Youness Ayaita 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").
>
But I don't think you can define a property this way. For example,
suppose you want to define "red". Conceptually it is the common
property of all things that are red. But this set isn't given, and it
can only be constructed (even in imagination) if you already know what
"red" is. For a strictly finite set you could use ostensive definition
to get the set, but I suspect you don't want to limit your set size.

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In any case I don't think "imaginable" and "describable in some
alphabet" are equivalent. People construct perfectly grammatical noun
clauses that don't correspond to anything imaginable, e.g. "quadratic
chairs".
Brent Meeker
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