U.S. Intellectual History Blog

What Is Linear Thinking? Logic, George Weigel, John Paul II, And Intellectual History

Today I come to you with an unusual USIH post. Rather than address a topic peculiar to U.S. intellectual history, this piece aims at larger issues: logic, discussing thought in history, and a case study from an widely acclaimed book on an international figure. But my thinking on these larger issues originates with what some would call a pet peeve: misgivings about the phrase “linear thinking.”

Since starting History and Education last year, one of the most consistently read posts there covers the subject of linear thinking. For every 100 visitors, or every 1.5 to 2 days, around 4 or 5 people read that post. I attribute those consistent viewings to a kind of at-large vagueness about the phrase’s meaning, and the subsequent desire for definition. I also noticed yesterday that a Wikipedia search for the phrase – as well as searches on “linear thought,” “non-linear thinking,” and “non-linear thought” – reveals nothing.

Thanks to Sitemeter, I know that the H&E post’s most common entry point is a Google search on the question “what is linear thinking.” But it’s not just Google that’s efficiently driving people to H&E: comments on the post (including my replies) display further attempts to delineate the boundaries of linear and non-linear thinking.

By way of summary, my first thoughts on the subject began with the idea that linear thinkers are simply logical – and that’s not such a bad thing. The corollary was that non-linear thinkers are not logical. There’s a bit more to the entry, but that was my gist. If I were to revise the original post I would expand on my introductory paragraph’s point that non-linear thinking is a synonym for thinking creatively, and perhaps a just another way of talking about the subject of “informal logic.” In many ways this USIH post is an expansion on that original H&E entry.

Here I want to dig deeper into the notions of linear and non-linear thinking. To help, I will eventually analyze a passage from George Weigel’s biography of John Paul II, titled Witness To Hope.[1] Because Weigel’s book is also a kind of intellectual history that received wide acclaim, his means and method should be of interest to intellectual historians. But before delving into Weigel I’d like to lay out some hopefully universal starting points about the study of logic.

To those who believe that logic is a subject admitting of innumerable types, with little common ground for discussion, then this post is not for you. Many members of the varieties-of-logic crowd believe that everyone operates under her or his own “logic.” Nonlinear and linear thinking, to them, are just more nominal categories in a morass that includes dialectic, the “logic of history,” symbolic logic, positivism, utilitarianism, and a multitude of other “isms” and philosophies.

For those believing that some universal rules apply within the subject of logic, common points of understanding exist. Traditionally, for instance, in basic texts like Irving M. Copi and Carl Cohen’s Introduction to Logic, two kinds of reasoning fall under the “formal logic” rubric: inductive and deductive. Both types utilize if-then statements and syllogisms (if in different ways), but differ with regard to cogency (or strength) and validity, for induction and deduction respectively. Induction works from the ground up (a posteriori) by observing phenomena and generalizing; deduction works from the top down (a priori) by applying universal principles to particular situations.

The category of “informal logic” includes fallacies, such as those illuminated by Plato in the Socratic dialogues. This especially important classification was covered exhaustively for historians by David Hackett Fischer in his 1970 book, Historians’ Fallacies.

There’s much more that could be said here about the contemporary scene in logic studies, but I’ll leave that for minds more competent than mine.

My point in elaborating on these means of reasoning, or subjects within logic, is to emphasize two things. First, logic is a viable field of study that concedes some inherent, universal organization in thought. Next, straight lines – or linearity – can be seen in all types of logical reasoning. Induction, for instance, can be seen as thinking that begins with the particulars, but proceeds in a kind of straight line that is visible in syllogisms. Even fallacies, although considered “informal logic,” can also be expressed “linearly” in faulty syllogisms. In many ways, then, being linear is often tantamount to simply attempting to be logical.

But what’s expressed by calling someone a “non-linear thinker?” This brings me to a passage I read recently in Weigel’s Witness To Hope. That passage, set in the context of Karol Wojtyla, Jr.’s development as an intellectual and a philosopher in the 1950s, defines linear thinking and addresses Wojtyla’s traits as a non-linear thinker. Here’s the paragraph (italics mine):

“Wojtyla-the-philosopher refined his distinctively phenomenological way of doing philosophy in [his] doctoral seminar. Many philosophers think in a linear way: they state a problem, examine a variety of possible solutions, and then, through a step-by-step process of logic, reach and state a conclusion. Wojtyla did not (and in fact does not) think linearly. His method was circular, but in the manner of walking down a spiral staircase, not going round-and-round a closed circle. He, too, would begin by identifying a problem: for example, what constitutes a just act? Then he would walk around the problem, examining it from different angles and perspectives. When he had gotten back to the starting point, he and his students would know a little more, so they would start walking around the problem again, reexamining it from this angle or that, but now at a deeper level of analysis and reflection. This continued through any number of perambulations, never forcing a conclusion before the question had been exhaustively examined from every possible point of view.[fn64] It was a power method of leading a seminar, a situation in which Wojtyla’s sharply honed capacity for analysis and making distinctions worked to great effect. Transferred to the printed page, however, it made for very difficult philosophical essays.” [2]

Lest we think this was just Weigel lionizing Wojtyla’s seminar method, the former forwarded the following in footnote #64: “Offered this once [by Weigel] as a description of his intellectual method, Pope John Paul II agreed that it was a reasonable depiction of the way his philosopher’s mind worked. [Author’s conversation with Pope John Paul II, December 11, 1996.]” (p. 899)

And make no mistake, here in a key passage of the book, Weigel’s acting as an intellectual historian. He’s attempting to explain someone’s thought processes to a reader.

But did Weigel do a good job of explaining the future pope’s manner of thinking? In terms of artistry, there’s no question. Weigel’s a superior writer. He set up Wojtyla’s dynamism, as well as the pope’s interest in hiking, in earlier passages. With that, the passage on Wojtyla’s “perambulations” is near perfect, at least in my estimation. It dovetails nicely Weigel’s caveated spiral-staircase analogy.

What of the notion of Wojtyla being a nonlinear thinker? Here I think Weigel did less than a perfect job as an intellectual historian. To me the phrases “linear way” and “think linearly” are unsatisfactory explanations of Wojtyla’s mind and method. But before I proceed, I want point out that my criticism is not meant as an overall indictment of Weigel’s book. I’m merely conducting a close reading, an intellectual historian’s reading, of one paragraph on one page in an 886-page book. The critique which I’m about to offer should be considered inconsequential in light of Weigel’s larger audience and goals.

With that in mind, I don’t see either of Weigel’s aforementioned phrases about linear thinking as helping toward his goal – to wit, showing that the future pope balanced traditional methods of thinking with those outside the box. Weigel’s definition of “the linear way” is reductionist in the context of the rest of the passage. How? The connotation is that linearity is insufficient, and that Wojtyla stands above or outside the rules of thinking.

I read Weigel’s passage as making Wojtyla appear to eschew traditional, formal logic and evade evaluations of fallacious thinking. Both are traits that’d normally be looked down upon in Catholic philosophical circles – especially traditional ones. I believe Weigel really wanted to demonstrate that Wojtyla was a hyper-linear thinker. Wojtyla took step two of Weigel’s definition of linear thinking to the max: the future pope examined “a variety of possible solutions” in an exceptional fashion. Wojtyla’s not a nonlinear thinker, he’s extraordinarily linear according to Weigel’s definition of the phrase.

I understand Weigel’s motivations to show Wojtyla’s creativity. Beyond admiring the workings of Wojtyla’s mind, the former wants to demonstrate how Wojtyla, as an old theater guy, steps outside of himself to look at problems from different angles. And the staircase analogy carries with it a certain step-by-step, logical connotation.

But the paragraph also gives the reader the feel that merely understanding a problem’s different appearances was Wojtyla’s goal. One might read this passage and believe that the future pope merely tried to empathize with everyone, and didn’t have a larger conception of the common good in mind (i.e. Wojtyla’s notion of the “law of the gift”). This clearly doesn’t describe Wojtyla accurately. The former pope was not afraid to draw conclusions and make judgments: to utilize the rules and maxims of formal logic. If he lacked those traits, he wouldn’t have become the universally acclaimed leader that he was.

One could also read Weigel’s passage and vaguely depart with the notion that Wojtyla was a kind of multiculturalist. While that may be true, that “kind” must be fleshed out. For instance, John Paul II will not be remembered for being a moral relativist, a position that is often attributed – rightly or wrongly – to multiculturalists. He most certainly applied traditional rules of logic to ethical questions.

Aside from this appearance of nitpicking by a sometime intellectual historian (me), I really like Weigel’s Witness To Hope. The book’s universal admiration is deserved. I’m no expert on John Paul II or the twentieth-century Catholic Church, but the book seems quite comprehensive. I’ve read about one quarter of it, and thus far it’s been a nice balance of biography and history. This seems to be what sells today, and Weigel does a fine job of engaging the two fields. I’ve learned more, for instance, about Poland’s cultural and religious history via Weigel than when I taught a world history course.

Finally, although it’s clear that I have a pet peeve about the notion of a “linear thinker,” no one – including Weigel – has convinced me yet that the irritation is unjustified. In writing here about it, and on Weigel’s passage in particular, my hope is that more care will be given to how the phrase is utilized.

What does the phrase ‘linear thinker’ mean to you? Does the notion of a “non-linear thinker” imply a lack of logic, or someone that ignores traditional logical categories? And if I haven’t treated Weigel justly, feel free to tell me how. – TL

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[1] I use Amazon links not because I’m a fan of the conglomerate, but because of the sometimes enlightening discussions in each book’s review sections. Here’s a link to Powell’s to see the contrast.

[2] George Weigel, Witness To Hope: The Biography of Pope John Paul II (New York: Harper Perennial, 2005), 138. This edition contains a Preface from 2005 written after John Paul II’s death.

11 Thoughts on this Post

  1. If we’re talking about logic, then I suppose *ahem* that I need to point out the following fallacy:

    “By way of summary, my first thoughts on the subject began with the idea that linear thinkers are simply logical – and that’s not such a bad thing. The corollary was that non-linear thinkers are not logical.”

    Actually, the only thing we can deduce from the proposition that linear thinking is logical is that non-logical thinking is not linear. We cannot logically conclude that non-linear thinking is not logical. While the original statement clearly states that if thinking is linear it is logical, it does not say that only linear thinking is logical. In other words, the possibility of logical, non-linear thinking is still left open by the initial claim.

    🙂

  2. Mike,

    I’m not sure how much of a difference this makes, but I meant for an If-Then proposition to be in that statement. It should read like this:

    “My first thoughts on the subject began with the idea that if one is a linear thinker, then one is logical – and that’s not such a bad thing. The corollary was the if one is not a linear thinker, then one is not logical.”

    I wanted convey the idea that logic is a subset of linear – at least insofar as my original H&E post was concerned.

    Should I change it?

    – Tim

  3. This issue also provides a perfect example of the value of American Pragmatism.

    For “linear” is a slippery term that I don’t remember being defined in the above post. What agreed-upon definition of the word would allow us to determine whether the future pontiff’s reasoning would be aptly so described? If I were to encouter a passage containing an argument, what should I ask in order to ascertain whether or not its reasoning is “linear” or “non-linear”? I honestly have no idea.

    But my hunch is that if it were properly defined in pragmatist terms, this dispute would disappear. If “linear” is defined, for example, as “following the rules of logic” than Tim’s point is correct, but only trivially so. If it is defined in a different fashion, then we would be able to ask whether linear reasoning is always logical, and whether or not it is the only thinking that can be so described.

    Until then, my suspicion is that this disagreement, such as it is, really concerns the value of certain political ideas rather the standards by which one can construct a compelling argument. In particular, it invokes to my mind the ongoing dispute between those who value objectivity as an important intellectual tool in the quest to understand reality, and those who see that objectivity itself as dangerously elitist.

  4. Several related and extended questions: First, by way of amplifying Mike’s point, I would still be very interested in learning how we decided to define “linear thinking” for this thread? I am afraid we may be using an allegory from Euclidean or analytical geometry here, so your use of the phrase “linear thinking” leads me to wonder about your evident distaste for non-linear thinking. When a process is “linear” it has to be functional, right? A math function implies a dependency, a monogamous marriage between each exogenous with one other endogenous variable, and these marriages must be between one “x” and one “y.” If we reject all mathematical “civil unions,” polygamous correspondences, and unstable relationships as “dysfunctional,” we are left with only functional one-to one correspondences. Ah, but only some of these functional relationships are to be described as “linear.” A linear relationship, and presumably “linear thinking,” assume that a dependent variable might be accurately predicted given only the value of the independent variable and the slope of the line upon which these pairings line up. The rest of the information is just to situate the rather arbitrary point of origin in “the right” place. So, like deduction itself, these kinds of functional relationships–“linear thinking”–depend on “if, then” statements. By chaining these kinds of “if, then” statements together, somehow along the same slope, we can be said to be doing “linear thinking,” if and only if the successive “if, then” pairings all line up along the same slope. Is this disciplined deduction what we mean by the term, “linear thinking.”
    Since reality does not seem to line up on any single slope, of course, we have to adjust our magnitude of observation through statistical methods. First, we might back up from the graph until the cloud of data seems to approximate a line. Second, we must recognize the many non-linear functions, i.e. curves (are we also calling these “linear?) that describe much of reality. We might also take a seemingly random cloud of three dimensional data and calculate (or more precisely, approximate) a line in two dimensions. Then this slope of our approximated line can be used to predict the future from regression techniques. But the accuracy of such an approach depends on how well the future approximates the past, and it almost never does. So, the application of this kind of “linear” technique to thought processes is just what most historians resist anyway. So I can not imagine we mean “linear thinking” in this way do we?
    Perhaps we do not mean “linear thinking” in a mathematical way at all. A line, after all, can only be represented, it can not be drawn (lines have no width.) They exist in the human imagination, but have never been experienced in reality, have they? Perhaps, you mean “linear thinking” as a proxy for “orderly thinking.” In which case, lines may not be progressive, they may curve and loop. And what may seem orderly for you may seem arbitrary to me. And the only objective way to decide what is “linear” is to find an objective point of observation (a place and time that probably does not exist.) Linear thinking may happen in a dialectical manner, as long as each synthesis unfolds from an earlier thesis and antithesis in an orderly way (if we allow linear to mean “orderly”). And “linear thinking” might even be used to describe an orderly process of natural selection, millions of evolutionary changes with species shaped by genetic branches, extinctions, restarts. Are family trees “linear?” If we mean “orderly” by the term “linear,” then even cyclical thinking can be linear, can it not?
    Of course, if we do allow the term “orderly” to stand in this discussion for the term “linear,” it may be helpful to describe the kinds of thinking that are “disorderly.” On the face of the term disorderly, I am very prepared to agree with you here. Disorderly thinking does seem to me to be illogical. But perhaps my own viewpoints are too limited to see the order that lurks in seemingly random reality.

  5. Joe,

    I appreciate your thinking on a number of points. I don’t know how to answer them all. The biggest question, however, seems to still be the original one: what is linear thinking?

    I do think that orderliness is important, but more important I think that the whole idea of “linear thinking” needs to be dropped. It’s useless. It seems that it is primarily used in order to talk about “non-linear thinking.” Well that just seems to the same as the old adages of “thinking creatively” and “thinking outside the box.” [Aside: Perhaps since boxes have 4 straight lines, somebody decided that inside-the-box thinking is linear.]

    Someone recently entered my site (H&E) via a Dogpile.com search on the phrase “define linear thinking.” The fist entry that came up in that search was this page from a consulting company. When I hit another link this next page came up.

    It seems that this company associates non-linear thinking with NOT using regression analysis to predict the future (hence the word “chaos” on the first page). The company says we live in a “non-linear era” where they can help with complex, creative solutions.

    In sum, the phrases “linear” and “non-linear” thinking still seem to me to be mere wordplay. They signify little to the conscientious reader, and they certainly don’t convey as much about someone’s thought processes as do the traditional categories of formal and informal logic, as well as the categories of deduction, induction, and fallacies.

    – TL

  6. Thanks Tim,
    I concur with your appraisal of so called “linear thinking.” With the summer freshman intake and advising schedule ahead for us both, I know you can appreciate my plea for more fluency with corkscrew type thinking patterns. “Dude, I want to major in Engineering because math is just so boring!” or “I’m putting down Sociology because I consider myself a very social person.” 🙂
    Best, Joe

  7. I have a similar pet peeve with regard to a common way of describing ethical distinctions: the rejection of a specific moral position on the grounds that the situation under consideration “isn’t that simple.” Most often, this comment is simply a device to avoid taking any position at all, or even one that contains the implicit argument that no one should have presented the issue as a moral one in the first place.

    I was reminded of this irritatingly common understanding by a review in this morning’s New York Times of Carl Bernstein’s new book on Hillary Clinton. Bernstein is quoted as saying of the Senator that her “’real-life education and sense of right and wrong (which became more complicated and relativist as she grew older) guided her away from rigid ideology’ and ‘led her to reject hard political dogma of any sort (including aspects of feminist theology).’” But what new beliefs did Ms. Clinton adopt? To say that the subsequent views were simply “more complicated and relativist” is hardly an answer; no one would be satisfied with such an account in the realm of, say, foreign policy or health care.

    Unfortunately, however, this is a common trope. The idea that certain situations are “complicated” morally and therefore do not admit of “easy answers” (or, similarly, that the issue is not “black and white” but contains “shades of grey”) should be an invitation to a deeper and richer examination of whatever situation is at hand. If the situation does not allow for easy answers, what are the hard ones? Or if these answers are too difficult, then what difficult quesitons does the problem raise?

    But this kind of follow-up seldom occurs. Most of the time, the advcate of the “shades of grey” position (often, one of my students) seems to think that this observation implies that there’s nothing more to be said about the subject. Yet it actually suggests just the opposite. And if the person who makes such a claim does not really want to delve into the more complicated issues that he/she claims to raise, then what is presenting itself as moral sophistication is closer to quietism or even cowardice.

    (Though I tend to associate the “shades of grey” position with liberals, one could make a parallel point regarding the claim for “moral clarity” that seems to come more often from conservatives. More often than not, the phrase means little more than “an unnuaced position that echoes my own.” Thus “clarity” frequently signals a dogmatism that might not be clearly reasoned at all.)

  8. Mike: The fact that this thread, straight and direct as it seemed, led you to that Bernstein review and to a denouncement of the annoying tendency by liberals to classify most issues as complex, and by conservatives to see issues as too simplistic, exercises–for me–the con of the postulate “is linear thinking the only rational thinking?” It is, of course, not that simple. I here spare you from a capacity/process interpretation of the various outlooks of the two political extremes, using an allegory of a little dump truck and a big dump truck. [ a big grin here, Mike!]

    On the matter of the thread, one of our best thinkers, Thomas S. Kuhn, carried the scars to his grave from a long battle over his notion of paradigm shifts. When scientists wanted to think of themselves as thinking in linear ways, and he [simply] wanted to show how historical evidence might show a non-linear structure to scientific progress. Now we seem to all be aware of the starts, dead ends, retrogrades, paradigm shifts, and revolutions that we call “scientific progress.” Aren’t we? Cheers, Joe.

  9. Ok, this is months later, but the term ‘linear’ thinking came into my mind today because I was trying to think of a good quote to use for a presentation.

    I find it interesting that what I am reading tells me that there is a debate on linear/nonlinear thinking. I also find that the few articles I have read put the terms into mathematical terms, logic vs chaos, and when I heard the term, I never even associated it with mathematical properties.

    In the late 1990’s, I was a computer novice, and since I learn from the top down, I would go to seminars or lectures or conventions just to hear what was out there. I knew what computers could do, and while I couldn’t afford it, I had a need to know what technology and software was being used.

    At a Macintosh convention, cdrom and quicktime was being introduced. I don’t know who said it, the presenter from Drexel University or the Representative from Apple, but it was said “People don’t learn in a linear manner, nor do computers teach in a linear manner.”

    I know it sounds really simple, but some things are just that, simple. From my point of view as an educator, what the presenter said made perfect sense. When you think, when you learn, you go off on tangents. The line is symbolic, you can go forward, you can go backward, but you stay on the line. In educational terms, what the Pope was doing is called scaffolding, it’s how kids learn. Scaffolding is exactly like walking around the spiral staircase, stopping at the beginning, and walking around again.

    Of course the line is always there, but non-linear thinkers sometimes bend the line to help them think, or they go off the line in a totally different direction before coming back to the line. Think of a game of tag, where the line is “touch base” or “safe”, then you are off again. Thinking is like that.

    I suppose I am simple, but if you take away all the labels and logic, and just read the words, they make perfect sense. Sometimes labels and categories are not worth the paper they are written on. Linear thinkers think in only one way, in a straight line. Nonlinear thinkers don’t. Scientists can be either or!

  10. Perhaps the term multiple intelligences can be added to the thread. Those who are defining linear represent one form of intelligence and there are other forms. Such concept more closely represents the spiral multi-perspective approach.

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