Order and Tolerance

Relationships Between the Natural Sciences and the Visual Fine Arts - I ORDER AND TOLERANCE 147 The problem of order seems to me closely connected with one of the oldest and venerable problems in the history of philosophy, that of universals. Both spacial and temporal orders presuppose an arrangement of elements that can be either identical or similar. It may be a moot point whether complete identity of elements can be found in nature (e.g. in the world of nuclear particles), but experientially the impression of identity or of similarity depends, of course, on a prior system of classification. Elements are alike or similar from a given point ofview; there must be a prior criterion that cannot, in the way of things, be derived from observation. Plato's solution of this dilemma was contained in the doctrine of anamnese, the soul remembered the idea of likenes like any other universal, having perceived it before entering the human body. Here as elsewhere it seems appropriate to replace the metaphysical doctrine by the postulate of a biological inheritance. One is born with more or less crude categories that allow one to compare experiences and also to refine their comparison. What one compares, however, are not the elements but one's reaction to them. Elements that elicit a similar reaction are classed as similar and can thus form the building stones of orders. Order in art is dependent on this relative crudity of one's discrimination. Different elements can do service as parts of an order. A good example of what is here meant is offered by the musical device of even temperament, a method of 'cheating' that permits the composer to modulate more freely from one key into another and, thus, to produce immensely satisfying orders that may, however, disturb musicians with a most discriminating ear. The problem of tolerance for disorder seems to me worthy of investigation in the context of this 'order' project. For the traditional opposition between rigid, mechanical and mathematical orders that are alleged to be 'dead' and the flexibility of 'living', 'organic' orders made, for instance by Ruskin in the 19th century and by Ludwig Klages (following Bergson) in the 20th century, seem to me philosophically naive. Even mechanical orders must be fuzzy around the edges and contain a random element; the experience of order presupposes tolerance. (Received 22 Oct. 1980) E. H. Gombrich 19 Briardale Gardens London. NW3. England ON A PRIORI ORDER AND ORDER TO BE DISCOVERED To do science is to discover an order in reality; to make an artwork is to impose on reality an order specific to the artist. 'To master reality it is sufficient to have a system, be it apparently illogical, unnecessarily complicated, strangely jarring', writes semi-humorously Roland Barthe [I]. 1. The Natural Sciences The aim of the natural sciences is to find laws of nature, to fit experimental facts into a general framework and to develop theories that enable one to predict these and other facts. In other words, the aim of the natural sciences is to discover order in nature. This order does not belong uniquely to nature; it depends in particular on the historical development of science. One can interpret nature within different kinds of order. There are, for instance, several more or less satisfactory hypotheses of fundamental particles that refer to different kinds of order. Still, what is clear is that, to say the least, these orders are not arbitrary. Assimilation [2] consists of making experimental facts fit into a pre-established order, one which has been presumed to be relevant to nature. When a new experimental fact isobtained that does not conform to the presupposed order, this order must be modified; this isthe process of accommodation [2].The successionof hypotheses in science is the seemingly unending passage from one order to another order. The axiomatic method used in mathematics, of which two striking examples are Euclidian geometry and the recent works of Bourbaki, consists mainly of presenting, as if it was an a priori order, an order that is the end of a chain ofanalyses. The historical order in which properties were found is replaced by a new, more logical order. Axiomatic methods thus...