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As you can see this is a composition of vertical and horizontal lines which will (in an abstract manner) have to express the idea of rising upwards, of magnitude. This is the same idea which used, for example, to be the guiding principle in the construction of cathedrals. Since only the manner of expression and not the representation has to express this general idea, I have not given any title. An abstract human mind will, of itself, receive the intended impression. I always confine myself to expressing the general.
--
letter to Theo van Doesburg, Amsterdam, 1915; as quoted in Letters of the great artists, Richard Friedenthal, Thames and Hudson, London, 1963, p. 234 (translation Daphne Woodward)

 

Piet Mondrian

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The cultivated man of today is gradually turning away from natural things, and his life is becoming more and more abstract. Natural (external) things become more and more automatic, and we observe that out vital attention fastens more and more on internal things.. ..Modern man –although a unity of body, mind and soul – exhibits a changed consciousness: every expression of his life has today a different aspect, that is, an aspect more positively abstract. It is the same with art. Art will become the product of another duality in man: the product of cultivated externality and of inwardness deepened and more conscious. As a pure representation of the human mind, art will express itself in an aesthetically purified, that is to say, abstract form.

 

Piet Mondrian

 

But one day, some painter used 'Abstraction' as a title for one of his paintings. It was a still life. And it was a very tricky title. And it wasn’t really a very good one. From then on the idea became something extra. Immediately it gave some people the idea that they could free art from itself. Until then, Art meant everything that was in it – not what you could take off it. There was only one thing you could take out of it sometime when you were in the right mood – that abstract and indefinable sensation, the aesthetic part – and still leave it were it was...

 

Willem de Kooning

 

The first remark we have to make, and which — though already presented more than once — cannot be too often repeated when the occasion seems to call for it, — is that what we call principle, aim, destiny, or the nature and idea of Spirit, is something merely general and abstract. Principle — Plan of Existence — Law — is a hidden, undeveloped essence, which as such — however true in itself — is not completely real.

 

Georg Wilhelm Friedrich Hegel

 

The consciousness of a general idea has a certain "unity of the ego" in it, which is identical when it passes from one mind to another. It is, therefore, quite analogous to a person, and indeed, a person is only a particular kind of general idea.

 

Charles Sanders Peirce

 

This music of yours. A manifestation of the highest energy — not at all abstract, but without an object, energy in a void, in pure ether — where else in the universe does such a thing appear? We Germans have taken over from philosophy the expression ‘in itself,’ we use it every day without much idea of the metaphysical. But here you have it, such music is energy itself, yet not as idea, rather in its actuality. I call your attention to the fact that is almost the definition of God. Imitatio Dei — I am surprised it is not forbidden.

 

Thomas Mann