Can i get a great definition for "inference"?

What is the meaning of each underlined word in these excerpts from "a modest proposal" by jonathan swift? i think it is agreed by all parties, that this prodigious number of children in the arms, or on the backs, or at the heels of their mothers, and frequently of their fathers, is in the present deplorable state of the kingdom, a very great additional grievance; and therefore whoever could find out a fair, cheap and easy method of making these children sound and useful members of the common-wealth, would deserve so well of the publick, as to have his statue set up for a preserver of the nation. some persons of a desponding spirit are in great concern about that vast number of poor people, who are aged, diseased, or maimed; and i have been desired to employ my thoughts what course may be taken, to ease the nation of so grievous an incumbrance. the word prodigious means . the word desponding means .