It is interesting to note that the Federalist papers are unique, as shown in this paper, because of the extreme amount of thought that was put into the design of the Constitution, as shown in Madison's original thought process that were penned in 51. Many, if not most, changes in institutional design, occur as the reactions of shortsighted people to what they perceive as more-or-less short-range needs. This is one reason the Constitutional Convention was a remarkable event. The Founding Fathers set out deliberately to design the form of government that would be most likely to bring about the long-range goals that they envisaged for the Republic. What is most unusual about Madison, in contrast to the other delegates, is the degree to which he thought about the principles behind the institutions he preferred. Not only did he practice the art of what nowadays is deemed institutional design, but he developed, as well, the outlines of a theory of institutional design that culminated in this essay.
The synthetic proof proceeds by shewing that the proposed new truth involves certain admitted truths. An analytic proof begins by an assumption, upon which a synthetic reasoning is founded. The Greeks distinguished theoretic from problematic analysis. A theoretic analysis is of the following kind. To prove that A is B, assume first that A is B. If so, then, since B is C and C is D and D is E, therefore A is E. If this be known a falsity, A is not B. But if this be a known truth and all the intermediate propositions be convertible , then the reverse process, A is E, E is D, D is C, C is B, therefore A is B, constitutes a synthetic proof of the original theorem. Problematic analysis is applied in all cases where it is proposed to construct a figure which is assumed to satisfy a given condition. The problem is then converted into some theorem which is involved in the condition and which is proved synthetically, and the steps of this synthetic proof taken backwards are a synthetic solution of the problem.