66 How to Win Every Argument
(It seems innocent enough, but the logic is fishier than the handy-
men. If we had used 'tax-dodgers' instead of fishermen, we would
have ended up saying 'no handymen are tax-dodgers', which
everyone knows is untrue. The fault lies with the two negative
premises.)The source of the fallacy is fairly clear. The three-liner relates two
things to each other by means of the relationship which each has
with a third. When both premises are negative, all we are told is
that two things lie wholly or partly outside the class of a third
thing. They could do this however they were related to each
other, and so no conclusion about that relationship can be
drawn:
Some brewers are not idiots, and some idiots are not rich, so some
brewers are not rich.
(Did you ever hear of a poor one? With two negative statements, the
idiots who are not rich do not need to be the same ones who don't
include the brewers among their number. If this sounds confusing,
remember two things: two negative premises do not prove anything,
and all brewers are rich.)The fallacy tends to occur because some people genuinely
believe that if a group is excluded from something, and that
group in turn is excluded from something else, then the first
group is also excluded from it. If John cannot get into the
Masons, and the Masons cannot get into the country club, it
seems plausible to assume that John doesn't stand a chance for
the country club. Of course, since the Masons cannot get in,
John might stand a better chance because he isn't one of them.
No pudding-eaters are thin, and some smokers are not pudding-eaters,
so some smokers are thin.