Open Journal of Philosophy
2013. Vol.3, No.1, 1-4
Published Online February 2013 in SciRes (http://www.scirp.org/journal/ojpp) http://dx.doi.org/10.4236/ojpp.2013.31001
Ants Are Not Conscious
Russell K. Standish
School of Mathematics and Statistics, The University of New South Wales, Sydney, Australia
Received September 10th, 2012; revised October 15th, 2012; accepted October 25th, 2012
Anthropic reasoning is a form of statistical reasoning based upon finding oneself a member of a particular
reference class of conscious beings. By considering empirical distribution functions defined over animal
life on Earth, we can deduce that the vast bulk of animal life is unlikely to be conscious.
Keywords: Anthropic Reasoning; Consciousness; Damuth’s Law; Power Law
Introduction
Consciousness is a bête noir of the physical sciences. Each
and every one of us is aware of his or her own consciousness,
and indeed it seems to be necessary in order to carry out science,
or at very least to give meaning to its theories and results. Yet,
the more neurophysiologists probe the workings of the brain,
the more of a phantom consciousness appears to be. Some ar-
gue that even if a complete neurophysical theory of the brain’s
function is determined, the “hard” problem of how phenomenal
experience is generated still remains (Chalmers, 1995). Related
to this issue is that we cannot prove definitively that any other
individual of the human race is conscious and not a zombie that
acts for all intents and purposes as conscious. Consciousness is
fundamentally a first-person phenomenon with scientific dis-
course relegated to comparing reports with our own experience.
Yet it is unreasonable to doubt the consciousness of other hu-
mans, who are constructed in the same way as ourselves, and
who act in the same way as ourselves. The same is not true of
other species, who are constructed from different body plans,
have very different neural structures, and act in significantly
different ways to ourselves. In the words of Nagel (1974)
“What is it like to be a bat?” answering the question of con-
sciousness in animals seems hopeless. Whilst Nagel was as-
suming that it is something to be like a bat, it is entirely rea-
sonable to ask the question of whether it is anything to be like a
bat. Most people would assume that on a scale of organism
complexity from human beings, through vertebrates, inverte-
brates, etc. through to non-living matter, a line can be drawn
between organisms experiencing phenomenal consciousness
and those that don’t. Descartes, for example, drew the line be-
tween humans and non-humans. Others would argue that some
other species of mammal, and possibly bird as well as some
cephalopods are probably conscious. Some even argue that
insects might be conscious (Tye, 1997).
In this paper, I define consciousness in an operational way by
noting that the reference class of anthropic reasoning (Bostrom,
2002) must consist of conscious entities, possibly restricted in
some way, such as the set of terrestrial animals. Anthropic rea-
soning is best known in the form of the Cosmological Anthro-
pic Principle (Barrow & Tipler, 1986) and the infamous Dooms-
day Argument (Leslie, 1989).
Anthropic reasoning has been criticized on a number of
fronts, particularly where it has been applied to produce counter
intuitive conclusions. For example, the fine tuning argument
has been used as evidence for a divine creator, or as evidence
for a multi-verse, and the doomsday argument suggests that the
human population will crash in the not too distant future. Most
of these objections have been rebutted in Bostrom’s book
(Bostrom, 2002), who makes a well-argued case that anthropic
reasoning can be done validly. It is not the purpose of this paper
to review to the structure of these arguments, objections raised,
nor rebuttals of those objections, as that is incidental to the
aims of this paper. However, two issues in particular are perti-
nent: the reference class problem, and the measure problem.
The issue of what constitutes the class of observers from
which the subject observer reasons he/she was randomly sam-
pled is known as the reference class problem. For many exam-
ples of Anthropic Reasoning, precisely what constitutes the
reference class does not bear much on the conclusions of the
reasoning. Bostrom (2002) gives examples of this. In this paper,
we very much turn the reasoning on it head, and ask what can
we establish about the reference class, given the observation of
what we are, and other information we might have at hand.
It might be argued that the reference class used for anthropic
reasoning should only include those observers capable of un-
derstanding anthropic arguments, or more widely, those con-
scious entities capable of introspection. It is not at all clear
whether this would include all humans, just a subset of humans,
or non-human species as well. Conversely, the widest possible
reference class is the set of all conscious observers, the inter-
pretation I wish to use here. An alternative reading of this paper
is that it is not talking about consciousness per se, but what is,
or is not, allowable within the anthropic reference class.
The measure problem comes from extending anthropic rea-
soning to infinite sets of observers, such as we would expect to
be the case in a multi-verse. In the set


=0,1,2,, we
might be tempted to say that the set of even numbers has mea-
sure 0.5. Yet if we write the set in a different order as


= 0,1,3,5,2,7,9,11,4,, the same line of argument pro-
duces a measure of 0.25. However, with respect to the argu-
ments given in this paper, this measure problem doesn’t arise,
as the measure is already known empirically.
To consider the title question of this paper, we only need to
note that there are considerably more ants than humans in the
world. It is estimated that ants monopolize between 15% - 20%
of the terrestrial animal biomass (Schultz, 2000), far exceeding

R. K. STANDISH
that of the vertebrates. A typical suburban house garden will
contain city-scale populations of ants. A nave application of
anthropic reasoning would conclude that ants could not be con-
scious, as otherwise we would expect to be an ant rather than a
human.
Unfortunately this usage of anthropic reasoning raises the
Chinese paradox. Why wasn’t I born in the most populous na-
tion on Earth, China, which has 50 times the population of my
country of birth, Australia?
Furthermore, ants are not a single species, but are taxonomi-
cally speaking a family, with which we are comparing a single
species homo sapiens. It would be better to rephrase the ques-
tion in a way that didn’t depend on a somewhat human-biased
taxonomic scheme.
In the rest of this paper I show that the Chinese paradox is
actually not a problem for anthropic reasoning, and in so doing
demonstrate a previously unknown process for generating
power law distributions. Then by recasting the ant conscious-
ness problem into a question of expected body mass, which is
an objective physical measurement rather than a possibly sub-
jective classification, and including the proper handling of the
Chinese paradox, we can conclude that the vast majority of
animal species (particularly the small ones) are unlikely to be
conscious (or in the reference class, if you prefer) by anthropic
reasoning.
Chinese Paradox
China has well over a billion people, and along with India,
has by far the biggest population of all the nations in the world.
I happen to live in Australia, for instance, a country with
around 1/50th the population of China. It would be absurd to
conclude that Chinese people are unconscious, so namely one
would expect on anthropic grounds to be Chinese or Indian. At
first sight this looks disastrous for anthropic reasoning, until
you realize that it is ill-posed. Suppose you asked the question
of what is the chance of being Chinese versus not being Chi-
nese. There is about a 20% chance of being Chinese, and 80%
not, so it then becomes unsurprising to not be Chinese.
We can rephrase the Chinese question in a different way:
What is the expected population size of one’s country of birth?
It turns out (see Figure 1) that there are far more countries with
fewer people, than countries with more people. The relationship
between population size and the number of countries looks
roughly proportional to 1/x, where x is the population of the
country. This law is an example of a power law, and it appears
in all sorts of circumstances, for example the frequency with
which words are used in the English language.
With a 1/x power law, the number of countries of a given
population size exactly offsets the population of those countries,
so anthropically speaking, we should expect to find ourselves in
just about any sized country, with the same probability. Being
in a country with a population the size of Australia’s would be
no more surprising than being in a more populated country such
as the US or China.
However, the actual distribution of country populations turns
out to be a log normal distribution1, whose probability dis-
tribution is
 


22
=expln 2px Cxx

  (1)
The parameters

and

can be found by means of the
maximum likelihood method outlined by Clauset et al. (2009).
In fact one can compare the likelihood of the lognormal dis-
tribution explaining the population data with the likelihood that
the 1/x power law explains it, and it turns out to be of the order
of 1011 times as likely. Similar results hold for other population
datasets in the range 1965-2005. So indeed it would be more
likely for one to find oneself in a middle ranked country like
Kuwait or Estonia, than in the most populous nations of India
or China. However, the effect is not marked. India and China
together have about 2.4 billion people, and the total number of
people living in countries with populations in the range 10 -
100 million is about 2.1 billion, and in the range 100 million to
a billion is about 1.5 billion.
Given the ubiquity of power laws, and the fact that a 1/x
power law exactly neuters any observer selection effect as in
the above case, might a 1/x power law be a signature of an
arbitrary, or random classification?
Mass Distribution of Animal Species
OK, well let’s get back to our ants, and ask the question of
what is the expected abundance of our species, assuming we are
randomly sampled from all conscious species on the Earth. The
distribution of species populations tends to follow a power law,
with a typical rank-abundance plot within a species size class
following a power law m
A
r with exponent m = −1.9 (Sie-
mann et al. 1999), where A is the abundance of the the rth most
abundant species. Rank-abundance plots are related to cumu-
lative size distributions (Newman, 2005):
 
=
A
rANpxx

d
(2)
where N is the total number of species in a size class, and


px the distribution of species abundances. Solving (2) im-
plies


pA is also a power law, with exponent −1.52. By the
argument in the previous section, we would therefore expect to
find ourselves to be one of the many species with few indi-
viduals, if all animals were conscious, as the distribution of
abundances falls off faster than 1/A. Yet our species abundance
is many orders higher (6 × 109) than the minimum abundance
for viability (approx 103). However, for the most part of our
species’ existence on the Earth, our abundance was much less,
and perhaps integrated over time, our total abundance is not so
different from that of other species of our size class.
However, let us ask a different question: “what is our ex-
pected body mass if we are randomly sampled from the re-
ference class of conscious beings?” For this we need the abun-
dance distribution


Pm as a function of body mass.
There is a well known biological law (called Damuth’s law)
(Damuth, 1991) that states the population density of a species is
inversely proportional to the 3/4ths power of that species’ body
mass, i.e. 34 Am

. To turn this result into the mass distribu-
tion of individuals


Pm, we need to multiply this law by the
mass distribution of species


Sm. Informally, we note that
there are many more smaller bodied species of animals than
larger ones; there are many more types of insect than of ma-
mmals, for example. The exact form of the distribution function


Sm is still a matter of conjecture. Some theoretical models
suggest that


Sm is peaked at intermediate body sizes (Hut-
chinson & MacArthur, 1959), and experimental results appear
to confirm this (Siemann et al. 1999), although it must be ad-
mitted that the latter study was confined to insects, and ignored
1Thank you to Aaron Clauset for pointing this out.
2

R. K. STANDISH
Figure 1.
Distribution of national populations in the year 2005, plotted on a log-log scale (US
Census Bureau, 2005). Also plotted are the best fits for a power law (slope −1.05)
and lognormal (μ = 14.8, σ = 2.5).
the huge diversity of nematodes. Of more interest was the find-
ing that Siemann et al. 1999 (Siemann et al.
use instead of ). Writing
 
0.5
Sm Pm

Pm

Im

 
12
34 34
PmSmmPm m

 (3)
we can solve for


Pm as


32
Pm m

 (4)
By the same arguments as above, we should expect to find
ourselves near the lower body mass of the class of conscious
animals, ruling out the vast majority of animals that are insects
etc.
Bayesian Formulation
The argument can be cast in a Bayesian framework in the
following way. Let A represent the hypothesis that all animals
are conscious, and B represent the observation that our ob-
served body mass is greater than (for arguments sake) 10 kg.
The previous argument could be criticised as suffering from
what is known as the “Prosecutor’s fallacy”. The value

pBA

can be computed from (4) by integration:


10 kg
=pBAPm m

d (5)
12
0
10 kg
=m




(6)
5
0
10with= 1μgm

 (7)
where 0 is the minimum mass of a conscious animal under
hypothesis A. A suitable choice for such an animal is C. elegans,
a 1 mm long nematode with a nervous system consisting of 302
neurons. The mass of an adult C. elegans is around 2 μg
(Knight et al., 2002). Even if we were to limit the discussion to
animals of the size of ants (our titular species) or bigger (60 μg -
2 mg (Kaspari, 2005)),
m


4
10pBA  .
However, the question we really want to know the answer to
is what is

p
AB —what is the likelihood of all animals being
conscious, given that our observed body mass is more than 10
kg?
Bayes law is written as



=pBA pA pABpB (8)
The term


pA represents our prior conviction in A. We
can, for the sake of argument, assume


=1pA here. Any
lesser value only increases the force of this argument.
The final term


pB is the probability of observing one’s
body mass greater than 10 kg. Since we don’t know the mass
distribution of conscious beings, we cannot calculate this value
directly. However, we can use a form of anthropic reasoning
introduced by Gott III (1994). In that case, Gott argued that a
number drawn at random from a uniform distribution on the
numbers 1
N
 would find its value to lie in the range


0.5 ,NN with confidence 95%. Suppose instead that the
numbers were ordered according to some attribute m, drawn
from some unknown distribution


M
m. Then by the same
argument, we can say that with 95% confidence

d> 0.05.
mMm m

 (9)
But the left hand side of (9) with m = 10 kg is just our term


pB, where


M
m is the unknown distribution of masses
of conscious observers. Thus with confidence


0,1c, we
can assume


>1pB c

.
Plugging this into (8), our confidence in hypothesis A being
wrong is

=1cpBA (10)
which is 99.7% for nematodes and 99% for ants. By contrast,
for the proposition that all mammals are conscious, our con-
fidence in this being wrong by (10) is only about 90%, using
the smallest known mammal mass of about 2 g for the Pygmy
Shrew. 90% is generally considered not statistically significant,
so anthropic reasoning cannot be used to rule out the conscious-
ness of all mammals without further refinement of


pA .

R. K. STANDISH
Conclusion
In this paper, the reference class of anthropic reasoning is
used as a way to reason about the species of animals that could
be conscious. Considering the reference class to be all con-
scious animals on the Earth, one applies known distributions of
species abundances to determine that: one’s nationality is not
expected to be any particular country, owing to a 1/x dis-
tribution of population sizes; that one’s body mass should be
near the lower limit of the set of conscious animals; and the
abundance of one’s own species should be near the lower limit
of species abundances.
Considering our body mass is substantially higher than the
average animal (who is an insect, or even possibly a nematode),
we can conclude that the vast bulk of the animal kingdom is
unlikely to be conscious. We might also conclude, based on the
high present abundance of humans, that most species of our
mass class are also not conscious, since we should also expect
to find ourselves near the lower limit of species abundance of
conscious species. But this would be a mistake—it is only na-
tural, assuming we’re born human, to be born in an era of high
human abundance. Integrated over our entire species lifetime,
the total human abundance may not be so different from that of
other species in our size class.
REFERENCES
Barrow, J. D., & Tipler, F. J. (1986). The anthropic cosmological prin-
ciple. Oxford: Clarendon.
Bostrom, N. (2002). Anthropic bias: Observation selection effects in
science and philosophy. New York: Routledge.
Chalmers, D. J. (1995). Facing up to the problem of consciousness.
Journal of Consciousness Studies, 2, 200-219.
Clauset, A., Shalizi, C. R., & Newman, M. E. J. (2009). Power-law dis-
tributions in empirical data. SIAM Review, 51, 661-703.
doi:10.1137/070710111
Damuth, J. (1991). Of size and abundance. Nature, 351, 268-269.
doi:10.1038/351268a0
Gott III, J. R. (1994). Future prospects discussed. Nat ure, 368, 108.
doi:10.1038/368108a0
Hutchinson, G. E., & MacArthur, R. J. (1959). A theoretical ecological
model of size distributions among species of animals. American
Naturalist, 93, 117-125. doi:10.1086/282063
Kaspari, M. (2005). Global energy gradients and size in colonial organ-
isms: Worker mass and worker number in ant colonies. PNAS, 102,
5079-5083. doi:10.1073/pnas.0407827102
Knight, C. G., Patel, M. N., Azevaedo, R. B. R., & Leroi, A. M. (2002).
A novel mode of ecdysozoan growth in C. elegans. Evolution and
Development, 4, 16-27. doi:10.1046/j.1525-142x.2002.01058.x
Leslie, J. (1989). Universes. New York: Routledge.
Nagel, T. (1974). What is it like to be a bat? The Philosophical Review,
83, 435-450. doi:10.2307/2183914
Newman, M. E. J. (2005). Power laws, pareto distributions and zipf’s
law. Contemporary Physics, 46, 323-351.
doi:10.1080/00107510500052444
Schultz, T. R. (2000). In search of ant ancestors. PNAS, 97, 14028-
14029. doi:10.1073/pnas.011513798
Siemann, E., Tilman, D., & Haarstad, J. (1999). Abundance, diversity
and body size: Patterns from a grassland arthropod community. Jour-
nal of Animal Ecology, 68, 824-835.
doi:10.1046/j.1365-2656.1999.00326.x
Tye, M. (1997). The problem of simple minds: Is there anything it is
like to be a honey bee? Philosophical Studies, 88, 289-317.
doi:10.1023/A:1004267709793
US Census Bureau (2005). IDB—Rank countries by pop ulation .
http://www.census.gov/ipc/www/idbrank.html
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