Models and metaphors we live by

George Lakoff and Mark Johnson’s Metaphors we live by is a classic, that has had a huge influence on parts of linguistics and cognitive science, and some influence — although less so, in my opinion — on philosophy. It is structured around the thought that “[m]etaphor is one of our most important tools for trying to comprehend partially what cannot be comprehended totally”.

The authors spend the first part of the book giving a very convincing argument that “even our deepest and most abiding concepts — time, events, causation, morality, and mind itself — are understood and reasoned about via multiple metaphors.” These conceptual metaphors structure our reality, and are fundamentally grounded in our sensory-motor experience. For them, metaphors are not just aspects of speech but windows into our mind and conceptual system:

Our ordinary conceptual system, in terms of which we both think and act, is fundamentally metaphorical in nature. … Our concepts structure what we perceive, how we get around the world, and how we relate to others. Our conceptual system thus plays a central role in defining our everyday realities. … Since communication is based on the same conceptual system that we use in thinking and actiong, language is an important source of evidence for what that system is like.

I found the book incredibly insightful, and in large agreement with many of my recent thoughts on the philosophies of mind and science. After taking a few flights to finish the book, I wanted to take a moment to provide a mini-review. The hope is to convincing you to make the time for reading this short volume.

Lakoff and Johnson present over 58 different metaphors with a series of examples. For instance, their opening metaphor, and one they return to frequently, is Argument is War. They present it with a series of examples:

Your claims are indefensible.
He attacked every weak point in my argument.
His criticisms were right on target.
I demolished his argument.
I’ve never won an argument with him.
You disagree? Okay, shoot!
If you use that strategy, he’ll wipe you out.
He shot down all my arguments.

Most of the metaphors they consider — like Ideas are Objects, Up is Good, and Down is Bad, or Understanding is Seeing — are so ingrained in our culture and literal seeming that I’ve never noticed them before their attention. Other examples are innovative and insightful; my favourite new metaphors are Love is a Collaborative Work of Art and Problems are Precipitates in a Chemical Solution.

Fundamentally, the book was motivated by linguistic motivations. It was “an attempt to answer influential claims about metaphor made by two major contemporary American philosophers — Donald Davidson, who claimed that metaphors are meaningless, and John Searle, who claimed that there are semantic and pragmatic principles that allow one to assign literal meanings to metaphorical sentences.” From the linguistics perspective, their response was largely a successes and resulted in a very different theory of truth and meaning than the standard analytic approach, and a theory of metaphors that departs from the common Aristotelian view of abstractions, and the more recent approach of weak homonyms. However, this is the only linguistics book I have ever read so I am reluctant to comment further.

I am more comfortable with cognitive science, where I think the book’s biggest impact lays. Here, taking the sensory-motor grounding of concepts seriously has resulted in the field of embodied cognition. In the 2003 Afterword, they push this connection to the extreme by discussing the neural basis of metaphor (for more detail, see Narayanan, 1997). In fact, I first heard about the book because of a recent article on the neurological evidence.

I am bit skeptical of how much clarify neuroscience will add, but I have greatly enjoyed embodied cognition over the recent years. I especially like Beer’s work on minimal cognition, but others aspects have been a turn off — especially Lakoff and Nunez (2010) grounding of mathematics leading to conclusions like: “Mathematics turns out not to be a disembodied, literal, objective feature of the universe but rather an embodied, largely metaphorical, stable intellectual edifice constructed by human beings with human brains living in our physical world.” Of course, such perspectives have a very large grain of truth to them, especially if one is a physicalist, but are poor reflections of how most mathematicians tend to conceive of mathematics. More importantly, they miss much of the philosophical depth that Lakoff and Johnson present when discussing truth and perspective more broadly. In particular, why accept your intuitions for the existence of an (objective) external world (or Kant’s sensible world) which holds your embodied self and others, but not accept a similar intuition for a shared (objective) “internal” world (or intelligible world — to borrow from the Kant of the Inaugural Dissertation) of mathematics? I could spill much keystrokes over this perspective — and probably will in future posts — but I don’t want to introduce too much of my own philosophy into this review.

This brings me to the general philosophy that the authors develop, which I found very insightful and — from my experience — under-appreciated in philosophic circles. They offer what they call experientialism as an alternative to the false dichotomy of objectivism versus subjectivism. They provide a nice origin story for these myths (not a derogatory term for authors focused on metaphor): “The myth of objectivism reflects the human need to understand the external world in order to be able to function successfully in it. The myth of subjectivism is focused on internal aspects of understanding — what the individual finds meaningful and what makes his life worth living.” More importantly, both myths detach person from environment, subjectivism through the struggle of alienation and objectivism through the disembodied observer. The authors try to bridge this by focusing on how our minds and their concepts are structured by our sensory-motor experience within the world. This results in a less objective view than the standard in science, but one where “scientific knowledge is still possible. But giving up the claim to absolute truth could make scientific practice more responsible, since there would be a general awareness that a scientific theory may hide as much as it highlights.” This awareness is something that I’ve attempted to get at — although, much less eloquently — with my discussion of moral methodology.

My real reason for reading the book was this sort of connection to science — especially the obvious connection between models and metaphors. Although the authors recognize that “[f]ormal scientific theories are attempts to consistently extend a set of ontological and structural metaphors”, they don’t focus on this perspective. However, I think that a mathematical or computational modeler can still benefit greatly from this book by simply replacing “metaphor” by “model” in much of the text. The book’s theory of truth and insistence on how metaphors (read: models) both focus attention and hide aspects of our experience should be of particular interest to the working modeler. Think of David Bastanta’s example of heuristic models as metro maps and how modeling is useful even when all models are wrong. You should expect several post in the coming months on more particular insights modeling inspired by Lakoff and Johnson.

Finally, unlike much of the technical work that I tend to read, the book offered some great lessons about society and everyday life. This passage on mutual understanding was particularly moving:

When people who are talking don’t share the same culture, knowledge, values, and assumptions, mutual understanding can be especially difficult. … you have to become aware of and respect both the differences in your backgrounds and when these differences are important. You need enough diversity of cultural and personal experience to be aware that divergent world views exist and what they might be like. You also need patience, a certain flexibility in world views, and a generous tolerance for mistakes, as well as a talent for finding the right metaphor to communicate the relevant parts of unshared experience or to highlight the shared experiences while deemphasizing others. Metaphorical imagination is a crucial skill in creating rapport and in communicating the nature of unshared experience. This skill consists, in large measure, of the ability to bend your world view and adjust the way you categorize your experience.

If that sentiment is not radical enough then their politics offer even more. In the closing lines of the book, they finish with a surprising anti-work sentiment that I did not know to exist in the 1980s (when the book came out):

Political and economic ideologies are framed in metaphorical terms. Like all other metaphors, political and economic metaphors can hide aspects of reality. … But virtually all major industrialized nations, whether capitalist or socialist, use the same metaphor [Labor is a Resource] in their economic theories and policies. The blind acceptance of the metaphor can hide degrading realities, whether meaningless blue-collar and white-collar industrial jobs in “advanced” societies or virtual slavery around the world.

I look forward to exploring some of the connections between Metaphors we live by and my own thought in the coming months. I have also added Lakoff & Johnson’s follow-up book Philosophy in the flesh to my reading list. If you have read either book then let me know what you thought of them in the comments.


Lakoff, G., & Johnson, M. (1980). Metaphors we live by. University of Chicago press.

Lakoff, G., & Johnson, M. (1999). Philosophy in the flesh. New York: Basic Books.

Lakoff, G., & Nunez (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.

Narayanan, S. (1997). Embodiment in language understanding: Sensory-motor representations for metaphoric reasoning about event descriptions. PhD Thesis (University of California, Berkeley)


About Artem Kaznatcheev
From the Department of Computer Science at Oxford University and Department of Translational Hematology & Oncology Research at Cleveland Clinic, I marvel at the world through algorithmic lenses. My mind is drawn to evolutionary dynamics, theoretical computer science, mathematical oncology, computational learning theory, and philosophy of science. Previously I was at the Department of Integrated Mathematical Oncology at Moffitt Cancer Center, and the School of Computer Science and Department of Psychology at McGill University. In a past life, I worried about quantum queries at the Institute for Quantum Computing and Department of Combinatorics & Optimization at University of Waterloo and as a visitor to the Centre for Quantum Technologies at National University of Singapore. Meander with me on Google+ and Twitter.

27 Responses to Models and metaphors we live by

  1. Terrific T says:

    I went to a talk by Siddhartha Mukherjee (the medical doctor who wrote The Emperor of All Maladies: A Biography of Cancer, and he mentioned that the metaphors and narratives used for a disease matters significantly to how people react to diseases and how treatments are developed. I agree with him wholeheartedly and thought that it is quite relevant to what you are describing here in this post.

    • Terrific T says:

      Also, he used “war” against cancer quite a bit, but he mentioned that while this metaphor works for him, it might not work for everyone; he said we should all find metaphors that work for us. Metaphors can indeed be quite subjective and changes from person to person, culture to culture.

    • This is a great point, the authors also discuss the medical considerations of metaphor, although mostly in the context of psychology.

      I would just go get a little picking on the first part of your last sentence: “Metaphors can indeed be quite subjective”. I am not sure if Lakoff and Johnson would necessarily use such language, although I think that they would agree with the spirit of your sentence. Many metaphors are so deeply embedded in our culture that there is almost no way for individuals to escape these perspectives. I would expect that health and death metaphors would be paradigmatic examples of this, and change of these metaphors is nearly impossible at the level of individual patients but must start early in the process of cultural education/integration.

      A position of power is often needed to propagate a new metaphor. Lakoff and Johnson have a particularly insightful passage for this in the context of how metaphors shape culture:

      New metaphors have the power to create a new reality. This can begin to happen when start to comprehend our experience in terms of a metaphor, and it becomes a deeper reality when we begin to act in terms of it. … Much of cultural change arises from the introduction of new metaphorical concepts and the loss of old ones. For example. the Westernization of cultures throughout the world is partly a matter of introducing the TIME IS MONEY metaphor into these cultures.

      Which metaphors do you think we need to introduce to make dealing with disease easier? I definitely think that in the case of cancer some new metaphor is needed to take attention away from the “where’s the cure?” perspective to a more preventing, delaying, or managing view.

  2. Boris Borcic says:

    There is an important point to make, I feel, about metaphor and language acquisition and evolution/drift, starting from the superficial but effective characterization of metaphor as using the name of something to speak of something else. The point is that restricted knowledge of language as is typical of budding speakers, allows via horizon effect, simultaneous illusions that (a) metaphor is marginal (b) language doesn’t evolve and (c) there is for every single word an unequivocal determination of what’s literal and what’s metaphorical use. I find it useful to consider on the contrary, that language evolves under the radar by allowing people to understand each other despite secret differences on the perception that are literal or metaphorical, uses of words that they do share.

    What prompts me to put this down, is the paragraph you quote with praise on the importance of metaphors between people who don’t share the same culture. Lakoff&Johnson’s I’ve found in general a powerful obstacle to convey attention to my view above, that competes with their compelling work as far as re-appraising metaphor is concerned. The problem is that their work suggests metaphors get defined outside and thus more stably than general linguistic convention, while I would on the contrary enroll metaphor as a gear of linguistic evolution. So my point on the paragraph you quote, is that the rightful recognition of the importance of (flexibility with) metaphor between people of widely different cultures, should not distract from the invisible but no less important dynamic role of metaphor between people with small cultural difference.

    • I don’t think I really understand your comment, so I will say things at you in hopes that you will respond with some clarification so we can reach some mutual understanding.

      The point is that restricted knowledge of language as is typical of budding speakers, allows via horizon effect, simultaneous illusions that (a) metaphor is marginal (b) language doesn’t evolve and (c) there is for every single word an unequivocal determination of what’s literal and what’s metaphorical use.

      This is the Aristotelian view of metaphor, Lakoff & Johnson stand in specific opposition to this view.

      The problem is that their work suggests metaphors get defined outside and thus more stably than general linguistic convention, while I would on the contrary enroll metaphor as a gear of linguistic evolution.

      This is probably due to my poor presentation of their work, but Lakoff and Johnson do not view metaphor as a linguistic artifact. For them, thought itself is structured in terms of metaphor which are then expressed as linguistic metaphors (that we are more familiar with) during communication. It isn’t that we just speak of time in terms of space, but we really think of time in terms of space.

      should not distract from the invisible but no less important dynamic role of metaphor between people with small cultural difference.

      I think that here you are trying to get at the important discussion of the importance of ambiguity in language. I agree that this is extremely important and a very powerful aspects of language that I feel is not discussed enough. Lakoff & Johnson do not touch extensively on it, but I am sure they are aware of the importance of ambiguity (especially given their extensive discussion of the limitations of the CONDUIT metaphor of language). However, the long quote on cross-cultural understanding that I include from them is from a section specifically dedicated to mutual understanding. I don’t think that they believe that mutual understanding is the purpose of language, but in this particular section they think about the case of: if mutual understanding is the goal for this particular discussion then how should we achieve it?

      Let me know if I completely missed the point of your comment.

  3. A great follow up on the topic is “From Molecule to Metaphor” by Jerome Feldman: It introduces a coherent view of language which has been developed by the author together with Lakoff and Narayanan and is called the NTL – the neural theory of language. The theory is presented in a very clear way as a sequence of concepts that would add up to a novel understanding for the majority of readers and possibly serve as inspiration for future research.

    • They discuss the neural theory of language extensively in their 2003 Afterword. I am actually not a big fan of this approach. I think it is actually less insightful than their more general approach of 1980 because NTL is so physicalist, I also don’t find the computational models of the sort they discuss as particularly insightful in most cases. I fear that they are succumbing to the curse of computing.

      In particular, I don’t find NTL as useful metaphor for understanding metaphor because I cannot understand any part of NTL (or any neural network) without further metaphors. In that case, why not use these further metaphor directly instead of first running through NTL? The only reason I can see is to capitalize on the ‘buzz’ of neuroscience and authority of physicalism.

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  5. I was an undergraduate at UC Berkeley in the 80’s, graduating in 1989 with a BA in Music. Somehow, my freshman year, I stumbled into Lakoff’s class on metaphor—his book had just come out—AND the class “Knowledge and it’s Limits” with Feyerabend.
    I’ve gone on to take it for granted that ALL systems of thought, even significantly the mathematical, start with unprovable assumptions and pile on from there. No system of thought, however well it anticipates and predicts the observational world, can ever actually reveal “Truth”. This by no means diminishes the power of Scientific Method but takes it off a certain pedestal.

    I’m curious how others more versed in these realms might respond this summation.


  6. Evelyn says:

    I think you missed adding a reference at “recent article on the neurological evidence”

  7. vznvzn says:

    reminds me of what are called “frames/ framing” in psychology (also “reframing” as a major element of CBT, cognitive behavioral therapy) & “spin” in politics. yes metaphors also have a big connection to memes and highly influence our thinking, and our thinking influences the metaphors.

  8. vznvzn says:

    re the nature/ epistemology of mathematical thought, you might enjoy Davies/Hersh, The Mathematical Experience.

  9. vznvzn says:

    oh yeah yet another interesting angle: political ideologies as having different basic worldviews and hence metaphors for understanding the world. and politics is a lot about arguing about the validity of these metaphors outside of objective scientific analysis. eg supply side economics as trickle down, voodoo economics, or “wealth/ job creators” etc. … and one could also study propaganda as a major aspect/ element of metaphor construction and “thought control”….

  10. Abel Molina says:

    Re: anti-work in the 1980s, according to there was actually a popular book written about it in 1985…

    Very interesting comment about the lack of sophistication/poor reflection of how many people think from the Lakoff and Nuñez book, definitely felt the same (though with very different views being defended) when reading Love and Math recently. Not sure to which degree there is a lack of awareness of other perspectives, and to which degree there is a lack of will to value/acknowledge them. Also not sure to which degree there is something anthropic going on (i.e., do less strong stances lead to to writing less books?)

    • Abel Molina says:

      (key word to get to that wiki article was “The Right To Be Lazy”, which incidentally feels like such a catchy title…)

    • Thanks for that link, I will be writing a review or brief commentary on Piketty’s Capital and I will probably touch on some of these themes (either in that post our in later follow ups) so it is useful to have the reference in your link. I haven’t read Russell in a while, so maybe In Praise of Idleness and Other Essays should be my next book by him.

      On the response to Lakoff and Nunez, I think that Frege had a nice pre-preemptive response that captures much of the spirit for me (although I will also write about this more, since I’ve learned some fun things about Frege’s metaphysics recently), quoting Anthony Kenny’s description of Frege’s thought:

      Even if psychology could give a causal explanation of the occurrences of the thought that ten squared is one hundred, it would still be totally different from arithmetic, for arithmetic is concerned with the truth of such propositions, psychology with their occurrence in thought. A proposition may be thought of without being true, and a proposition may be true without being thought of.

      I like this stance to some extent, although I would soften it from having separate realms to differing perspectives on an otherwise ineffable single realm. But I do have some issues with the last sentence of that quote. I think that there are different degrees to which we can ‘think’ or ‘believe’ a proposition. If we use Heinlein’s grok as the expression of the most intimate thinking or understanding of a proposition, then I would argue that a false proposition of mathematics cannot be groked (you can’t grok a square circle). The second clause needs a little modification as well, although any particular proposition may not have been thought of, all true propositions of mathematics are thinkable (although I am not sure if they are all grok-able).

      I like your thought about anthropic effects. I wouldn’t be surprised if strong stances are more likely to be written. I do recall that the first rule of philosophy is to be provocative. On the other hand it seems that the synthesis or middle-ground of two warring strong stances often has prominence, too (I am thinking of Kant, here). Although maybe that can be taken as provoking both extremes?

      • Abel Molina says:

        Yeah, that seems closer to the more common views of mathematicians about mathematical truth being something “out there”, that human thoughts manage to reflect sometimes. Then there is the opposite extreme where all that “exists” is a bunch of people talking.

        How to take some value from views along both of these lines is definitely an interesting task, the Kantian ideas mentioned seem definitely very helpful at that.

        Another attempt might try to focus on the universality between several people saying “1+1=2”, and associate mathematical truth with whatever ontological status one gives to that pattern.

        Another direction that comes to mind, within a physicalist point of view, is trying to ground mathematical truth as something apart from humans by defining it in terms of something machines can verify/produce. Godel incompleteness-like ideas make some issues with this arise, but maybe they can be sidestepped by changing mathematical truth to “human-discoverable mathematical truth”.

        Re: not being able to grok false mathematical propositions, I remember seeing the same argument today (except with a word choice I like less : ) ) in Sam Harris’ Waking Up book. Not feeling like I know well enough what understanding is to have much of an opinion, either from personal exploration or neuro literature. Though think I remember feeling like I had grokked something that wasn’t correct in the end, but if I remember correctly it was because of starting with a wrong assumption.

    • Another direction that comes to mind, within a physicalist point of view, is trying to ground mathematical truth as something apart from humans by defining it in terms of something machines can verify/produce.

      I am not sure how much more useful this approach is.

      If you actually mean machines in the narrow everyday sense of the word (like my laptop, say) then you have the issue that we designed these machines and their decision procedures, so it is really no different than just saying “humans”. In practical terms, though, this is a conversation that’s been had since the partially computerized proof of the 4 colour theorem (and I wrote about it briefly: Four color problem, odd Goldbach conjecture, and the curse of computing). This takes us into a very culture-centric view of mathematics, where a proof does not count as proof unless it is intelligible to the members of our mathematical community, which — at least at this point — does not extend to machines.

      If you mean machines in some human-independent sense — how Gandy might have meant it — then you are left with the same issue that all empiricism-leaning philosophers since Aristotle faced: how are these mathematical principles ‘abstracted’ from the concrete cases of the physical? In Aristotle’s words: how do we get universals from particulars?

      Godel incompleteness-like ideas make some issues with this arise, but maybe they can be sidestepped by changing mathematical truth to “human-discoverable mathematical truth”.

      This realm would have very strangely defined boundaries, and feels unsatisfactory in many ways to me. However, I can see how we could defend it. I think modern formalists would fall in this camp. My real issue with these threads, is that when mathematics is done, it doesn’t feel deductive, it feels like rationalization; at least to me in most cases.

      To unpack the above a bit: I feel like a lemma or theorem “pops to mind” and then I have to work actively to find the deduction that justifies it. In other words, I rationalize it after I arrive at it. Very rarely do I arrive at a theorem by actively deducing from first principles and valid rules of inference and “stumbling upon” something useful. Of course, there are ways around this — ways that I often use in my description of what it feels like to do mathematics — like saying that my mind was working on the problem subconsciously, only notified my conscious of its progress when it found something cool, and now I have to reconstruct (or maybe remember, in homage to Plato) it’s deduction.

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