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I say again that there are a variety of points of view from which thoughtful and useful study of poetry can be made. Poetry is also a social document, and may be made use of by the historian, the moralist, the social philosopher or the psycho-analyst. Nor do I say that the critic should not be aware of these aspects. He is only required to know what he is doing.

My problem is that I don't know why the writer used "nor" introducing his second statement when the first one is not negative. So I cannot find out if the second statement is negative or not. Does he say that the critic should not be aware of these aspects? Or does he say the critic should be aware of them?

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    I just read it as Nor [contrary to what you might suppose, from what I've said so far] do I say blah blah. A very slightly quirky / dated alternative to [Contrary to what you might suppose,] I do not say blah blah. A sort of "literary flourish", if you will. – FumbleFingers Dec 20 '19 at 18:16
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    Does this answer your question? “Nor” following the positive sentence – Edwin Ashworth Jan 4 at 19:36
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According to https://guidetogrammar.org/grammar/conjunctions.htm

It is possible to use nor without a preceding negative element, but it is unusual and, to an extent, rather stuffy:

George's handshake is as good as any written contract, nor has he ever proven untrustworthy.

Regarding your specific questions . . .

Does he say that the critic should not be aware of these aspects?

No

Or does he say the critic should be aware of them?

Pretty much (or that it is okay for the critic to be aware of them). Of course, it is possible that the author didn't mean to say this; the original intention is difficult to determine.

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According to CGEL, the fact that the first sentence is not negative is characteristic of a relatively formal style. What the sentence expresses, most likely, is this:

For all I know, it could be permissible for the critic to be aware of these aspects.

Discussion

Here is what CGEL says about that construction (pp. 1309-1310); the example closest to yours is [51iv].

Nor with subject-auxiliary inversion

The following non-correlative use of nor differs from that in [50ii] [see below] in that nor is not here replaceable by or:

[51]   i  The Germans haven't yet replied; nor have the French.
         ii  He didn't attend the meeting, nor was he informed of its decisions.
        iii  He was one of those people who can't relax. Nor did he have many friends.
        iv  The hotel had good views and a private beach; nor were these its only attractions.

In this use nor introduces a clause (normally a main clause) and triggers subject-auxiliary inversion. Some speakers allow a preceding and or but (cf. %The Germans haven't yet replied and nor have the French), so that for them nor here is a connective adverb, like the neither that could replace it (... and neither have the French). For many,however, this nor cannot combine with and and but,30 and hence is again best regardedas a coordinator, though it very often occurs in sentence-initial position, as in [51iii].

This use also differs from that in [50ii] with respect to polarity. In [50ii] the first coordinate is within the scope of a negative; in [51] the first clause is usually negative, as in [i-ii], but in relatively formal style it need not be. In [iii] the first clause contains a negative but it is within the subordinate clause: the main clause itself is syntactically positive, though it has an obvious negative entailment, "He couldn't relax". In [iv], however, the first clause is completely positive.

30This is particularly so in AmE, but in other varieties too we find coordinator + neither much more often than coordinator + nor.

For completeness, here is [50ii]:

[50]   ii  a.  The change won't be [as abrupt as in 1958 nor as severe as in 1959].
              b.  No state shall have a share [less than 50% nor more than 70%].
              c.  Serious art is not [for the lazy, nor for the untrained].

How to figure out the meaning of your sentence

Here is how to see that the sentence in question,

Nor do I say that the critic should not be aware of these aspects.

expresses

For all I know, it could be permissible for the critic to be aware of these aspects.

Let P="the critic should not be aware of these aspects." Starting with the original sentence (Nor do I say that P), we proceed as follows:

[1] Nor do I say that P.
=
[2] I do not say that P.

Why doesn't the writer say that P? A fair interpretation is that what the writer is really saying is this:

[3] It is not known that P

And a fair interpretation of [3] is

[4] For all I know, it could be that not-P.

Let's now see what not-P is:

[5] not-P=Not[the critic should not be aware of these aspects]
=
[6] Not[for all x, if x is a critic, then x should not be aware of these aspects]

Now let

P1="x should not be aware of these aspects."

Substituting that into [6], we get

[7] not-P=
Not[for all x, if x is a critic, then P1]

Now we use the fact that

not[For all x, A(x)]=there is at least one x such that not[A(x)].

We get

[8] there is at least one x such that not[if x is a critic, then P1].

But

not[if A, then B] = A and not-B

Using that in [8], we obtain

[9] there is at least one x such that x is a critic and not-P1.

And what is not-P1? It is this:

not-P1=it is permissible for x to be aware of these aspects.

Putting not-P1 into [9], we get

[10] not-P=there is at least one x such that x is a critic and it is permissible for x to be aware of these aspects.

And, finally, putting not-P from [10] into [4], we get

[11] For all I know, it could be that there is at least one x such that x is a critic and it is permissible for x to be aware of these aspects
=
[12] For all I know, it could be that it is permissible for the critic to be aware of these aspects.

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