Heh. Reminds me of one of Lewis Carroll's sylogisms:<p><pre><code> Premise A: "No one, who means to go by the train and cannot get a conveyance, and has not enough time to walk to the station, can do without running";
Premise B: "This party of tourists mean to go by the train and cannot get a conveyance, but they have plenty of time to walk to the station".
Does the conclusion "This party of tourists need not run" hold?
</code></pre>
It actually doesn't; here's a non-formulaic reason:<p>[Here is <i>another</i> opportunity, gentle Reader, for playing a trick on your innocent friend. Put the proposed Syllogism before him, and ask him what he thinks of the Conclusion.<p>He will reply “Why, it’s perfectly correct, of course! And if your precious Logic-book tells you it <i>isn’t</i>, don’t believe it! You don’t mean to tell me those tourists <i>need</i> to run? If <i>I</i> were one of them, and knew the <i>Premisses</i> to be true, I should be <i>quite</i> clear that I <i>needn’t</i> run—and I should walk!”<p>And <i>you</i> will reply “But suppose there was a mad bull behind you?”<p>And then your innocent friend will say “Hum! Ha! I must think that over a bit!”<p>You may then explain to him, as a convenient <i>test</i> of the soundness of a Syllogism, that, if circumstances can be invented which, without interfering with the truth of the <i>Premisses</i>, would make the <i>Conclusion</i> false, the Syllogism <i>must</i> be unsound.]