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The finite and the infinite

Immediate experience is always definite and finite. A defining property of an infinite set is that you can add something to it without changing it. For example you can map the even integers onto all integers. Both sets have the same number of elements. A defining property of immediate experience is that if you add something to it you change it. Conscious experience is a gestalt whole. Change it and you have a different experience.

The finiteness of direct experience leads to a second simplest possible assumption about the nature of existence. By giving essence to existence we give substance to the question of what it would mean for an infinite structure to exist. They cannot exist as gestalt wholes. This does not necessarily mean that there a fixed fine limit to conscious gestalts. There may be two classes of existence. The first is immediate gestalt experience. The second is the collection of all such experiences. This collection may be infinite and is not itself an immediate gestalt experience. Mathematics already has such a distinction between sets and classes. This was necessary because of the contradictions that arise from assuming there can be a set that contains all sets. There is a class of all sets that cannot be a set. We are suggesting that this necessary boundary occurs between the finite and the infinite.

Conscious gestalts are what is. Each gestalt is finite but there may be no limit to the unfolding of gestalt experiences. What is a gestalt and where are its boundaries? In mathematics the unifying relationship is set membership. Everything is a set and all relationships are determined by set membership. A set is an arbitrary collection of other sets. Our conscious experience seems to follow a mathematical construction. Aspects of the physical mathematical structure of our brain seem to not simply mirror but are the structure of our conscious experience.

Mathematics studies all possible structures. The only constraint is logical consistency. The same constraint would seem to apply to a gestalt. When we have an immediate conscious experience it is a definite unique event. It may have many ambiguous interpretations but the experience itself is exactly what it is. A patch of color cannot be red and also not red. As mathematics is the study of all possible logical structures it is also the study of the structure of all possible gestalts.

Consciousness evolves. It changes over time. Reproducing molecules have become the human mind capable of the most incredible ecstasy and unspeakable horror. This evolutionary process need not have an end. We do not know if time and space have finite boundaries. We know from mathematics that there is no limit to fundamentally richer and deeper structures. If the universe is potentially infinite than the evolution of consciousness may expand forever. Could this be where our instincts our pointing when they lead us to a sense of the spiritual and divine? Does not creativity itself have survival value? Could we not evolve instincts that lead us to pursue unbounded creativity? Is that not where we get our desire to explore the world and the universe?


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Next: Mathematics and physics Up: expth Previous: External and internal reality


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