Abstract

What gives notational systems their power ? Are they merely convenient collections of arbitrary tokens and rules that just happen to have a useful application in the real world ? Or might there be a deeper connection between notational systems and reality ?

This talk explored this question, and answered in the affirmative. However, the position taken is not standard philosophical realism. We discussed the conventional definitions of "abstraction" and their inadequacies, and seeked a new definition. We sketched a theoretical framework -- a metaphysical system that attempts to account for the law-abiding nature of physical objects, the nature of laws, and , ultimately, the nature of abstractions.

The talk discussed the notion of an "abstraction space" such as the field of numbers, and how three such spaces historically have been explored and tokenized ("settled"). The talk concluded with a brief outline of a plan for improving humanity's abstraction space settlement process. This plan is essentially an agenda for the proposed new field of "notational engineering".