Robert Altemeyer’s The Authoritarians (abbreviated as “TA” hereafter – freely downloadable from the preceding link) is a truly important work not because of the originality of the work (the original work was all published in the peer-reviewed literature over the course of several decades), but because of the accessibility it brings to such an important constellation of ideas. I had an opportunity to revisit TA recently, in the form of an audio book as I was driving some distance. So I thought I would write a few entries touching on some of those themes from Altemeyer’s book that come especially close to my own focal areas here. This time around, I want to look at issues that fall under Altemeyer’s heading (from Chapter Three of TA) “illogical thinking.” In a later entry, I’ll talk about “compartmentalization,” which can only be separated from the other topic by some significant compartmentalization of its own. But for now I want to talk about failures of formal reasoning beyond just and only those that Altemeyer discusses (especially as one very dramatic example did not come out until after Altemeyer published his book.)

On page 76 of TA, Altemeyer gives the example of a syllogism that authoritarian types of persons have a great deal of trouble with:

All fish live in the sea.

Sharks live in the sea..

Therefore, sharks are fish.

(To be technically correct, there should be an “All” before “sharks” on both the second and third line. But that quantifier is presupposed in the presentation of the syllogism.) Even the most casual acquaintance with formal logical reasoning will enable a person to recognize that this is not a valid line of reasoning. The problem here is not that the conclusion is false, but that the conclusion does not follow from the premises. Quite aside from the numerous counter-examples that can be offered (whales live in the sea, but whales are not fish; coral lives in the sea, but coral are not fish, etc.), there are trivially simple tests one can apply to easily demonstrate that the reasoning in the above is not valid. (The formal name for the fallacy in the above syllogism is an “undistributed middle.”) Part of the problem in Altemeyer’s example is that people generally already know that sharks are fish. But this fact does not follow from the information provided, hence the argument is invalid.

One way of testing such an argument is to introduce formal symbols, and then substitute various contents for the non-logical parts (in this case, the ideas about “fish,” “sharks,” “lives in the sea”) to see if the argument still works. A valid argument will still hold regardless of what terms are substituted into the abstract, non-logical letters (within certain technical limits that we need not go into here.) Thus, allowing “A” to stand for “All” (which is a logical part of the argument, and thus cannot be altered willy-nilly), “F” to stand for “fish”, “S” to stand for “sharks,” and “L” to stand for “lives in the sea,” the formal syllogism is (the underline stands for “therefore”):

A F L

A S L   

A S F

Now, substitute “whale” for “shark” in “S” (we get to do this because “whales” and “sharks” are not formal, logical structures, but things that exist in the world empirically), and it is clearly an invalid argument.

By the bye, if one reverses the position of the invalid conclusion and the second premise, so that one has:

A F L

A S F    

A S L

Then one has a formally valid argument. (All fish live in the sea; All sharks are fish; Therefore, All sharks live in the sea.) Notice that the “F” term now stands diagonally across the two premises (that is, in the lines above the underline that marks the “therefore.”) This is the “middle” term which was unidistributed in the previous (which is to say, invalid) versionbut which is now distributed across the premises, and is therefore valid.

A very real example of this sort of egregious failure of basic reasoning can be found in Johah Goldberg’s recent Liberal Fascism (2008). In this book, Goldberg offers the galactically fallacious argument that,

Some Nazis were vegetarians

Some Liberals are vegetarians

Therefore, Liberals are Nazis!

We can formalize this as,

I N V

I L V     

A(?) L N (The quantifier on Goldberg’s conclusion is a bit ambiguous.)

The “I” in the above stands for “Some” (I’ll say more on this in a moment.) For the moment, look at the form of the argument. Notice that, as with Altemeyer’s example, the middle term is not distributed. The only term which could be a middle term, the “V” which appears in both premises, does not stand diagonally across from itself in those premises. In this example, “N,” “L,” and “V” stand for “Nazis,” “Liberals,” and “Vegetarians” respectively. But qua formalization, these are just arbitrary letters, and could as easily have been “F,” “S,” and “L,” in line with Altemeyer’s example. However, Goldberg’s actual argument only seems to be as bad as Altemeyer’s case; in point of demonstrable fact, Goldberg’s arguement is far, far worse. This is because Goldberg really did talk about “Some,” rather than “All,” in the premises of his argument, and this means that the possibility of drawing any manner of conclusion is altogether absent. Which is to say, even if Goldberg had distributed the middle of his argument, (thus avoiding that fallacy) it would still be the case that no valid argument of any kind would have been available from his premises. Recall here that what Altemeyer presented was actually fixable by swapping the conclusion with the second premise. Nothing of the kind can save Goldberg’s argument.

This is not a casual error, which “anyone” might make. Rather, Goldberg drew a galactically invalid conclusion – which he evidently supposed was valid – a conclusion which any first-year in a 100-level Critical Thinking class would easily see through. Why didn’t Goldberg see through it? Why didn’t his editors? I’ll speculate on that in a later post. But the fact is that neither Goldberg, nor his editors nor, apparently, his defenders, managed to notice this grotesquely outlandish piece of illogical twaddle which any college freshman would reasonably be expected to recognize and dismiss as the nonsense it obviously is.

This is all old news; many persons have long since commented on this piece of sophomoric absurdity from Goldberg. Let me add that I have no definitive proof that Goldberg would score high on Altemeyer’s spectrum of authoritarian thought and belief. I strongly suspect that Goldberg would score very high on that scale if he were objectively evaluated, based upon his many other published statements. But my primary reason for using this piece of very public illogic is mainly to emphasize that Altemeyer’s categories are not mere abstractions. People really do fail to reason in the ways that Altemeyer highlighted, and these failures tend to come in systematic clusters, clusters that typically express themselves in authoritarian styles of belief.

I promised to say a few words about the letters used to represent the quantifiers, the “all” and “some,” etc. “A” for “all” seems obvious (actually, it isn’t), but why “I” for “some”? Well, the reason has to do with the millenia of tradition underlying the discussion of formal logic, going back to the Greek and Latin authors who established the subject within the Western Philosophical tradition. That tradition settled “A” = “all,” “I” = “some,” “E” = “none” or “not any”, and “O” = “some not.” These letters are coming from languages that are not English, but they come with the weight of thousands of years of tradition. Regardless of whether they seem to make sense now, these are the established symbols for quantifiers in formal syllogisms.