Re: [lojban] non-ka properties

["John E. Clifford" <kali9putra@yahoo.com>]

I'm not following; the question was, I thought, whether the number of tokens was uncountable.  So all that is relevant is the number of types (at most aleph-null) and the number of situations in which a token of that type might be issued.  That there are more properties than expressions for them was never at issue, nor particularly relevant to the discussion, insofar as I understand it.  But I see I did make my favorite error and spoke here of predicates (linguistic expressions) rather than the properties meant.  And I suppose the talk of description later adds to the confusion.  The point is merely that every possible situation that is counted under one property will also be counted under other properties as well, but that duplication does not bring the count down from in denumerable to denumerable. So, yes, the size of the set of potential tokens is indenumerable.

Sent from my iPad

On Jun 19, 2011, at 16:11, Jorge Llambías <jjllambias@gmail.com> wrote:

> On Sun, Jun 19, 2011 at 4:28 PM, John E Clifford <kali9putra@yahoo.com> wrote:
>> Are you sure?  I get confused in infinity (as any right-thinking person should)
>> but I have aleph-null types and aleph-null situations giving aleph-null squared
>> potential tokens.  aHAH! There must be more than aleph-null situations because
>> there are more than aleph-null predicates, each of which can occur alone in at
>> least one situation.  And we can't reliably reduce these variant properties down
>> to others, even if every situation under one description is also another
>> situation under another, Never mind.
> 
> I don't think the number of situations is at all limited by the number
> of predications. Situations are the territory, predications are the
> map. By the very nature of things, most situations won't be fully
> describable by a predication.
> 
> It's not that complicated really. For example, for every real number
> x, there is the property of being that number. There, already, you
> have a cardinality of properties larger than aleph-null, most of which
> won't have a ka-expression to express them. The number of expressions
> is strictly limited by the discrete nature of language (or a language
> like Lojban at any rate).
> 
> mu'o mi'e xorxes
> 
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