How we cite our quotes: (Paragraph.Line)
Quote #1
Realizing that we cannot live unto ourselves alone, we have contributed of our resources and our counsel to the relief of the suffering and the settlement of the disputes among the European nations (1.6).
Coolidge knows that the world has become too interconnected for the U.S. to just sit back and watch other world powerhouses destroy each other and the world economy.
Quote #2
The physical configuration of the earth has separated us from all of the Old World, but the common brotherhood of man, the highest law of all our being, has united us by inseparable bonds with all humanity. Our country represents nothing but peaceful intentions toward all the earth, but it ought not to fail to maintain such a military force as comports with the dignity and security of a great people (5.5-6).
Sometimes appealing to people's inner moral compasses gets them on your side. Sometimes it doesn't. We can't know for sure how much Coolidge's "we are all people and should help each other" argument convinced his audience—the U.S. was planning to loan a ton of money to Germany to help them repay war reparations—but he definitely takes the moral high ground. He also argues here for having a strong military, even though he actually pushed for de-militarization in the U.S. and abroad.
Quote #3
We cannot barter away our independence or our sovereignty, but we ought to engage in no refinements of logic, no sophistries, and no subterfuges, to argue away the undoubted duty of this country by reason of the might of its numbers, the power of its resources, and its position of leadership in the world, actively and comprehensively to signify its approval and to bear its full share of the responsibility of a candid and disinterested attempt at the establishment of a tribunal for the administration of even-handed justice between nation and nation. The weight of our enormous influence must be cast upon the side of a reign not of force but of law and trial, not by battle but by reason (9.4-5).
This is a long-winded way of saying that Coolidge supports the U.S. joining the Permanent Court of International Justice. He stayed out of the League of Nations, but was okay with the court as long as it didn't limit American sovereignty. His use of the words "sophistries" and "subterfuges" suggests that some people weren't being entirely candid or truthful about the reasons for or against joining the Court.
Quote #4
We have never any wish to interfere in the political conditions of any other countries. Especially are we determined not to become implicated in the political controversies of the Old World […] We have not failed, nor shall we fail to respond, whenever necessary to mitigate human suffering and assist in the rehabilitation of distressed nations (10.1-2, 5).
It's true that the U.S., with its fairly isolationist platform, had generally avoided getting involved in other country's business, unless it saw some sort of tyranny. It's also true that Coolidge meddled with Latin American countries so much they almost passed serious anti-U.S. legislation. Apparently it's only the Old World politics that need to be avoided—the New World is up for grabs.
Quote #5
While there may be those of high intelligence who violate the law at times, the barbarian and the defective always violate it. Those who disregard the rules of society are not exhibiting a superior intelligence, are not promoting freedom and independence, are not following the path of civilization, but are displaying the traits of ignorance, or servitude, of savagery, and treading the way that leads back to the jungle (22.1-2).
Yeah, standards of political correctness were a bit different in 1925. There are always people who view civil disobedience or even anarchy as a sign that they're more enlightened than other rigidly rule-bound folks. Coolidge doesn't buy this one bit. He's a law-and-order guy right down the line.