If someone doesn't believe in "the" theory of category mistakes

Question

There are actually a bunch of these theories (per the SEP entry).¹ But so suppose that one believed in no "ontological categories" at all. Or suppose someone were a skeptic about ontological categories, at least.

More finely still, suppose one can juggle levels of skepticism concerning the multiplicity of theories about why silly sentences aren't just silly, they're "category mistakes." For example, maybe one is less skeptical about the idea that there is a cross-contamination of semantic content than they are that there is a distortion of some sentence's alethic value. And so on and on... To the extent that some (possible) person (possibly) doesn't believe in the concept of "making category mistakes," is it even possible for that person to make category mistakes? I.e., no matter how silly their sentences, would any of them count as "category mistakes"?

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¹The initial historical matter pertains to Gilbert Ryle, who the article says first used the phrase "category mistake" in his anti-dualism treatise, not in reference to what Quine called "silly sentences," such that the article questions the connection between "silly sentences" and a semantic argument against dualism as such.

Answer 1

Category-Error equivalents across fields

It is remarkable to note that from Aristotle on and through Kant, fundamental categories has been a staple of philosophy but philosophy has not dealt with category errors quite as well as other disciplines.

First let me tabulate how the basic notion of ‘category error’ looks elsewhere:

Area	Name
Philosophy	Category Error
CS	Type Error
Logic	(non)WFF
Physics	Dimension error
Math	“Infinity error”
Rhetoric	Zeugma/Syllepsis

The short answer

This is to your title question from the CS world:

• Category mistakes are type errors if your programming language is syntactically typed; in CS jargon in statically typed languages.
• In dynamically typed languages there is no such typing and so no category errors. This of course makes (what would be) a category error into a different kind of error, often more problematic for the programmer/user.

Under the assumption that the above is not very intelligible to folks without a CS background, I expand on this a bit below.

Pauli principle

In response to a particularly garbled physics paper, Wolfgang Pauli said “(There is right wrong and) not even wrong”

A longer more detailed version runs: “What you said was so confused that one could not tell whether it was nonsense or not.”

Zeugma/Syllepsis

This is the lightest of the many fields but is an outlier because unlike all the others where it is unintended and undesired, here is is deliberately used for amusing effect:

• When he said, 'What in heavens', she made no reply, up her mind, and a dash for the door
  More here
• Miss Bolo rose from the table considerably agitated, and went straight home, in a flood of tears and a Sedan chair
  Dickens Pickwick papers
• The farmers in the valley grew potatoes, peanuts, and bored

Logic

What is going on here is that from Aristotle's excluded middle/non contradiction, through Boole and then Frege, logic has always been fundamentally binary. But that doesnt work in practice; sometimes we want to say More wrong than wrong!

Now you can if you wish flatten out your world into 2 saying everything that is not right is wrong. But this turns out to be way clumsier than it may appear.

Take logic. One could say eg.
P ∧ Q ⇒ P
is universally true (tautology);
P ∨ Q ⇒ P
is not. And
P ∧ ¬ P
is always false. But what about this?
P Q ⇒ P ¬∧

This is why logicians have come up with a ‘pre-pass’ to doing logic called WFF. We make sure we dont have just any symbol mishmash but a subset which has passed a syntactic sanity check. That sanity check is described once in the book/lecture and then assumed to always be cleared in all further discussions.

CS

CS has taken this to the most refined level in the model of the compiler pipeline.

And at every stage in the pipeline what is processed has passed the sanity check of the earlier stages. Using the logic WFF-paradigm at each stage a putative formula, which may or may not be well formed, the non well formed case is filtered out. IOW at every stage the universal set of formulas is subsetted to a smaller guaranteed not not-even-wrong set for the next stage.

Of these the type-analyse phase comes closest to philosophy category errors, although as pointed out above every stage can be taken to filter category errors, just that the categories are different at each stage.

Answer 2

You ask:

To the extent that some (possible) person (possibly) doesn't believe in the concept of "making category mistakes," is it even possible for that person to make category mistakes?

I believe Scott and Mauro's comments have generally answered the question, but it wouldn't hurt to flesh out the explanation. A category mistake is a theory in regards to natural language ontology (SEP). The particulars of the nature of a category mistake may vary from theorist to theorist, but the broad overview of the category theory, IIRC which comes from Concept of Mind, is the intuitive sense that one applies a rule for one language category to another. It is a semantic error in regards to an ontology, and is often reflected grammatically.

For instance, in German, one applies essen (to eat) to people: Die Leute essen. (The people eat.) This is in distinction to the use of fressen, which is used with animals: Die Schweine fressen. (The pigs feed.) It would be a misapplication for a foreign language student to use fressen with people. That would be a simple example of a category mistake. Of course, to a fluent speaker, it might actually be used to be an insult: Er frißt wie ein Schwein. (He eats like a pig, or less idiomatically, he feeds like a pig.) A similar relationship between nouns 'feed' and 'food' are observed in English.

What's important is that this rule is an objective error, and exists independently of a person's grammatical knowledge. Thus, when an exchange student commits this type of category mistake, the syntactic type, for instance, their awareness of their error is immaterial to it being committed. In this way, a category mistake presupposes a normalized version of grammar. On the semantic approach, however, one might ask, if the category mistake is rooted in a particular flavor of metaphysics, and the sentence is not overtly nonsensical, by what standard should an error be measured? This is why someone thinkers reject that "Colorless green ideas sleep furiously" is, strictly speaking, nonsensical.