
Re: Foundations of mathematics... the order of bootstrapping the foundations
Posted:
Aug 21, 2013 2:36 AM


Lax Clarke wrote: > Please correct me if I'm wrong please: > > This is the order of bootstrapping the foundations of mathematics: > > 1) Naive logic (like the ones the Greeks played with).
The Greeks had no theory of nary relations, did they? Not even n=2 iirc.
Was it Boole or De Morgan or one of those fellows who pointed out that the valid inference
A horse is animal  Therefore the head of a horse is the head of an animal
cannot be handled by Greek logic?
> 2) Use 1) to talk about Naive Set theory (like Halmos' book). > 3) Use 2) above to define Mathematical Logic / FirstOrder Logic > 4) Use 3) above to define axiomatic set theory.
One might begin by asking if mathematics has a foundation, or if it needs one.
 Sorrow in all lands, and grievous omens. Great anger in the dragon of the hills, And silent now the earth's green oracles That will not speak again of innocence. David Sutton  Geomancies

