Horse and Horses

--- Thanks to J for engaging in metaphysical views about how uncriminal to be a dualist is.

In Homer, when he refers to Achilles's two horses, Homer uses a 'dual number'. This is very odd. It's like the Greeks could say:

. That horse is running.
. Those horses are running.

---- BUT

if it's

TWO horses running, they used a still different form (dual plural): 'Two horses arer running', say.

This seems a bit otiose.

Apparently, if you used the REGULAR plural (for n>2) when referring to or predicating something about the TWO horses, you were misusing the system.

I'm not sure if it would come as FALSE that 'Two horses are running', with 'running' in plural, rather than dual.

For one, modern Greek lost the dual-number altogether.

There are relics of duality in things like "Both my eyes are blue" (as David Bowie cannot say").

"My eyes are blue" seems to be informative enough. But surely Grice who can speak of Martians, and in fact has written about Martians having 'our ordinary set of eyes, plus an extra pair, as it were', may want to say that "My eyes are blue" only IMPLICATES (rather than say) that I have two eyes.

Joshi et al held a symposium in Pennsylvania ("Elements of dicourse understanding", Cambridge University Press) and they noted how intuitive our criteria of grammaticality are. At least for males. They discussed the example:

"My ball itches".

Apparently, there is an unwanted 'implicature' (of the conversational kind) there that the utterer only has one ball, but I disgress. Barbara Partee said she couldn't opine on the topic, since she lacked the proper 'linguistic' intuition.

----

In general, while monism, pluralism, dualism, etc, seem all wrong -- they can be fun.

In general, logicians avoid 'number' altogether. If we speak about Nellie, the Loch Ness monster, we may speak about a class (the class of monsters inhabititng Loch Ness), a set, or a "Menge".

(Ex)Mx

-- there is a monster

--- there is at least one monster

---- there are monsters

------------- all refer to the same logical form.

Warnock (in "Metaphysics in Logic", repr. in Flew, Conceptual Analysis -- Warnock belonged to Grice's generation or play group) argued that if we don't feel to comfy about:

------- "Some cities in England are called "London""

just because ONE city is thus called -- that's an ordinary-language problem, not a logical one. It may well be argued that Grice's whole point about the implicature is to justify an apparent 'divergence' between the logical form and the ordinary language counterpart as merely 'implicatural'.

----

The point about collective or mass nouns is still a different one. But it does seem to relate to our ideas of plurality. It would be VERY OTIOSE if Americans and British (according to the wiki on 'collective nouns'), since they differ in the grammar for 'collective nouns' -- 'The police are late', 'The police is late' -- also differ in the logical form of what they say. Or not.