On Categorizing Errors of Reasoning

Anyone who is interested in self-reflection and rationality often grapples with categorizing errors of reasoning.  The motivation behind this is evident – to make sense of the myriad of mistakes we make, we must learn the patterns.  (Please see the list of cognitive biases for a good starting point, if you are not already familiar with it.)

Today I surprised myself with a realization about the type of categorization.  I will present my thesis after I present the context, followed by a visual metaphor.

I noticed, after several days of observation, that a certain individual, who I will call Gatsby, had made a series of errors.  They were:

  1. He failed to understand the distinction between general and specific.  When called on to provide a specific example, he simply rephrased his vague idea, believing that he had provided the example that was requested.
  2. He failed to notice sarcasm on several occasions where everyone else in the room picked up on the rhetoric immediately.
  3. He made a series of category errors, mistakenly identifying elements of one trend as belonging to another.
None of these errors were particularly attention-grabbing.  But I naturally began analyzing these errors and looking for a general category under which they fall.  I asked myself, “If I were Gatsby, what single error-making pattern might I have that would cause me to make these errors?”

Now I will take a quick detour for my visual metaphor.  Consider an archer, shooting arrows at a target far away.

The skill of an archer is measured by the distance between the target and the point that the archer hits.  A great archer will have striking points that cluster close to the target, whereas a bad archer will have striking points scattered all across the target (and off it entirely).

What causes an archer to miss?  Well, a great archer might miss for reasons that are somewhat predictable.  He may have misjudged the wind, or improperly calibrated his bow, or miscalculated gravity’s effect on the arrow, or possibly his arm was sore.  If you ask a expert archer why they fired a bad shot, he would likely be able to explain to you, with some amount of certainty, what mistake he made.

What causes a bad archer to miss?  It could be just about anything.  It will likely be a combination of many errors, including errors caused by the archer’s lack of knowledge on what he is even supposed to be doing.  If you ask a bad archer why he missed, he will likely have no idea.

At this point, perhaps you see what I’m getting at.  The structure of the categories of errors that people make differs widely between people.  When I analyzed Gatsby’s behavior, I assumed a certain structure for the categorization of his errors.  More specifically, I committed the mind projection fallacy, as I assumed that Gatsby’s structure for the categorization of his errors would resemble the structure of the categorization of my errors.

In this case, I have come to believe that Gatsby, at least in the context that I observed him, is a bad archer.  His errors do not fall under readily-identifiable categories.  Like the bad archer, if I asked him why he made these errors (after getting him to admit that he erred), he would likely not be able to explain their origin.  His arrows, in my opinion, were flying wildly away from the target.  I should expect at least as much difficulty categorizing his errors as I would categorizing the errors of a bad archer.  In fact, it will be much more difficult, as I can observe a bad archer setting up his shot, whereas with Gatsby I cannot see his cognitive process.  I only see the resulting striking points.  It is as if I had to identify the flaws of a bad archer by looking only at where his arrows land.

The general lesson I learned from this encounter is that I should be more diligent with my starting assumptions about a particular person’s structure for the categorization of his or her errors.  The better an archer I think they are, the more applicable a categorization schema is, and the more likely I should be to find the schema.  A great archer will occasionally miss the target for no apparent reason, but in most cases the error will be explainable, and similar to previous errors.

I will close with several responses to anticipated rejoinders.  Firstly, I will emphasize that I do believe I have the authority to deem others to be good or bad archers.  To the extent that they miss, and to the extent that they identify why it is that I miss,  I have sufficient information to determine their proficiency in archery.  Of course this process is error-prone, but it is still a very reasonable deduction for me to make.  Secondly, one might respond that we must mind-project to a certain degree in order to derive any theories of concerning the thoughts of others.  Without mind-projection, one could argue, we can’t postulate any structure for the categorization of the errors of others.  This is true; however, the extent to which you assume that other people think similarly to you can vary.  When I say I committed the mind projection fallacy, I mean simply that I overestimated the similarity between my and Gatsby’s thought processes.  Instead of asking, “What category of mistakes might I be committing, were I to have committed Gatbsy’s mistakes?”, I should have asked, “What category of mistakes might I be committing, were I to have committed Gatsby’s mistakes and have a similar intellectual framework to Gatsby?”  This latter question is much harder to answer, but crucial if we are to learn from the mistakes of others.

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One Response to On Categorizing Errors of Reasoning

  1. Jerry says:

    There is more to this than you improperly projecting your mind fallacy. You have, a priori, decided that even the bad archer has structure. You look to understand the structure of Gatsby’s reasoning errors. Too often there is no structure. Often reasoning is random and fickle. Reasoning is commonly unreasonable. The assumption of structure in Gatsby is your greatest error.

    Yes, you can analyze and explore the good archer because his structure is not a semi-solid glob of slime wandering this way and that. Good archers are few and far between.

    On the other hand, Gatsby got all the money but was still rejected because he was not born of good blood. In the end, all his wealth could not get him the acceptance that he wanted. Oh, wait, I think my structure just went back to high school literature. Sorry.

    More importantly, without using polar coordinates, how can I EASILY derive the surface area of a sphere from the area of a circle. I am running into the same problem as when I tried to derive the volume of a shpere. At least I now understand the derivation of the volume of a cone. I am far too lazy to find this on the internet or watch one of the calculus classes on Roku.

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