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Background
This exploration of abstraction is directly related to the use of abstraction to explore the debates surrounding a fundamental underlying reality.
The search for an underlying reality, a higher level of form, and the revelation of this through intuitive means, characterised the early 20th century strivings in abstraction by Piet Mondrian and Wassily Kandinsky. Both of these artists developed distinct visual languages that owed much to the optimism which had been brought about by the success of science, and more particularly, mathematics in describing the world.
now I find myself at the end of the 20th century trying to make sense of the success and failure of science and mathematics; trying to grasp the deeper meanings that are implied by the explorations of the world through rationalist, logical methods. Popper 1 has been and gone, leaving only traces of a philosophical position which seems to be the fall back position for many. Kuhn 2 has thrown out a challenge only to retreat from its deeper implications. Feyerabend 3 has upset the notions of purity by shouting loudly about the failure to produce precise method. Wittgenstein 4 remains hanging over all the debates as a series of whispers that cut deeply into all areas, but do not take on the force of an all out onslaught. Whilst Kurt Gödel's Incompleteness Theorem has dealt a body blow to the very core of the mathematical and scientific rationalist beliefs.
Method and reality are left in tatters with each position lurching into another position. Unsure of which way to turn, I return to the representation of underlying structure; the questions of whether the structure lies 'out there' or is a construction of ourselves, whether there is structure at all, and what are the parts played by rationality and intuition.
Reflections
Allusions to purity
Attempts to define theories / religions / philosophies which allude to some form of purity are based upon the belief that there exists some form of fundamental underlying reality. These are all permutations of the belief in the Platonic universe, which is totally consistent and reliable, and is thus preferable to our experience of limited consistency, illusions and contradictions. The belief that there is some form of underlying reality may induce a sense of security and may appeal but this does not mean that it is real or true.
The Imposition of Conceptual Structure
We impose structure upon the world. Our perceptual system draws our attention to patterns and the breaking of patterns (boundaries / borders).
We construct theories of reality that act as conceptual nets which we throw over our sensory impressions. We compare one area of experience to
another by finding analogous distortions in the nets we have thrown over them.
The basis of knowledge resides with these acts of throwing nets and finding analogous distortions. We can never be sure to what extent the structures
are 'out there' or a construction of ourselves.
The whole of this process is always incomplete and we revisit it every time we experience anything.
Pattern / Net / Boundary / Perceptual Unity / Analogy / Knowledge
Waiting for the Theory of Everything
I sit and stare into the space that has been created by the triumph of rationalist means. I wonder if there is something that could possibly bring together the disparate strands of relativity and quantum physics, whilst also remaining consistent with observed reality. I create structures / patterns that develop and disintegrate; each taking hold of my mind and building itself. Are they any more consistent than any theory? Do they represent anything more or less fundamental?
Bibliography
1 Karl Popper, Conjectures and Refutations
2 Thomas Kuhn, The Structure of Scientific Revolutions
3 Paul Feyerabend, Against Method
4 Ludwig Wittgenstein, Central Texts, trans. G. Brand
Michael Polanyi, Personal Knowledge