Atheism and Theism 17Faulty Anthropic ArgumentsThe matter many be illustrated by a faulty argument of G.J. Whitrow in the
appendix to the second edition of a book published in 1959^27 and earlier in
a paper in The British Journal for the Philosophy of Science.^28 This was some
time before Brandon Carter formulated his ‘anthropic cosmological principle’,
and there is some similarity between Whitrow’s reasoning and Carter’s, and
yet an important difference. Carter’s reasoning was not faulty in the way (as
I shall show) Whitrow’s was. This is because Carter connected his anthropic
principle with a ‘many universe’ hypothesis which I shall discuss shortly.
Whitrow begins by assuming plausibly enough that in a space of s+ 1
dimensions there would be an inverse sth power law of gravitational attrac-
tion. (This is the case in Newtonian dynamics and is approximately true
in general relativity.) Whitrow also assumes, perhaps plausibly, that life, and
hence observers, would not have arisen on a planet which had a very eccentric
or unstable orbit. He then goes on to make use of a theorem in classical
mechanics that a stable and near circular orbit can occur only in a space of
either two or three dimensions. He makes use of an argument to the effect
that a brain would not be possible in two-dimensional space: only in a space
of three or more dimensions could many neurons be connected in very many
ways so as to form a complicated network. (Whitrow acknowledges a sugges-
tion by J.B.S. Haldane and a mathematical discussion with M.C. Austin.)
Whitrow thus concludes that ‘the number of dimensions of space is neces-
sarily three, no more and no less, because it is the unique natural concomitant
of the higher forms of terrestrial life, in particular of Man, the formulator of
the problem’ (Whitrow’s italics).
Modern cosmologists play around with theories that space has ten or more
dimensions and a complicated topology, but they still hold that macroscopic-
ally it has three dimensions and a Euclidean type of topology. (Compare the
way in which an oil pipe hundreds of miles long would look like a straight
line from far enough away in space, whereas looked at closely its surface is
seen to be two-dimensional, with the topology of the surface of a cylinder.)
That space has three dimensions at least macroscopically is good enough for
Whitrow’s argument and we can agree that it does follow from Whitrow’s
premisses, together with some uncontroversial mathematics, geometry,
mechanics and natural history, that humans could not exist unless the number
of dimensions of space was (macroscopically) three. Nevertheless, insofar as
he put the argument as an explanatoryone, it is quite preposterous. The
supposed explanation is back to front.
Surely we should think that it is the three-dimensionality of space that
explains the existence of habitable planets containing intelligent life. I do not
think of ‘explanation’ as a very clear notion, and its use depends a good deal