 
                         20060101.01

     I have much occasion to reflect on my failures: my
failure to become a musician and my failure to become a
mathematician.  It is clearly impertinent of me to presume to
redefine, to recalibrate mathematics in such a way as to
mitigate the significance of my own failures in the field.
Yet that is precisely what I do, when I point out that the
validity of mathematical discovery is unavoidably mediated by
social, that is to say, by political factors.  Like any other
(philosophical) theory, the mathematical discovery (or
invention) unavoidably requires validation by society; and if
not so validated, it will be lost.  But this validation of
the theory in turn is only incompletely a matter of its
functional cogency.  This validation is also a consequence of
the social dynamics of the group to which it is presented,
and in which it is considered.  I doubt that the axiomatics
which attracted such lively attention when David Hilbert
presented them in Paris would have been taken nearly so
seriously, if they had been offered by an unknown neophyte.
Consequently their validity, such as it may be, is an
expression not only of the compulsion of their logic, but
also of the professional prestige of their author.

     It is, I think, important to recognize the extent to
which knowledge - and purported knowledge as well - may be
accepted on the authority of the teacher. A student
presumptuous enough to venture to disagree would be
stigmatized as being stupid.  Is that why Thomas Aquinas was
nicknamed the Dumb Ox?  The autos ephe with which the
Scholastics put down the questioner, strikes me as a mere
emblem of the mass of scholastic reasoning, which, as I
interpret it, required the uncritical and unquestioning
acceptance of dogma. To the extent that he who was indoc-
trinated was not required to understand, in the sense of
being able explicate or to replicate that which he was
expected to believe, its validity depended on the reputation
of its promulgators.  In other words, knowledge was required
to be accepted on faith.

     Turning now to the scientific knowledge of which I am
aware, much of which I do not understand in the sense of not
being able to explicate or to replicate it, I have no
alternative but to acknowledge that I am, nonethless,
expected to accept it as true, again, as a matter of faith.
What is accepted as true without being understood includes,
of course, the vast assemblage of the assertions of physics,
of chemistry, biology, and other sciences; but even more
significant: it includes the assertions of statistics that
purport to define the reality of the present and to
rationalize the anticipation of the future. My point is, that
from the perspective of accepting as true what we don't
understand, we are all of us scholastics.  And, given given
the impenetrability of statistical reasoning to most of us,
the statistician is the contemporary soothsayer par
excellence.

     This issue, the reliable anticipation of the future is
the crux of knowledge. It is the mental function which makes
possible the life of humans, and perhaps also of all other
animals; inasmuch as the gathering of food and the avoidance
of danger, which require some knowledge of the future, are
prerequisite to survival.  The anticipation of the future is
far from reliable.  Statistics is the mathematical technique
by which prediction of future events is to be enhanced.
Obviously it is not unconditionally successful in this
endeavor: for simple formulas prove to be inadequate. The
more complex ones, even as they claim to be more reliable,
become at the same time inscrutable, and to the point where
one cannot understand them and must accept them on faith.
Back in the Middle Ages again.

     Thus the limitations of understanding, specifically, the
limitations of _my_ understanding lead to a situation which I
am unable to distinguish from Scholasticism, a situation
where I have no choice but to accept premises and reasoning
that lead to essential conclusions about the world and about
myself, and to accept such conclusions on faith, on faith no
different from that which would have been required of me if I
were living in the Middle Ages, and had to give my assent to
the reasoning of the Scholastics.


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Copyright 2006, Ernst Jochen Meyer
