Completed second draft of this book

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Structure and essence

As science has become more mathematical and abstract it has created an opening to reconnect with values and meaning. For the ultimate content of mathematics is the empty set or nothing at all. Mathematics describes only structure or how complex entities are constructed out of simpler ones. For example the number one is defined as the set containing the empty set. The number two is the set containing zero (the empty set) and one. All mathematical objects are defined in this way using the relationship of set membership. The empty set is the only primitive object not constructed as a set of simpler objects.

This high level of abstraction forces all assumptions about structure to be explicit. There are no inherent properties. There are only properties explicitly constructed with the relationship of set membership. Making all assumptions explicit avoids attributing logical necessity to implicit assumptions such as the parallel postulate in Euclidean Geometry.¹But reducing everything to structure makes it clear that something profoundly important is missing from our mathematically based scientific understanding. In fact everything that has intrinsic value is missing.

For these abstractions are explicitly free of meaning and value. This contrast with older metaphysics such as the one based on earth, air, fire and water. These each had an inherent nature and through that nature gave meaning and value to the objects that were constructed from them.

Completed second draft of this book

PDF version of this book