By presenting the anticipated outcomes before detailing the actual proposal, the speaker tries to win us to his side before actually going into the specifics, which he may suspect we will reject without due consideration. He talks about the sad sight of beggar women and their many children and how these women do not have the opportunity or time to procure gainful employment because they must care for these children. Thus, the reader feels sympathy for them, and the speaker points out what these women need to be useful: fewer children.
He writes, however, that his proposal will not only present a way to make the "children sound, useful members of the commonwealth," but it will "take in the whole number of infants . . . who are born of parents . . . as little able to support them as those who demand . . . charity in the streets." Therefore, his scheme seems to benefit not only those who have been reduced to panhandling but also those who are nearly as desperate. He also comments on the women who commit infanticide rather than bear the cost or the shame of having a baby out of wedlock. His plan, he purports, will solve this problem too.
The first thing the speaker actually says of his own plan is,
I shall now therefore humbly propose my own thoughts, which I hope will not be liable to the least objection.
In other words, he has anticipated objections to his plan and has attempted to remedy them, before they can even be voiced, by enumerating the wonderful outcomes of his proposal.