Subject: Re: [lojban] More about quantifiers

From: "Jorge Llambias" <[email-masked]>
Date: Wed, 13 Mar 2002 19:45:53

la pycyn cusku di'e

>If you check other pages, you will find that Helman is not dealing with
>restricted quantification as such but using the notation as a stage in the
>process of translating English into symbols in ordinatry first-order logic.

On the contrary, he specifically defines restricted universal
quantification and unrestricted universal quantification, and
then gives the following "principle of equivalence":

(Ax: Sx) Px =||= Ax (Sx -> Px).

(where <A> should be inverted). What's more, in the chapter
about existential quantification he also has the equivalence
between the restricted and unrestricted forms:

(Ex: Sx) Px =||= Ex (Sx & Px)

and also the principle of obversion:

¬ (Ax: Sx) Px =||= (Ex: Sx) ~Px

which works only if the restricted universal is A-.

>Once the block attached to the quantifier is correctly filled in, the whole
>can then be correctly moved into the formula in the usual way. But the
>"restricted quantifier" (as the regular use of "thing" suggests) is just a
>passing phase of translation, not a part of the logic.

I'm sorry, I don't understand the difference. I would put
the above formulas in Lojban as saying that {ro da poi broda cu brode}
is {roda zo'u ganai da broda gi da brode} and that {su'o da poi broda
cu brode} is {su'o da zo'u ge da broda gi da brode}.

>Alas, I fear that agreeing about As and Is will not yet help us to
>agree about {ro} and {su'o} even in ultimate forms ({ro} does always imply
>{su'o} and you can work it out, but that is unconvincing somehow to some).

Saying "you can work it out" is unconvincing. Maybe if you actually
did work it out it would be more convincing, but since in the end
it is just a matter of definitions...

mu'o mi'e xorxes

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