Diagonalisation (?), behaviour, and meaning ...

Does something like this work:

Suppose we were to give a behavioural account to of how to say things in a language - say a list of noises, and what they meant.  The list could include not only 'primitive' expressions but also any complexes constructed from them.  If we could describe the records in this list, then the list would be enumerable.

Notice that while one side (say the left side) of this list comprises specific physical circumstances (behaviours, or noises), the other side (the right side) is a list of contents, and so can only be identified intentionally.


If we can describe records in the list, then we can describe the contents of each left side of each element.  (This means, among other things, that the descriptions of the physical behaviours must also appear as the contents of the intentional side somewhere else in the list, and so have their own describable physical counterparts.)


Everything that can be said could be somewhere in this list, linked up to a way of saying it.

Although the list is formally interminable, however, any actual statement would have to be finite.  This is a barrier to the actual list containing the behaviour which counted as a description of itself, since this would require something like infinite repetition of nested representations of the list.

Also, although the list would contain statements about whether some statement was a member of the list, the number of these would be 'smaller' than the number of items in the list - otherwise the only thing the list could contain would be statements about what was in the list.

Since a description of the list would containt a complete statement of what was in the list, this description could not be in the list since there have to be some statements which do not have membership statements in the list.