Date: Tue, 19 Sep 1995 11:32:52 +0200
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To: conlang@diku.dk
From: mmg@risc.iris.firenze.it (Maurizio M Gavioli)
Subject: CONLANG: The Click language and sets of sets
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Reply-To: mmg@risc.iris.firenze.it (Maurizio M Gavioli)
Status: OR

To my question about distinction between sets and sets of sets in Click,
doug@NETCOM.COM (Doug Merritt) replies:

>It is not needed. It is reasonable of you to point out that
>self-referential paradoxes appear to be allowed. It is not reasonable
>to say that (a) they cannot be allowed, nor (b) that having multiple
>kinds of sets (as in the mathematical Theory of Types) is the
>only way to avoid such paradoxes.

I have said neither a) or b); I have simply noticed that auto-refrential
paradoxes are possible.

You correctly point out that they are possible in natural languages. Whether
this is good or bad for Click is something that only its author can define.

My point is that, having defined the language based on set operations
(albeit informally), some sentences exist for which these operations cannot
be performed without contradiction (and please note that contradiction is
another thing than ambiguity!)

Then, some additional "rule" has to be introduced to deal with these
sentences: 1) they are not grammatical, 2) they are grammatical and mean
that the auto-referential barber always shaves himself, 3) never shaves
himself, 4) is always chosen among peoples affected by alopecia, 5) ...
whatever you like, but you have to deal with them.

Additionally, you have to define in some way which words are elementary sets
and which are sets of sets, even by a dictionary list (taking the place of
the native speaker competence).  Otherwise you would not know when and how
apply the above rules (whatever they will be).

Maurizio M. Gavioli
--------------------                          
  Maurizio M. Gavioli                       Associazione IRIS
mmg@risc.iris.firenze.it    via di Vincigliata 26, I-50135 Firenze - Italy
                             phone: +39 55 603 251 - fax.: +39 55 603 383