18th Century British-English - "Know not" vs "Don't know"

Solution 1:

Robinson Crusoe, which was published in 1719, includes the phrases:

He was now grown old, and had left off going to sea, having put his son, who was far from a young man, into his ship, and who still used the Brazil trade. The old man did not know me, and indeed I hardly knew him. But I soon brought him to my remembrance, and as soon brought myself to his remembrance, when I told him who I was.

I knew I had been here now almost eighteen years, and never saw the least footsteps of human creature there before; and I might be eighteen years more as entirely concealed as I was now, if I did not discover myself to them, which I had no manner of occasion to do; it being my only business to keep myself entirely concealed where I was, unless I found a better sort of creatures than cannibals to make myself known to.

It seems that know has fairly 'modern' uses too:

I had, God knows, more sincerity than knowledge in all the methods I took for this poor creature’s instruction

As you can see, the traditionally archaic 'She doth know' isn't actually relevant - I couldn't find 'doth' in Robinson Crusoe. As Spagirl points out in the comments below, admittedly these examples aren't directly proof of your 'She doesn't know me either', but hopefully shows that language was still relatively similar to modern usage.

_{Worthy of note is that the social class/upbringing of the speaker is extremely significant, as is the origin. You may want to check other, more appropriate books in which case.}

Solution 2:

"A New Grammar, English and French" (1734) includes

He doesn't know me

as a 'familiar phrase' in translation, suggesting that "doesn't know" is perfectly normal conversational phrasing for that time.

One of Jane Austen's letters (LXIX, 1813) includes the sentence

I am not known to her by name, however.

So perhaps: I am not known to her, either.

Solution 3:

After reading the answers and comments that others have offered, I’m a bit confused what you’re asking. Your question seems to be about where the negation belongs in the statement, not about replacing the word “know” with some synonym, as suggested by several people.

Anyhow, I looked around 18th-C. English literature and found no hard rule. The word “know” is sometimes used to indicate that people know each other, but occasionally synonyms are used. The contraction is sometimes used, and sometimes avoided. And different degrees of fanciness of expression occurred in the 18th Century, just as they do today.

I have no special experience with this issue, but just my general sense of the way language sounds, plus a bit of research included below. But to me, some of the suggestions in your question sound strangely out of balance; “either” seems to indicate one of two considerations, and supplying both of these might help a reader follow you more easily. But the following sound to me like possible 18th Century constructions.

• I know her not; neither does she know me.
• She neither loves me nor even knows me.

Moll Flanders, by Daniel Defoe, offers the following examples.

• 'I tell you,' says he again, 'she is a wife and no wife; you don't know what I am, or what she is.' 'That's true,' said I; 'sir, I do not know what you are, but I believe you to be an honest man…
• 'You don't know that neither,' says the brother.
• 'You don't know those sort of people, child,' says she;
• At last I resolved to go to my old governess, and acquaint myself with her again.

Gulliver’s Travels, by Jonathan Swift, appears to contain no instance of “n’t.” It offers the following examples.

• … neither did I know any artist in that country so nice and exact, as would undertake to make me another
• … neither do the most learned know what sort of mortals inhabit beyond those mountains…
• … for I soon began to be known and esteemed among the greatest officers…

And from The Spectator, Vol’s 1 To 3, by Addison and Steele:

• I don't know but it might be exactly where the Coffee-house is now.
• I do not know whether I have observed in any of my former Papers
• .. an old Acquaintance of mine, a Person of Worth, whom I would have bowed to in the Pit, at two Yards distance did not know me.