Re: pc answers

[jorge@phyast.pitt.edu]

la djer cusku di'e

> >> 2. E(z1)(w1) t(z1,w1).    For some z1, For each w1, touches(z1, w1).
> >> 5. (w1)E(z1) t(z1,w1).
> jorge said:
> >2. says that there is at least one man, such that he touches each
> >   of the three dogs.
> >5. says that each of the three dogs is touched by at least one man.
> >In 2., it has to be the same man that does the touching, while in 5.
> >it can be a different one for each dog.
> djer adds:
> In (2.) it does not have to be the same man [singular] that does the
> touching.

Yes it does. At least one man has to touch all three dogs. It is
irrelvant what the other two men do. In (5.) it is not necessary
that any single one of the men touch all three dogs.

> (2) states, "for some z1..." where  z1 is clearly defined by
> pc to be the set {x,y,z} of three men.

That's right.

> We have the existential
> quantifier E on z1.  It is read as "for at least one..and less than
> all".

No, the last part is not claimed. It could very well be true
for all of them. The claim is that it is true for at least one.
If it also happens to be true for all, then the claim is still
true for at least one.

Jorge