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A philosophy of mathematical truth

The mathematics described in this chapter is standard. The approach that focuses on properties of computer programs is unconventional but not controversial. In contrast our philosophy of mathematical truth is radical.

The real numbers have no physical existence. They are a human creation and thus a product of biological and cultural creation. Denying the objective existence of completed infinite totalities including the reals leads to a very different notion of mathematical truth.

Mathematics is about the structure of immediate experience or bessense and the potentially infinite progression of sequences of such experiences. Mathematics involves the creation of truth which has an objective meaning. This is truth about what a computer does if it is allowed to run forever perhaps following an ever expanding number of paths. The ordering of events associated with such a process is the creative aspect of mathematics. Mathematical statements that cannot be interpreted as questions about events all of which will occur in a potentially infinite deterministic universe are neither true nor false in any absolute sense. Of course, they may be useful properties that are either true or false relative to a particular formal system.

The essence of physical objects is immediate experience. This widens the implications of mathematics as the study of all possible structures. It implies that biological evolution is an evolution of consciousness and the structure of that evolution can be understood mathematically. Number is the mediator between the reality of here and now and our deeper existence as part of the unbounded creative process of evolving consciousness. Mathematics gives us some sense of what is possible and establishes some of the conditions necessary to realize those possibilities.

The subtlety and richness of human consciousness has evolved mainly to deal with other brains. If we survive as a species, the future not just of our species but of the entire evolutionary process will fall into our hands. If we do survive, evolution will have passed the most remarkable turning point of its existence. Evolution will become conscious of what it is creating and will take conscious control of creation itself. Mathematics is crucial to understanding the conditions for unbounded creativity as we assume this extraordinary power and responsibility.


Completed second draft of this book

PDF version of this book
next up previous contents
Next: Digital physics Up: Creative mathematics Previous: Is the cardinality of   Contents


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