Axioms and Barbarism

Jusepe de Ribera - Euclid - 2001.26 - J. Paul Getty Museum

"An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα (axíōma), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.

The term has subtle differences in definition when used in the context of different fields of study. As defined in classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. As used in modern logic, an axiom is a premise or starting point for reasoning.

The word axiom comes from the Greek word ἀξίωμα (axíōma), a verbal noun from the verb ἀξιόειν (axioein), meaning "to deem worthy", but also "to require", which in turn comes from ἄξιος (áxios), meaning "being in balance", and hence "having (the same) value (as)", "worthy", "proper". Among the ancient Greek philosophers, an axiom was a claim which could be seen to be self-evidently true without any need for proof."


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Poverty of experience. This should not be understood to mean people are yearning for new experience. No, they long to free themselves from experience; they long for a world in which they can make such pure and decided use of their poverty – their outer poverty, and ultimately also their inner poverty – that it will lead to something respectable. Nor are they ignorant or inexperienced. Often we could say the very opposite. They have “devoured” everything, both “culture and people,” and they have had such a surfeit that it has exhausted them. No one feels more caught out than they by Scheerbart’s words: “You are all so tired, just because you have failed to concentrate your thoughts on a simple but ambitious plan.” Tiredness is followed by sleep, and then it is not uncommon for a dream to make up for the sadness and discouragement of the day – a dream that shows us in its realised form the simple but magnificent existence for which the energy is lacking in reality.

[...]

Barbarism? Yes, indeed. We say this in order to introduce a new, positive concept of barbarism. For what does poverty of experience do for the barbarian? It forces him to start from scratch; to make a new start; to make a little go a long way; to begin with a little and build up further, looking neither left nor right. Among the great creative spirits, there have always been the inexorable ones who begin by clearing a tabula rasa. They need a drawing table; they were constructors. Such a constructor was Descartes, who required nothing more to launch his entire philosophy than the single certitude, “I think, therefore I am.” And he went on from there. Einstein, too, was such a constructor; he was not interested in anything in the whole wide world of physics except a minute discrepancy between Newton’s equations and the observations of astronomy. And this same insistence on starting from the very beginning also marks artists when they followed the example of mathematicians and built the world from stereometric forms, like the Cubists, or modelled themselves on engineers, like Klee. For just like any good car, whose every part, even the bodywork, obeys the needs above all of the engine, Klee’s figure too seem to have been designed on the drawing board, and even in their general expression, they obey the laws of their interior. Their interior, rather than their inwardness; and this is what makes them barbaric.

Walter Benjamin, Experience and Poverty