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are we supposed to make of that?” So I thought I could sweeten or lighten
this problematique if I tried above all to present the ideas so clearly that
they became transparent. And when something is transparent, then one no
longer sees it: the problems disappear. And as a second idea, I thought I'd
bring from California a trio of American jewels for our birthday child
Niklas Luhmann that are probably somewhat known here already but may
still amuse the birthday child in their special birthday edition.
The first present I've brought along is an essay by Warren McCulloch,
written about a half a century ago. It is the famous article with the title “A
Hetarchy of Values Determined by the Topology of Nervous Nets” (1945).
I find that this article is of such great significance that I'd like to draw your
attention to its existence once more. So that you can see what field he
worked in, I'll read you a sentence from the last paragraph. It rests on the
idea of a circular organization of the nervous system: “circularities in pref-
erence.” These circularities arise when one prefers A to B , prefers B to C ,
and, again, C to A . In classical logic one then speaks of being illogical. Nev-
ertheless, McCulloch says that is not illogical, it is logic as it is actually used.
Therefore: “Circularities in preference instead of inconsistencies, actually
demonstrate consistency of a higher order than had been dreamed of in our
philosophy. An organism possessed of this nervous system—six neurons—
is sufficiently endowed to be unpredictable from any theory founded on a
scale of values.” A system of six neurons is, in the framework of existing
theories, unpredictable in principle. That is present number one.
Present number two that I've brought along with me is an article by Louis
Kaufmann, a mathematician who is fascinated by self-reference and recur-
sion. The article is called “Self-reference and recursive form” (1987). And
so that you can see why I find it so important, I'll read you the last sentence
of this article. The last sentence of this article is: “Mathematics is the con-
sequence of what there would be if there could be anything at all.”
Present number three is by my much admired teacher Karl Menger, a
member of the Wiener Kreis (Vienna Circle), to which I am pleased, even
today, to have fallen victim! When I was a young student I enthusiastically
attended Karl Menger's lectures. The article by Karl Menger, which I've
brought here as present number three, is “Gulliver in the Land without One,
Two, Three” (1959). You may ask, why I've brought such an article to a
group of sociologists! In this article Karl Menger already developed the
idea of functors, that is, of functions of functions, which I consider
wholly decisive for the theoretical comprehension of social structures. Here
too I'll read the last sentence, so you can see what it's all about. The last
sentence is: “Gulliver intended to describe his experiences in the Land
without One, Two, Three in letters to Newton, to the successors of Descartes,
to Leibniz, and to the Bernoullis. One of these great minds, rushing from
one discovery to the next, might have paused for a minute's reflection upon
the way their own epochal ideas were expressed. It is a pity that, because
of Gulliver's preparations for another voyage, those letters were never
written.”
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