What do you mean by "actual q= uantification"?

Quantity and quality (universal-particular, affirmative-negative) as well a= s import.

<Right, except I'm not sure what you mean with those {..}.

You cannot insert another term in there for the equality to hold.>

In case broda has arguments attached.

<Which one is the traditional system?>

All + with the assumption that all classes mentioned as subject are n= on-null (and maybe a few less certain things as well). Using {ro brod= a} and {ro da poi} as the usual quantifiers of course already guarantees th= e assumption -- in true sentences anyhow.

<If you mean (A-,E-,I+,O+),>

I never would, since it is unlojbanic in its first two members and lacks su= balternation.

<

>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 lo= gic.

On the contrary, he specifically defines restricted universal

quantification and unrestricted universal quantification, and

then gives the following "principle of equivalence":

(A= x: Sx) Px =3D||=3D Ax (Sx -> Px).

(where 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 =3D||=3D= Ex (Sx & Px)

and also the principle of obversion:

=AC (Ax: Sx) P= x =3D||=3D (Ex: Sx) ~Px

which works only if the restricted universal is A-.

>Once the block attached to the quantifier is correctly filled in, the w= hole

>can then be correctly moved into the formula in the usual way. Bu= t the

>"restricted quantifier" (as the regular use of "thing" suggests) is jus= t a

>passing phase of translation, not a part of the logic.>

Well, I didn't read the whole book, just a few sections that talked about r= estricted quantification. I never saw any evidence that it was develo= ped as a separate system. In fact all the cases I saw were parts of t= ranslation exercises, like the one you sent me to originally: "(AxFx)Gx" as= a more or less Englishy sentence that could then be converted into "Ax(Fx = =3D> Gx)", but not used in proofs or derivations. Obversion is jus= t a device for making "not every" a bit more readable, as I read him. = But I will look at some more (and of course it works for an all positive s= et as well -- under the standard condition -- no empty subjects).

Of course, the restricted quantifier is -, since it just is the ultimate fo= rm in a minorly gussied up way. Part of the gussying is, alas, to hid= e the real subject of the of the final quantifier, namely the universal cla= ss.

<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...>

Every universal quantifier (in a non-empty universe) entails every instance= of its matrix, every matrix with a free term entails its particular = closure on that term:

AxFx therefore Fa therefore ExFx. That is about as thorough a working= out as I can think of.

--part1_73.1c499a40.29c12d14_boundary--