Re: [mizar] 'element'

[Josef Urban <josef.urban@gmail.com>]

On Fri, Aug 24, 2012 at 9:52 AM, Jesse Alama <jesse.alama@gmail.com> wrote:
> trybulec@math.uwb.edu.pl wrote:
>
>>> How about 'thing', 'object', or 'item'?
>>
>>
>> I see no strong arguments for changing notation. I do not see strong
>> arguments for 'element', either.
>
>
> Here's a linguistic reason.  In the context of chemistry, one can say,
> e.g., 'hydrogen is an element'.  But in the context of set theory,
> 'element' to me can only mean 'element of something'.  So 'element' as
> a new radix (non-dependent) type strikes me as an awkward name.

The reason why I do not object too much is that in NBG, sets indeed
are defined as classes that are elements of other classes. So I can
perfectly imagine that in NBG, the terminology would be element/set
instead of set/class (but then, shifting the traditional meaning of
"set" to "class" probably would not be acceptable to the creators of
NBG). Also, set-theorists seem to be happy with "urelement".

Josef