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The descriptions of science are widely accepted because of their utility. Our assumptions have the potential for similar practical results. The psychologist, Carl Jung, had an intuition that number was the archetypal mediator between the physical world and the higher world[1, par 778][3]. Mathematics can help us understand spiritual truths that have previously been only intuitions.
Central to the evolution of consciousness is the development of ever more subtle and complex levels of self reflection. This has culminated in the human mind aware of its own mortality and able to develop science and mathematics. We can understand aspects of these structures in mathematical hierarchies of iteration or self reflection. Our assumptions establish a structural equivalence between consciousness and these mathematical hierarchies.
An implication of Gödel's famous proof of the incompleteness of mathematics is the absence of any single finite formulation that can capture the potentially unlimited levels of ever more powerful forms of self reflection that can exist in a mathematical system. The only way to explore all these possibilities is through a divergent process that follows an ever increasing number of paths as biological evolution has done in creating the human mathematical mind.
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