[EMAIL PROTECTED] wrote: > > 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.

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