Agreed. But there may be a price associated with being rigorous.
> So, I see a continuum from natural language to a kind
> of "strict" natural language (where every word is previously defined,
> for example) to formal logic to mathematics.
I'm not sure that it is continuous.
> What you gain is consistency and completeness; what you give up is
> semantic distance from what you're really talking about.
If you are giving something desirable (or necessary) up, then you may have
incompleteness. In this way, formal systems are consistant, but not
complete.
Of course, competence in mathematics has two advantages:
(1) It has many very important uses in our world
(2) IF there are applications that are not expressible by
mathematics, we would have to have a very good understanding
of our mathematics to know this.
Jeff Prideaux