When To Run For The Train

I mean to return to the subject brought up Monday, about the properties of things that don’t exist, since as BunnyHugger noted I cheated in talking briefly about what properties they have or don’t have. But I wanted to bring up a nice syllogism whose analysis I’d alluded to a couple weeks back, and which it turns out I’d remembered wrong, in details but not in substance.

     “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;
     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.
         ∴ This party of tourists need not run.”

His conclusion: there’s no conclusion to be drawn. That is, they might not need to run, and they might need to run. The lovely explanation (past one in diagram that appears on page 69, at least if I’m understanding the HTML version correctly) is this:

[ Here is another 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.

He will reply “Why, it’s perfectly correct, of course! And if your precious Logic-book tells you it isn’t, don’t believe it! You don’t mean to tell me those tourists need to run? If I were one of them, and knew the Premises to be true, I should be quite clear that I needn’t run — and I should walk!

And you will reply “But suppose there was a mad bull behind you?”

And then your innocent friend will say “Hum! Ha! I must think that over a bit!”

You may then explain to him, as a convenient test of the soundness of a Syllogism, that, if circumstances can be invented which, without interfering with the truth of the Premisses, would make the Conclusion false, the Syllogism must be unsound. ]

There is much I admire in the above: for one, how what can be an example confusing to logic students is explained with vividness and clarity and humor that makes its point perfectly clear; for another, enough use of italics to keep the Linotypist earning his pay; for another, the spelling “premisses” which inexplicably delights me; and of course the putting of a mad bull into a logic puzzle. I haven’t had the occasion to teach logic in a decade, but if I do get the chance again I intend to plunder Carroll for style and cases, since the books are chock full of puzzles that could just as easily be done in pure symbols (Carroll even puts it that way: the premises are “No M’ and X’; All Y are M; therefore, All Y are X’,” where ‘ means false), but with much less educational weight.

Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.

5 thoughts on “When To Run For The Train”

  1. Most of the time philosophy departments have managed to stake a territorial claim on that sort of logic. And, I’d say, rightly so; we don’t have as many service classes that we can teach as the math folks do. Plus, you know, Aristotle was one of ours.


    1. Well, yes, Aristotle was one of yours, although he’s often credited for quite a few mathematical accomplishments by people who’ve got him mixed up with Archimedes.

      I should perhaps confess (not to BunnyHugger, who knows already) that I wasted my chance to actually learn something a little outside my majors as an undergraduate by taking a logic course which satisfied the liberal arts requirement of taking philosophy classes without actually taking me away from what I was already doing in mathematics. The symbols were a little bit different but getting the hang of a different set of symbols isn’t much.


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