From: utzoo!decvax!harpo!npoiv!alice!rabbit!ark
Newsgroups: net.misc
Title: Re: Logic and the Quality of Food: Survey Results
Article-I.D.: rabbit.650
Posted: Sun Aug  1 12:29:29 1982
Received: Mon Aug  2 01:23:23 1982
References: watmath.3159

No the statements are not equivalent, in the sense that the formulae
do not capture all the information usually inferred from the English.
When I say "good food is not cheap," what I am really saying is:
"good food is usually not cheap."  Similarly, when I say "cheap food is
not good,"  I am really saying "cheap food is usually not good."  These
two statements are definitely NOT equivalent.  Consider a situation in
which all food is good, and a tiny bit of it is cheap too.  Then the
first statement is true but the second is not.

To convince yourself that the "usually" belongs there instead of "always,"
suppose someone told you that good food is not cheap and the next day
you found a restaurant that did indeed serve cheap good food.  Would
you think that that single counterexample demolished the claim?  Probably
not:  you would think: "remarkable -- here's a restaurant that serves
cheap good food.  Let's file that with the rare exceptions."