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Posted by dorayme on 12/31/43 11:44
In article <541jg3-mpa.ln1@ophelia.g5n.co.uk>,
Toby Inkster <usenet200604@tobyinkster.co.uk> wrote:
> Davémon wrote:
>
> > Lists with no items? That doesn't make any sense to me at all!
>
> The mathematical equivalent for the UL element would be what is called a
> "set".
>
> A set is a group of numbers/shapes/letters/vectors/whatever. Some examples
> are the set of all positive integers, the set of letters that directly
> follow vowels in the alphabet, and the set of all people called Kevin.
>
> The set is an abstract concept, and can be dealt with mathematically, in
> many cases without worrying about how many (if any) elements it contains.
Indeed, a main point here being that a class or set can have no
members. One can have a building that no one has yet occupied or
fled from, or a club that has yet to get a member or no longer
has members. It is thought by some that classes exist
independently of their members. And so they can exist without
members at all.
In a book called Principia Mathematica, written by Bertrand
Russell, a philosopher, with Alfred North Whitehead, a
mathematician, there was a serious attempt to reduce mathematics
to logic. Principal tool of the attempted reduction was the
logical notion of class. This notion is also used in mathematics,
maths employing, naturally enough, much logic.
There are some possibly deep questions peculiar to lists - but I
can't think of any at the moment.
But questions about number are quite prevalent in and out of
philosophy and mathematics:
In Farewell My Lovely, a Raymond Chandler thriller, Marlow, over
the phone, says to Moose Malloy, something like, "Have you heard
of Baxter Wilson Grayle?" and Moose replies "How many people is
that?"
--
dorayme
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