March 5

On the value and limits of borders

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The central question of this essay was to me: Why will binary systems always only be decideable or complete but never completely decideable? And: What does that mean for me?

Horos (ancient Greek ὅρος) denotes the border, the boundary stone. The human frisson to cross such a border is stylized in horror films in modern times, specifically made tangible. Where in former times mostly natural conditions, like rivers, marked as demarcation lines the difference between here and there, man soon invented terms to distinguish between this- and beyond-that.
Systems theorists have developed this two-valued logic into theories and have shown the value for social systems - i.e. states, religious communities, etc. - if it is successful to enforce two-valued logics. It is only the difference that allows one to respond to a counterpart, to meet as a human being. And so it has its value when a system establishes its boundaries, reaches its limits.
But I would like to address a particular aspect of boundaries that rarely receives attention - because it is uncomfortable to think about, especially among studied folk. To do so, I want to draw on three traditions or thinkers that I think have created powerful images of language that make this difference denominable.

  • ancient Greek mythology, which makes a clear distinction between the Appolinian and the Dionysian - which Nietzsche aptly unfolded in his "Genealogy of Morals" and also in "Beyond Good and Evil."
  • Wittgenstein, a thinker whose early writings were so Appolinic: One thinks of the Tractatus, which says: "The limits (sic!) of my language, are the limits of my world" - at the same time a thinker whose late writings overcome the limitations of this perspective until it can be said: "The meaning of a word is its use in language".
  • Gottlob Frege, who states in his Begriffsschrift that two-valued systems are always either decidable or complete - but never decidable and complete at the same time. And thus mathematically substantiates what Schiller criticized in his Kant critique or the Bacchants criticized in Apollo for centuries, but could not prove in logical and mathematically clean formulas, which is why every two-valued logical thinker could dismiss it as sentimental nonsense.

The exciting point for me now is that although Luhmann and co. have laid out that limits must be reached, are necessary, these limits are not capable of making all essential decisions. Man, if he is to succeed in the project of life, must develop other figures of thought and decision-making practices beyond two-valued thinking in order to move forward. He must therefore not only overcome borders, but also overcome thinking in borders, which always know only a here or there.


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