The title is an ironic gesture to a disturbingly cheerful (some, like me, might say saccharin) tune by Bacharach and David, but my intention is to talk about what is less happily categorized as circular reasoning. This is one of those fallacies that has been recognized for so long that the medievals gave it a Latin name: petitio principii. It is also one of those painful failures of basic reasoning that goes beyond the narrow confines of formal logic, or introductory critical thinking classes. This is one of those monsters of bad thinking that empower authoritarian minded individuals and their enablers to unshamefacedly spout about “alternative facts” and other infantile drivel. You see, the problem with a circle, as well as with a mind that reasons in one, is that the circle is closed; inquiry, on the other hand, is (by necessity) open and ongoing.

I’ve talked before (several times, in fact) about what Altemeyer describes as the “compartmentalization” that occurs in authoritarian belief and ideology. One can scarcely dignify this latter as “thinking,” regardless of the degree of sophisticated cleverness employed in maintaining those compartments as air tight against all facts and logic. Authoritarian thinkers, following Hamlet’s example, keep their minds, bounded in a nutshell and count themselves kings of infinite space, were it not that they have bad dreams. (Of course, Hamlet was being ironic, and mocking his interlocutors, something the Mango Mussolini’s enthusiasts entirely fail to grasp.) The thing is, these people choose to be bounded by a nutshell, all the while imagining themselves in princely command of infinite space. Meanwhile, their bad dreams (which are the trailings of reality, dogging them despite their dogmatism) are the sources of their willing embrace of Trumpian neo-fascism. Because the nutshell – the “nut house” – in which they have bound their minds is a tightly enclosed circle that permits no entry from reality.

Circular reasoning basically occurs when the conclusion one is arguing for is already contained in the premises. The analogy with compartmentalization is easily drawn: Certain conclusions are held, and justified, dogmatically, so that a belief cannot, and will not ever, be challenged by logic, principles, evidence, or facts. That means all pretenses of justification must come from within the compartment. This in turn means that the belief itself must, at some point, become a premise in its own defense. Sometimes that defense is as brief as “X because X.” Sometimes, it is a bit more elaborate. But regardless of elaboration, the purpose is to maintain a closed system against any incursion of genuine inquiry, which is inevitably developmental, creative, and accretive.

Some people have criticized formal logic for being, in one sense or another, inevitably circular in its reasoning: nothing can appear in the conclusion that did not already appear somewhere in the premises. As a simple example, we have as a premise, “If A then B” (A → B) and as a second premise we have “A”. From this, we can conclude “B.” Schematically, this is:

A → B
A            
B

All we seem to have here is just what we started with.

Another example – one that I’ve used before, but which has gained a certain urgency given SCOTUS nominee Neil Gorsuch’s less than clear standing with regards to privacy – is the syllogistic argument against the right to privacy. This is a little more complicated than the first example, but I believe it is worth following all the way through. I will present the central clauses of the argument within quotation marks, and their schematic substitutions directly below. As typically presented, the argument looks like This:

“There is no” “mention in the Constitution” of a “right to privacy”
E                                      M                                                     P
Therefore
“There is no” “right that exists” which is a “right to privacy”
E                                   R                                                 P
But this is not a formally valid argument; there is a missing premise! (The above is what is technically known as an “enthymeme.”) If we are acquainted with the formal structures of the syllogism, we can reconstruct that missing premise from the information given:

“All”  “Rights that exist” are “mentioned in the Constitution”
A                        R                                                  M

The complete syllogism is now:

“There is no” “mention in the Constitution” of a “right to privacy”
E                                        M                                                   P
“All”  “Rights that exist” are “mentioned in the Constitution”
A                             R                                                   M
Therefore
“There is no” “right that exists” which is a “right to privacy”
E                                      R                                              P

This is schematically represented as:

EMP
ARM   
ERP

Now, indeed, all of the terms (the “E” and “A” are not terms per se; rather they are quantifiers) that are found in the conclusion are also found in the premises. But look at that second premise, the one that was initially hidden, the “ARM” claim that “all rights that exist are mentioned in the Constitution.” Had we not filled in the formal gaps in the argument, we might never have noticed it. But having now noticed it, we easily see that, while the argument is “formally” “correct,” its conclusion is manifestly false, since that second premise is explicitly denied by the 9^th Amendment:

The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.

What this illustrates is that formal logic is not “circular;” rather its purpose is to illuminate what our premises are so that those premises can be held up for genuinely logical (in the broad sense of “theory of inquiry”) critique. Everything that is in the conclusion is in the premises, but the ways things are ordered and arranged have been changed so as to highlight how they are related.

This is fundamentally different from circular reasoning. In a circular argument, such relatedness will often enough be obfuscated – and, often enough, deliberately so – by the form which the presentation of claims as premises takes. Few arguments will take the fideist position of “X because X” (although various religious absolutists will go that direction) so circularity of reasoning will tend to be buried in long chains of premises, or in premises that are asserted as obvious, yet which are not only not obvious, but are consequences of the conclusion being argued for, and hence presuppose that conclusion. Authoritarian minded individuals, with their walled-off ideological positions, seldom if ever face the challenges posed by additional facts or hidden premises to their claims, so their positions frequently take on such circularity. (For example, the compartmentalization of belief around the frequent denial as to the existence of a right to privacy is maintained by shutting out the second premise of their argument and disregarding the enthymemic character of their argument.)

In the case of genuine inquiry, however, even when there is a sense in which the conclusion is presupposed as a premise (certain types of scientific experiment can appear this way), because inquiry is a process, the conclusion of that inquiry (which is typically only a moment of relative pause in a larger process) has informed that premise, and altered or deepened its meanings and logical connections. This leads to what Nelson Goodman many years ago said was not a vicious circle, but a “virtuous spiral.” The processual nature of inquiry leads to growth in knowledge and understanding that is entirely different from, and other than, the stasis of compartmentalized ideology. Absent such process, no matter how many times one goes around in a circle, one never actually goes anywhere.