Handbook of the History of Logic: - Fordham University Faculty

The Development of Supposition Theory in the Later 12 th through 14 th Centuries 183
Every woman’s donkey is lame..
A donkey every woman’s is lame.
Some woman’s some horse sees every donkey
in which the last proposition is to be read something like: Regarding some woman,
some horse sees every donkey of hers. These forms may be confusing in English; to
increase comprehension I will always use the ‘of ’ form in the English transliterations.
Thus, although the following are not standard English, you should easily be
able to figure out what they mean, so long as you keep in mind that the left-to-right
ordering of the denoting phrases corresponds to their logical scope:
Of-every woman a donkey is lame
A donkey of-every woman is lame
Of some woman some horse sees every donkey
where the last proposition is ambiguous regarding whether it is the horse or the
donkeys that belong to the woman.
2.8.1 What the Genitive means
Some common nouns, such as ‘mother’, ‘owner’, . . . are inherently relational;
others such as ‘woman’, ‘chair’ are not.
Non-relational nouns: Typically the genitive construction used with a nonrelational
noun indicates some kind of possession (‘a horse of Fred’s’) or something
analogous to possession (‘Mary’s job’), or almost any other kind of relation that
can be doped out from context (‘Mary’s hill’ = the hill Mary has been assigned to
climb).
Relational nouns: Usually the genitive construction used with a relational noun
indicates the relation conventionally associated with the noun; ‘Mary’s mother’
usually means the female person who gave birth to Mary. Relational nouns also
have nonrelational uses, as in: ‘Four mothers showed up’. I assume that these nonrelational
uses are best construed as homonyms; ‘mother’ can be a non-relational
noun meaning e.g. “mother of someone”. These non-relational nouns then also
enter into the first kind of genitive construction, so that ‘Mary’s mother’ can mean
the mother (of someone) to whom Mary has been assigned as a case worker. 32
For simplicity I’ll concentrate on examples involving non-relational nouns.
When a genitive is used, the “possessed” term is parasitic, just like a participle
of a transitive verb. In ‘Cicero’s donkey is an animal’ the term ‘donkey’ doesnot
stand for donkeys in general; it is restricted to standing for donkeys owned by
Cicero. So the semantics has to take this into account. Intuitively, it is as if the
denoting phrase containing the possessor term binds a variable in the possessed
term. Like this:
(Cicero x)(a donkey-of-x y)(an animal z) y is z
32 Because of this, constructions with relational nouns are ambiguous. A popular illustration
of this was the sophism: “This dog is yours. This dog is a father. So this dog is your father.”