okeefe.r.a.@edxa@sri-unix.UUCP (10/14/83)
From: RICHARD HPS (on ERCC DEC-10) <okeefe.r.a.@edxa>
The resolution of the paradox lies in realising that
"cheap apartments are expensive"
is not contradictory. "cheap" refers to the cost of
maintaining (rent, bus fares, repairs) the apartment
and "expensive" refers to the cost of procuring it.
The fully stated theorem is
\/x apartment(x) & low(upkeep(x)) =>
difficult_to_procure(x)
\/x difficult_to_procure(x) =>
high(cost_of_procuring(x))
hence \/x apartment(x) & low(upkeep(x)) =>
high(cost_of_procuring(x))
where "low" and "high" can be as fuzzy as you please.
A reasoning system should not conclude that cheap
flats don't exist, but rather that the axioms it has
been given are inconsistent with the assumption that
they do. Sooner or later you are going to tell it
"Jones has a cheap flat", and then it will spot the
flawed axioms.
[I can see your point that one might pay a high price
to procure an apartment with a low rental. There is
an alternate interpretation which I had in mind, however.
The paradox could have been stated in terms of any
bargain, specifically one in which upkeep is not a
factor. One could conclude, for instance, that a cheap
meal is expensive. My own resolution is that the term
"rare" (or "rare and highly sought") must be split into
subconcepts corresponding to the cause of rarity. When
discussing economics, one must always reason separately
about economic rarities such as rare bargains. The second
assertion in the syllogism then becomes "rare and highly
sought objects other than rare bargains are (Zadeh might
add 'usually') expensive", or "rare and highly sought
objects are either expensive or are bargains".
-- Ken Laws ]