This question has been interesting to research and has given me more insight into Galatians chapter 3, so I thank the OP for presenting it.
On page 231 of his book 'Beyond the Basics' (in the middle of no less than eighty-five pages of discussion on this very subject) Daniel B Wallace presents a flow chart which plots how to discover, in any particular context, how the Greek article is being used, under six headings : Simple Identification, Generic, Deictic, Monadic, Abstract, Par Excellence, Well-Known and Anaphoric.
I thoroughly recommend a study of the subject as the article is a very important factor in the translation of Greek into (particularly) English, since English (unlike both Hebrew and Greek) insists on having both a 'definite article' and an 'indefinite article' the latter causing all sorts of problems, conceptually.
I would point out just two simple issues, firstly, that the article names a concept by using a 'label' (which we call a 'noun') and in Greek often introduces that concept anarthrously (without an article) thereafter locating that concept (as the one previously identified) by using the article anaphorically. This makes abundant sense when we realise that the article is a development of the demonstrative pronoun ('this''that''these'those' etc).
And I would point out, secondly, that the article may be present in locating (not 'defining') either the whole body of Christ 'the church' or may locate a representative portion of the whole, 'the church', referring, say, to the church in Corinth.
Definitions are either taken for granted (by using a well known noun) or by discussion within the context of the text.
Locate - not define . . . . the whole or a representative part.
It seems to me that Paul uses the word 'law' without article in three places, first, making it clear that law as such (all law, any law, absolute law) is
-
- Not worked by the Spirit already received (verse 2)
-
- Not worked by He who supplies that Spirit (verse 5)
-
- Puts all who work under it - under a curse (verse 10)
Paul, having introduced the universal concept of law anaphorically then locates that law - by directing the reader to 'the book of that law'. And he advises, anyone who wishes to proceed with working that, that they must attend to 'all things which have been written in that book' . . . . to do them.
For the book of the law is the book that (and that only) fully expresses the obligations incumbent on any person wishing to justify themselves by legal means. No other inferior representation of law will adequately express the absolute requirements of law as such.
Paul then returns to law (no article, anarthrous) as such, law in its essence, law absolutely as a concept, and states, categorically and absolutely, that in law (or by law) it is manifestly apparent that nobody is justified with God for . . .
-
- The just shall live by faith (verse 10)
-
- That law (article, anaphoric) is not of faith (verse 12)
-
- The one who works these things shall live by them (verse 12)
-
- Christ has ransomed us from the curse of that law (article, anaphoric) having become curse for us (verse 13)
There are eight more references to law, five being anarthrous and three being anaphoric and I leave them to be discovered according to the above principles and according to Daniel B Wallace's explanations on pp55-206 of 'Beyond the Basics'.