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Robert Motherwell: Would you say that a fair statement of your position is that the "meaning" of a work of art consists of the relations among the elements, and not the elements themselves?
Hofmann: Yes, that I would definitely say. You make a thin line and a thick line. It is the same with geometrical shapes. It is all relationship. Without all these relationships it is not possible to express higher art.
--
Interview in Modern Artists in America, First Series (1952), edited by R. Motherwell, Ad Reinhardt, and B. Karpel, p. 19, 39

 

Hans Hofmann

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The Buddha said, "Elements come together and form this body. At the time of appearing, elements appear. At the time of disappearing, elements disappear. When elements appear, I do not say "I" appear. When elements disappear, I do not say "I" disappear. Past moments and future moments do not arise in sequence. Past elements and future elements are not in alignment. This is the meaning of ocean mudra samadhi."
Closely investigate these words by the Buddha. Attaining the way and entering realization does not necessarily require extensive learning or realization. Anyone can attain the way through a simple verse of four lines. Even scholars of extensive learning can enter realization through a one line verse.

 

Dogen

 

But if some mind very different from ours were to look upon some property of some curved line as we do on the evenness of a straight line, he would not recognize as such the evenness of a straight line; nor would he arrange the elements of his geometry according to that very different system, and would investigate quite other relationships as I have suggested in my notes.
We fashion our geometry on the properties of a straight line because that seems to us to be the simplest of all. But really all lines that are continuous and of a uniform nature are just as simple as one another. Another kind of mind which might form an equally clear mental perception of some property of any one of these curves, as we do of the congruence of a straight line, might believe these curves to be the simplest of all, and from that property of these curves build up the elements of a very different geometry, referring all other curves to that one, just as we compare them to a straight line. Indeed, these minds, if they noticed and formed an extremely clear perception of some property of, say, the parabola, would not seek, as our geometers do, to rectify the parabola, they would endeavor, if one may coin the expression, to parabolify the straight line.

 

Roger Joseph Boscovich

 

Carnap calls such concepts as point, straight line, etc., which are given by implicit definitions, improper concepts. Their peculiarity rests on the fact that they do not characterize a thing by its properties, but by its relation to other things. Consider for example the concept of the last car of a train. Whether or not a particular car falls under this description does not depend on its properties but on its position relative to other cars. We could therefore speak of relative concepts, but would have to extend the meaning of this term to apply not only to relations but also to the elements of the relations.

 

Hans Reichenbach

 

Nature consists of the elements given by the senses. Primitive man first takes out of them certain complexes of these elements that present themselves with a certain stability and are most important to him. The first and oldest words are names for "things". ... The sensations are no "symbols of things". On the contrary the "thing" is a mental symbol for a sensation-complex of relative stability. Not the things, the bodies, but colours, sounds, pressures, times (what we usually call sensations) are the true elements of the world.

 

Ernst Mach

 

We speak of concrete and not abstract painting because nothing is more concrete, more real then a line, a colour, a surface. A woman, a tree, a cow; are these concrete elements in a painting? No. A woman, a tree and a cow are concrete only in nature; in painting they are abstract, illusionistic, vague and speculative. However, a plane is a plane, a line is a line and no more or no less than that. "Concrete painting". Spirit has arrived at the age of maturity…

 

Theo van Doesburg