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Essence as a Platonic ideal

Platonic philosophy attempted to capture essence in a different way. Plato thought what we see in the physical world is a dim reflection of the true ideal thing. For example circular objects are crude approximations to the ideal perfect circle. Platonic philosophy aims to understand reality in terms of the ideals that capture the real essence that is dimly reflected in physical existence.

Today mathematics comes close to capturing the ideal circle of Plato. It cannot be constructed, but its properties, like the area it covers, can be computed with any desired degree of accuracy. Mathematics can do this in a purely structural way building all objects including circles from the essence free empty set.

Essence free arguments are not the norm even in mathematics. Geometrical arguments are still phrased in terms of geometrical properties. Only they are done in such a way that it is clear how to convert them to arguments about sets. In normal discourse we take the merger of structure and essence as given. It is how we visualize the world and how we think. The problem is that the essence we attribute to external objects is from our own experience. It is not something that is part of the external objects. A soft touch, sharp slap, beautiful sunset or ugly wound, are things created in us when we have particular experiences.

We are not perceiving external reality as it truly is nor are we dimly perceiving some ideal platonic reality. We are creating the world in our conscious experience. There is a related external structure that our perception is causally connected to. But the perception of, for example, color is far more a construction of our sensory and nervous system than it is an effect from light of a particular frequency.

The idealization and abstraction of mathematics had a profound an unexpected impact. It lead to something called Gödelization. That is the ability to assign unique numbers to all mathematical expressions. Today Gödelization is a practical reality for all of us as we store documents, images and movies digitally as a series of numbers in a computer. But in the 1930's it was a deeply creative observation that led to a result that shook the world of mathematics and exploded the idea that there could be an absolute Platonic ideal even for mathematical truth.


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Next: Gödel and unfathomable complexity Up: Structure and essence Previous: Essence and chemistry   Contents


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