The limits of my language are the limits of my world.

3 June 2011


One of the many famous aphorisms that have been plucked out of Wittgenstein’s Tractatus Logico-Philosophicus is, “The limits of my language are the limits of my world” (“Die grenzen meiner sprache sind die grenzen meiner welt” section 5.6). Like much in the Tractatus, this gnomic aphorism invites interpretation and can never be exhausted.

One way to construe this Wittgensteinism very broadly would be to think of it as the limits of my idiom are the limits of my world, with “idiom” construed broadly to include any way of talking about the world, and not merely a particular language. If you’re of a continental persuasion, you could say the limits of my discourse are the limits of my world. It amounts to pretty much the same thing.

Particular theories about the world are idioms for talking about the world, forms of discourse, if you will. Scientific theories are scientific idioms for talking about the world. Now, scientific theories often broaden our horizons and allow us to see and to understand things of which we were previously unaware. But a scientific theory, being a particular idiom as it is, may also limit us, and limit the way we see the world.

The limitations we take upon ourselves by thinking in terms of particular theories or speaking in particular ways are human limits that we have chosen for ourselves; they are not intrinsic limitations imposed upon us by the world, and this, of course, is something that Wittgenstein wanted to bring to our explicit attention.

We very frequently mistake the idioms we employ, and the particular ways in which we understand these idioms, to constitute the very fabric of the world. When in this frame of mind we make claims for our theories that are not supported by the theories themselves, but rather reflect our particular, limited understanding of very difficult matters. This has been the case with the general theory of relativity and quantum theory, both of which are very young sciences, but which now dominate physics. Because of the dominant position of these theories, and of particular interpretations of these theories, we forget how young they are, and how far we have to go in really coming to an adequate understanding of them.

Our inadequate understanding of quantum theory, in particular, has been glossed so many times by physicists seeking to give a popular account of quantum theory that one might be forgiven for supposing that quantum theory is a form of mysticism rather than of science. (For example: “For those who are not shocked when they first come across quantum theory cannot possibly have understood it.” Niels Bohr) It is inevitable that, as our understanding of the world gradually and incrementally improves, much in quantum theory that now seems inscrutable will eventually make sense to us, rather than the theory being a mere systematization of a mystery.

A recent paper in Science by Sacha Kocsis, Boris Braverman, Sylvain Ravets, Martin J. Stevens, Richard P. Mirin, L. Krister Shalm, and Aephraim M. Steinberg, Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer, points to new ways of thinking and talking about quantum theory. Here is the abstract of the paper:

“A consequence of the quantum mechanical uncertainty principle is that one may not discuss the path or “trajectory” that a quantum particle takes, because any measurement of position irrevocably disturbs the momentum, and vice versa. Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles. We sent single photons emitted by a quantum dot through a double-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the result of a strong measurement of photon position in a series of planes. The results provide an observationally grounded description of the propagation of subensembles of quantum particles in a two-slit interferometer.”

There is a good article by Jason Palmer of the BBC, Quantum mechanics rule ‘bent’ in classic experiment, about the paper and its ramifications. Palmer writes that researchers, “say the feat ‘pulls back the veil’ on quantum reality in a way that was thought to be prohibited by theory.” If one wanted to go seeking headlines, one could say something dramatic like “Scientists break the laws of quantum physics” — you get the idea.

But what has been thought to be prohibited is in large measure a limitation upon the current language of quantum theory and, to a certain extent, an artifact of particular experiments. As more sophisticated experiments are conceived and conducted, we may someday know quite a bit more about quantum theory than has been thought possible to date.

In Palmer’s BBC story there is an excellent quote from Marlan Scully of Texas A&M University:

“The trouble with quantum mechanics is that while we’ve learned to calculate the outcomes of all sorts of experiments, we’ve lost much of our ability to describe what is really happening in any natural language.”

“I think that this has really hampered our ability to make progress, to come up with new ideas and see intuitively how new systems ought to behave.”

Progress in understanding quantum theory will, as implied by Scully, ultimately take the form of being able to discuss it in natural language and to formulate the theory in an intuitively perspicuous manner. We do not yet have the language or the concepts to do this, but each advance like the recent results reported in Science bring us a little closer, chipping away at the limits of our language that currently constitute the limits on our world.

. . . . .

Since writing the above I have learned that the method used in the experiment described is called “weak measurement” (as mentioned in the abstract quoted above) and has been employed in other recent experiments (as well as having been criticized quite harshly). I have written further on weak measurement in some comments on the paper Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment.

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8 Responses to “The limits of my language are the limits of my world.”

  1. […] The limits of my language are the limits of my world. ( […]

  2. Lyle Upson. said

    when I read this stuff, am I exercising my mind?

    • geopolicraticus said

      Hopefully so!

      Best wishes,


      • Lyle Upson said

        i note you have several essays that are of interest to my own work. I hope to soon refocus on your ecological temporality and maybe develop the ideas further if I can… (ha ha, time will tell)

      • geopolicraticus said

        Hi Lyle,

        Thanks for your encouragement. I hope to bring together my work on ecological temporality in a short manuscript, but I feel that I have not yet reached a level of rigor in my formulations that is appropriate. So I continue to work on these ideas, and have several more blog posts that I’m working on in relation to ecological temporality.



  3. anonymous said

    sooo who is it then??? cant they jus tell ya a simple answer goosshhhh

  4. walt paynter said

    Nick, you say “The limitations we take upon ourselves by thinking in terms of particular theories or speaking in particular ways are human limits that we have chosen for ourselves” Maybe. But unforeseen theoretical implications/deductions that may constitute limitations in subsequent thinking are not limits we have “chosen for ourselves”, nor are they “human limits”, rather I would say they are incidental logical/theoretical consequences of incomplete/inadequate reasoning. And “When in this frame of mind we make claims for our theories that are not supported by the theories themselves” needs revision/clarification because theories aren’t self-supporting unless they are tautologies. These caveats aside the main point of this article seems advocate Whorfianism and a Kuhnian view about the influence of paradigms on thinking and speaking, two highly contested views with which, however, I concur. Dissenters are usually those pushing for a physicalistic reduction of language and everything else social/cultural. However, Wittgenstein’s later work on “Certainty” and what Braver calls “Groundless grounds” suggests he later may have changed his opinions about the limits of language when he stressed knowing either “by doing” or as a presupposition of “doing” or “saying”.

    • geopolicraticus said

      Hi Walt,

      Thanks for your perceptive comments. If I were to write this over again now, or to write a longer exposition a bit more carefully, it is unlikely that I would make the sweeping claim that, “The limitations we take upon ourselves by thinking in terms of particular theories or speaking in particular ways are human limits that we have chosen for ourselves.” In spirit I still agree with this, but it needs emendation and qualification. Certainly some of our limitations are imposed upon us from without, while some limitations we have chosen for ourselves.

      That aside, in regard to, “unforeseen theoretical implications/deductions that may constitute limitations in subsequent thinking are not limits we have ‘chosen for ourselves,’ nor are they ‘human limits,’ rather I would say they are incidental logical/theoretical consequences of incomplete/inadequate reasoning,” I agree with the latter formulation, but incomplete and inadequate reasoning is a human limitation (perhaps not always one we have chosen), and the logic we employ in the exposition and development of a theory is the logic we chose for that theory. One of the great contributions of the rigorization of formal thought that began in the late 19th century was the realization that, along with stipulating our axioms (formation rules) we also need to stipulate our logic (transformation rules). Now, in ordinary physical theory most scientists don’t bother to stipulate the logic they will employ to derive their conclusions, but I think this will change over time, and it already began to change in the twentieth century when several quantum theorists began toying with trivalent logics. So even though I accept your formulation, I think I would still insist that human limits, some chosen and some native to the human condition, play a role here. Maybe not the dominant role, but still a decisive role.

      What I think I was trying to say by invoking what we say in a given frame of mind is that scientific theories (well, all theories when I think about it) can be entertained on a number of levels. There are rigorous formulations for formal occasions, off-the-cuff versions for informal occasions, popularized versions for speaking beyond the circle of communicants, and so on. We all know examples of scientists, mathematicians, philosophers, and others who give one version to sympathetic colleagues, another version to unsympathetic colleagues, and another version yet when writing a popular book. It is not unusual in expositions to sympathetic and popular audiences that one takes liberties and claims more for a theory than that theory strictly entails.

      Note that I wrote, “The limitations we take upon ourselves by thinking in terms of particular theories or speaking in particular ways are human limits that we have chosen for ourselves.” I take the qualification, “by thinking in terms of particular theories” to be important. To think in terms of a particular theory is to adopt a particular frame of mind, and this frame of mind is not permanent. We may enter it or leave it aside — hence the old joke about mathematicians being Platonists Monday to Friday and formalists on the weekends.

      I consider the later Wittgenstein an entirely different animal, and in using the earlier Wittgenstein to discuss the evolution of our understanding of quantum theory I am not making any generalizations about Wittgenstein’s thought on the whole. As you note, the later Wittgenstein, especially in On Certainty in which the paradigm case argument plays a prominent role, would involve an entirely different perspective on the limitations of thought and the relation of these limitations to our “world.”

      I’m not a dogmatic Kuhnian, and I don’t consider myself a Whorfian at all. That being said, I cannot object to your formulation in terms of, “the influence of paradigms on thinking and speaking.” There is an influence, the hard question is how much of an influence.

      I haven’t done justice to all the interesting issues you raise in your comment, but I will be thinking about them.

      Best wishes,


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