Re: SUO: Re: Re: Foundations for Ontology
Seth,
This is pure and simple mathematics. It is indeed profound,
and it is also true.
JS> By repeated contraction, expansion, and analogy, any theory
> or collection of beliefs can be converted into any other.
> Multiple contractions would reduce a theory to the empty or
> universal theory at the top of the lattice that contains
> only the tautologies that are true of everything. Multiple
> expansions would lead to the inconsistent or absurd theory
> at the bottom of the lattice, which contains all axioms and
> is true of nothing.
SR>Wow! ... that's fairly profound :) .... is it really true ??
However, you have to realize that the lattice is infinite.
Each individual step of contraction or expansion is easy
to do *provided that* you know what step to take. But for
any theory with N axioms there are N possible contraction
steps (i.e., any axiom can be deleted) and infinitely many
possible expansion steps (i.e., infinitely many possible
axioms could be added). That is a lot of options to consider.
Just look at the example of how Niels Bohr transformed
Newton's theory about planetary motion to his own theory
of the hydrogen atom. Each step is *easy* after you have
seen it done. But Bohr won the Nobel prize for discovering
those steps *before* anyone had shown them to him.
Bottom line: If you are lost, it is easy to take the right
steps to get from where you are to where you want to be.
The hard part is knowing what steps to take.
John Sowa