day no. 14,551: in all the churches

1 Corinthians 11:3-5, 16
But I want you to understand that the head of every man is Christ, the head of a wife is her husband, and the head of Christ is God. 4 Every man who prays or prophesies with his head covered dishonors his head, 5 but every wife who prays or prophesies with her head uncovered dishonors her head, since it is the same as if her head were shaven. If anyone is inclined to be contentious, we have no such practice, nor do the churches of God.

1 Corinthians 14:33-36
For God is not a God of confusion but of peace. As in all the churches of the saints, 34 the women should keep silent in the churches. For they are not permitted to speak, but should be in submission, as the Law also says. 35 If there is anything they desire to learn, let them ask their husbands at home. For it is shameful for a woman to speak in church. 36 Or was it from you that the word of God came? Or are you the only ones it has reached? 

Whatever "prophesying" with her head uncovered is supposed to mean in 1 Cor 11:5 it certainly has to mesh with what is said later in chapter 14, which seems pretty absolute. Without exception. Concrete. Hard to work around. 

So we have to figure out what contexts he means this hard and fast rule to be applied. You can't apply this limp-wristed to any situation or you go against the clear, authoritative thrust of it. It is relentlessly clear. If 1 Timothy 2 is controversial in saying, "I permit no woman to teach or exercise authority," this possibly amps it up even more by saying "I permit no woman to speak" in church. 

And notice he says, "in all the churches" multiple times. This is not a Corinthian problem (or an Ephesian one for that matter) Notice that he appeals to things bigger and larger and more timeless like the Law and nature itself. He says it would go against the Law to have a woman speaking in this context. He says it is shameful for women to speak in this context. It goes against nature. It is repulsive or to borrow OT Law language (since Paul goes there) it would be an abomination. That is no small thing and I cannot see how it so easily gets disregarded merely because a few chapters earlier Paul infers that a woman who prophesies with her head uncovered should be ashamed, embarrassed, etc… He is using the same language in 1 Cor 11 (shame, nature, the Law of God in creation) to make the same case. And DO NOT lose sight of the fact that the point of 1 Cor 11:5 is not that women may be permitted to prophesy. That's not his point. His point is that whatever prophesying they do must be done under authority, under headship for any praying or prophesying that is out from under headship is shameful, embarrassing, against God and His angels, etc…

So if Paul implies that women are to be praying or prophesying a la 1 Cor 11:5 (granted it being in a manner that is veiled, covered, under authoity), then he also must be implying that they must not be praying or prophesying in church since it would require speaking. That is clearly prohibited by his comment a few chapters later 1 Cor 14:34. So it seems at the very least that in church or when doing "churchy" things or things that may be considered under an official church capacity, Paul is forbidding women to speak or exercise authority in those capacities.