[This is the start of Section Two, Reason and the First Person. An index with links to all parts of the work as they are posted can be found [url=https://forum.evangelicaluniversalist.com/t/sword-to-the-heart-reason-and-the-first-person/1081/1]here.]
[This series constitutes Chapter 14, “The Golden Presumption”.]
In geometry, as every high-school student is taught, all theorems and other geometric rules can be deduced from axioms. The axioms you use, determine the type of geometry you have. In Euclidian geometry (the kind normally taught in high-school), there are three axiomatic assumptions which cannot be proven, and upon which everything else depends. Points have no dimensions; lines consist of an infinite number of points in one dimension; and planes consist of an infinite number of lines in two dimensions. Solid-body or 3-D geometry extends the classically Euclidian axiom set to include a volumetric space with an infinite number of planes in three dimensions.
No one can prove any of this, but not to assume these axioms can lead to nonsense. [Footnote: Curiously, the chief axiom–that points must be presumed to exist yet also to have precisely zero [u]physical characteristics–might itself be considered nonsense in light of a naturalistic philosophy.] Nonsense does not necessarily follow by changing these axioms; that is how non-Euclidian geometries were developed. But the more basic and fundamentally necessary the assumption, the more likely that any alternate assumption will lead to nonsense.
The most basic and fundamentally necessary assumption should therefore be one that would be nonsense to deny. Such a key assumption (or presumption) will be the bedrock from which trustworthy deductions may be drawn about the rest of reality–it will be a reliable foundation, because to deny it leads precisely nowhere.