[FOM] Solution to Buckner?

[Lucas Wiman]

 >The most important constraint embedded in natural
 >language is (I believe) that there are no infinite sets, i.e. objects to
 >which infinitely many objects bear the "membership relation".  I.e. it
 >embeds an Axiom of Finity, if you like.

What about statements like ``all English sentences contain at least one 
word"?  On the surface, this seems to involve reference to an infinite 
totality--all English sentences.  You can, of course, interpret this to 
mean that there given an arbitrary sentence in English, it is the case 
that it contains at least one word.  But what about ``all English 
sentences can be generated by a single computational procedure"?  This 
seems to involve infinite totalities in a less trivial way, as checking 
an arbitrary sentence individually fundamentally changes the meaning of 
the statement.  Certainly an arbitrary sentence can be generated by a 
computational procedure (the sentence is finite), but saying that a 
computational procedure generates all English sentences seems different.

Anyway, the fact that the surface structure of these sentences involves 
infinite totalities seems to argue against any such thesis:  you have to 
recast them to get a finitistic meaning out of them.  But if they have 
no finitistic meaning to begin with (until translated), then how could a 
finitistic being understand them in the first place?

Best regards,
Lucas Wiman