(Originally appeared in Lognet 97/2)
[We] all know how the basic syllogism goes. Given that
All Ruritanians are rich.
John is a Ruritanian.
None of us will hesitate to come to the conclusion:
John is rich.
Slightly more difficult: Given that
No fruitpicker is a sailor.
All Ruritanians are fruitpickers.
One can logically deduce that:
No Ruritanian is a sailor.
Now the poser. Given the premises:
All members of the cabinet are thieves.
No composer is a member of the cabinet.
What logical conclusion can we draw from this [that concerns composers and thieves]?
Those of you [who are] skilled in the arts of formal logic, please refrain from drawing truth tables and such and see what your intuition tells you. We want a conclusion that’s as easy to come by as John is rich was.
While you’re thinking, let me tell you what this is about. I’ve just read a book called Inevitable Illusions: How Mistakes of Reason Rule Our Minds, by Massimo Piattelli Palmarini. The above example is from pages 37 and 38.
His thesis is that, just as there are optical illusions, where our perceptual system tells us one thing (like that one line is longer than another) even when we know it isn’t true (because we’ve just measured them), there are also “cognitive illusions”, where our minds fail to make a simple logical leap or make a leap that is completely incorrect.
Most of his examples show that human beings have really crummy intuitions about probability, but there were a few, like the one above, that were pure logic.
If you’re like most people (and like me) you probably concluded that there was nothing to be concluded about composers and thieves. This is incorrect. Keep trying.
One of Loglan’s claims is that it “makes logic speakable”. JCB wrote somewhere (was it L1?) that by writing if...then... as anoi (meaning or not), the fact that the truth tables of if...then... and ...or not... are the same becomes obvious to a native speaker. This is supposed to make logical deductions about them easier to make.
My question is, can Loglan help us solve the above problem? Can writing it in Loglan make the logic clear enough to draw the right conclusion? Or does a brana logli still have to take that freshman logic course before [l] can deduce that
Some thieves are not composers?
My impression is that Loglan doesn’t help much. It might help to cast the problem into a rather specialized Loglan that’s only used in freshman logic courses in Loglandia, but the rather specialized English used in freshman logic courses would do just as well. I must confess, however, that I took that course so long ago that I couldn’t remember how to solve this problem.
Does anyone care to agree or disagree?
Hue Djeimz Djeninz
Hue Djeimz Salsman:
Thanks for your question. You say:
“... My impression is that Loglan doesn’t help [syllogistic reasoning] much. ... Does anyone care to agree or disagree?”
I agree. Thad Polk did a study of such things in his 1992 Carnegie Mellon Computer Science thesis (CMUCS92178); here’s the abstract:
Hue Qad Pok:
Previous theories of human reasoning have all been based on what might be called the transduction paradigm: people encode the problem statement into an internal representation, then reason using processes devoted specifically to that purpose, and then decode the result. The nature of the intermediate reasoning process has been a major source of debate among cognitive psychologists. Some researchers have proposed that this process can best be characterized as the application of formal rules of inference while others have argued that it corresponds to a search for alternative mental models of the problem statement. I believe that the transduction paradigm itself is in error, at least for the standard tasks that have been used in studying human deductive reasoning. My thesis is that most untrained subjects lack sophisticated reasoningspecific mechanisms for solving these tasks, and that, in their absence, they attempt to make progress by repeatedly applying linguistic processes to encode and reencode the problem statement. I refer to this type of behavior as verbal reasoning. The ideas of verbal reasoning arose out of VR, a computational model of human behavior on categorical syllogisms. It simulates human behavior on every variant of the syllogism task using purely linguistic processes.
VR models all of the standard phenomena that have been discovered about syllogistic reasoning and makes a number of novel predictions that have been empirically confirmed. Furthermore, using a set of individual difference parameters, it has been tailored to fit the behavior of individual subjects with an accuracy that rivals the testretest reliability of the subjects themselves. Since VR only uses linguistic processes, it provides compelling evidence that human syllogistic reasoning can best be characterized as verbal reasoning. Finally, to show that verbal reasoning generalizes to other tasks, I analyzed JohnsonLaird and Byrne’s recent attempt to provide accounts of behavior on all the standard deductive reasoning tasks. In most cases, their explanations depend on assumptions about how the problem statement is comprehended and thus constitute verbal reasoning accounts. In the few cases in which their explanations depend on reasoningspecific mechanisms, verbal reasoning provides a more parsimonious account.
Hue Djeimz Salsmyn:
I like Loglan because of its features as an interlingua; how it organizes semantic constructs in a way that English (and most natural language grammars) do not; it seems to be better organized and more orthogonal, so it would seem to be easier to write programs that translate into Loglan and then out to another language than directly from one natural language to another.
This is an encouraging, and yet surprising, result. I thank James Salsman for bringing it to our attention. And, of course, Thad Polk for investigating the phenomenon in the first place.
James Jennings’ remark about our possibly needing to take “freshman logic” in Loglandia, too (before we can solve such puzzles as the Members, Thieves, and Composers problem), reminds me of an after-class conversation I had with Mary Shaw, my teacher of freshman logic at the University of Minnesota in or about the year 1939. She had just shown us Venn Diagrams—from an inspection of which, by the way, the solution to the Members, Thieves, and Composers problem is actually quite simple—and it was obvious that they conveyed much more “logical information”, per unit chalk, than normally linear symbolic logic did! So I caught up with her at the door and said something impudent like “Why don’t we devise a speakable notation that is as good as Venn Diagrams for presenting syllogistic information?” “It would have to be two-dimensional,” said she; “and speech isn’t.” “Hah!” I said. And there the matter rested...and probably still rests.
Actually, there are plenty of two-dimensional notations that contain as much—or even more—information (per unit chalk) than Venn Diagrams do; the notation of the calculus does. But, of course, like all mathematical notations, calculus expressions are intended to be written, and so to be examined up and down and backwards and forwards at the examiner’s leisure. So it isn’t just the linearity of speech, but much more importantly its temporarity, that makes speech a poor instrument for conveying syllogistic information. Polk’s result about the predominance of VR in human thinking is even more suggestive when viewed from this perspective.
By the way, JJ’s first impression was correct. Before the conclusion Some thieves are not composers can be drawn, an existential assumption, Some members of the cabinet exist, must be made. Without this additional premise—which is often justified, of course—no relation between thieves and composers can be drawn. For consider what happens when we replace members of the cabinet in this example with Martians! —JCB
Copyright © 1997 by The Loglan Institute. All rights reserved.