Verses 13-15 bring Paul’s argument on the practical level to a conclusion by appealing (1) to the reader’s judgment (verse 13), (2) to nature (verse 14), and (3) to Christian custom (verses 15-16; also in Jewish custom).

In verse 13 Paul’s appeal to the reader’s judgment recalls 10.15, “judge for yourselves.” This phrase may refer to judgment that is either “in your hearts” or “among yourselves.” Since Paul is addressing a community of Christians, “among yourselves” is more probable.

The opening words of verse 13, Judge for yourselves, show that the following question is not rhetorical, though Paul doubtless expected the answer “No.” Judge for yourselves may also be expressed as “I want you to decide for yourselves.”

Proper means “fitting,” “right behavior.”

Other translation models for this verse are:
• I want you yourselves to decide whether it is right for a woman to pray to God in public worship with no covering over her head.

Or:
• I want you yourselves to decide: if a woman prays to God in public worship with no covering over her head, isn’t she acting in a disgraceful manner?

Quoted with permission from Ellingworth, Paul and Hatton, Howard A. A Handbook on Paul’s First Letter to the Corinthians, 2nd edition. (UBS Handbook Series). New York: UBS, 1985/1994. For this and other handbooks for translators see here .