Cleaning Up One’s ProseNovember 19, 2006
Philip J. Davis
Nonsense: A Handbook of Logical Fallacies, Revised Edition. By Robert J. Gula, Axios Press, Mount Jackson, Virginia, 2002, $10.00.
"Shut up," he explained.
--Ring Lardner, The Young Immigrants
Reader: Are you stressed out by submersion in the intricacies of monadic second-order logic? Are you somewhat confused by the proof that GCH is provable in ZFL? Does the ontological status of the hyper-hyper-inaccessible cardinals give you heartburn? If so, let me recommend the late Robert Gula's Handbook for instant relief---even, I might say, for comic relief. With the exception of a few Venn diagrams at the end of the book, the logic treated here is not of the Whitehead and Russell or the Tarski sort; it is rather the logic or the illogic of everyday rhetoric that appears in oral communications and that bombards us from all directions in the media.
If you say, for example, "Ambassador Taylor flunked his college swimming test and therefore his views on foreign policy are at best dubious," you are indulging in what Gula and the old classic rhetors term an ad hominem argument, and in a logical irrelevancy to boot. If you assert that "No one has yet gotten ptomaine from eating in Flax's Coffee Shop, so go in and enjoy," you are resorting to an argumentum ad quietam---an argument from silence (often used by historians and just as often derided by other historians). If you suggest evasion---"Let's wait for a while and see what happens"---you have pulled out the "procrastinator's argument." An ad claiming that "A recent survey shows that more doctors prescribe Brand Z" indulges in "vague statistics." These examples give an idea of the kinds of statements that Gula calls logical fallacies.
Gula, who taught at Groton School and wrote educational materials, has catalogued more than one hundred fifty logical fallacies, which he has divided into 14 categories. His categories range from the "emotional"---appeals to guilt, fear, hope, flattery, status, etc.---all the way to the "semantic," i.e., the stuff of Math Logic 101 that focuses on the tricky use of such words as "and" and "or" plus incorrect syllogisms. Larded with quotes from a variety of sources, the book offers many a laugh.
One of my favorite fallacies---or simply infelicities of prose---is what Gula calls "syntactic ambiguity" or, as the great orator Cicero might have termed it, "amphiboly." One such infelicity takes the form of a pile-up of modifiers in which you can't figure out what is modifying what. I remember this one from a course in logic: "A pretty little girls' camp." Placed out of context, what, exactly, does this mean? A rather small camp for girls? A pretty camp for little girls?
How would Gula have classified the famous one-liner of Ring Lardner that I used as an epigraph for this article? And I wonder what he would have made of this two-liner:
He: "What's for supper, dear?"
She: "You should lose some weight, you
Or of Bill Clinton's asking what the meaning of is "is" to explain certain of his actions.
Are these evasions? Glitches? Illogical non-sequiturs? Nonsense? Was Clinton creating a new and uncatalogued type of logical fallacy or simply raising a deep existential question? Regardless of what we call them, they are certainly instances of language that sparkles and bristles. Moreover, there are implications in the lines that most readers will grasp, silently "connecting the dots" and restoring the logic.
Granted that in some strict sense all of these are indeed fallacies and that we ought, as Gula suggests, to clean up our statements. I'm right with Gula when I think of my hatred for jargon, double-speak, inflated language, in-group terminology, particularly when spouted by a customer service person (or electronic robot) in response to a question I have raised. Poor soul: I think that he/she/it has no linguistic resource other than an answer that to me is pure gobbledygook.
In putting together a book that provides rules for proper argumentation, Gula comes on as a prose puritan. A good teacher must have a few molecules of the pedant. Yet, if it were possible to avoid all hundred fifty types of logical fallacy, we should hardly be able to communicate at all. We would be deprived of the use of the hundreds of figures of speech, many of which overlap the logical fallacies---generalization, irony, hyperbole, understatement, metaphor, sarcasm, parody, the creation of straw men and scapegoats. I, personally, would feel bereft, and my writing, though precise, would have all the charm of the Providence telephone book.
It's clear, then, that there are acceptable logical fallacies as well as unacceptable ones; many among the hundred fifty have their use and their misuse. Let me now consult my mathematical soul and see how it reacts to Gula's list.
Fallacious logic in the mathematical sense (and in Gula's sense) includes turning a proposition around: If A implies B and B is true, then A must be true. Sometimes, but not always. If A is an equilateral triangle, then it is an isosceles triangle and two of its angles are equal. The converse---If two angles of a triangle are equal, the triangle must be equilateral---is not true.
But then consider the heuristic principles that George Pólya described and emphasized as roads to discovery in his book How to Solve It. One instance is: If A implies B and if B is true, then A becomes more credible.
Example: If it rains, the grass will be wet. The grass was wet. Therefore it is credible that it rained. The mathematician/philosopher Charles Sanders Peirce dubbed reasoning of this kind "abduction." Deduction goes forward to a conclusion, while abduction goes backward from a conclusion. (The latter can be linked up with Bayesian subjective probability.)
Metaphors: Mathematical models are often described as metaphoric. An instance: The Navier–Stokes equations describe in symbols what takes place dynamically with real-world fluids.
Jargon: Mea culpa. I certainly use in-group terminology when I say "in algebra" something that I might have grave difficulty in finding a way to say "in plain English."
Regarding inversion: The German mathematician Carl G.J. Jacobi (1804–1851) said, "Man muss immer umkehren." (One must always turn things around.) Of course, Jacobi was thinking of his great discovery that if you invert the elliptic integrals, you get doubly periodic functions.
Generalization: Jacobi also said (I forget in what context), "Man muss immer generalisieren." And generalization and abstraction are so endemic, so ingrained in the mathematical work habits, that some critics have warned against pointless, sterile generalizations.
Testimonials: We are inclined to support an argument if some prominent individual is for it. Call this "proof by authority," and consider this lovely story: In a letter to the 19th-century scientist Alexander von Humboldt, Jacobi wrote that
"If Gauss says he has proved something, it seems very probable to me; if Cauchy says so, it is about as likely as not; if Dirichlet says so, it is certain."
False dichotomy, or the "black and white fallacy": either this or that, and nothing in between. Whole reservoirs of ink have been expended in arguments as to whether mathematical statements are true or false.
Gula called his compilation a handbook, and so it is. It can serve as a handbook for debaters, political speech writers, Madison Avenue types, for all those who want to learn how to answer questions by evasion, obfuscation, or by a spate of non-sequiturs. Perhaps I have it backward; maybe communicators of these types need no instruction. They are already past-masters of logical fallacies, and what we have to do is listen to their nonsense, identify the fallacy, realize what's going on, and then laugh. It's lucky that most of us know how to filter out nonsense.
My Merriam-Webster says that one meaning of the word "fallacy" is "an often plausible argument using false or invalid inference." Plausible? Yes, in the sense that none of us is immune from the blandishments of illogic, and we may occasionally be taken in by such arguments. The past decade has given us many instances in which fallacious rhetoric has created very serious problems and done great damage.
Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island, and can be reached at email@example.com.