# Re: No(-)Justification Justifies The Everything Ensemble

```[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
```
Brent Meeker

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