Andrew Chapman wrote:What Payne is describing (see his first several examples) is negated parallelism. The fact that it is negated is more or less irrelevant.
οὐ γὰρ πάντες οἱ ἐξ Ἰσραὴλ οὗτοι Ἰσραήλ· 7) οὐδ’ ὅτι εἰσὶν σπέρμα Ἀβραὰμ πάντες τέκνα, ἀλλ’· ἐν Ἰσαὰκ κληθήσεταί σοι σπέρμα. [Rom 9.6b-7]
Even if οὐδέ were joining equivalent expressions here, as Payne claims, it hardly helps his case. Obviously, if two ideas are the same, then adding one to the other leaves you with just one. This isn't the same type of 'single idea' as he is arguing for in 1 Tim 2.12.
But in this text especially, they are not the same at all. The whole point of the following discussion about the seed of Abraham is that it was only one line that were the inheritors of the promises. Ishmael and Esau were excluded.
Right. And most of the first group ...
"1. οὐδὲ Joins Equivalent Expressions to Convey a Single Idea"
… don't qualify as "Equivalent Expressions". And if they did, it would not prove anything relevant to 1Tim 2:11-12 for the simple reason that the syntax doesn't determine the semantics. This is not rocket science. The structure made up of a sequence of particles OU|OUK|OUDE …. OUDE … ALL' or something similar doesn't tell us anything about the meaning of constituents between the particles.
The way Payne breaks the examples out into four groups reminded me of some classic treatments of biblical parallelism. Paul very frequently falls into a cadence in his rhetoric that imitates the poetic structures of the Hebrew scriptures.
Payne's first sample text (p237)
Rom. 2:28 οὐ γὰρ ὁ ἐν τῷ φανερῷ Ἰουδαῖός ἐστιν
οὐδὲ ἡ ἐν τῷ φανερῷ ἐν σαρκὶ περιτομή,
29 ἀλλ᾿ ὁ ἐν τῷ κρυπτῷ Ἰουδαῖος,
καὶ περιτομὴ καρδίας ἐν πνεύματι οὐ γράμματι,
οὗ ὁ ἔπαινος οὐκ ἐξ ἀνθρώπων ἀλλ᾿ ἐκ τοῦ θεοῦ.
The second statement expands on the first statement. It is not strictly equivalent. It is characteristic of Hebrew parallelism that the parallel constituents are rarely strictly equivalent, in as much as that defeats the purpose of parallelism. One certainly could argue that Paul uses parallelism to demonstrate a single complex concept. But that wouldn't help us much with the exegesis of 1Tim 2:12.
1Tim. 2:11 Γυνὴ ἐν ἡσυχίᾳ μανθανέτω ἐν πάσῃ ὑποταγῇ·
12 διδάσκειν δὲ γυναικὶ οὐκ ἐπιτρέπω
οὐδὲ αὐθεντεῖν ἀνδρός, ἀλλ᾿ εἶναι ἐν ἡσυχίᾳ.
The only thing parallel here is the use of an infinitive. Functionally γυναικὶ is the agent of διδάσκειν where as ἀνδρός is the patient of αὐθεντεῖν. So on semantic functional level this is not a parallel structure. If we understand οὐκ ἐπιτρέπω as assumed but omitted from the second line, this is common in parallelism, then perhaps we could see a somewhat complex sort of parallelism, but the agent-patient semantic roles are not in favor of that analysis.
None of this really matters for Payne's project. It is just an observation that cropped up tangential to the critique of this paper.
 Andrei Desnitksy, PhD., "Classifying Biblical Parallelism" https://www.dropbox.com/s/43mc92n9tjyyy ... cation.pdf
See also my previous quote on parallelism from Lee Irons, PhD.