I believe that Gilbert Ryle introduced the term "category mistake", but I am struggling to apply the term.
Could you please give me an obvious and less obvious instance of a category-mistake?
And if something is a "category mistake" then what does that tell us about how to think about it?
The most common category errors generally go by separate names with which most folks are more familiar. Included are things like
You can get the definition from the family resemblance between these examples: They involve lifting a property that needs a given context out of that context and presuming it has a value where it doesn't belong. Green ideas are not an oxymoron, they are a category mistake.
Anachronism is an example that is simple because it is so extreme. "When there were no clocks it must have been quite hard to catch a train." -- We are attributing modern intentions to ancient people, the need to catch a train is a property that those living before clocks just didn't have.
More subtle category errors common in our world right now include things like failing to see that faith in natural law is in fact faith because it is part of science and not religion or accepting success at Capitalism or some (other?) sport as the basis for one's judgment of someone's moral character.
A category mistake is when, for the ontology of any particular domain of discourse, an element of a set is unjustifiably excluded from the set.
An obvious example of this is the statement, "It is a time before time". Time cannot be before time because the extension of time includes the extension of every statement of something being before or after something else (i.e. every B-series statement) such that "a time before time" falsely excludes "time" from the extension of "time".
A less obvious example is the statement, "It is before time", however this statement has similar problems to the one before because it is to say, "It is at an earlier point in time than time." This falsely excludes a point in time from time, which is false by contradiction.
The SEP's article on category mistakes opens with a few good examples:
Category mistakes are sentences such as ‘The number two is blue’, ‘The theory of relativity is eating breakfast’, or ‘Green ideas sleep furiously’.
These sentences are incorrect in a fundamentally different way than the sentences '2+2=5' or 'The first president of the USA was Thomas Jefferson'. According the same article, the best way to recognize a category mistake is the fact that we react to them differently than regular, incorrect sentences.
In my experience, when one person accuses someone of making a category mistake during an argument, they are actual say something along the line of 'You are fundamentally misunderstanding such and such'. This is not really what a category mistake means though. Since the category mistakes are best identified by the fact they are instantly recognizable as incorrect in a weird way, no person making a sincere argument would make a category mistake. In my opinion, if something is not obviously a category mistake, it should not be labeled as such. For this reason, I cannot provide a "less obvious instance of a category-mistake".
A friend and I are arguing over queer theory. I have given the example below of a category error - though I am open to correction. I only read philosophy as an undergrad.
"One of the most notorious examples of Foucault's failure of integrity was his deliberate creation of a category error in an attempt to reframe the sexual element in rape and paedophilia as harmless. He claimed that we should judge a sexual assault only on the degree of its violence. It is not for a man to deny the reality of a survivor in finding that the sexual element makes the assault many times worse. Psychiatry, and society as a whole, were guilty of doing just that as a way of diminishing child sexual abuse for the first 70 years of the last century, because they were not prepared to deal with it."
I'm not surprised that you are struggling to apply the term "category mistake".
I think it is most helpful to focus on Ryle's use of the term. It is, as you say, how the term was introduced into modern philosophical discourse.
At the time he wrote, there was a widespread consensus that there was a clear distinction between correct and incorrect English (and for other languages, of course). That idea has been widely questioned and is now very much in retreat. So, as you have found, the term is now used in many ways, which do not correspond exactly to Ryle's use of it, and are not always particularly helpful. However, I do not think it is appropriate to rigidly classify all these uses as correct or incorrect by reference to Ryle's use of it.
You will find a useful article at Category Mistakes - Stanford Encyclopedia of Philosohy. This may not bring the clarity you are looking for, but will show how complicated this topic has become since Ryle wrote.
The best help I can offer is to look more closely at Ryle's use of the term, which is relatively clear.
Ryle was articulating a demolition of Cartesian dualism of mind and body. The key element in this theory is the claim that mind and body are different substances. For Descartes, this was a technical term, originating in Aristotle's metaphysics.
Ryle is adapting "category" which is another technical term, also originating in Aristotle. His philosophical programme was to return philosophy from the traditional forest of technical terms, including the technical terms of formal logic, to "ordinary language". But in this argument, his philosophical heritage is important to understand what he is saying.
Ryle's diagnosis of Descartes' mistake is that Descartes is misled by the grammatical similarity between the word "mind" and the word "body" into thinking that a mind is something rather like a body.
To make this clearer, we have to appeal to analogies. Hence his famous slogan about the ghost in the machine. Another famous example that he cites in the classic book "The Concept of Mind" is the visitor to Oxford who tours the city and sees the various colleges and the Bodleian library and so forth and then asks, "But where is the University?" This is a misunderstanding. There is no building that is the University. The University is the institutional organization of the buildings that they have seen.
The SEP article above shows how people have tried to articulate his idea in more detail. What you are grappling with is the complication and variety of ideas that have been produced by this process. It would have been good to have pinned his idea down, but I'm afraid that philosophy is not very good at producing that kind of answer, or rather it is very good at producing many answers.
A philosophical category mistake can be thought of as an ordinary category mistake on steroids. There's no philosophical problem about the mistake of putting tomatoes in the vegetable aisle, even though tomatoes are actually a fruit and belong with the apples and pears. But in philosophy, such mistakes promote misleading and unhelpful comparisons - even what is plainly nonsense.
