In their book on Davidson, Lepore and Ludwig suggest that when davidson says an expression E is a semantic primitive if "the 'rules which give the meaning for the sentences in which it does not appear, do not suffice to determine the meaning of sentences in which it does appear'", he means that:"someone who knows [these rules for how to use all sentences not containing E] is not thereby in a position to understand" sentences containing E.
Intuitively, I presume the idea is supposed to be something like this: "big cat" is not a semantic primitive, since you could learn its use just by hearing expressions like "big dog" and "orange cat" but "cat" is a primitive, since you wouldn't be able to understand this expression without previous exposure to sentences containing it.
However, I think this definition turns out to be rather problematic.
Firstly, by 'rules' Lepore and Ludwig later clarify that they don't mean consciously posited rules which we might have "propositional knowledge" of. So they don't mean something like "i before e, except after c". Rather, the relevant rules are supposed to be tacit, or unconscious.
So it seems like we can restate the criterion by saying something like:
E is a semantic primitive iff merely learning how to use expressions that don't contain E doesn't put one in a position to understand the use of E.
But now here's the problem.
-If "being in a position to understand" the use of E means being able to logically derive facts about the use of E then all words are semantic primitives. There's nothing logically impossible about a language in which there happens to be a special exception where, where by combine "big" and "cat" this means hyena rather than big cat.
- On the other hand, if "being in a position to understand" the use of E means being likely to use E correctly, this is a fact about about the relationship between a language and varying aspects of human psychology.
Here's what I mean:
Model someone learning a language as having a prior probability distribution over all possible functions pairing up sentences of a language they know with propositions, and then reacting to experience by ruling out certain interpretation functions, when they fail to square with the observed behavior of people who speak the relevant language. On this model, theories like Chomskian linguistics amount to saying that babies assign 0 prior probability to certain regions of the space of possible languages.
We can imagine a contiuum of logically possible distributions of prior probability, ranging from the foolhardy tourist who assumes that everyone is speaking English until given strong behavioral evidence against to the poet who feels sure he knows that a "fat sound" is the very first time he hears fat applied to things other than physical objects, to the anxious nerd who asks for examples of "fat" vs. "thin" sounds, to they hyperparainoid person who worries about the possibility that the combination of "fat" and "cat" might fail to mean a cat that's fat, just as the combination of "toy" and "soldier" fails to mean a soldier that's a toy.
Presumably actual (sane) people won't differ too much in their linguistic priors. [Though I wouldn't be surprized if babies and adults differed radically in this regard.]
But notice that being a semantic primitive turns out to have nearly nothing to do with the role of a word in a language. Rather it has to do with our cautious or uncautious tendency to extend examples of verbal behavior in one way rather than another. For the foolhardy tourist no English words are semantically primitive (on hearing a single word he comes to understand everything in one swoop) whereas all expressions are semantically primitive for the hyperparanoid person. Two people could learn the same language, and a word would be a semantic primitive for one of them, but not for the other.
Thus, so far as I can tell, the notion of 'semantic primitive' is incorrectly, or inadequately, defined for Davidson's purposes.
There's no limit to how complex a language a finite creature could "learn" on the basis of even a single observation. Whatever pattern of brainstates and behaviors suffice for counting as understanding the language, we can imagine a creature could just start out with a disposition to immediately form those, if it ever hears the sound "red". The only real limit on complexity of languages has nothing to do with learning, but rather with the complexity of the kind of behavior which competence with a given language would require. Our finite brains need to be able to produce behavior that suffices for the attribution of understanding of the relevant language.
Thus, I think, the claim that all human learnable languages have to have only finitely many 'semantic primitives' adds nothing but giant heaps of philosophical confusion and tortured metaphor to the (comparatively) clear and obvious claim that there have to be relatively short programs capable of passing the Turing test.