Specifying Sets

There are two methods of specifying the contents of a set.

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.

LIMITATIONS OF THE METHODS
For 1), the method of enumeration, we make no distinction between a set and a list. Rather than write {The President of the United States, Donald Rumsfeld, 2005}, we ought to write 'The President of the United States, Donald Rumsfeld, 2005'.

For 2), the method of description, we make no distinction between a set and 'all'. Rather than write {x: x is blond}, we ought to write x: x is blond, or, all blonds.

DISCUSSION
There's no reason why the objects in a set can't be looked at as lists or as 'all', but the methods of enumeration and description seem to pass by the central concern of establishing what it is to be an object in a set. We put the cart before the horse when we try to specify what it is to be an object in a set before we have established what it is to be a set.
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Relevant Pages

  • Re: Specifying Sets
    ... x such that x is blond, or the set of all blonds. ... Donald Rumsfeld, 2005}, we ought to write 'The President of the United ... No, you can put it in language or shorthand, whichever. ... There's no reason why the objects in a set can't be looked at as lists ...
    (sci.logic)
  • Re: Specifying Sets
    ... {The President of the United States, Donald Rumsfeld, 2005} ... x such that x is blond, or the set of all blonds. ... Donald Rumsfeld, 2005}, we ought to write 'The President of the United ... There's no reason why the objects in a set can't be looked at as lists ...
    (sci.logic)
  • Re: Specifying Sets
    ... {The President of the United States, Donald Rumsfeld, 2005} ... x such that x is blond, or the set of all blonds. ... Donald Rumsfeld, 2005}, we ought to write 'The President of the United ... There's no reason why the objects in a set can't be looked at as lists ...
    (sci.logic)
  • Re: Specifying Sets
    ... {x: x is blond}: the set of all x such that x is blond, or the set of all blonds." ... I got that quote from a logical encyclopaedia. ... The President of the United States, ... The method of enumeration lists the contents or objects of the set ...
    (sci.logic)