So, this question is inspired somewhat by Do we Need to help a baby learn to soothe itself? as well as my own experience with other people's children and my own.
Many mothers are reluctant to let their children cry at all, but there are times when a child just isn't consolable, there is sleep training that includes letting them cry and a host of times when a parent might just need to take a deep breath and a minute or two in order to regain patience for listening to a baby cry such as a colicky baby and step away for a bit to calm themselves. I generally felt that it was my job to teach my baby I was there for her and that meant responding in some way when she cried - even if my response didn't always stop the crying, but I don't remember reading anything that made me "know" that.
It seems to me there are a lot of beliefs around how much crying a baby should be allowed to do, or not. While I don't buy into this line specifically (considering it an old wife's tale), I've even heard, "let her cry, it'll help her lungs develop" from my mother in law.
What is actually known about when babies should be allowed to cry without consoling (I know sleep training methods all pretty much agree never before six months - but why six months and not seven? What is the developmental sign they are ready to cry a little without consoling?). Even then, for how long should they be allowed to cry? Are there scientific studies that show certain lengths of time at certain ages to either be helpful or harmful? What can a mother of a child that just can't be soothed be told in regard to how much crying is okay and how much is too much?