Re: Specifying Sets

On Thu, 13 Nov 2008 19:55:03 +0000, John Jones <jonescardiff@xxxxxxx>
said:
Chris Menzel wrote:
...
Indeed, in ordinary discourse, "set" is entirely ambiguous. This is
hardly news, and it is not of the least significance for mathematics.
"1) The method of enumeration lists the contents or objects of the set
{The President of the United States, Donald Rumsfeld, 2005}
2) The method of description states what condition must be satisified
for something to be a member of the set. {x: x is blond}: the set of all
x such that x is blond, or the set of all blonds."

If you reread that, it is plain that the intention was to read 'list' in
much the same way as we read a shopping list, ie. unordered. I got that
quote from a logical encyclopaedia.

You may well have -- though I'd be curious what "logical encyclopedia"
this is from. Be that as it may, all you've done is illustrate that
point that "set" and "list" don't have precise meanings in ordinary
language -- you do recognize that the above is just an ordinary language
use of "list", right, and not a mathematical definition of the term?

The term list used in the quote is different from the list you claim
is used by mathematics.

Indeed, it is just an ordinary language use.

What is the mathematical term for the list as it is used in the quote?

The list? There is no list referred to in the quote. "list" is being
used as a verb there. The example given is of a set, whose elements we
can list as follows: The President of the United States, Donald
Rumsfeld, 2005.

Just use that.

There is no that to use.

And that, moreover, it is not even talking about lists, just about
two different informal ways of picking out a set?

The list in the quote doesn't pick out a set,

Again, there is no list in the quote. A set is referred to in the
quote, one whose elements can be listed as above; or any permutation
thereof.

informally or formally, or anything that could be considered being
called a set.

You don't think there is a set containing Bush, Rumsfeld, and the number
2005?

The trap is to think that where the word 'set' is used, we have a new
property, or something substantive, but we don't. A list and 'all'
didn't pick out a 'set' in the quoted material, despite the fact that
the author thought that they did.

There you go again, just makin' crazy, incomprehensible stuff up instead
of cracking a book.

It's the sort of thing one might see in the introductory chapter of
an elementary set theory text where the author provides an intuitive
introduction to the subject before actually getting into the
mathematics proper.

The greatest battles are fought before the first elementary textbook can
make an appearance.

Ah, well, then, no wonder you refuse actually to learn any mathematics:
you think our present day mathematics is fundamentally confused and the
task falls to you to rethink all 2000+ years from the ground up. Well,
good luck to you, sir! You've made an impressive start!

.

Relevant Pages

  • Re: Wistar conference math quote mining. QMP needs to cover this
    ... It is not unusual to see creationist quote ... Is there anyone familiar with the math of evolutionary biology who ... reluctant to embrace mathematics, except for population genetics, and ... mutation and selection" in which it is unclear whether the "random" ...
    (talk.origins)
  • Re: Hamiltons Rule In The Mirror
    ... >>far as the academical studies were concerned, ... I attempted mathematics, and even went during the summer of ... > Nice quote. ... Regarding this last item, Gould writes: ...
    (sci.bio.evolution)
  • Re: all the incompleteness proofs are worthless untill...
    ... The development of mathematics in the direction of greater exactness ... quote which you have just provided provides some support for your view ... it is obvious that godel considered the rejected version of PM he used was ... The methods of reasoning which were accepted by the mathematical ...
    (sci.logic)
  • Re: Bug/Gross InEfficiency in HeathFields fgetline program
    ... calling a tail a leg does not make a tail ... areas of mathematics. ... <end quote> ... But OF COURSE in c.l.c the ONLY opinion that counts is the opinion ...
    (comp.lang.c)
  • JSH: Groupthink
    ... and I think you can see what groupthink is in a dramatic area. ... math journals on process of formal peer review--putting your judgement ... Now then, you're just a gaggle of people, but the United States is the ... why groupthink is no match for mathematics. ...
    (sci.math)