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This project is defined in "finite math". Though we talk about "infinity" and "the infinite" and "the continuum", all our structures -- or most of them -- are defined in discrete increments defined by boundary values in an interval.
We can build this structure up from the continuum, because we approach the continuum as a limit, and form an approximation to "the real number line" as "close as we wish" -- under the control of "acceptable error tolerance".
But these increments are always digital.
And these digital objects can be combined to build very complex structure that remain stable, because they are all defined in the same terms, and constructed in the same way.
So we make the claim that all human conceptual structure is defined within the single interval defined in the loop as bounded by "the infinite" at the top of the cascade and "the infinitesimal" at the bottom.
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In this framework, the continuum is defined as a range of "pure uncertainty" within a bounded digital increment. It is approached as an ideal. We are exploring the idea that the continuum is somehow "orthogonal to" the incremental digital level above it in the decomposition cascade.
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Inside this framework, we expect to build "all symbolic structure" -- by which we mean
- All symbols -- letters, numbers, alphabets -- all "terminal characters", which are each unique and have some constructive role in assembling complex composite structures.
- All words
- All meaning, defined under context-specific top-down dimensional stipulation
- Definitions of all mathematical and logical operations constructed from these elements
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