Wittgenstein's Philosophy of Mathematics and the Search for Extraterrestrial Intelligence

Abstract

Humanity, its scientific members in particular, has long been fascinated by the
possibility of extraterrestrial intelligence. Although the idea of creatures
inhabiting nearby heavenly bodies lost credence after expeditions to the Moon and
Mars, several members of the SETI Institute (the institute for the search of
extraterrestrial intelligence) still maintain on statistical grounds that "alien
civilizations in the galaxy are likely to number anywhere from 10,000 to one million"
(Broad 1998). But, what does it mean: "extraterrestrial intelligence"? The first
association most readers will probably have is the prototype of a Martian: a green,
and slimy creature in which all sorts of human traces, mental as well as
physiological, can be discerned. Furthermore, this creature - let us call him Joe -
is very intelligent; in particular, he excels in mathematics. In fact, the very way
in which we got in contact with Joe was by means of mathematics: large
radiotelescopes picked up sequences of prime numbers, which we returned with part of
the sequence of Fibonacci numbers… and he arrived on earth. There is an underlying
assumption of tremendous importance: mathematics is a language shared by all
civilizations, it is a universal language, so to speak. This assumption has had
enormous consequences for the SETI project. It has restricted the definition of
"extraterrestrial intelligence" in the same way as old-fashioned IQ tests have done
with the notion of human intelligence: intelligence is equated with the outcome of
the test, discarding the possibility of an external criterion for the correctness of
the test; analogously, "extraterrestrial intelligence" has been declared equivalent
to "possession of mathematical abilities similar to ours." But, why would
extraterrestrial civilizations have the same mathematics as we do? Is not a different
mathematics possible? That is, how can we be sure that the above definition of
"extraterrestrial intelligence" does not exclude civilizations that do their math in
a different way, but are interesting to get in contact with anyway? Do such
civilizations exist? Can such civilizations exist? In this paper, I will argue that
Wittgenstein's philosophy of mathematics provides an interesting view on the
assumption that mathematics is a universal language. The argument as I give it here
will probably not convince someone who is not familiar with Wittgenstein's thought.
For a different audience, I would have elaborated on different points. Furthermore, I
have not dwelt upon any connections with, say, the problems of other minds and
cultures, relativism, and the like. Altogether, it is only a short note on what I
think is not an unimportant issue.