Hi RBrown,
I would like to answer some of your questions here.
First, linguistics is part of humanities, like history or anthropology. Thus it is not exact science, like physics or chemistry. E.g. there may be several explanations to a historical event. Like, why did the first world war start?
Scientific explanation can be valid on three grounds. I remember two of them at the moment. The first one is that the explanation is true. That is quite self explanatory. The second one it that the explanation explains the data. This is what linguists are aiming at. We do not need to prove that something we assert is true, we only need to prove that it explains the data. If we get more data that does not fit the explanation, then we need to revise our explanation.
Explanations need to be falsifiable. Thus for example the notion of UG or universal grammar that we are born with, is a hypothesis that cannot be falsified, so it is not a scientific hypothesis.
The most simple explanation wins. If there are two competing explanations that both explain the data, the most simple explanation wins. For example, if there is one explanation that explains the word order in Spanish, and it has 15 rules and then there is another explanation that has only one rule, the latter explanation wins.
One interesting web page I found:
http://www.philosophypages.com/lg/e15.htm
Then to your questions.
1. Categories.
I understand that to mean verbs, noun, adjectives and the like.
The answer is that categories are based on form and distribution.
Form here means the internal structure of the words. Nouns can take plurals: cat, cats, ox, oxen. Verbs cannot: I looked at him, *I lookeds at him.
Distribution here means that nouns can function as the head of a noun phrase, verbs cannot.
A practical consequence of this is that in some languages there are no adjectives, instead they have static verbs. Thus the category adjective is not universal, i.e. it does not exist in all the worlds languages.
2. What is valid linguistic observation?
Linguistics, as all sciences, work on a spiral of inductive-deductive reasoning. Before one starts to analyse a language, one has some notions about languages in general and about the specific language in particular. That is the deductive part. Then one starts to gather data. Texts for example. When one analyses the texts, that is the inductive part. After analysing some texts, one creates hypothesis, which may be different from the notions one had before one started the analysis. When one has formed a hypothesis, one starts to check it. That is again the deductive part.
Thus from the beginning it is all valid. The question is, how probable it is that the hypothesis is valid for the whole language? it is possible to form a linguistic hypothesis from analysing one text. But it would be insane to claim that that is the final word on the language. Thus the validity of the hypothesis correlates with the validity of the data. The validity of the data depends on the quantity of the corpus, the quality of the corpus, the representativeness of the corpus etc. Text are the best data compared for example to elicited sentences. But one cannot analyse a language only based on texts. One has to have elicited data also. But texts must be the basis and foundation, not the elicited sentences.
Thus, if one has a valid corpus and the hypothesis i.e. the grammar is based on that corpus with the proper inductive-deductive method, then one has a valid linguistic observation.
As a practical example: is the actor focus in Philippine languages in fact anti-passive, or is it normal transitive clause? Or is the main category of Greek verbs aspect or tense? One needs to gather data from Philippine languages and prove one hypothesis and disprove the other.
3. How much can we know about language?
We can know as much about a language as we can know about history of the every day life of hunter gatherers in Papua New Guinea.
4. Does a linguistic observation make a difference in the lives of individuals?
If we think of Greek and Hebrew, we can say that understanding the Bible correctly is important to us. That is not possible without descriptive linguistics. James Barr's book on the The Semantics of Biblical Language (1961) was a good example of linguistic observation making a difference.
Also in translation, linguistics makes a real difference. People who do not know how language works cannot translate accurately or idiomatically.
5. Special problems with biblical languages.
The main problem is that we have no respondents to ask questions from. We cannot ask Paul, what did you mean with x?
Yours,
Kari