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."