Re: Motions 5 and 6 under discussion --

[John Pryce <prycejd1@xxxxxxxxxxxxx>]

P1788 members

On 4 Aug 2009, at 11:44, Arnold Neumaier wrote:
> J. Wolff v. Gudenberg schrieb:
> >   a short note on motion 6 section 3 .5.2
> > last paragraph:
> >  "we treat [-oo.-oo]  and [oo,oo] as having no meaning (rather  
> > than being empty)"
> > This sentence introduces a 3rd kind of emptyness, emptyset and NaI  
> > are the first 2
>
> No. It is not a kind of empty set, but a semantically forbidden
> construct, since by definition, a lower bound is never +oo,
> and an upper bound never -oo.

Arnold has interpreted my intent correctly. This sentence occurs in  
section 3.5, which is about level 1, the mathematical concepts. My  
choice is to make [oo,oo] semantically meaningless (hence it has  
undefined value) in the same way as, say, 0/0 is semantically  
meaningless over the reals, or 99 is semantically meaningless over  
the set of octal representations of integers. This does NOT mean that  
some new datum is being defined -- that would be a level 2 notion.

John Pryce