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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 analysis aims to understand the physical world in terms of the ideals that capture the real essence that is dimly reflected in physical existence.

Today the ideal world that captures the true circle is mathematics. Unlike Euclidean geometry, contemporary mathematics has no primitive objects with innate properties. In mathematics everything is structure. Mathematical captures the mathematical properties of the ideal circle as an abstract structure.

Removing essence from primitive objects in mathematics serves a valuable purpose. It forces all structure to be explicit. One avoids implicit assumptions about objects by way of assumed properties of those objects. For example it was long thought that logic required that parallel lines never meet. Eventually mathematicians realized that this was an assumption that is true in some geometries and not true in others. In particular it is not true on the surface of a sphere which is the geometry we inhabit.

Mathematics avoids making implicit assumptions by limiting itself to one primitive entity, the empty set, with no structure of its own. It is far more difficult to construct a geometry from the empty set than it is from the axioms of Euclid. But when mathematicians do it in the contemporary way they fully characterize the structures they are building. This helps them to see other ways in which a different geometry might be constructed. It also helps them to understand how seemingly disparate fields of mathematics may be structurally similar and able to borrow results from each other.

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 exists as its own immediate experience. Our perception is causally connected to this structure. But the perception of for example color is for more a construction of our sensory and nervous system than it is an effect from light of a particular frequency.