> On Sep 13, 11:47 pm, Youness Ayaita <[EMAIL PROTECTED]> wrote:
>> I see two perfectly equivalent ways to define a property. This is
>> somehow analogous to the mathematical definition of a function f: Of
>> course, in order to practically decide which image f(x) is assigned to
>> a preimage x, we usually must know a formula first. But the function f
>> is not changed if I do not consider the formula, but the whole set
>> {(x,f(x))} instead, where x runs over all preimages.
>> Concerning properties, we normally have some procedure to define which
>> imaginable thing has that property. But I can change my perspective
>> and think of the property as being the set of imaginable things having
>> the property. This is how David Lewis defines properties (e.g. in his
>> book "On the Plurality of Worlds").
>> If you insist on the difference between the two definitions, you may
>> call your property "property1" and Lewis's property "property2".- Hide 
>> quoted text -
> Surely you are just talking about the well-known distinction between
> intensional and extensional definitions:
> http://en.wikipedia.org/wiki/Intensional_definition
> "An intensional definition gives the meaning of a term by giving all
> the properties required of something that falls under that definition;
> the necessary and sufficient conditions for belonging to the set being
> defined."
> http://en.wikipedia.org/wiki/Extensional_definition
> "An extensional definition of a concept or term formulates its meaning
> by specifying its extension, that is, every object that falls under
> the definition of the concept or term in question."
But both have difficulties for Youness.  You can't use extensional 
definitions for infinite sets.  On the other hand, using properties 
leads to Russell's paradox unless limited in some way.

Brent Meeker

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