Re: Undefinedness

JOG wrote:
> Word up CDT. How the devil are you all? Well, I return with a question
> that as ever highlights my complete lack of formal mathematical
> training, and in light of knowing no logicians in my daily life (funny
> that), I was hoping that one of you kind folks might be able to
> advise:
>
> Say I had a set of 3 encoded propositions:
> R := { {(Name, Tom), (Age, 42)}, {(Name, Dick), (Age, 16)}, {(Name,
> Harry)} }
>
> (note that Harry's Age is missing, so instead of adding a null, i've
> intentionally just left the attribute out. Just ride with such oddness
> for now if you would.)
>
> What if I deigned to create a simple 'adults' subset of this set of
> propositions, by creating a predicate that only returned the elements,
> p, which contained an age attribute greater than 18. Could I state
> this as (where E signifies set membership):
>
> Adults := { p E R | EXISTSx ( x > 18 && (Age, x) E p ) }
>
> My question obviously hinges around Harry's missing age attribute. In
> this case would the EXISTSx (...) part of the set's intension simply
> return a FALSE, or will I end up in the quagmire of 3VL with an
> UNDEFINED? My instinct is that I am still in 2VL given there is no
> null floating about, but since the recent, excellent discussions of
> Jan's DEF operator, and having delved into beeson's logic of partial
> terms, I am not at all confident.
>
> Any comments are much appreciated, and regards to all, Jim.

I look at it and ask: Does the pair exist? And the answer of course is No. Received on Wed Nov 21 2007 - 17:50:39 CET