[FOM] Solution to Buckner?

[Dean Buckner]

Dean:
>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.

Lucas:
>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.

No it doesn't.  Even if English contained infinitely many words, which I don
't think it does, your sentence just means " Every English sentence contains
at least one word" which means the same as " No English sentence contains
less than one word"

Where's the "infinite totality"?

Lucas:
>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?

As I said, the surface structure involves no such thing.

As to your second point: in translating a Latin sentence to an English I aim
to replace the Latin one with an English one that has the same meaning.
That's what translation is.  So how can something that does not have a
"finitistic" meaning be translated to one that does have a "finitistic"
meaning?  If the meaning is not the same, it's not an accurate translation
in the first place.  If it is an accurate translation then both, or neither
of them, have a "finitistic" meaning.

Dean Buckner
London
ENGLAND

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