Man is a historical being : The realisations of the powers of human individuals living at any one time takes the cooperation of many generations (or even societies) over a long period of time. By contrast with humankind, every individual animal can and does do what for the most part it might do, or what any other of its kind might or can do that lives at the same time.

There are various ways you might define the common good, but that would be one way you could do it.

Man is a historical being : The realisations of the powers of human individuals living at any one time takes the cooperation of many generations (or even societies) over a long period of time. By contrast with humankind, every individual animal can and does do what for the most part it might do, or what any other of its kind might or can do that lives at the same time.

A political conception just applies to the basic structure of a society, its institutions, constitutional essentials, matters of basic justice and property, and so on.

I live in a country where 90 or 95 percent of the people profess to be religious, and maybe they are religious, though my experience of religion suggests that very few people are actually religious in more than a conventional sense.

The fairest rules are those to which everyone would agree if they did not know how much power they would have.

Now the good of political life is a great political good. It is not a secular good specified by a comprehensive doctrine like those of Kant or Mill. You could characterize this political good as the good of free and equal citizens recognizing the duty of civility to one another: the duty to give citizens public reasons for one's political actions.