In one of the first lectures in the syntax class I'm taking, the prof discussed this three way distinction found in Chomsky's Aspects. Chomsky claimed there were three levels of adequacy for any grammar: observational, descriptive, and explanatory. A grammar is observationally adequate if it tells you whether any given string of words comprises a sentence in the language. A grammar is descriptively adequate if it associates with each grammatical sentence a syntactic structure (not sure if it also associates a structure indicating why the string is not grammatical if it isn't). A grammar is explanatorily adequate if it explains why descriptive grammar works. Chomsky thought that syntactic theories should ideally meet all three levels, although they must only meet the first two. The first two certainly look easier, but I was a bit puzzled what made that the natural boundary. Looking at the levels of adequacy reveals a pretty natural reason. Observational and descriptive adequacy are the sorts of things that are naturally completed by an algorithm. They are clearly mechanizable. An observationally adequate grammar would be a program that took a string and ran through sentences of the language until it found the sentence or exhausted the sentences of the proper length. It would be the characteristic function of the set of sentences of the language. Similarly, the descriptively adequate grammar would build a syntactic structure for each sentence that the observationally adequate grammar told it was good. That's a bit more difficult, but still mechanizable. Explanatory adequacy crosses the boundary (barring some assumptions about the mind being a Turing machine) into what one wouldn't expect a program to do. It would need to bring in stuff outside the language the grammar is designed to describe. In particular, it would need to be able to cite (on a Chomskyan way of looking at things) universal grammar, parameters, language modules, and a host of other things about the ins and outs of language and linguistics. That'd require creativity on the part of a full blown artificial intelligence with a fair amount of world knowledge (that's an awful wastebasket phrase). Chomsky, rightly, thought it might be a bit demanding of the syntacticians to have their grammars do all that.