Branching quantifiers.

In the "nonfirstorderizability" thread, the following comments
were made about "branching quantifiers", a topic that resurrects
every so often here. [apologies for losing the attributions]

______________________

> It is claimed that branching quantifier constructions occur
> in natural language.
______________________

> writers about branching quantifiers use some odd examples,
> e.g. Hintikka's

> Some relative of each villager and some relative of each townsman
> hate each other.
______________________

> My first approximation to formalizing that would be:
> AxAyEzEu((Vx -> Rzx) & (Ty -> Ruy) & (Hzu & Huz))

> Well, it's not at all what Hintikka intended.
______________________

> How about Axy[ Vx&Ty -> Euv[ Rxu & Ryv & Huv & Hvu ] ]

> Or is 1 hating villager supposed to be a relative
> of every villager, while the 1 townsman who hates
> her is a relative of every townsman? The sheer
> ambiguity of the natural langauge is problematic
> to begin with. Presumably they would've said
> "some relative of all villagers" as opposed to
> "some relative of each villager", if they meant that.
______________________

> suppose they intend for the relative of the villager to be
> chosen independently of the townsman and vice-versa.
> That seems like a somewhat eccentric interpretation of
> the English phrase.

> The thing is, I don't know whether such usage details are
> especially relevant to whatever point they mean to make.
> Is it that they want to show it's "natural" for people to
> want to express things that can be expressed in terms of
> branching quantifiers?
________________________


If the task is to find a natural example of branching quantifiers,
wouldn't the following sort of thing do?

"Every citizen has a representative, all of whom talk to one another."

A very everyday and democratic example.

If the main clause describes too simple a property, that may be
circumlocuted some other way, a more technical alternative might be

"Every citizen has a representative, pairs of whom formally
match up for voting procedures."

Anyway; isn't that the natural kind of context?

---------------------------------------------------------------------
Bill Taylor W.Taylor@xxxxxxxxxxxxxxxxxxxxx
---------------------------------------------------------------------
In a democracy, your vote counts.
In feudalism - your count votes.
---------------------------------------------------------------------

.

Relevant Pages

  • Re: Nonfirstorderizability
    ... |Those who write about branching quantifiers ... |use some odd examples, such as Hintikka's ... | of each townsman hate each other. ... I suppose they intend for the relative of the villager to be ...
    (sci.logic)
  • Re: Nonfirstorderizability
    ... >> of each townsman hate each other. ... Or is 1 hating villager supposed to be a relative ... Prev by Date: ...
    (sci.logic)