9. Philosophical Aspects. The appraisal of the phil-
osophical significance of a new field of science, or of
a fundamental turn in its treatment, or of the appear-
ance of a new scientific language expressing new con-
cepts, is an extremely delicate matter. Hence little shall
be said here as it may be premature to do so. But if
we attribute philosophical meaning to the fact that the
study of decision-making under a wide set of circum-
stances has not only affected significantly sciences like
statistics, but is spreading to other fields as a new
mathematical discipline—game theory—and is influ-
encing even pure mathematics, then we are justified
in speaking of a philosophically relevant development.
While raising no claims of equal importance, the
development of game theory has created a shift of
standpoints in viewing the social world and human
behavior, just as relativity theory and quantum me-
chanics have provided a new outlook on physical real-
ity. It is too early to be very specific: in those other
two areas it took years before the strange new concepts
of space curvature, of an infinite but bounded space,
of the Heisenberg uncertainty relationship, and of
Bohr's principle of complementarity (to name only a
few) were properly incorporated into philosophy, and
it is doubtful whether this process has already come
to an end. Consequently it will likewise be many years
before the philosophical discussion of the new outlook
due to game theory will have crystallized.
In statements about the philosophic significance of
a scientific area it would help if it were unambiguously
clear what is meant by “philosophy.” Philosophy has
a difficult but fairly well defined scope when it comes
to analyzing problems of knowledge, of verification,
of the meaning of truth. But to determine the philo-
sophical meaning of a new scientific development is
almost impossible while that change is rapidly pro-
gressing. Therefore only some tentative remarks shall
be made in which there is no attempt to order them
according to their significance or to be exhaustive. Nor
can one be sure that the principal philosophical mean-
ing does not lie elsewhere.
(a) We are confronted with a new development
concerning our understanding of reason and rationality
as the previous sections have indicated. Both being
possible human attributes we are now in possession of
precise concepts that were lacking or undefined for-
merly. We have a mathematical theory that is largely
combinatorial in character and whatever ultimate
crises mathematics itself may be afflicted with there
has never been any doubt cast on the final character
of combinatorics. The new light thrown on the problem
of rational behavior has shown that there is here not
one problem but many, that they inevitably lead to
formulations requiring mathematical analysis, that one
is now capable of providing such analysis at consid-
erable depth and that actual computations are possible,
though limited by physical processes such as speed and
memory of the computers.
Mathematics thus has encroached on another field
of human activity in a decisive manner, and it is certain
that it will never be dislodged from it again. We also
note that axiomatics, so far the ultimate formal expres-
sion we are capable of giving to theories, has now for
the first time firmly established itself in the social
sciences.
(b) A further step has been taken in the behavioral
sciences by the replacement of determinism by the
new, extended, role which has been assigned to proba-
bility though the indeterminacy introduced is not in
all respects that of a probabilistic nature (as is shown,
e.g., by the uncertainty regarding which imputation
in a solution set in an n-person game will be chosen).
This also affects the ideas held concerning prediction:
neither deterministic nor probabilistic approaches need
to work, as uncertainty of a different kind appears to
prevail in many social setups and decision situations.
(c) Modern decision theory has thrown new light on
the nature and role of information, its flow from indi-
vidual to individual and on the value and cost of
obtaining it or preventing it from spreading. In the
same spirit mention must be made of the fact that one
has gained control—no doubt in an initial manner
only—of the troublesome notion of utility by tying it
firmly to expectations and various forms of probability.
(d) The immense complexity of social actions and
their interplay has been laid bare. It is seen that it
is greater by several orders of magnitude over what
earlier writers in the social sciences had contemplated,
and it has been shown—though only in part and so
far mainly indirectly—how and why the classical
formalistic approaches must fail. It is probably no
exaggeration to state that social science will prove to
be far more difficult than physics and that it will re-
quire (as indicated earlier) the development of new
mathematical disciplines.
There is, in particular, one philosophical conse-
quence that must be stressed because it seems to have
escaped proper attention thus far: it was emphasized
above that certain formal system of society will of
necessity work in a manner different from the inten-
tions of the designers. More generally we state that no
complete formalization of society is possible: if a
formalization is made, it is either incomplete or self-
contradictory. Hence the attempt can only be to for-
malize as much as possible and to supplement the
formalism by new formalistic decisions in those con-
crete situations where it fails. Every social theory must
therefore be dynamic, proceeding from one formalism
to another. The axiomatization of games conforms to
this fact, since the axioms require neither categoricity
nor completeness because new games can always be
invented and these can serve as prototypes for new
social arrangements.
The theory of finding optimal strategies in decision-
making has thus produced a new paradigm for the
social and behavioral sciences. It will take considerable
time before the full impact of this development is felt.
But one philosophical meaning cannot be missed even
now: the push towards a more general theory firmly
based on combinatorial mathematical concepts and
procedures.
However, before philosophy reaches its ultimate
state of becoming the most general abstract science,
in the sense of Leibniz' Mathesis universalis, philo-
sophical activity may itself be viewed as a game. This
only appears to be a heretic idea. Plato in Parmenides
did speak of philosophy as a game and the Sophists
engaged openly in philosophical contests. Philosophical
schools have always competed with each other, as is
the case in all sciences in different stages of their
development. The same applies to art; it suffices to
recall the contests between Leonardo da Vinci and
Michelangelo. With this remark we return to the
opening observation in this paper which showed the
deep roots of games in human affairs to be such that
we may speak rightly of man as Homo ludens.
