The category mistake: useful but tricky.

In the recent article about the lottery fallacy I talked about how to spot this fallacy but also how not to "overspot" it and start seeing it even if it's not there. Let's do the same with the fallacy known as the category mistake or category error. I decided to write this article after I read this recent article talking about a mistake some climate science doubters make. They say that it's premature to act on conclusions of climate science if those conclusions are not completely "settled". The article says this is a mistake and specifically a category mistake.

When I was reading it, I was in full agreement that it's a mistake: it's irrational to think we should wait until a danger is scientifically proven beyond doubt before needing to protect yourself from it. If you were 50% sure you just ingested deadly poison you would probably happily take the antidote! But the claim that it's a category mistake struck me as dubious. I did more research to double-check myself and my opinion solidified. But I also discovered something interesting: finding a correct definition of exactly what the heck a category mistake is may just well be impossible!

Look at what the Stanford Encyclopedia of Philosophy, a great resource on tricky concepts, says:

Category mistakes are sentences such as ‘The number two is blue’, ‘The theory of relativity is eating breakfast’, or ‘Green ideas sleep furiously’...

[one page later]

One might have expected this entry to start with a definition of ‘category mistake’. However, giving an explicit informative definition of category mistakes is no easy task. A typical dictionary definition looks like this: “The error of assigning to something a quality or action which can only properly be assigned to things of another category, for example treating abstract concepts as though they had a physical location” (Stevenson 2010). But such definitions are at best too vague to be useful, and at worst simply incorrect.

So it explains the idea of a category mistake by examples as opposed to a definition. But what is so difficult about giving a definition? For example, what is wrong with the one it quotes? The problem is that there are examples of sentences that fit the definition but are not considered category mistakes. For example:

1. "The number two is odd". This is just a false statement, not a category mistake. But it seems to fit the above definition: it assigns the number two, an even number, a quality (being odd) that nothing in the "even numbers" category can ever have.
2. "The king of the US is bald". The US doesn't have a king but it's again not a category mistake. However, the definition is satisfied: the sentence talks about the US as if it belonged to the category of monarchies.

So what's going on here? Maybe that particular definition is bad but others are better? Well, let's look at some others. 

From Oxford Reference:

A statement about something that belongs to one category but is intelligible only of something belonging to another category, as when the mind is referred to as if it were a physical entity.

From Cambridge English Dictionary:

A mistake in which something is said or believed to be in one category (= group) when in fact it belongs to another; a mistake in which something is said to have a particular quality, or be able to do a particular thing, that only members of another category (= group) of things can have or do.

From Wikipedia: 

A semantic or ontological error in which things belonging to a particular category are presented as if they belong to a different category, or, alternatively, a property is ascribed to a thing that could not possibly have that property.

Well, you get the gist, the picture is the same. These definitions are too vague, they don't exclude non-examples of category mistakes like "Two is odd" and "The king of the US is bald". So how are we supposed to identify category errors? From examples, just like we learned most words (in our native tongues). 

Thankfully, examples abound. Let's list some, from the same sources and some others:

• Two is blue.
• The theory of relativity is eating breakfast.
• (After seeing buildings, playing fields, classrooms on campus, and assuming "the university" is just another structure) That’s great that you showed me all these things, but you haven’t shown me the university yet. 
• Most Americans are over 15 minutes long.

These are very obvious cases, it's unlikely that somebody would actually make a mistake that obvious. Let's now look at more real-life examples:

• To treat atheism as a belief system alongside varieties of religious belief is simply a category mistake. (This assumes the common definition of atheism as a lack of belief in God, i.e. it's not in itself a belief in any proposition.)
• It is a category mistake to talk about a research programme as being falsified, because only theories can be falsified - research programmes can at most be discredited.
• To evaluate the efficacy of a product independently of [how it] is used is to commit a... category error... Educational products can’t be efficacious or not. Learning interventions [involving those products] can, though. 
• If philosophy is a sport, fretting over its lack of progress is a category error. (This relies on the debatable assumption that a sport is not the kind of thing that can experience progress.)

Can we now generalize from these examples? Can we articulate a standard for calling something a category mistake and make sure that standard doesn't apply to non-examples like "Two is odd" or "The king of the US..."? In case you want to create your own formulation, I'll put a "category-mistake-y" picture here and give you my version below it.

The key to all the examples, I think, is that they refer to statements (maybe implicit statements like beliefs) that are not just wrong, but unintelligible, nonsensical in a specific sort of way. The key phrase that they invite is something like: "That's not even the kind of thing that could...". 

For example, in response to somebody saying "You have shown me all the buildings on campus, can you now take me to see the university?" we could say: "But the university is just not the kind of thing you could be taken to see like another structure in addition to all the buildings." 

What about the pesky non-examples that spoiled the definitions we looked at before? With "Two is odd", can we say something like "That's not just wrong, two is not even the kind of thing that could possibly be odd"? Not really, that would be a strange thing to say, the statement is just wrong. 

What about "The king of the US is bald"? Can we say "The US doesn't just lack a king, it is not even the kind of thing that could have a king"? No, the statement is perfectly sensible, and in fact maybe in some parallel world the US does in fact have a bald king. 

We can summarize the definition I'm proposing this way:

Suppose we have a statement of the form "Thing X has property P". It commits a category mistake if it's justified to say: "It's not merely wrong, X is not even the kind of thing that could have a property like P".

Of course, as with any definition, there's always some degree of subjectivity. I am sure in some cases reasonable people will disagree on whether it makes sense to say "X is not even the kind of thing..." But that would not be a big problem, almost all concepts have borderline cases. 

Let me know in the comments if you agree with this definition or whether you came up with one you like more.