(CNN) -- As America celebrates its birthday on July 4, the timeless words of Thomas Jefferson will surely be invoked to remind us of our founding ideals -- that "All men are created equal" and are "endowed by their Creator" with the right to "Life, Liberty and the pursuit of Happiness." These phrases, a cherished part of our history, have rightly been called "American Scripture."

But Jefferson penned another phrase, arguably his most famous after those from the Declaration of Independence. These far more contentious words -- "a wall of separation between church and state" -- lie at the heart of the ongoing debate between those who see America as a "Christian Nation" and those who see it as a secular republic, a debate that is hotter than a Washington Fourth of July.

It is true these words do not appear in any early national document. What may be Jefferson's second most-quoted phrase is found instead in a letter he sent to a Baptist association in Danbury, Connecticut.

While president in 1802, Jefferson wrote: "Believing with you that religion is a matter which lies solely between Man and his God, that he owes account to none other for his faith or his worship, that the legitimate powers of government reach actions only, and not opinions, I contemplate with sovereign reverence that act of the whole American people which declared that their legislature should 'make no law respecting an establishment of religion, or prohibiting the free exercise thereof,' thus building a wall of separation between Church and State ... "

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The idea was not Jefferson's. Other 17th- and 18th-century Enlightenment writers had used a variant of it. Earlier still, religious dissident Roger Williams had written in a 1644 letter of a "hedge or wall of separation between the            garden of the church and the wilderness of the world.who founded Rhode Island with a colonial charter that included religious freedom, knew intolerance firsthand. He and other religious dissenters, including Anne Hutchinson, had been banished from neighboring Massachusetts, the "shining city on a hill" where Catholics, Quakers and Baptists were banned under penalty of death

As president, Jefferson was voicing an idea that was fundamental to his view of religion and government, expressed most significantly in the Virginia Statute for 

Religious Freedom, which he drafted in 1777.

Revised by James Madison and passed by Virginia's legislature in January 1786, the bill stated: "No man shall be compelled to frequent or support any religious worship, place, or ministry whatsoever, nor shall be enforced, restrained, molested, or burthened (sic) in his body or goods, nor shall otherwise suffer on account of his religious opinions or belief ..."

It was this simple -- government could not dictate how to pray, or that you cannot pray, or that you must pray.

Jefferson regarded this law so highly that he had his authorship of the statute made part of his epitaph, along with writing the Declaration and founding the University of Virginia. (Being president wasn't worth a mention.)

Why do Jefferson's "other words" matter today?

First, because knowing history matters -- it can safeguard us from repeating our mistakes and help us value our rights, won at great cost. Yet we are sorely lacking in knowledge about our past, as shown by a recent National Assessment of Educational Progress.

But more to the point, we are witnessing an aggressively promoted version of our history and heritage in which America is called a "Christian Nation."

This "Sunday School" version of our past has gained currency among conservative television commentators, school boards that have rewritten state textbooks and several GOP presidential candidates, some of whom trekked to Ralph Reed's Faith and Freedom Coalition conference in early June 2011.

No one can argue, as "Christian Nation" proponents correctly state, that the Founding Fathers were not Christian, although some notably doubted Christ's divinity.

More precisely, the founders were, with very few exceptions, mainstream Protestants. Many of them were Episcopalians, the American offshoot of the official Church of England. The status of America's Catholics, both legally and socially, in the colonies and early Republic, was clearly second-class. Other Christian sects, including Baptists, Quakers and Mormons, faced official resistance, discrimination and worse for decades.

But the founders, and more specifically the framers of the Constitution, included men who had fought a war for independence -- the very war celebrated on the "Glorious Fourth" -- against a country in which church and state were essentially one.

They understood the long history of sectarian bloodshed in Europe that brought many pilgrims to America. They knew the dangers of merging government, which was designed to protect individual rights, with religion, which as Jefferson argued, was a matter of individual conscience.

And that is why the U.S. Constitution reads as it does.

The supreme law of the land, written in the summer of 1787, includes no references to religion -- including in the presidential oath of office -- until the conclusion of Article VI, after all that dull stuff about debts and treaties: "No religious Test shall ever be required as a Qualification to any Office or public Trust under the United States." (There is a pro forma "Year of the Lord" reference in the date at the Constitution's conclusion.)

Original intent? "No religious Test" seems pretty clear cut.

The primacy of a secular state was solidified when the First Amendment was included in the Bill of Rights. According to Purdue history professor Frank Lambert, that "introduced the radical notion that the state had no voice concerning matters of conscience."

Beyond that, the first House of Representatives, while debating the First Amendment, specifically rejected a Senate proposal calling for the establishment of Christianity as an official religion. As Lambert concludes, "There would be no Church of the United States. Nor would America represent itself as a Christian Republic."

The actions of the first presidents, founders of the first rank, confirmed this "original intent:"

-- In 1790, President George Washington wrote to America's first synagogue, in Rhode Island, that "all possess alike liberty of conscience" and that "toleration" was an "inherent national gift," not the government's to dole out or take away

-- In 1797, with President John Adams in office, the Senate unanimously approved one of America's earliest foreign treaties, which emphatically stated (Article 11): "As the government of the United States of America is not in any sense founded on the Christian Religion, -- as it has in itself no character of enmity against the laws, religion or tranquility of Musselmen (Muslims) ..."

-- In 1802, Jefferson added his famous "wall of separation," implicit in the Constitution until he so described it (and cited in several Supreme Court decisions since).

These are, to borrow an admittedly loaded phrase, "inconvenient truths" to those who proclaim that America is a "Christian Nation."

The Constitution and the views of these Founding Fathers trump all arguments about references to God in presidential speeches (permitted under the First Amendment), on money (not introduced until the Civil War), the Pledge of Allegiance ("under God" added in 1954) and in the national motto "In God We Trust" (adopted by law in 1956).

And those contentious monuments to the Ten Commandments found around the country and occasionally challenged in court? Many of them were installed as a publicity stunt for Cecile B. DeMille's 1956 Hollywood spectacle, "The Ten Commandments."

So who are you going to believe? Thomas Jefferson or Hollywood? On second thought: Don't answer.