SUO: Practical Consistency Through Persistent Modeling
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SUO Working Group,
When it comes to worries about the consistency of a set of postulates,
let me reccommend to you the following strategy, which has the advantage
having been field-tested by many generations of people who actually prove
non-trivial theorems about difficult objects.
Examples! Examples! Examples!
That's how it was told to me, so please excuse the exclamations.
For example, when I say that there is a non-commutative group of six elements,
I can justify my claim by constructing a non-commutative group of six elements.
That example, say G, is a "model" of the following postulates:
1. G satisfies the axioms for a group.
2. G is not commutative.
3. G has six elements.
Now, any exercise in formal semantics or model theory is nothing but
a translation from one language to another, and this is no different.
At no point do my signs leave the medium, and so even these concrete
styles of construction are really just a matter of passing from more
abstract signs to interpretive signs that we view for some reason as
more concrete, but it can hardly be denied that a certain measure of
confidence in one's postulates is genuinely gained in the process.
Jon Awbrey
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