In early America the very understanding of the word "oath" meant that the person taking it believed in God.

Oath: "A solemn affirmation or declaration, made with an appeal to God for the truth of what is affirmed. The appeal to God in an oath, implies that the person imprecates his vengeance and renounces his favor if the declaration is false, or if the declaration is a promise, the person invokes the vengeance of God if he should fail to fulfill it. A false oath is called perjury" [Webster’s Dictionary (1828)].

This understanding is reflected in how "Article 6" was explained in the ratifying conventions. For example, one may consider the words of James Iredell at North Carolina’s ratifying convention:

Wednesday, July 30, 1788
The North Carolina State Ratifying Convention

'According to the modern definition of an oath, it is considered a "solemn appeal to the Supreme Being, for the truth of what is said, by a person who believes in the existence of a Supreme Being and in a future state of rewards and punishments, according to that form which will bind his conscience most." It was long held that no oath could be administered but upon the New Testament, except to a Jew, who was allowed to swear upon the Old. According to this notion, none but Jews and Christians could take an oath; and heathens were altogether excluded. At length, by the operation of principles of toleration, these narrow notions were done away. Men at length considered that there were many virtuous men in the world who had not had an opportunity of being instructed either in the Old or New Testament, who yet very sincerely believed in a Supreme Being, and in a future state of rewards and punishments . . . (Mr. Iredell describes a British court case involving a man from India who was neither a Christian nor a Jew and then concluded) It appeared that, according to the tenets of this religion, its members believed in a Supreme Being, and in a future state of rewards and punishments. It was accordingly held by the judges, upon great consideration, that the oath ought to be received; they considering that it was probable those of that religion were equally bound in conscience by an oath according to their form of swearing, as they themselves were by one of theirs; and that it would be a reproach to the justice of the country, if a man, merely because he was of a different religion from their own, should be denied redress of an injury he had sustained. Ever since this great case, it has been universally considered that, in administering an oath, it is only necessary to inquire if the person who is to take it, believes in a Supreme Being, and in a future state of rewards and punishments. If he does, the oath is to be administered according to that form which it is supposed will bind his conscience most. It is, however, necessary that such a belief should be entertained, because otherwise there would be nothing to bind his conscience that could be relied on; since there are many cases where the terror of punishment in this world for perjury could not be dreaded' [Elliot, Jonathan, ed. The Debates in the Several State Conventions on the Adoption of the Federal Constitution as Recommended by the General Convention at Philadelphia in 1787. . . . 5 vols. 2d ed. 1888. Reprint. New York: Burt Franklin, n.d., Volume 5, Amendment I (Religion), Document 52, emphases mine].

The Establishment Clause: Why no Mention of God in the National Constitution?

Thomas Jefferson's 1802 letter to a group of Baptists of Danbury, Connecticut states that the purpose of the First Amendment was to build "a wall of separation between church and state." Yet what President Jefferson meant by this wall is patently obvious from the weight of historical evidence cited above: namely, that this did not mean that there could be no point of contact between church and state. Civil governments have all kinds of laws that churches must obey: building codes, fire safety codes and zoning ordinances. None of these violate the liberty of churches to worship God according to their own liberty of conscience. Furthermore, there are times when the members of ecclesiastical bodies are simply unable to decide issues without submitting to the judgment of civil courts. A prime example of this would be contentions over the ownership of the church's property.

Thomas Jefferson's phrase in 1802 must be understood in light of what he said in his “Second Inaugural Address,” in 1805:

"In matters of religion I have considered that its free exercise is placed by the Constitution independent of the powers of the General Government. I have therefore undertaken on no occasion to prescribe the religious exercises suited to it, but have left them, as the Constitution found them, under the direction and discipline of the church or state authorities acknowledged by the several religious societies" (emphasis mine).

According to Thomas Jefferson, the reason why God and Christianity are not mentioned in the Constitution of the United States is in order to allow the individual states to reflect their own peculiar religious perspectives: "the Constitution found" "religious exercises" "under the direction and discipline of the state authorities" (emphasis mine). There is, indeed, a profound "wall of separation" built into the Constitution, but that wall is not between the individual states and various religious bodies; it is between the Federal government, what Jefferson calls the General government, and the governments of the individual states. The Tenth Amendment makes this very clear: "The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people" ("Amendment X," The Constitution of the United States of America).

That this understanding is the only way correctly to read the Constitution is reflected in The Northwest Ordinance, (July 13, 1787) stated in Article 3: "Religion, morality, and knowledge, being necessary to good government and the happiness of mankind, schools and the means of education shall forever be encouraged." The United States Congress passed this ordinance during the time that the Constitutional Convention met (May 29 through September 17, 1787). This is the same Congress that approved the United States Constitution and sent it down to be ratified by the states.

That is why Justice Josiah Brewer could write on February 29, 1892, "Our laws and our institutions must necessarily be based upon and embody the teachings of the Redeemer of mankind. It is impossible that it should be otherwise; and in this sense and to this extent our civilization and our institutions are emphatically Christian" [Church of the Holy Trinity v. United States, 143 U.S. 457-458, 465-471, 36 L ed 226. (1892)].