Alan Wachtel writes:

If I were teaching a class in inductive logic, the negative test of the flying saucer detector [in Leaving Small’s Hotel] would be a perfect illustration of Hempel’s raven paradox. 
   In inductive logic, we can confirm the generalization “All ravens are black” by examining particular ravens and determining that they are black.  The German logician Carl Hempel pointed out that this statement is logically equivalent to its contrapositive, “All non-black objects are non-ravens,” and concluded that we could equally well show that all ravens are black by looking around the room for non-black objects and determining that they are non-ravens. 
   I can't claim any familiarity with the lengthy philosophical debate that Hempel provoked—I know only a few popular accounts—but I’ve never found this result paradoxical, just a little unexpected.  We confirm that “All ravens are black,” with a certain degree of confidence, by examining a great enough number of more or less randomly sampled ravens.  If we knew just how many ravens there are in the world, we could make a precise statistical statement about the degree of confidence inspired by our sample, but even so we might have some subjective sense of how many ravens we need to look at to feel we’ve had a reasonable chance of seeing one that is non-black, if there is one. 
   In the same way, we can confirm that “All non-black objects are non-ravens” by examining enough more or less randomly distributed non-black objects to feel we’ve had a reasonable chance of seeing one that is a raven, if there is one.  Since there are so many more non-black objects in the world than there are in the room, and since the room is not even a very good sample of the world—rarely including, unless your name is Poe, a raven of any color—our confidence after inspecting the room should not be very high.  (And since there are so many more non-black objects in the world than there are ravens, looking at ravens is more efficient than looking at non-black objects.)  On the other hand, I could quickly establish that “All telephones are black” is false by looking at its equivalent “All non-black objects are non-telephones.” 
   Now here’s the new part (new to me, anyway).  Consider the statement “All unicorns are white”—equivalently, “All non-white objects are non-unicorns.”  Again, looking around the room wouldn’t give me much confidence in this generalization, but I could, in principle, exhaustively enumerate all the non-white objects in the world and determine that they are non-unicorns, proving that all unicorns are white.  And this would, in fact, be a true statement, but only in the empty sense that any statement about the null set is true.  So looking at non-black objects may help to show that all ravens are black, but it does not help to show that there are any black ravens.  The negative test of Peter’s saucer detector helps to show that flying saucers disturb the local magnetic field, but not that there are any flying saucers in the first place.  At an intuitive level we know this, and that's why it’s funny. 
   John Allen Paulos, a Temple University mathematician who is famous for grumpy books like Innumeracy bemoaning popular understanding of mathematical concepts, earlier wrote a book called Mathematics and Humor that attempts to explain, in the tradition of Freud and Bergson, but this time using catastrophe theory, why jokes are funny.  I’m afraid he wasn’t very successful.  The most you can hope for, I think, which is what I’ve tried to do here with the saucer detector joke, and what the saucer detector does with saucers, is to show that if jokes (or flying saucers) exist, they are associated with certain attributes.  But the detector doesn’t show that there are any flying saucers, and analyzing a joke won’t make you laugh at it.

A Topical Guide to the Complete Peter Leroy (so far) is a work of fiction. The characters, incidents, dialogues, settings, and businesses portrayed in it are products of the author’s imagination and are not to be construed as real. Any resemblance to actual events or persons, living or dead, is entirely coincidental. 

All rights reserved. No part of this guide may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the author. 

Portions of A Topical Guide to the Complete Peter Leroy (so far) were first published by Voyager, Inc., as part of The Complete Peter Leroy (so far).

The illustration at the top of the page is an adaptation of an illustration by Stewart Rouse that first appeared on the cover of the August 1931 issue of Modern Mechanics and Inventions. The boy at the controls of the aerocycle doesn’t particularly resemble Peter Leroy—except, perhaps, for the smile.