When is vagueness a virtue in science?

Like a lot of people, I think precision is a virtue in science. One sign of scientific progress is increasing precision, often but not necessarily expressed mathematically. For instance, Darwin got a lot right without using any math–but we’ve since learned a lot more about evolution than we could have otherwise by expressing Darwin’s ideas more precisely and mathematically. Or think of how the vagueness with which ecologists define “biodiversity” and “ecosystem function” leaves us vulnerable to critical scrutiny. Or think of how Bob May’s math undermined and corrected previous verbal intuitions about how “diversity” or “complexity” might relate to “stability” in ecology. Thereby forcing future ecologists working on that topic to quit waving their arms and instead say exactly what they meant. We need math because the consequences of our assumptions often can’t be worked out without math, and because our choice of words often misleads us in subtle but important ways. Some profound scientific ideas can’t even be expressed verbally, at least not without doing the math first.

So in the spirit of being contrarian with myself,* here’s a question: can vagueness rather than precision ever be a virtue in science? Vagueness is sometimes inevitable, such as when some new idea is first being developed. But is it ever desirable, so that we wouldn’t want to get rid of it even if we could?

Some smart people would say yes. For instance, here’s philosopher Ken Waters**, writing in 2013 about vagueness in the definition of “gene”:

What about biologists? What do they say when repeatedly pressed by philosophers to answer the question, ‘What is a gene?’ In my own experience, after being shown that their answers are vague, admit exceptions, or are ambiguous, biologists typically shrug their shoulders. Many quickly concede that they do not know exactly what a gene is. Reflective biologists add that trying to answer the question with the kind of rigor that philosophers demand would be
counterproductive. Progress in genetics, they say, has depended and continues to depend on “muddling through”. Science, they insist, would be stymied if geneticists were forced to agree on using a clear and unambiguous concept of the gene.

The example of “gene” hints at one kind of situation in which vagueness might be a good thing: some bit of biology is messy and complicated. There’s a range of cases that are obviously similar in important ways, but that also differ in various ways and it’s hard to pin down exactly which similarities and differences matter for what purposes. So rather than risk pinning them down in the wrong way, we muddle through with vague definitions. Although personally, I might describe such cases as cases in which vagueness is inevitable rather than advantageous. Or to put it another way, in such cases the greatest level of precision possible or reasonable may not be all that precise in an absolute sense (Peter Godfrey-Smith recently wrote about this in an evolutionary context). Put still another way, it’s not as if we ever want as much vagueness as possible–there’d be no point to defining genes as “molecular thingies that do stuff”. So whether you want to say vagueness is good rather than merely unavoidable probably depends on what baseline you’re comparing it to. I’d say the same about other vaguely-defined terms in ecology and evolution, like “species” and “ecosystem”.

It occurs to me that the best example of a usefully-vague term in ecology might be…[wait for it!]…”ecology”. Ecologists all share some interests, and it’s good for all of us to recognize those shared interests, even though they’re quite vaguely defined. Recognition of shared interests encourages us to see each other as colleagues involved in a shared intellectual project that’s worth pursuing. But if you tried to define those shared interests more precisely, you’d either end up with an empty definition (which is just vagueness by another name), or you’d end up with a definition sufficiently precise as to exclude some people whom everybody considers ecologists. I’m thinking for instance of Cooper’s The Science of the Struggle for Existence, a philosophical work framed around a search for the definition of ecology. As I recall, the definition Cooper ends up with basically defines ecosystem ecology as not ecology. I’m also thinking of various people who’ve defined ecology as “scientific natural history”, or otherwise emphasized the primacy or centrality of natural history or field work to ecology, in a way that defines me and Ben Bolker out of the field (I’m sure that wasn’t the intent***, but that’s the effect). Tyler Cowen has noted that many political unions and other partnerships are based on “creative ambiguity”.**** Perhaps the field of ecology is one such union.

Another way vagueness can be useful is by allowing an idea to draw greater interest and more research effort than it otherwise would. If progress depends on having a critical mass of people working on a problem, and if defining the problem too precisely (at least initially) would discourage lots of people from working on it, then maybe vagueness is a good thing. Of course, you can have too much of any good thing–a vague idea that attracts a lot of research interest is a good way to start a bandwagon.

One important distinction here is between vaguely defined concepts, and concepts that have various precise but contrasting definitions. As noted earlier in the post, “stability” is now an example of the latter, having previously been an example of the former. I don’t think it’s ever helpful to mix up different definitions of stability, or be vague about which definition you’re using. More broadly, I suspect there are various ways scientific ideas can be vague, and it’s probably important to distinguish between them. Maybe somebody needs to write the scientific equivalent of Seven Types of Ambiguity.

*For which this is the best illustration, given my credentials as a zombie fighter. 🙂

**A conversation with whom got me thinking about this. And as an aside, if you’re looking for philosophy of science to read and you’re interested in genetics and evolution, you should add some of Ken’s stuff to your reading list.

***At least I hope not! 🙂

****Such as academic departments. As Cowen writes:

We find the same in many academic departments.  Things can be going along just fine, but once the department has to write out an explicit plan for future growth and the allocation of slots across different fields or methods, all hell breaks loose.

24 thoughts on “When is vagueness a virtue in science?

  1. Wonderful post, Jeremy! Two quotes came to mind immediately as I read it:

    “Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.” -Archimedes

    “I think I can safely say that nobody understands quantum mechanics.” -Richard Feynman

    When I think of Archimedes, ecology, and my own journey through science (35 yrs & counting)- it really rings true concerning the “pure love” of mathematics. While its hard to know what Archimedes meant by this, as the language had very different contexts during the third century BCE, I have taken his utterances to mean COMMITMENT.

    Love is all about commitment- through thick & thin, good & bad, better or worse. I know for myself I did not have a love of mathematics until about 30 yrs into my career. It started out as a necessary evil, then became evil, and then at long last became a true love of mine. Patience, understanding, forgiveness, curiosity, anticipation, awe, compassion… and yes, love of mathematics are now very much a part of my work. We are united in our commitment to science.

    The lion’s share of ecologists I’ve worked with either had the view that mathematics were to be applied for what was already obvious concerning ones hypotheses, or that on rare occasion a click of the mouse button might, during a fishing expedition, reveal something really very kewl. So in my experience, for what it’s worth, most ecologists seem to avoid mathematics except when they are developing hypotheses or crunching data. Obviously folks such as you and I differ because of our theoretical underpinnings.

    My view of ecology as a whole is that it very obviously is a data/ statistics-driven endeavor. The numbers tend to be the name of the game. Yet, many of the folks I’ve collaborated with only had a “working man’s/ blue collar” understanding of mathematics. Just think about the litany of ecology publications where authors never bothered to check the basic assumptions of their test statistics. To me this is indicative of an avoidance of mathematics in the discipline. And so when I look at ecology as a whole, I get the sense it is at the stage of viewing mathematics as the “necessary evil”… as I did for many years early on in my career. Hopefully the field matures and finds a way for a greater commitment… for a true love of mathematics. I believe an era such as this, where the lion’s share of practitioners embraced the philosophy of Archimedes, would advance the discipline by light years.

    And speaking of light years… yes, vague concepts can be of profound impact. Quantum theory and nuclear power generators are proof positive of that. Show me an electron and I will nominate you for one of several Nobel Prizes… .

  2. As Jerry Coyne put it (Nature, 357, 289–290), species concepts are like barnacles on a whale. They retard progress; but not much. I think the same can be said of many of the ‘vague’ concepts you highlight in this piece. Making them more concrete is a difficult task and not one that will alter the overall trajectory of science.

    • So if we define ecology so as to exclude me, progress won’t instantly grind to a halt?! Um, actually you’re probably right. 🙂

      In seriousness, good point Markus. Will need to think more about it to see if I can think of any cases where vagueness seriously held back progress in ecology, or any other field.

      As an opening bid, could you argue that vague “good of the species” thinking seriously held back evolutionary biology’s ability to understand the evolution of many animal behaviors before G. C. Williams & co. came along? Where does vagueness stop and misunderstanding begin?

      • I wonder whether there’s a difference between vague definitions of entities (species, genes etc.) versus ideas (concepts, theories). As Darwin put it in ‘On The Origin…’, everyone knows roughly what they mean when they talk about a species. Uncertainty in the definition didn’t interfere with developing the theory. An ill-defined theory, on the other hand, would have gone nowhere.

      • “I wonder whether there’s a difference between vague definitions of entities (species, genes etc.) versus ideas (concepts, theories).”

        Hmm. I’m not sure there’s a clearcut distinction between “entities” and “concepts”. For instance, part of what’s vague about the “gene” concept is its physical referrant. So you might have a point, but first I’d want to see the distinction between “entities” and “concepts” fleshed out…

    • An excellent compendium of species concepts and their meaning/ usefulness is provided in: Species Concepts and Phylogenetic Theory: A Debate (Wheeler & Meier 2013). I found chapter 6 to be especially compelling as it concerns the evolutionary species concept (Wiley & Mayden).

      Mayden in particular has published several excellent manuscripts on this topic. Essentially, he asserts that “existing and revised versions of the integrated framework of species concepts all are not new species concepts, but versions of the evolutionary species concept, because they treat the evolutionary (or lineage) species concept as the concept for species category.” (Wiley, Mayden, de Queiroz, & Naomi 2011)

      I believe Mayden presents sound logic and objective reasoning in advocating for the evolutionary species concept. As described, I think it eliminates much of the vagueness you mention while providing a good working hypothesis with practical applications.

  3. The use of the word “biodiversity” as a broad, maybe vague, term is to my mind an advantage as it allows a lot of people from otherwise disparate fields (ecology, taxonomy, evolutionary biology, sustainability science, agriculture, forestry, medicine, etc.) to come together under a single umbrella and to begin to find common goals related to understanding and conserving the natural world. The problem lies when we try to use the word in a more prescriptive manner, especially when it’s considered synonymous with “species richness” or (even worse) “high species richness”. That’s the point at which people start to talk past each other and why I think “biodiversity” as a word is disliked by many.

    • “The use of the word “biodiversity” as a broad, maybe vague, term is to my mind an advantage as it allows a lot of people from otherwise disparate fields (ecology, taxonomy, evolutionary biology, sustainability science, agriculture, forestry, medicine, etc.) to come together under a single umbrella and to begin to find common goals related to understanding and conserving the natural world. ”

      So the vagueness of “biodiversity” serves the same purpose as the vagueness of “ecology”.

      “The problem lies when we try to use the word in a more prescriptive manner…”

      Isn’t this a little in tension with the idea that “biodiversity” brings us together around common goals of conservation? Because conservation surely is prescriptive. Or is the problem when “biodiversity” gets treated as synonymous with quite *specific*, and debatable, conservation goals like “high species richness”?

      • “So the vagueness of “biodiversity” serves the same purpose as the vagueness of “ecology”.”

        Yes, I’d agree with that.

        “Or is the problem when “biodiversity” gets treated as synonymous with quite *specific*, and debatable, conservation goals like “high species richness”?”

        Yes, it’s definitely that specificity that I’d see as (sometimes) a problem.

      • Where I have observed dysfunction as it concerns the use of the term “biodiversity” relative to conservation is that it can obscure many other relevant ecologic processes in discussions/ debates and application of protocols in the field. You are correct to point out that richness receives far too much attention- especially concerning restoration work.

        The frustration expressed by restoration ecologists is significant in this regard, I think because where it takes us in policy-related matters is a very bad direction. Increasing richness, for example, via active reveg or introductions of other taxa, absent repairs to the underlying disturbances simply provides a superficial and short-term solution that is doomed to fail over the long term.

        But it is also important to understand that at the level of policy, where you are working with non-scientists, can be a difficult bridge to erect. Communication is key, which requires we find ways to effectively communicate scientific concepts to non-scientists. This is our responsibility, not theirs.

  4. I think the key here is to figure out when vagueness helps or retards progress. Because there are definitely times when it does either. Most people seem to fall into one camp or the other (always helps or always retards), but I think it can do either.

    I think for the field as a whole, vagueness helps. For example, doing a keyword search or picking a symposium by having the word competition is helpful. I don’t want to just find people who think about these topics the way I do. There is a real ecological concept in there and like the metaphor with the blind men and the elephant, different lenses are more illuminating than a single lens.

    But I think when we start getting quantitative, we get into a lot of trouble. We retain our (helpful) vagueness and assume that different measures of competition are all comparable and say the same thing but they don’t. Just as an example within competition, the issue of whether effect on a neighbor should be normalized by the size of the impacting individual wasted years of fruitless debate because people were using different measures. Or when people talking about aboveground (light) and belowground (nutrient) competition ignored the fact that these two resources are fundamentally different.

    In short vagueness helps when we are doing vague things (finding people in our field) and hurts when we are doing precise quantitative models, meta-analysis, etc.

    • “In short vagueness helps when we are doing vague things (finding people in our field) and hurts when we are doing precise quantitative models, meta-analysis, etc.”

      I agree 100% with your specific examples. Still thinking about the general point. Not sure it’s always obvious when we’re doing a vague thing vs. a precise thing. Many philosophers would argue that there lots of non-quantitative situations in which precision is both obtainable and essential.

      • And some would argue that numbers don’t make vague things more precise.

        I agree with Brian that vague things should be left vague and precise things made precise; and with Jeremy that its often not easy to tell the diff

      • “And some would argue that numbers don’t make vague things more precise. ”

        Yes, that’s a good point, probably worth a post of its own. It’s common in the scientific literature for someone to propose a quantitative measure of a previously-qualitative and perhaps vague concept. Often, those proposing the quantitative measure will claim to have made the concept “operational” or “precise” or “measurable” or “quantitative”, thereby opening the door for more rigorous research based on the concept. When in fact, all they’ve done is disguised vagueness and imprecision.

        Arguably, the literature proposing and arguing over various indices of the “intensity” or “importance” of competition provides an example. See Rees et al. 2013 J Ecol: http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2745.2011.01946.x/full. UPDATE: Quoting from the final paragraph of Rees et al.: “Imbuing a term in common usage with an alternative technical meaning is a recipe for confusion and indeed much of the confusion in the literature is a simple consequence of not stating explicitly what competition is important to, or relative to.” I agree with their assessment of the literature on competitive “intensity” and “importance” indices, and I’m sure the same problem crops up in other contexts.

  5. In 1973(or maybe 1974) I took a graduate with the title Concepts of the Gene. A bit of a stretch for an ecologist, but very interesting to me. My take home lesson was that there were at least three main concepts of the gene. All of the concepts were useful in understanding genetics. I don’t think we would have a better understanding of genetics if any one concept was crowned the true gene concept. I guess you could always explicitly label which cocept you were using (transcriptional-gene), but I expect that it was pretty obvious from context. Maybe things have gotten more ambiguous since I stopped trying to understand molecular biology (approximately 1974 :-).

    Ecologists have always had a lot of interest in inventing words and arguing about definitions. I would guess that banishing vagueness and requiring precision would lead to spawning a large number of new terms with limited domains. And there would still be papers pointing out misuse of definitions stifling our otherwise sure progress.

  6. Vagueness is good in science communication with non-scientists. Your examples are all cases in point: gene, species, ecosystem. If you were trying to write a pop sci article or create a video to engage non-scientists, you’d be shooting yourself in the foot to get all persnickety on the mathematical definition that you had in mind for that particular piece of communication.

    • Good point, though I was thinking about communication with other scientists. Which raises the question: are there situations in which communication with other scientists is analogous to communication with non-scientists?

      Brian’s raised the example of bringing together scientists who have different perspectives on some broad topic. And perhaps in some venues, like a conference talk (or a blog post!), it would be counterproductive to be over-precise.

      Although I also think it’s important (or at least useful) to be able to let those with whom you’re communicating know that the precise, technical underpinnings are there. That’s what references and links are for. One annoying thing I run into sometimes when reading scientific papers is people who make some statement and then give a bunch of references, only some (or none!) of which actually support that statement. Vagueness with the *appearance* of precision is really pernicious, I think.

  7. Great post. I think ‘vagueness’ is a virtue, for ecology specifically. In other scientific disciplines, e.g. medical research, we would most likely be concerned if scientists were a bit ‘vague’ about what they were doing! But ecology is a science of uncertainty. Isn’t trying to be too ‘precise’ about ecosystems & interactions almost an insult to the complexity & contextual variability of nature? Sometimes it can also do more harm than good, i.e. the potential issues with overuse of causal language in observational/field studies that I wrote about a couple of weeks ago.
    Maybe working out when vagueness is good or bad depends on the context, i.e. where the vagueness stems from. Is it vagueness from ignorance or imprecision, or vagueness simply arising from inexplicable complexity? Have you ever tried to explain the meaning & usage of words like “the” “when” “there” etc. to a non-English speaker, especially one who doesn’t have equivalent words in their own language?

    • “But ecology is a science of uncertainty. Isn’t trying to be too ‘precise’ about ecosystems & interactions almost an insult to the complexity & contextual variability of nature? ”

      Hmm…On its face, I think that’s actually kind of dubious. For instance, you use the example of medical research as a field where even a bit of vagueness would be worrisome. But the human body is hugely complicated, and there’s lots among-patient variation in all sorts of relevant respects.

      As you say, whether vagueness is good or bad presumably is context-dependent–but it’s not easy to be very precise about that context-dependence.

      Re: inexplicable complexity, I have a couple of old posts on this. The first argues that, if ecology seems overly complex, well, that’s our fault and not nature’s. The second kind of pushes back against the first and asks if there are any ecological phenomena that are just too complex for us ever to really understand, drawing on an analogy to irreducibly complex chess endgames:



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