The White Queen's "Confusing" Implicature: "Jam Every Other Day"

--- by JLS
--------- for the GC

--- I AM GLAD Kramer's wife coincides that I do not use natural English! I mean, recall this is an exercise for the Grice Club. Anyway, when I was researching into 'or' -- years after having already submitted my PhD and getting full grade for that --, I started to consider Jennings with some serious detail. If Horn's initial claim to fame was his "Natural History of Negation", and we don't have a celebrity doing "And", the credit for the second connective, 'or' must go to Jennings's "The genealogy of disjunction." As he notes, 'or' originally meant 'second'. Cfr. German 'oder' -- 'other' --. Surely 'second' is NOT an Anglo-Saxon word -- and the fact that such an important notion as the second ordinal ('first', 'second', 'third', ...) BE NOT Anglo-Saxon is telling ('zahl' means number in German, cognte with 'tell').

But why? Well. Jennings suggest that 'other' STILL means 'second', as in 'every other' ---. This etymological explanation goes over Alice's head when the White Queen makes fun of it:

Form the Alice books:

----- It's Carol Lombard in the film version -- and a pleasant song, too:

ALICE: But really you should have a lady's maid.

THE WHITE QUEEN. I'm sure I'll take you with pleasure! -- Twopence a week, and jam every other day.

ALICE (laughing). I don't want you to hire me -- and I don't care for jam.

THE WHITE QUEEN. It's very good jam, you know.

ALICE. Well, I don't want any today, at any rate.

THE WHITE QUEEN. You couldn't have it if you did want it. -- The rule is: jam tomorrow and jam yesterday, but never jam today.'

ALICE. It must come sometimes to "jam today.

THE WHITE QUEEN. No, it can't. It's jam every other day. To-day isn't any otherday, you know.

ALICE. I don't understand you. It's dreadfully confusing.

----- Etc.

The White Queen is trading of course on an ambiguity, too?

"any other" -- meaning, 'whatever'.

But note that she aequi-vocates, as Grice would say (Grice notes that aequivocality is used aequivocally).

For the Queen first says:

i. You will have jam EVERY other day.

And then she turns, in a slight sneaky way, to

ii. You will have jame ANY other day.

So Alice could have objected that while 'today' indeed is NOT, and never can be 'every other day', today can become 'any other day'? Or rather vice versa:

iii. Indeed, today is NOT 'any other day': it is TODAY. It is an important 'date', and while we do say, "Oh, today was just like any other day", or "today was just any other day" (well, ...)

iv. Yet, today can be 'every other day'.

------

Alice's point is the logic of the ontology

Suppose we date the jam


Sunday-Monday-Tuesday-Wednesday-Thursday-Friday-Saturday
JAM ---NO JAM -- JAM -- NO JAM -- JAM -- NO JAM -- JAM

There seems to be an aequivocation here, but surely the NEXT Sunday would be NO JAM.

What Alice is objecting. Suppose she starts working for the Queen on a Monday. No Jam. But surely Alice is right that if the rule is: "Jam every other day", she SHOULD have jam on Tuesday. But then the Queen may want to say that when the rule is read on Tuesday, the other days become the past Monday and the following Wednesday.

At this point Alice could object that, as a matter of fact, or fare, she was not given jam on Monday, and that the rule thus indicates that she should have it on Tuesday.

But I suppose the Queen would have the last word on this. I wonder how much jam you can buy with twopence. I'm glad it's not twopence ANY other day. Or something.