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Expediting organised experience: What statistics should be?

The above diagram is by John F. Sowa and it depicts a high level view of C.S. Peirce’s classification of the sciences of discovery (you have been warned). The dotted lines indicate what on the right should be informed by what is on the left.

I think there is a missing spot (or better an opportunity) for statistics in this diagram. Were and what should statistics be?

First, to quickly give a sense about the diagram, starting on the far left, Peirce construed mathematics as experimenting (manipulating) representations as representations, to discern what they purport (could be taken) to represent. That is discover their implications if taken as exactly true. A concrete example would be manipulating diagrams to learn about their inherent properties (e.g. moving around the lines depicting a triangle to prove the angles always add up to 180 degrees). More abstractly, it could be the contemplating of any aspect of any sort representation to learn only about the representation itself.

Moving to the right, under the philosophical branch, phenomenology is a discernment of what is present in consciousness. Peirce argued these are possibilities, necessities and construals (reflective inferences of varying degrees). Consciousness was argued as always being some mix of these three. Next to the right are the Normative Sciences of Esthetics, Ethics and Logic. They were discussed here. But to keep the focus here,  Esthetics was discerning what to value (grasping empirical “reality” being suggested as the best), Ethics how to deliberately conduct oneself to achieve what is valued and Logic how to deliberately think by representing empirical “reality” least wrongly and re-representing it without making it more wrong (e.g. truth preserving manipulations). Metaphysics was the discernment of “reality” as it most  generally could be so as to not misguide, block or hamper organised experience of the world as it is.

Finally the right most branch Empirical – which is the bottom line for most of us – being Organised Experience split into Natural versus Social Science.

What should statistics be and where should statistics be placed in this diagram?

Why not subtitle the Empirical branch with Statistics as the expediting of organised experience?

OK, taking charge of Natural and Social Science might be aiming a bit too high – but something to the right of Natural and Social Science but under Organised Experience with dotted lines to both.  Natural and Social Science should be informed by Statistics – right?

Now expediting (in the sense of encouraging better economy of research) could be the primary focus. That is guiding research efforts of empirical researchers and enabling them in ways that they will get less wrong in the long run. Is that not what the statistical discipline is or should be aspiring to be?


A more detailed but complicated diagram (for connoisseurs).

A review of a book long treatment of Peirce largely focusing on the diagram above.





  1. Mike Maltz says:

    Rather than look on statistics as a node, why not look on it as a path, uniting the mathematical with the empirical, with information flowing in both directions?

    • Keith O'Rourke says:

      I think statistics should be more than just math informing the organisation of experience (learning from observations).

      Rather I think it should be minimizing the hazards and maximizing the opportunities in the organisation of experience or at least empirical experience. There could be a loop going back to math as there should be minimizing the hazards and maximizing the opportunities of learning new things about abstract representations as well.

      Mostly I think a lot of important activity some statisticians engage that requires more than math and that has been increasing lately.

      At some point after other’s comment I’ll try to set that out with some examples.

  2. Terry says:

    Is there a reason why the lowest words in the graphic slope down from left to right? Why is Metaphysics lower than Phenomenology? Why are Social Sciences lower than Natural Sciences, and why are both lower than everything else?

    And is there supposed to be an optical illusion where Empirical appears to be lower than Philosophical and Mathematical?

    • Keith O'Rourke says:

      One would have to ask the artist (John F. Sowa) but my guess is that was just to allow for the dotted lines.

      Now the dotted lines perhaps should have arrows on them as being informed runs from left to right. I think it is pretty clear that normative science should not inform what is present to the mind (an ought does not inform an is) but should Social Sciences inform Natural Sciences?

  3. How intriguing. I will look at it more assiduously this weekend. I have a different conception, but hey that’s the fun of it.

  4. Thanatos Savehn says:

    Well, since it’s the internet and I (a lawyer and no scientist) get to vote I’ll channel R. A. Fisher and cast my ballot for “Mathematical”. What is an electron shell if not a mathematical construct? What is our perception of the fact that individuals examined collectively make heaps (h/t Sorites) around 0 if not a tease, a taunt, towards emergence’s predictability? A theory of variability more refined than “people/cancer/voting/whatever are like playing cards” would be huge.

    • Keith O'Rourke says:

      Not sure that is an accurate assessment of R. A. Fisher as he often railed about math and in particular mathematicians that did not have hands on research experience.

      Also his late reflections on design of experiments suggesting optimization was distracting from the more important task of making assumptions less critical and more likely to be true. Now, worrying about assumptions not being true to me is not really part of math as there you take assumptions as exactly true even if embedding them in layers (e.g. what happens if you assume linear but it is quadratic). This would also apply to checking assumptions.

    • Terry says:

      There seem to be a lot of lawyers and people in law-related jobs in the comments. Why? Extensive experience in identifying dishonest argumentation?

      • Keith O'Rourke says:

        > Extensive experience in identifying dishonest argumentation?
        Definitely an important skill for any statistician – especially if they are really trying to minimize the hazards and maximize the opportunities in the organisation of experience. Here in particular, drawing on many things from Social Science that one should not choose to disregard.

      • Thanatos Savehn says:

        Because we are tasked with making decisions. You cannot un-hang a man.

  5. Erin Jonaitis says:

    I kind of want Statistics to be connected to all three of the “head” branches in some way. I see the field as one that uses mathematics as a toolkit to operationalize the philosophy of science in a way that then informs the empirical sciences. I admit I don’t fully understand the layout of this diagram (and actually I seriously doubt that all of these dotted lines operate in only one direction in reality!) but I think that would put Statistics somewhere right of (informed by) Philosophy and left of (informing) Empirical Knowledge.

    • Keith O'Rourke says:

      Erin: > Statistics somewhere right of (informed by) Philosophy and left of (informing) Empirical Knowledge.
      That is where I would put it too informed by Math and Philosophy though mostly informed by the Normative branch of Philosophy (and I think Phil Dawid would want a meta-statistics added just the the left of statistics).

      > seriously doubt that all of these dotted lines operate in only one direction in reality!
      Agree (its not my plot) though I think one could distinguish the stuff on the right should not disregard lines coming from the left (i.e. in statistics you have to get the math right) whereas vice versus it can be disregarded (i.e. something from social science giving rise to a metaphor for physics that might be useful in some sense can be disregarded).

      p.s. being dyslexic I am taking a risk referring to right and left in the graph.

  6. Paul says:

    Statistics wants to be the field of Organized Experience itself. Its practitioners just don’t realize it yet. Hadley Wickham is proof that statisticians should be thinking about how to organize data and not just limiting themselves to (a narrow subset of) mathematical functions of random variables.

  7. daniel says:

    Statistics is a sub-branch of Metaphysics. P values of < 0.05 represent BEING. All others represent NON-BEING. Obviously.

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