for (Christian) marrying, it is essential that I should not be already married with a wife living, sane and "undivorced", and so on (Austin, 1962)
If "undivorced" implies married, what does that sentence mean?
Undivorced does not simply mean 'married'. It means never having been divorced.
To clarify, the following people are "undivorced":
The sentence refers to all the impediments to marriage which Christians must avoid for the marriage to be legal and binding. It gives illustrative examples (already having a wife, having an ex-wife, and being of sound mind).
There are two kinds of impediments to marriage. The examples in the sentence are all of the more serious kind, diriment (separating) impediments, which cause a marriage to be null and void in the view of the church. The other kind, prohibitory impediments, are those which do not nullify a marriage, but cause it to violate church law.
A marriage is null and void in the view of the church if, at the time of marriage, one of the parties is:
A marriage is also null and void if contracted without the blessing of the church or without witnesses, or if the marriage contract includes conditions which are incompatible with marriage (such as a promise of divorce).
A marriage violates church law if it violates:
A marriage also violates church law if one of the parties is a baptized Christian of a different denomination.
Basis in Semitic and Roman law
In brief, these impediments go back to Semitic and Roman law. Many can be considered social custom, but some arise from the Jewish religious view of marriage as an irreversible union of flesh:
Any union of the flesh creates a valid marriage in the eyes of God. This is why the Jewish law obliges a rapist to pay the bride price and treat the victim as his wife:
Denominational differences render some of these impediments moot. For example, some Protestant denominations do not sanction vows of chastity, establish an ecclesiastical calendar which prohibits marriage at certain times of the year, or prohibit interdenominational unions.
In The Bible Jesus at one point (Matthew 19:9) basically says that marrying a divorced person is no different than adultery. Based on this, many devout Christians don't (and particularly 50 years ago didn't) believe in the validity of divorce. As far as they are concerned, once you are married you are married until one of the pair dies, no matter what the state says.
So what this is saying is that the person in question would not be an acceptable person if they've been divorced.
The word undivorced here refers not to 'me' but to 'a wife'. After a wedding, the (hypothetical) person Austin married remains his wife lifelong. However, both civil and church law in 1962 allowed in certain circumstances for divorce, and for a marriage to be annulled in the case of incurable insanity (in which case of course she could not consent to a divorce). So it appears that Austin is drawing a distinction between married in the sense of 'having taken part in a wedding' (which might include widowers, those married to the insane, "and so on") and in the sense of 'in a state of Christian marriage'.
Without reading the book, I'm unsure whether he puts inverted commas round undivorced because the validity of divorce is questionable (as T.E.D. says), or simply because it was a neologism in the 1960s.