"A Modest Proposal" is a satire couched in the kind of logical, scientific language used in publications by the Royal Society. Swift was profoundly skeptical of the value of many of the proposals emanating from Britain's leading scientific academy. He satirizes its work in Gulliver's Travels when Gulliver reaches Laputa, a society in which, among other things, absent-minded scientists conduct pointless experiments, such as attempting to extract sunbeams from cucumbers.
It's entirely appropriate, then, for Swift to use the rhetorical device of logos in the "Proposal," as this would've been how scientists of the Royal Society presented their findings. Examples abound:
The question therefore is, How this number shall be reared, and provided for? which, as I have already said, under the present situation of affairs, is utterly impossible by all the methods hitherto proposed.
This makes it seem that the author of the pamphlet has thought long and hard about the solution to this "problem" and that the proposal he's about to make will be set out with impeccable logic. Again, the tone of disinterested curiosity lends the proposal the necessary air of scientific respectability.
One of the elements of Swift's critique of scientific discourse is the way it turns human beings into objects to be studied, manipulated, and controlled. This process of de-humanization allows the author to resort to unflattering comparisons between poor women and breeding animals. This is an example of parallelism:
Men would become as fond of their wives during the time of their pregnancy as they are now of their mares in foal, their cows in calf, their sows when they are ready to farrow; nor offer to beat or kick them (as is too frequent a practice) for fear of a miscarriage.
Under the terms of the "modest proposal," men would come to value their wives as much as they would their animals, as their womenfolk would, by giving birth and selling their children for meat, contribute greatly to the household's prosperity.
But "A Modest Proposal" doesn't simply rely on cold logic to make its point. There's also considerable room for pathos, or an appeal to the emotions. The author wants to make it clear that he is motivated by the very purest of intentions in advancing his radical solution to such a seemingly intractable social ill:
These mothers, instead of being able to work for their honest livelihood, are forced to employ all their time in strolling to beg sustenance for their helpless infants: who as they grow up either turn thieves for want of work, or leave their dear native country to fight for the Pretender in Spain, or sell themselves to the Barbadoes.
The fact that such an appeal to the emotions comes in the very first paragraph is instructive. The author is trying to play on his readers' heart-strings, to soften them up in order to make them more amenable to the somewhat distasteful proposal he's about to put forward. If he gives this proposal a clear moral objective from the outset, that will make it more difficult for opponents to attack his ideas as the product of cold-hearted, dispassionate logic.