This is a mixture/edit of answers I've posted to the following questions on BH.SE:
Perhaps Paul didn't mean 'absolute silence at all times' in the churches
Paul permits women to speak elsewhere, and Paul must be read in harmony within the context of his entire letter to the Corinthians. Earlier in his letter, St. Paul exhorts:
...but any woman who prays or prophesies with her head unveiled dishonors her head—it is the same as if her head were shaven (NRSV).
The context of the verses in chapter 14 are also prophecy (specifically, weighing prophecy).
I have a few notes on various aspects of this text. I will begin with the second half of v. 33 since this is part of the same sentence in v. 34 (verse numbers and chapter divisions as we have them today weren't added to the text until the mid-16th century, so they should not be considered logical breaks in the text when interpreting the text):
- v. 33b. Paul's use of the phrase ὡς ἐν πάσαις ταῖς ἐκκλησίαις τῶν ἁγίων ("as in all the worshiping assemblies [churches] of the saints") makes it clear that the worshiping assembly at Corinth is not being singled out for this teaching; it is the practice of all assemblies at this time. We should not strictly interpret ἐκκλησία (ecclesia) as 'church,' because the literal meaning at this point in history was "a gathering of citizens called out from their homes into some public place, an assembly," and this did not always imply gathering for worship. It is very important to note that in 1st century Greek culture, it was customary for women to refrain from speaking in public assemblies (ἐκκλησίαις). It is also important to note that we should not equate early assemblies with 'churches,' and thus this is likely not a transcultural principle. We read our 3rd–21st century bias into the text when we interpret ἐκκλησία as 'church' (and when we refer to buildings in our communities as 'churches,' which would have been foreign to the original hearers, who did not consider ecclesia and synagogues to be an apt comparison).
- v. 34. The word for 'woman' and 'wife' is the same in Greek (γυνή). Because of the reference to husbands in v. 35, the word may be translated 'wives' here. But in passages governing conduct in assemblies like this (cf. 11:2-16; 1 Tim 2:9-15), the general meaning 'women' is more probable.
- v. 34. Total silence is not implied in other New Testament texts that use the verb σιγάω or the noun-form, σιγή (cf. Luke 9:36; 18:39; Acts 12:17; 21:40-22:2). Nor is absolute silence implied by the synonym ἡσυχάζω (noun form: ἡσυχία), cf. Acts 11:18; 21:14; 22:2; 1 Timothy 2:11-12. 1 Timothy 2:11 is a major point in this discussion because the author (likely not Paul) is making the same argument and yet uses the synonym that does not mean entirely silent. Thus the distinction between these two terms is largely a moot point in understanding this text. However, some scholars take the fact that Paul effectively makes this exhortation three times to mean that it is an absolute silence, which is worth noting.
- v. 34. In light of 1 Corinthians 11:2-16 which allows for women to pray or prophesy in the assemblies, the silence commanded here does not seem to imply the absolute restriction of women speaking in the assembly. Therefore some take "be silent" to mean not taking an authoritative teaching role, and others relate it to the preceding regulations about evaluating the prophets (v. 29). Here Paul would be indicating that women should not speak up during such an evaluation, since such questioning would be in violation of the submission to male leadership that is called for in Old Testament law.
And so it's possible that St. Paul only intended for women to remain silent during the evaluation of prophecy, which is the immediate context of this passage.
Paul may not have said this
Pauline authorship of the pastoral epistles is heavily disputed, and so using them as support that Paul made a similar statement in his epistle to the Corinthians is a moot point. These are the only other epistles containing such commandments about the role of women 'in the churches'. Even more interestingly, there is strong support that 1 Corinthians 14:33-35 is an interpolation (that is, a later addition to the text).
I am going to attempt to walk through the major literature in this discussion, which will be a lot of back and forth. I have linked to all the major works referenced, however not all of the articles and books are freely available online (some must be purchased).
Both Gordon D. Fee and Philip B. Payne are notable scholars who believe that 1 Corinthians 14:34-35 is an interpolation. Other scholars who hold this position include Straatman, Fitzer, Barrett, and Ruef. In his article entitled Fuldensis, Sigla For Variants in Vaticanus, and 1 Cor 14.34–5, Payne points out that
"...scribes in that period simply did not take the liberty to rearrange the argument of Scripture in this manner. We do not have even a single parallel example of a scribe rearranging the sequence of an original text of any of the NT letters to make it more logical. Furthermore, even if Bishop Victor felt he had the authority to rearrange the sequence of the text, there is no adequate reason why the text would make more sense reinserted at the end of the chapter."
In his article MS. 88 as Evidence for a Text Without 1 Cor 14.34–5, Payne claims that
"The evidence that ms. 88 was copied from a text of 1 Corinthians 14 without vv. 34–5 provides additional external support for the thesis that vv. 34–5 were not in the original text of 1 Corinthians 14."
Curt Niccum wrote an article entitled The Voice of the Manuscripts on the Silence of Women: The External Evidence for 1 Cor 14.34–5 that claimed the bar-umlauts themselves were added to the text at a later date and are thus not indicative of an interpolation, but rather of a paragraphos (marginal note).
Payne co-authored an article with Paul Canart entitled The Originality of Text-Critical Symbols in Codex Vaticanus where they argue their point based on new findings concerning the ink used in the Codex; from the introduction to the paper:
"The discovery that the ink of text-critical symbols in Codex Vaticanus matches the original ink of the codex breaks new ground for textual criticism. A scribe in the Middle Ages, apparently concerned with fading, traced over the original ink of every letter or word of Vaticanus unless it appeared to be incorrect. Thus, unreinforced letters and symbols reveal the original ink of the codex. The most obvious examples of the original ink are the few places its scribe inadvertently duplicated a word, phrase or clause. In these cases the reinforcer traced over only one of the duplicates, so the other reveals the original ink."
Payne and Canart make the case that this finding further proves that the original manuscript omitted 1 Corinthians 14:34-35.
Payne based some of his beliefs about these texts being an interpolation on the work of J. Edward Miller who had posited that various umlauts (distigmai) might have been an indication of scribal uncertainty concerning the authenticity of these passages. However, after Payne cited Miller's work, Miller wrote an article entitled Some Observations on the Text-Critical Function of the Umlauts in Vaticanus, with Special Attention to 1 Corinthians 14.34-35 to refute Payne's position, arguing that Payne misinterpreted his findings. Payne wrote a followup article in response to this entitled The Text-Critical Function of the Umlauts in Vaticanus, with Special Attention to 1 Corinthians 14.34-35: A Response to J. Edward Miller, where he makes the case that the bar-umlaut does indeed have a special meaning.
Further work was published in 2007 studying umlauts in Codex Vaticanus, although it is not specifically related to the text in question (but sheds light on it). Unfortunately the work was published in French (and I am not aware of an English translation).
In 2009, Payne published his book Man and Woman, One in Christ: An Exegetical and Theological Study of Paul's Letters which contains his most current thoughts and most compelling arguments for 1 Corinthians 14:34-35 to be considered an interpolation, along with his views on all of the other passages dealing with gender roles in Paul's letters. The book is very scholarly and does a great job considering multiple viewpoints, employing both historical-grammatical interpretation and textual criticism to make his points.
Despite Payne and others scholars' findings concerning distigmai in the text, conservative scholars still insist that this is insufficient evidence that 1 Corinthians 14:34-35 is an interpolation. Daniel B. Wallace summarizes this perspective in an article entitled The Textual Problem of 1 Corinthians 14:34-35, where he argues that despite the variance in where verses 34-35 are placed in the text, they must have been a part of the original text because they exist in all of the early manuscripts. Wallace makes the case that the Apostle Paul himself added the paragraphos.
In summary, there has been significant research conducted on both sides of this issue. Future work remains to be done concerning the meaning and dating of distigmai in manuscripts. Even so, the internal and external evidence for an interpolation is weighty and must be considered even at the present state of research into such manuscript features.