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Everything that can be said can be said clearly.

The title as many may know, is a quote from Wittgenstein. It is one that has haunted me for many years. As a first year undergrad, I had mistakenly enrolled in a second year course that was almost entirely based on Wittgenstein’s  Tractatus. Alarmingly, the drop date had passed before I grasped I was supposed to understand (at least some of) the Tractatus to pass. That forced me to repeatedly re-read it numerous times. I did pass the course.

However, I now think the statement is mistaken. At least, outside mathematics in subjects where what is being said is an attempt to say something about the world – that reality that is beyond our direct access. Here some vagueness has its place or may even necessary. What is being said will unlikely be exactly right. Some vagueness may be helpful here in the same way that sheet metal needs to stretch to be an adequate material for a not quite fully rigid structure.

Now, what I am thinking about trying to say more clearly at present is how diagrammatic reasoning, experiments performed on diagrams as a choice of mathematical analysis of probability models utilizing simulation, will enable more to grasp statistical reasoning better. OK, maybe the Wittgenstein quote was mostly click bait.

My current attempt at saying it with 4 paragraphs:

Grasping statistics more thoughtfully and more widely may be achieved by trying to understand experiments themselves more thoroughly. Experiments understood as making observations and making sense of them in terms of what to repeatedly expect in future observations. Now, as indicated above, experimental reasoning can be extended to include mathematics. That being the manipulation of diagrams or symbols taken beyond doubt to be true – experiments performed on abstract objects rather than chemicals – diagrammatical reasoning. An abstract diagram is made, manipulated and observed to understand the diagram as thoroughly as one can. It is simply a choice of method of mathematical analysis.
Now, probability models can be represented as diagrams and understood by experimenting on them by repeatedly simulating outputs from them. Given most statistical methods are based on probability models (though sometimes only implicitly) statistical methods are likely best grasped by that means. It is simply a choice of method of analysis.  So to more fully grasp statistical methods one needs to first fully grasp probability models. It’s all about sense making in statistics being formalized in assessments of what would repeatedly happen in some reality or possible world. That “what would repeatedly happen” is most explicitly defined in probability models.
Here, the proposed approach offers two advantages. The first being avoiding the need to learn formulas and their manipulations as well as rules for their use. The second being the ability to experiment with statistical methods in fake worlds where the underlying truth can be set and known. In this setting, the study of the performance of statistical methods and especially what to make of them might be easier to grasp. The intent is to enable some amount of do it yourself verification of statistical recommendations to avoid having to just take someone’s word for it.
No formulas will be required, just probability diagrams and repeated simulation. However, any real learning of something new is a painful struggle (there are likely biological reasons for that). One needs to develop an experimental attitude and persistent curiosity about how things really are. Devoting time to both defining more and more realistic like possible worlds. Using appropriate compositions of probability diagrams. Then gaining sufficient experience in these designed fake worlds where the truth is known. The challenge then becomes the application of that knowledge that in the real world where the truth is uncertain. That is transporting what is learned in the fake worlds to making sense of what is observed in this world.


  1. Adede says:

    Er… looks like one big paragraph.

  2. Christian Hennig says:

    “However, I now think the statement is mistaken.” Many think that Wittgenstein himself believed later that this statement is mistaken, as can be at least indirectly taken from his Philosophical Investigations. There are also quite varied readings of the “Tractatus”, including one that would take it as a development of a certain position that Wittgenstein was more curious about than that he held it himself. There is however hardly any doubt that he preferred, at least at the time of writing the Tractatus, statements about observables to speculative statements about “truths” that could ultimately never be checked.

    • Keith O’Rourke says:


      The quote was from Wittgenstein but just taken at face value. A post on Wittgenstein’s Tractatus and post Tractatus views would have been much longer.

      As a distraction, there is a nice discussion of Ramsey frustrations being saddled with supervising Wittgenstein’s thesis revisions in Cambridge Pragmatism: From Peirce and James to Ramsey and Wittgenstein

      So the distraction here is this confirmation bias by me to notice this excerpt from the wiki entry on Bayesian Probability

      “Ramsey and Savage noted that the individual agent’s probability distribution could be objectively studied in experiments. Procedures for testing hypotheses about probabilities (using finite samples) are due to Ramsey (1931) and de Finetti (1931, 1937, 1964, 1970). Both Bruno de Finetti[30][31] and Frank P. Ramsey[31][32] acknowledge their debts to pragmatic philosophy, particularly (for Ramsey) to Charles S. Peirce.[31][32]

      The “Ramsey test” for evaluating probability distributions is implementable in theory, and has kept experimental psychologists occupied for a half century.[33] This work demonstrates that Bayesian-probability propositions can be falsified, and so meet an empirical criterion of Charles S. Peirce, whose work inspired Ramsey. (This falsifiability-criterion was popularized by Karl Popper.[34][35])”

      So many more things to correct me on, than in this brief post ;-)

  3. jim says:

    It does not say:

    “whatever can be **KNOWN** can be known precisely and exactly and precisely and exactly expressed”.

    It *does* say: “whatever can be said can be said clearly”.

    I feel like your paragraph has a lot of philosophizing in it that’s confusing the point. The point is what you’re doing and why it works.

    Here, I’ll give it a try:

    Lots of people don’t “get” probability or the statistics that are used to describe it. This is a (bummer, problematic, unfortunate) because statistics and probability are increasingly widely used to explain the world we live in, and it’s important for people to understand how they work – and how they don’t work.

    Given most statistical methods are based on probability models (though sometimes only implicitly) statistical methods are likely best grasped by understanding probability models. Probability forecasts the range of outcomes – the variation of outcomes – if an given process is repeated over and over.

    One way to investigate how probability actually works is with graphical experiments rather than physical experiments. The graphical method can allow people to experiment and see the results without struggling with equations. In this scenario, the underlying truth is set and known, but the learner plays through the processes to see how data accumulates and get a feel for how data variation influence our perception of reality. The ultimate purpose is for the student to gain a conceptual understanding of statistics work so that conceptual understanding can be applied to real worlds situations.

    If I got something wrong please say so.

    • illiterate says:


      there’s nothing wrong with philosophizing. Actually the quote is not accurate as it’s a translation and not the full quote. The full quote is:

      Alles was überhaupt gedacht werden kann, kann klar gedacht werden. Alles, was sich aussprechen lässt, lässt sich klar aussprechen. (4.116)

      Everything that can be thought at all can be thought clearly. Everything that can be said can be said clearly. (Ogden, 4.116)

      Obviously this can’t be understood in isolation. Also note that ‘aussprechen’ can be translated more closely as ‘to utter’.

      • jim says:


        I agree, there’s nothing wrong with philosophizing per se.

        Why do you say: “it can’t be understood in isolation.”? To me it makes fine sense on it’s own. One of humanities biggest problems is that people read and hear things that aren’t and weren’t written or said and become confused and misinformed by what they thought was there but isn’t.

    • Keith O’Rourke says:

      Thanks – looks fine.

      To me there are important reasons to bring in the philosophical connections to better grasp the centrality of this type of experimental reasoning as an integral part of scientific reasoning which includes mathematical reasons.

      However, for an audience that will be turned off by that, your version is much better. Trust I can reuse it? If so, I credit anonymous?

      • jim says:


        If it’s helpful use it however you want. No need to credit. Nothing wrong with the philosophical discussion per se. Just one too many things going on there for me to sort out. I guess I wasn’t really that clear on it either. Perhaps a separate paragraph?

        • Again, thanks.

          Sometimes I have had a paragraph on the desirability of being clear on what scientific enquiry should be (appears like philosophy) and how statistics needs to support that.

          • jim says:

            I guess one way to work out any piece of writing that’s giving you fits is to outline it. The old fashioned game of topic sentence, supporting sentences, closing and transition really works, so if you can’t fit it into that format then you gotta tear it apart, sort out the pieces and rebuild.

  4. Olav says:

    There’s a quote by a different famous philosopher that’s appropriate here:

    “Our discussion will be adequate if it has as much clearness as the subject-matter admits of, for precision is not to be sought for alike in all discussions, any more than in all the products of the crafts.” –Aristotle

    • Olav says:

      The more extended quote (from the Nicomachean Ethics):

      “Our discussion will be adequate if it has as much clearness as the subject-matter admits of, for precision is not to be sought for alike in all discussions, any more than in all the products of the crafts. Now fine and just actions, which political science investigates, admit of much variety and fluctuation of opinion, so that they may be thought to exist only by convention, and not by nature. And goods also give rise to a similar fluctuation because they bring harm to many people; for before now men have been undone by reason of their wealth, and others by reason of their courage. We must be content, then, in speaking of such subjects and with such premisses to indicate the truth roughly and in outline, and in speaking about things which are only for the most part true and with premisses of the same kind to reach conclusions that are no better. In the same spirit, therefore, should each type of statement be received; for it is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits; it is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician scientific proofs.”

  5. Mendel says:

    Hmm, people may not have the time to say *everything* clearly that could be said clearly:

    A member of the Cabinet congratulated Wilson on introducing the vogue of short speeches and asked him about the time it took him to prepare his speeches. He said:

    “It depends. If I am to speak ten minutes, I need a week for preparation; if fifteen minutes, three days; if half an hour, two days; if an hour, I am ready now.”

  6. Michael Nelson says:

    Interesting parallel between summarizing the information in data as one or two numbers, and summarizing ideas you wish to express as words. If only it were as inexpensive to replicate your own (or others’) studies as it is to reiterate drafts of your own (or others’) writing. Put another way: Imagine if putting together a written passage took as much effort/money/expertise as conducting a study does. Then we’d have massive blow-ups between scientists over matters of pure composition. Rather than admitting their mistakes and retracting work that took months to complete, some people would stubbornly claim that, for example, knowledge really doesn’t start with a “k” or that sentences are more clear without verbs or that the word “yes” can be used to mean “no.”

    Andrew, the next time you criticize someone’s refusal to recognize and correct mistakes in their work, perhaps you should tell them: “Making up your own scientific rules when analyzing data is like making up your own grammatical rules when reporting data. Either way, your statements are meaningless.”

    • Michael,

      I think your matters of composition actually does apply to mathematical experiments. Various diagrams and manipulation of diagrams could be equivalent proofs a long with numerous symbolic implementations of the same proof. And some mathematicians do have blow ups over different styles of proofs. In fact, diagrammatical proofs were largely dismissed as “real” proofs until recently.

      • Michael Nelson says:

        Yeah, I remember reading about a controversy over symplectic geometry, where a famous mathematician had written a key paper that apparently only gave the outline of a proof, without sufficient detail for anyone else to follow. Later someone wrote papers to “correct” his, and he wrote papers to “explain” why he was right in the first place, and a fight over credit for the proof ensued. So yeah, just like some mathematicians seem to believe that following meticulous rules for communicating important ideas is not real math, many social scientists want to tell a story or advance a perspective and see the technical details as impeding that.

        The difference between the two fields, though, is that a proof is either correct or incorrect. But bad science isn’t just incorrect, it tends to also be unfalsifiable, which is then taken by the bad scientist as evidence of its truth. In other words, social science has a problem with ignorance of methodology that is compounded by a problem with ignorance of epistemology. Can diagrams be proofs? Sure, if you want them to be. What constitutes a proof is a social construct among mathematicians. Logic is malleable in a way that the physical world is not–just add an axiom. But the scientific method and all it entails are not just logically true, they’re empirically true, and the “rules” we follow have been carefully tailored to fit the real world (most of the time).

  7. Martha (Smith) says:


    At first reading, I thought your suggestion to Andrew was a good one. But after a moment’s reflection, I realized that someone who might be accused of “making up their own scientific rules when analyzing data” might actually think that they *are* using “standard scientific procedures” (“That’s The Way We’ve Always Done It), and that their critic is the one who is making up their own rules.

    • Michael Nelson says:

      Fair point. I was really just suggesting an original way to mock them. I actually think a better approach–if you’re trying to convince someone, not just hector them–is to say:

      “Either you are wrong about the consequences of conducting X analysis in Y way, or thousands of statisticians and methodologists, with all their proofs and simulations, are all wrong. If you’re going to stick to your guns and not correct your paper, you must believe you are the one who’s right, and certainly you must know *why* you are right and *why* they are wrong. In which case you have a moral obligation as a scientist to explain the rightness of your approach in a paper that you submit to a major quantitative journal. By setting the rest of us straight, you will have an immense impact not only on the field of statistics, but also on what thousands of social science students are taught every year, because we’ll have to rewrite all the textbooks to include your reasoning. In fact, if your shortcut analysis is just as rigorous as the preferred one, then you’ll be saving millions of dollars by reducing the complexity of studies. You will have done your duty as a scientist and you will be richly rewarded for it. If you are truly convinced that the way you were taught is the better way, what could possibly be stopping you?”

  8. Flaffer says:

    I would also add that WIttgenstein spent the latter half of his thinking time on refuting the Tractatus. Certainly he spent much time arguing that at certain points, language’ “spade is turned”. Vagueness lives in the places where language is used in a game it is not meant for and therefore is ambiguous. For a philosopher, this refuting of his early work is quite a unique intellectual journey.

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