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What Is "Linear Thinking?" A Lament On Logic’s Diminished Status In Schooling And At Large

February 5, 2007

This past weekend I had an extensive conversation with my sister-in-law, a former high school math teacher, about the phrase “linear thinking” and the notion of a “non-linear thinker.” She used the latter to describe a colleague with whom she’s had trouble interacting. In the context of the arts and creativity, non-linear thinking is often prized. But in the situation we discussed, being ‘non-linear’ was clearly not an attribute. This particular ‘non-linear thinker’ was unorganized and generally unable to put together a good plan.

This use of ‘linear’ or ‘non-linear’ in relation to thought processes has bothered me before, but until this weekend’s conversation I hadn’t forced myself to articulate why. I told my sister-in-law that, while I was pretty sure I understood what she meant, the phrase ‘non-linear thinker’ was itself trendy nonsense. I conceded that I have heard others mention the phrase a number of times in recent years, but I maintained that traditional terminology would be more useful. To me the use of ‘non linear’ with regard to ‘thinker’ or ‘thinking’ was a just a fashionable, two-word, four-syllable synonym for ‘illogical.’ But then I discovered the following, this morning, in the online Oxford English Dictionary:

————————————————–

“ADDITIONS SERIES 1997

linear, a. and n.

Add: [A.][3.]c. Of causation, evolution, time, etc.: progressing in a single direction by regular steps or stages, sequential.

– 1948 E. WHITTAKER Space & Spirit xxxix. 126 In the argument as usually presented..all chains of causation are simple linear sequences.
– 1954 A. P. USHER Hist. Mech. Inventions (ed. 2) ii. 30 The cultures of antiquity do not fit the patterns of the linear sequences of social and economic evolution developed by the German Historical Schools.
– 1972 R. D. WALSHE in G. W. Turner Good Austral. Eng. xi. 228 The McLuhan thesis that..‘linear thinking’..had been rendered obsolete by the new ‘in-depth’, ‘all-at-once’ thinking of the electronic media.
– 1979 P. MATTHIESSEN Snow Leopard i. 60 The Australian aborigines..distinguish between linear time and a ‘Great Time’ of dreams, myths, and heroes, in which all is present in this moment.
– 1983 P. LIVELY Perfect Happiness viii. 112 Time, that should be linear, had become formless.
– 1992 Forum Mod. Lang. Stud. Jan. 22 It is impossible to over-emphasise the importance of the poet’s decision to keep the inexorable linear flow of time intact on each occasion when a-temporality is alluded to.”

————————————————–

What caught my attention in the above usage sequence, of course, was the 1972 citation of McLuhan. That instance by itself proved I was at least partially wrong in my assertion of trendiness: the phrase and idea of ‘linear thinking’ were both at least thirty-five years old.

But based on McLuhan, as well as the 1948 and 1954 usage citations, the use of ‘linear’ as an adjective does involve chronology and causation. The phrase appears particularly amenable to conversations about history, especially its logical underpinnings. It seems clear that ‘linear thinking’ involves the basic “if…then” progression: IF (sufficient condition) THEN (necessary outcome). The results, then, of ‘linear thinking’ are old-fashioned syllogisms, and ‘linear thinking’ is therefore synonymous with traditional, critical thinking terminology and associated wtih the discipline of logic.

But what’s wrong with using the older, simpler terminology? Why does someone have to be called ‘non-linear’ rather than illogical? I think the reason behind the avoidance is simply that few people today are practiced in the discipline’s relation to the humanities and social sciences. Studying the fundamentals of logic is out of fashion: it’s not seen as necessary to today’s liberal arts curriculum. Most contact with logic comes in mathematics. Even there it is studied in its symbolic form.

Moreover, I think that designating someone’s argument ‘illogical’ strikes one today more as a “put down,” or an ad hominem, than a critical evaluation. When an argument is deemed illogical, the argument’s author sees the act as a personal attack. Could it perhaps be the case that the development and use of the phrase “non linear” came about as a way to soften criticism? If so, and if this is necessary today, are we just too sensitive for direct criticism? Are we too prideful to accept logic’s conclusions?

To return to an earlier point, it seems safe to say that misunderstandings about logic have everything to do with the subject’s devaluation in the United State’s system of education. With that in mind, I wonder if anyone’s written a ‘history of logic in U.S. curricula’? If so, when did the study of logic – in the humanities and social sciences – go out of style? Why? When was it at its height? What would it take to renew wide-scale appreciation of the subject? Or is the study of logic in the context of the humanities simply dead? – TL

[Update, 6/21/2007: See this post at USIH for more thoughts on “linear” and “non-linear” thinking. – TL]

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26 Comments
  1. I've often wondered if these sorts of things are true–do fewer people study logic than used to? Or more to the point, are fewer people studying logic than SHOULD BE?

    More people go to college, and clearly, not all of them study logic. But that doesn't mean that no one does. I know my experience wasn't typical, but every freshman at my undergraduate institution had to take at least once class specifically on logic, and 4 philosophy classes overall. Not everyone studied logic back in the day, either; college was more rarified air. So do we have a lower “logic quotient” in our society at large?

    Think of it this way:

    1900: x% goes to college, 90% of x take logic classes.

    2000: 10x goes to college, 15% of x takes logic courses.

    Or some variation of the foregoing. It is entirely conceivable to me that MORE people actually take logic at a time when it is less prevalent than ever (in a generic sense) in college curricula.

    Think, for example, how many people take statistics courses anymore. Statistics is a basic training in some basic logical principles. (esp: correlation does not equal causation!)

    thoughts?

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  2. CM: You make a good point. In absolute terms, perhaps more study logic now than ever. And, with the increased numbers of scientists (and science-lite types) in the twentieth century, more now than ever in human history have likely encountered the rudiments of symbolic logic. As you noted, most undergraduates learn that correlation doesn't equal causation.

    But what if the relative percentage of logic students remained high, as in the case of the hypothetical 90 percent you posed, and they actually applied that study to the humanities? I'll even take a lower percentage. With that, what if 60 percent of the at-large public could identify common fallacies in political speeches with relative ease? If 60 percent could, with little effort, catch straw man and false dichotomies, wouldn't the electorate be that much better off for the increase? – TL

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  3. Anonymous permalink

    Q: Why does someone have to be called 'non-linear' rather than illogical?
    A: Because they're not the same thing.

    It seems illogical to treat “non-linear” and “illogic” as interchangeable or synonymous.

    But since you've given “linear” a definition and citations, you might consider giving the same treatment to “non-linear,” “logic,” and “illogic.” So all your terms will then be defined, and your arguement strengthened.

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  4. Dear Anonymous,

    But it would seem from the OED definition that 'illogical' and 'non-linear' are pretty much the same thing? I'll assign that similarity an 85 percent value, with my 15 percent variable being the 'artistic' aspect discussed in my post.

    While I could do it as a matter of courtesy (and I will below), I'm not really obligated to define the traditional categories of 'logic' and 'illogic.' The burden of proof for that is on the one (my sister-in-law, for instance) trying to change these useful, time-tested, and proven categories of thought (or non-thought, as may be).

    For the sake of argument, however, I refer you to the following online sources for definitions of logic:

    1. Stanford Encyclopedia of Philosophy (see Aristotle's Logic);
    2. Wikipedia (quite useful for an introduction); and
    3. The Philosophy Pages (search for logic).

    For a print resource, few books outdo Copi and Cohen's “Introduction to Logic.” – TL

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  5. Anonymous permalink

    Based on the OED, it does not seem that “illogical” and “non-linear” are the same thing at all.

    If one followed an argument that
    1. logic is the opposite of illogic,
    2. linear is the opposite of non-linear, and
    3. logical thinking equals linear thinking,
    then maybe you could draw the conclusion that illogic is the same as non-linear.

    But I don't find that argument particularly solid. The notion that non-linear is a synonym or a softened criticism for illogical just seems, respectively, a bit off the mark.

    Illogic is non-sense; non-linear is just another way of thinking things through. I won't argue that linear thinking has its merits, but I wouldn't entirely discount, down-play, or ignore non-linear thought either.

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  6. John Kutlich permalink

    When I went to college, I was told the purpose of education was to teach us how to think. I was told this by enough professors that I assumed it was the prevailing attitude of the times (late 60s). My favorite courses were the my electives in philosophy, especially logic.

    In those days I felt the natural human quest for knowledge was the driving force behind a steady advancement of civilization, and would continue indefinitely, to the benefit of us all.

    At some point since those days, the quest for knowledge in western societies has ended. It seems nobody, whether politician, educator, businessman, journalist, or whatever, is interested in the truth about anything. Special interests, greed, political correctness, diversity, a conservative agenda, a liberal agenda, ANYTHING but a desire to arrive at the truth drives all discourse.

    In my opinion, western civilization was on the right road, and has lost its way. I don't think the tide will turn back, I truly feel our best days are behind us and it's downhill from now on. The human mind/soul has simply proven itself to be not up to the task of continued progress.

    Maybe I misread things in my youth, maybe it was never like I thought. But I don't think even my young mind could have missed the level of irrationality we suffer through today, had it existed then.

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  7. John,

    Thanks for the post. I mostly agree with your additional lament. I only have a problem with your second-to-the-last paragraph.

    Even though our intellectual histories of the West have shown us that the intellectual class did believe in progress, I'm not sure our civilization did as a whole. Considered from that perspective, it's not so much that the West is off track, but rather that the quality of our leadership has changed. More leaders today seem to be ideologues than thinkers.

    Is this the fault of our education system? Perhaps. I do think that fewer professors believe in the notion of progress today than they did even in the 1950s. But I'm not so concerned with the West, as a whole, believing less in progress.

    I think a significant portion of the general population still believes that progress is possible (i.e. science for sure), it's just more variable in our leadership class of intellectuals and politicians. – TL

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  8. Would it be reasonable to work from a theory concerning the comments surrounding “progress” that western civilization simply needs to grow into the progress already attained?
    Would you also agree or not if the absence of the desire to attain truth, would be an outward personification of the prevailing lack of self worth that seems to me to be at or close to the root cause for the reduction of desire?
    Thanks fo taking the time I've found some help here.

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  9. Have you found any histories of the role of logic in education? Your lament is one I share, and have recently begun to investigate what is written on the topic, and if anyone is already organized to work on this issue. (This is how I found your blog.) Anything you have found on the topic would be welcome information.

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  10. Chris,

    I have no recommendations off the top of my head. Of course my post was anecdotally based, but this particular link has received an incredible number of hits. If I had the time I'd write this history myself.

    – Tim

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  11. Drevin permalink

    Being an analytic person in a long-term relationship with a professed 'non-linear thinker', I've had occasion to tread this ground a few times over the past years.

    I agree with Mr. Lacy that 'logical' and 'linear' are, in terms of thought, synonymous. It is necessary to observe, however, than a logical statement is not necessarily a true statement.

    My wife describes her thinking as a gestalt of experience from which, should she desire to communicate, she must reverse-engineer articulation.

    That seems rather awkward to me, but nonetheless intelligible:

    The key is that she is still moving from cause to effect (her gestalt being acquired through experience), she is simply less aware of the ground she covers between origin and destination. I'm told it's akin to being aware of something, but not the specifics of what initiated that awareness.

    I suppose that 'fuzziness' frees her to reach further for connections than would the more concretely minded…doubtless why, to the artist, it seems a fount of possibility and creativity, while to the scientist it seems simply an unnecessary increase in uncertainty.

    In any event, the role of logic in education is of professional interest to me, and, oddly enough, it's possible to trace its withdrawal from the humanities to the rise of Modern Logic around the beginning of the twentieth century.

    In a nutshell, prior to this, most any college student would receive instruction in the Trivium, the classical study of logic, rhetoric, and grammar.

    This was Aristotle's logic, founded on an analysis of language. Unsurprisingly, the Trivium translated very well to the humanities (with rhetoric and grammar having since been wholly absorbed by them, in fact).

    Modern logic, by contrast, is largely symbolic rather than verbal, and represents the attempt to elevate logic more firmly into being considered a science by identifying it with mathematical operations. One of the turning points down this path was the publication of the Principia Mathematica by Alfred North Whitehead and Bertrand Russell.

    This structural emphasis, by identifying formal logic so specifically with science, pushed it in like degree away from the humanities as a whole.

    A unfortunate state, and an altogether ironic culmination of Aristotle's own passion to divide reality into more digestible mind-bites…the flip side of which being that we treat as separate things those that are integrated in truth, if no longer so in practice.

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  12. Dr. Joe permalink

    My interest in thinking has to do with business where it is normal to reduce most things to Yes or No, Black or White, when in reality most issues are shades of gray. We need to add more dimentions to our thinking process which some refer to as Systems thinking.
    I tend to think of it as more What if or What will happen based on this decision rather than if it is in our best interests or not.
    One of our more recent blunders seems to have been the War in Iraq. We did not adequately explore all the outcomes of the basic decision of whould we invade or not?
    We didn't fully understand their culture, what their reactions might be and what it would take for us to get out.
    Maybe if we used a more sophisticated decision making process we would have not gone, gone it and got out immediately by turning the country over to the Iraq people and let them sort out the mess.

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  13. I think this subject has more to do with progressive thinking rather than correlative thinking. We each as individuals have our own definition of what defines “progression.” That is, whether or not a conversation has taken a direction which we deem as advantageous is highly subjective, and the attempt to define in words this subjective approach to communication results in the ambiguous term that we are so fervently pondering within this blog.
    That is, it's not a question of logic, but rather a question of what drives us forward.
    A person who dwells on the negative and highly emotional side of things might define linear thinking as that which delves deeper into the dark depths of the human psyche.
    A more practical person who errs on the side of pragmatism will define linear thinking as that which in that person's viewpoint will achieve a “greater end.”

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  14. David,

    I agree with you, to some extent, on the subjectivity that can arise within the applications of logic. Logic is a tool that can be abused. Many who use logic start with false or inadequate premises, and others use logic to oversimplify complex human behavior and ways of thinking. In this way, I agree that linear thinking is based, at least in part, on what drives the individual forward.

    – TL

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  15. Angelica Graue permalink

    I don't know how relevant this is for this specific discussion, but I recently figured out my cognitive development pattern based on Jung theory, and it's Ni/Fi + Fe/Ne + Ti/Si + Se/Te. This is unusual, I guess, because I straddle the J and P patterns (J = Ni, Ti, Se, Fe as primary processes); (P = Ne, Te, Si, Fi as primary processes). This is supportable by the fact that I only tested slightly J when I took the Myers-Brigg. but what it means is that because you only have four processes as your primary ones, my Thinking and Sensing functions are subverted. Ti specifically seems to mean linear thinking, although Te also seems adequate for the type of logical reasoning you were suggesting. But I have neither function as a primary function and I find that my difficulty in thinking linearly causes me to have great difficulty writing (because it's a major ideal to try to put my thoughts into a coherent and linear structure). This has made writing essays a dreaded experience for me, and writing in-class essays a particular hell. I usually don't finish.
    Anyway, my point is that my current inability to think linearly when i need to puts me at a disadvantage, and I'm going to work on developing it. Linear thinking, just like anything else, is something that should be cultivated, regardless of what your personal preferences are, as it is ubiquitously useful for being better rounded as an individual.
    Sorry if this wasn't entirely clear. I didn't know how to say it more directly without going into Jungian cognitive theory, and it's better explained on the following sites:

    http://www.cognitiveprocesses.com/16types.html
    http://www.timeenoughforlove.org/Functions.htm

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  16. This is based on an incorrect interpretation of what linear vs. non-linear thinking is. Your perception of linear thinking is correct. Your definition of non-linear thinking is incorrect; non-linear does not imply illogical. Non-linear implies “not in a line”. This means that leaps of logic can be made, thought can happen in a “webbing/network”, eg., “multiple strands” of thought can be happening at once.

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  17. Dear George,

    Thanks for the comment. Please remember that some of my definition of non-linear here was affected by the circumstances in which it was introduced to me. Logic implies the ability to detect a line of thinking. But my sister-in-law found neither lines nor logic in her boss' thinking. I understand your point that something can be logical even if we don't immediately see the steps (i.e. hidden premises). But I think that some use “non-linear thinking” to denote someone who thinks outside the box, whether logical or not. In that case, non-linear means more than just not in a straight line.

    – TL

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  18. Everyone writes as if some people are linear thinkers and some are non-linear. People are not limited to one method of processing data.
    In decision making and analysis, linear and non-linear thinking are two different tools one could and should use and develop. Why not have more tools at your disposal.

    Tim's observations in his initial post illustrate the propensity of Americans to squeeze words into a box, making them difficult to use when communicating with a person that doesn't own or use a dictionary.

    Ever heard someone say people in certain countries (France, Britain, or Canada) are rude. I believe this broad stereotype to be a result of intimidation by said countries citizens having a better command of language and communication.

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  19. Perhaps what is required here is the coining of a new word for this thought process that is outside the purview of logic, since a “line” of thought can certainly be curved and still come to the same, truth-based conclusion, no? I'm thinking of getting rid of the offensive prefix “ill” and going with perhaps something like extralogical to simply denote a less simple method of arriving at the same place than that of a straight line (aka “quickest”) and (in that process) side-stepping the offensive connotation of the “ill” applied to the “logical.”

    But, if I do so I am left with a question about my motivation for doing so; it hearkens back to the original post. Am I merely worried about stepping on the toes of the creatively inclined? Am I so entrenched in the quagmire of political correctness that I need to fashion new words for the job (or hyphenate existing ones)?
    Ah, behold! The flux and glory of the English language!

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  20. If linear is the black and white, my has experience has resolved tha that Comprehensive thinking encompases the gray areas as well and give equal weight to all.

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  21. Wow, my cut and paste jibberish needs some attention, Translation of the above post: If linear thinking is the black and white, comprehensive thinking encompasses the gray areas as well, and equal weight is given to all.

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  22. Anonymous permalink

    Interesting discussion. I have often found that predominantly linear thinkers equate non-linear with illogical, whether they know they are doing so or not. However, nothing, could be further from the truth.

    In reality a disposition for one way of thinking over another has little to do with logic, and a lot to do with memory (specifically working memory).

    The predominantly linear thinker tends to have a larger working memory for data points than the non-linear thinker. The non linear thinker has a greater ability to hold abstractions.

    Linear thinking might be better described as imperative or sequential thinking, and non-linear as being descriptive thinking.

    So linear thinking is a way of thinking which focuses on the verbs, where as non-linear focuses on the nouns.

    We can take an example from logic to explain. X -> Y (the condition x implies the condition y).

    An example of linear, but illogical thinking might be of the following.

    (a) X implies Y, Y is true therefore X is true.

    This is linear, but not valid logic. The linear, logical thinking would be.

    (b) X implies Y, Y is true, we know nothing about X.

    The non-linear thinker sees x -> y more like ~( X /\ ~y), which is logically equivalent. ( It is not the case that x is true and y is not true ).

    The non-linear thinker _sees_ the implication as a statement about the falseness of one out of 4 possible conditions.
    Those conditions being

    XY

    FF – T
    FT – T
    TF – F
    TT – T

    The non-linear thinker is not likely to make the reverse implication made above in (a), specifically because they do not process the information linearly. The down side of this way of thinking is that the non-linear thinker either understands, and understands completely, or doesn't understand at all. Where as the linear thinker may understand partially, but also be partially wrong.

    If the linear thinker never comes across a case in which Y is true and X is not true, their partial understanding will be sufficient. The linear thinker can form often successful generalizations more quickly, unfortunately these generalizations are typically not complete. The non-linear thinker may take much more time to come to a conclusion, but once achieved, these conclusions are usually complete.

    About the earlier statement dealing with memory. It is believed that many predominantly non-linear thinkers are so because they lack the working memory to be successful at linear thought. Basically they must think non-linearly because they can not hold the data points in their memory ling enough to make it though a sequence.

    The linear thinker is such, on the other hand, because he or she, can hold enough data long enough to successful make it through most sequences and therefore non-linear, or descriptive thought is never a necessity.

    The logic calculus used here is of a very simple form, and often not the proper tool. In fact predominantly linear thinkers often have difficulty with other forms of logic.

    Consider that both statements (X->Y) and ~(X/\~Y) could be considered very different in the amount of information they encode. Just because something is not false does not necessarily mean that it is true. And just because something is not false, does not necessarily mean that it is true.
    Those who have not studied such systems of logic may find this difficult, but in fact such thinking may be necessary to understand quantum physics.

    Consider (X->Y)
    XY

    FF – ?
    FT – ?
    TF – F
    TT – T

    and ~(X/\~Y)
    XY

    FF – ?
    FT – ?
    TF – F
    TT – ?

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  23. Anonymous permalink

    Thank you Anonymous. It was such a relieve to read your post!

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  24. Just to add something about linear thinking and the arts:

    When an art teacher tries to take someone's 'linear thought' away in terms of drawing, it's not an attempt to 'liberate' them from some traditional 'stale' dogma or what not. It's rather to help them see things as they are

    It's why a great many adults, when asked to draw something from life, seem to create works that came from a grade schooler. In terms of linear thinking, they won't draw a face as they actually see it, but rather how they *think* they see it. They believe all eyes have a certain shape, mouths have a certain shape, etc. (in other words, the value of 'X' facial feature never changes). “To create a face, follow these steps”. They use a symbol of systems rather than actually perceiving what they see. Once they are 'free' from a symbol/step system, they draw what they see incredibly well. Anyone can do this

    The best artists then aren't strictly non-linear thinkers as I believe they are stereotyped as by 'intellectuals'. They use steps and decision making to create their works just as in any other trade or situation, but also tie in that 'non-linear' thinking into their 'linear' thought process when appropriate. It's not a conscious switch obviously

    If anything is 'diminished' in status in today's education, I think I would place the blame on the extreme ends of linear/non-linear schools of thought. They love to downplay each other to death, while not realizing that both are integral to what they all do

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  25. Anonymous permalink

    What if one is dyslexic?

    That is definitely my problem. Trig was murderous for me and gave me headaches. I can remember the many arguments I had with my teacher about my failed tests because even though I had the answers correct, my equations were always wrong. xy+(a-m)=qkn will never make sense to me.

    And this is carried into my thought process. I can't string thoughts sequentially but bounce all over pulling something from one area and shoving it into a second while extracting from a third. On face value, none of those three have anything to do with each other, but in my mind I can see the link. And eventually I can and do make my point.

    I'm just wondering if dyslexia might account for a non-linear thinker's thought process.

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