrity (or something similar), which stipulates that weare typical observers. But of course we need not be, and furthermore we may be typical of oneclass of observers and atypical of another (as in the Googolverse example above).Despite the vagueness of WAP2, one might prefer it to WAP1, since it suggests that wecondition on a broader (but unspecified) reference class. However, WAP2 must be supplementedby the principle of mediocrity, a principle which, unlike other typicality assumptions such asthe Copernican principle and the cosmological principle, is invoked not as a working hypothesisbut as a principle of reasoning about one’s working hypothesis (the multiverse theory).4 Itsfailings in this regard are readily seen from its application to the Googolverse scenario above.In short, WAP2 is a kind of fuzzy generalization of WAP1 which nevertheless leads to no newpredictions unless supplemented by the principle of mediocrity, a principle which lacks anyindependent justification in the abstract and is often wrong in the concrete.4 ConclusionWAP1 and WAP2 are both interpretations of the weak anthropic principle, and both areincontrovertibly true. Why, then, have we suggested that one should use WAP1 rather thanWAP2? Because the WAP1 directly yields testable predictions, while WAP2 requires one toboth identify a particular class of observers and apply the principle of mediocrity with respectto the class chosen. To be sure, WAP1 makes the simultaneously trivial and strong claim thatif the theory assigns a non-vanishing probability to the parameter values we do observe, thenthat is what we should expect to observe. If on the other hand the theory assigns a probabilityof zero to the values that we observe, then of course the theory is ruled out.With respect to theory confirmation, one should certainly not say that the fact that theuniverse we observe is predicted with some probability (however small or large) serves asa confirmation of the theory. But then, why would anyone expect that one could reasoninductively from a single data point in the first place?References[1] A. Vilenkin. Birth of inflationary universes. Phys. Rev., D27:2848–2855, 1983.[2] A. Linde. Eternally existing self-reproducing chaotic inflationary universe. Phys. Lett. B,1986.[3] R. Bousso and J. Polchinski. Quantization of four-form fluxes and dynamical neutraliza-tion of the cosmological constant. J. High Energy Phys., 06:006, 2000. hep-th/0004134.[4] L. Susskind. The anthropic landscape of string theory. 2003. hep-th/0302219.[5] S. Kachru, R. Kallosh, A. Linde, J. Maldacena, L. McAllister, and S. Trivedi. Towards in-flation in string theory. J. Cosmol. Astropart. Phys., 2003(10):013, 2003. hep-th/0308055.4See [15] for an excellent discussion of the Copernicus, Kant, and the anthropic principle, and see [16] fordiscussion of the roles that the Copernican and cosmological principles have historically played in cosmology.5[6] B. Freivogel, M. Kleban, M. Rodriguez Martinez, and L. Susskind. Observational conse-quences of a landscape. 2005. hep-th/0505232.[7] B. Carter. Large number coincidences and the anthropic principle in cosmology. In M. Lon-gair, editor, Confrontation of cosmological theories with observational data; Proceedingsof the Symposium, Krakow, Poland, September 10-12, 1973, pages 291–298, Dordrecht,1974. D.Reidel.[8] A. Vilenkin. Anthropic predictions: The case of the cosmological constant. 2004. astro-ph/0407586.[9] M. Rees. Numerical coincidences and ‘tuning’ in cosmology. In N.C. Wickramasinghe,G.R. Burbidge, and J.V. Narlikar, editors, Fred Hoyle’s Universe, pages 95–108. Kluwer,2003. astro-ph/0401424.[10] P.C.W. Davies. Multiverse cosmological models. Mod. Phys. Lett., A19:727–744, 2004.astro-ph/0403047.[11] J.B. Hartle. Anthropic reasoning and quantum cosmology. 2005. gr-qc/0406104.[12] N. Bostrom. Anthropic Bias: Observation Selection Effects in Science and Philosophy.Routledge, New York, London, 2002.[13] L. Smolin. Scientific alternatives to the anthropic principle. 2004. hep-th/0407213.[14] A. Aguirre and M. Tegmark. Multiple universes, cosmic coincidences, and other darkmatters. J. Cosmol. Astropart. Phys., 2005(01):003, 2005. hep-th/0409072.[15] S. Roush. Copernicus, Kant, and the anthropic cosmological principles. Stud. Hist. Phil.Mod. Phys., 34:5–35, 2003.[16] G.F.R. Ellis. Cosmology and verifiability. Q.Jl R. astr. Soc., 16:245.6

Anthropic reasoning in multiverse cosmology and string theory

PhilSci Archive

Anthropic Bias: Observation Selection Eﬀects

Anthropic predictions: The case of the cosmological constant.

Anthropic reasoning and quantum cosmology.

Birth of inﬂationary universes.

Copernicus, Kant, and the anthropic cosmological principles.

Cosmology and veriﬁability. Q.Jl R.

Eternally existing self-reproducing chaotic inﬂationary universe.

Large number coincidences and the anthropic principle in cosmology.

Multiple universes, cosmic coincidences, and other dark matters.

Multiverse cosmological models.

Numerical coincidences and ‘tuning’ in cosmology.

Quantization of four-form ﬂuxes and dynamical neutralization of the cosmological constant.

Scientiﬁc alternatives to the anthropic principle.

The anthropic landscape of string theory.

Towards inﬂation in string theory.

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5 Anthropic reasoning in multiverse cosmology and string theory∗

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Anthropic reasoning in multiverse cosmology and string theory∗
Steven Weinstein†
Perimeter Institute for Theoretical Physics, 31 Caroline St, Waterloo, ON N2L 2Y5 Canada
Dept. of Philosophy, University of Waterloo, Waterloo, ON N2L 3G1 Canada
Dept. of Physics, University of Waterloo, Waterloo, ON N2L 3G1 Canada
July 31, 2005
Abstract
Anthropic arguments in multiverse cosmology and string theory rely on the weak an-
thropic principle (WAP). We show that the principle, though ultimately a tautology, is
nevertheless ambiguous. It can be reformulated in one of two unambiguous ways, which
we refer to as WAP1 and WAP2. We show that WAP2, the version most commonly used
in anthropic reasoning, makes no physical predictions unless supplemented by a further
assumption of “typicality”, and we argue that this assumption is both misguided and un-
justified. WAP1, however, requires no such supplementation; it directly implies that any
theory that assigns a non-zero probability to our universe predicts that we will observe
our universe with probability one. We argue, therefore, that WAP1 is preferable, and note
that it has the benefit of avoiding the inductive overreach characteristic of much anthropic
reasoning.
1 Introduction
Over the last twenty years or so, inflationary cosmologists have been toying with theoretical
models that postulate the existence of a multiverse, a set of quasi-universes (henceforth “uni-
verses”) which are more-or-less causally disjoint [1],[2]. String theorists, who once hoped to
predict a unique supersymmetric extension to the standard model, now find themselves con-
templating a similar scenario, with perhaps 10500 or more metastable low-energy vacua (the
“landscape”) realized via inflationary mechanisms as essentially distinct universes [3],[4],[5],[6].
The vast majority of the universes in these scenarios look nothing like our universe, the values
of the fundamental physical parameters (e.g., the cosmological constant) differing markedly
from the values we observe.
A significant number of physicists have understood this situation — in particular, the fact
that universes like ours are atypical — to be problematic because, it is felt, it reveals a lack
of explanatory or predictive power. Others seem more concerned with our inability to either
confirm or falsify such theories. It is in addressing these concerns that anthropic reasoning
enters the picture.
∗Thanks to Rob Caldwell, Jim Peebles, and Lee Smolin for helpful discussions and comments on an earlier
draft.
†Email: sw@uwaterloo.ca
1
Anthropic reasoning is reasoning based on the use of the (weak) anthropic principle, artic-
ulated by Carter as
WAP: “What we can expect to observe must be restricted by the conditions nec-
essary for our presence as observers.” ([7], p. 291).
This seems unobjectionable; in fact, it is a tautology. As such, one wonders how it can do any
explanatory or methodological work, much less be the object of heated disagreement. We will
argue that the anthropic principle, as stated by Carter, contains what Bohr might have called
an “essential ambiguity”, and that the problematic aspects of anthropic reasoning stem from
the use of a form of the principle which requires recourse to an additional and unsupported
assumption of “typicality” in order to make contact with observation. Though the crucial
importance of the “principle of mediocrity” which encodes the assumption of typicality is
understood by some, its connection to a particular form of the WAP and its status as a
distinct and unargued-for assumption seems not to be well understood.
2 Anthropic arguments
2.1 General
The general strategy of an anthropic argument is as follows. Begin with some mulitiverse
hypothesis, a hypothesis which gives:
• a set of possible universes parametrized by the values taken by the cosmological constant,
the dark matter density, and other physical parameters, and
• a probability distribution describing the relative frequency of occurrence for these uni-
verses in the (generally infinite) ensemble.
Now, in accordance with WAP, restrict attention to the subset of universes that support the
existence of observers, since these are the only universes we could hope to observe, and consider
the distribution of the parameters over this “anthropic” subset. These are the universes it is
possible to observe, and so the predictions for what we can expect to observe should be based
on this subset.
Given the restriction to the anthropic subset, one has a new probability distribution for
each parameter reflecting the relative frequency with which the various values of the parameter
occur in the anthropic subset. If the parameters take on a continuous set of values, or even a
large but finite number, the probability of any particular value will be absurdly small, so that
no particular outcome is to be expected. What, then, does anthropic reasoning predict?
It is here that one must introduce an assumption of typicality, such as Vilenkin’s “principle
of mediocrity,” which he describes as “the assumption that we are typical among the observers
in the universe.” He elaborates,
Quantitatively, this can be expressed as the expectation that we should find our-
selves, say, within the 95% range of the distribution. This can be regarded as a
prediction at a 95% confidence level. ([8], p. 2)
2
Equipped with this further assumption, one can infer that the observed values of the parameters
will lie within the 95% range.1 In short, if we assume we are typical (i.e., if we apply the
principle of mediocrity), we get a range of predicted outcomes which is a proper subset of the
anthropic subset.
From here, the anthropic reasoner will generally conclude that the observation of an (an-
thropically) typical value by us means that the theory has successfully explained the value
(since we are a generic prediction of the theory). Furthermore, she will judge that the obser-
vation of a typical value offers inductive support to the theory.
Similarly, observation of an atypical value is judged to constitute a disconfirmation, even
falsification, of the theory [9],[10]. However, from a logical standpoint, all that has been shown
by a failure to observe an anthropically typical value is that the conjunction of the theory
and the principle of mediocrity is inadequate. One might just as well impugn the principle of
mediocrity rather than the theory. The following example brings this out.
2.2 Example: The Googolverse
Consider a multiverse theory which postulates the existence of a “Googolverse”, an infinite
ensemble made up of 10100 (a googol) different sorts of universe, where “different sorts” means
that the universes are characterized by different values of one or more physical parameters.
The postulated theory also provides a probability distribution over the parameters, so that one
can talk about “typical” and “atypical” values. Suppose, finally, that the values we observe
are atypical, lying outside the 95% confidence interval. In such a situation, we might turn to
the anthropic principle in order to assess the theory.
Upon doing an anthropic analysis of this multiverse, let us suppose we discover that 105 of
the 10100 universes support observers. In accordance with the anthropic principle, we reason
that these are the only universes we could possibly observe, and we go on to ask whether what
we observe — the value of the cosmological constant, the electron mass, and so on — is typical
of this observer-supporting, “anthropic” subset. In other words, would a generic observer
expect to see something like what we see? The anthropic reasoner says that if the answer is
no, then our theory should be regarded as an explanatory failure, and our observation of the
atypical values should count against acceptance of the theory.
So far, so good... perhaps. But suppose we analyze the observer-supporting subset further,
and discover that there are really only two general sorts of observers, Humans and Aliens (the
reader is encouraged to envision insect-like creatures akin to those portrayed in the film Alien),
and that Aliens are by far the dominant form of life in the observer-supporting subset. In fact,
we discover that only 17 of the 105 sorts of universes support the existence of Humans (Aliens
are far more adaptable, apparently), and that these account for only 0.1% (i.e., 100) of the
universes in the observer-supporting subset. Statistical analysis reveals that of this Human-
accommodating subset of 17 universes, the values we observe in our universe, one of the 17,
are entirely typical.
In short, we come out looking like an atypical member of the Googolverse, an atypical
member of the observer-supporting subset, and a typical member of the Human-supporting
subset. Most anthropic reasoning seeks typicality (or “mediocrity”) amongst the broadest
1But note that the notion of typicality, of lying within some confidence interval, is not well-defined for all
probability distributions. For example, a flat distribution has no “typical” values. What, for example, is a
typical outcome of the roll of a fair die?
3
possible subset of observers, judging that “it is prudent to condition probabilities, not on a
detailed description of ‘us’, but on the weakest condition consistent with ‘us’ that plausibly
provides useful results.” ([11], p. 5). Thus most anthropic reasoners would presumably con-
clude that the observed values are not explained by the Googolverse hypothesis, and a fortiori
that these values do not support the hypothesis. On the other hand, the typical member of the
small subset of the human race who is not completely flummoxed by the idea of a multiverse
might well disagree, noting that the Googolverse hypothesis succeeds very well in explaining
what we observe, since we are Humans, not Aliens.
3 The Essential Ambiguity
The Googolverse example is of course a caricature, but it highlights the way in which the
particular choice of a reference class can make an enormous difference to the outcome of an
anthropic argument. It does so via the additional requirement of typicality with respect to
the reference class of observers.2 Given the seemingly uncontroversial nature of the WAP, it
is surprising that its application can be so contentious. In this section, we will see that this is
a result of an ambiguity in the principle itself.
Consider once again the Weak Anthropic Principle, “What we can expect to observe must
be restricted by the conditions necessary for our presence as observers.” How are we to under-
stand the phrase “our presence as observers”? Are we to understand it as talking about our
presence, or the presence of observers, in general. The difference is pivotal.
Given that we are observers, the conditions necessary for our presence as observers are no
different from the conditions necessary for our presence, and we might reformulate the WAP
accordingly:
WAP1: “What we can expect to observe must be restricted by the conditions
necessary for our presence.”
This is an uncontroversial claim, since “we” can only observe the properties of worlds that
allow our presence. So for example, we cannot observe a world or a universe in which we failed
to evolve, even if that universe has earth-like planets and other DNA-based life forms.3
Clearly, most proponents of anthropic reasoning understand Carter’s principle in a different
way, interpreting WAP as,
WAP2: “What we can expect to observe must be restricted by the conditions
necessary for the presence of observers.”
Application of WAP2 requires one to establish what “observers” are, and then to identify the
conditions necessary for their presence. The constraint is much looser than the constraint
imposed by WAP1, in that it admits universes which do not contain “us”, do not contain
human beings at all. Furthermore, although WAP2 tells us that what we can expect to observe
is restricted by the conditions necessary for observers, it does not tell us anything about the
likelihood of our observing particular conditions, even though it does instruct us to calculate
the probability distribution of the parameters over the sub-ensemble of universes that support
2See [12] and [13] for further discussion of the problem of the reference class.
3Interpreting the weak anthropic principle in this way more or less implies the “top-down” approach of [14].
4
the existence of observers. In order to extract concrete predictions from WAP2, it must be
supplemented by the principle of mediocrity (or something similar), which stipulates that we
are typical observers. But of course we need not be, and furthermore we may be typical of one
class of observers and atypical of another (as in the Googolverse example above).
Despite the vagueness of WAP2, one might prefer it to WAP1, since it suggests that we
condition on a broader (but unspecified) reference class. However, WAP2 must be supplemented
by the principle of mediocrity, a principle which, unlike other typicality assumptions such as
the Copernican principle and the cosmological principle, is invoked not as a working hypothesis
but as a principle of reasoning about one’s working hypothesis (the multiverse theory).4 Its
failings in this regard are readily seen from its application to the Googolverse scenario above.
In short, WAP2 is a kind of fuzzy generalization of WAP1 which nevertheless leads to no new
predictions unless supplemented by the principle of mediocrity, a principle which lacks any
independent justification in the abstract and is often wrong in the concrete.
4 Conclusion
WAP1 and WAP2 are both interpretations of the weak anthropic principle, and both are
incontrovertibly true. Why, then, have we suggested that one should use WAP1 rather than
WAP2? Because the WAP1 directly yields testable predictions, while WAP2 requires one to
both identify a particular class of observers and apply the principle of mediocrity with respect
to the class chosen. To be sure, WAP1 makes the simultaneously trivial and strong claim that
if the theory assigns a non-vanishing probability to the parameter values we do observe, then
that is what we should expect to observe. If on the other hand the theory assigns a probability
of zero to the values that we observe, then of course the theory is ruled out.
With respect to theory confirmation, one should certainly not say that the fact that the
universe we observe is predicted with some probability (however small or large) serves as
a confirmation of the theory. But then, why would anyone expect that one could reason
inductively from a single data point in the first place?
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6


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