Then again maybe the quality of Lincoln's literacy defies it.

What does it mean for two people to be "equal"? Obviously, it cannot mean they are equal in strength and in quality. There are people who are excellent, and excellent in many ways, and people who are mediocre or poor in quality in many ways. People are also morally diverse, ranging from the virtuous and the saintly to the thuggish and the depraved.

No, this equality is an equality of basic human dignity. It rests with human nature: our dignity is rooted in our rationality and freedom to make chose. Incidentally, this is also the basis for human rights.

Historically, however, most cultures did not believe in human equality or equality of dignity. You only see that with a robust account of natural law and in its fullness within the Imago Dei; living up to it is another matter. Liberalism [0], as an offshoot of this tradition, takes for granted this notion, but when pressed, it has trouble offering justification. That's why political appeals to equality now appear more frantic and strident. When there is an underlying uneasiness about the rational basis of one's convictions, this often transmutes into emotional defensiveness. But mere assertion has little force. Over time, emotion and pure assertion does not maintain its grip, which makes these quotes that much more interesting.

[0] Another fun case are materialists who simultaneously believe in equality. If there is anything that would dash the very notion of equality, it is materialism.