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Brooke Allen claims in her article “Our Godless Constitution” that America “was founded not on Christian principles but on Enlightenment ones.”  The Enlightenment is a term used to describe a period in eighteenth-century Europe and America when reason, coupled with advances in science, was declared to be the principal source of intellectual and moral authority. Ideas had to be argued rationally and demonstrated empirically to be true. The Greek philosopher, logician, and theoretician Aristotle (384–322 B.C.) was the model for an older worldview where often untested theories were promulgated as universal laws. It is unfortunate that up until the 15th century, a majority of scientists, church scientists included, adopted his untested theories and made them scientific and church dogma.
It would have been a simple thing for Aristotle and any of his later disciples for 2000 years to demonstrate empirically that objects of differing weights fell at the same rate of speed by actually testing the theory. Instead, Aristotle deduced and reasoned that different weighted objects should fall at different rates of speed.  He did a similar thing when it came to explaining our solar system. He reasoned that the earth was the center of the universe based on philosophical reasons. Each element has its “natural place” in the universe. The earth’s natural place is at the center. He further argued that the sun, moon, and planets were perfect spheres that revolved around the earth in circular orbits because the sphere and circle are perfect shapes. This geocentric—earth-centered—Aristotelian cosmology became part of scientific and religious dogma until the time of Nicolas Copernicus (1473–1543) and the publication of his De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres), published just before his death in 1543, and the later observations and writings of Galileo Galilei (1564–1642). But even after the publication of Galileo’s observations and findings, the scientific establishment had its reservations. Aristotle’s ideas seemed logical as they might seem logical to lots of people even today.
Aristotle’s physics is complex and differs greatly from what is now taught as science in our schools, but it would be a great mistake to suppose that it was therefore foolish or self-evidently wrong. . . . [T]he reader must remember that the majority of early-seventeenth-century astronomers were Aristotelians for reasons defended in logic and observation. 
Those who claim the Enlightenment was an overthrow of a Christian worldview seem to have forgotten that the scientific world had made Aristotle’s view of the universe the source of truth. Even scientists associated with the Church read the Bible through the writings of Aristotle. The battle the Church had with Galileo was because his new cosmology contradicted Aristotle! In reality, “it is the Christian world which finally gave birth in a clear, articulate fashion to the experimental method of science itself.” 
Before science as we know it today could get started in proposing theories, certain assumptions about the way the world works had to be understood to be valid and operationally consistent. These universal laws operated predictably because the majority of people—scientists included—accepted that they were God’s laws, established and upheld by Him, even if they did not know how the world worked the way it does.
It has even been suggested that such a view played a key role in the successful development of science in the Western cultures, and did so because they were influenced by the Judaeo-Christian tradition which fostered faith in the underlying rationality and orderliness of Nature during periods of history when human ideas were inbred by all manner of magical and occult notions. 
Life is predictable because God is predictable. Even those who did not embrace a biblical worldview knew that they could not develop an ordered world without the shared belief that God was necessary to make it happen.
In cultures where progress was made in mathematics, science, medicine, political theory, and law, people assumed that the world was not an illusion, that truth mattered, and man was a rational being created by a rational God even though at times man behaved irrationally and believed irrational things. Cultures that believed that spirits inhabited trees, rocks, and animals made very little progress culturally and scientifically because they never knew what the spirits might do. There was never a guarantee that what people did one day could be repeated on another day. The world was at the mercy of forces controlled by capricious gods who were always changing the rules. The Bible makes it clear that neither people nor things are controlled by impersonal forces. The world was created by God (Heb. 1:1) and is held together by Him in terms of physical laws that He established (Col. 1:17).
It’s true that many “Enlightenment thinkers rejected the idea that religion can be a source of truth, and believed instead that the application of reason to the evidences of the senses is the sole source of the truth.”  For them, reason was in, and the Bible was out. These early Enlightenment figures were not atheists; they were deists. Deists believe in God, but they do not believe in divine revelation or that God interacts with His creation. God can only be understood through the right use of reason and the study of nature. “A deist is described by the poet Alexander Pope (1688–1744) as a ‘Slave to no sect, who takes no private road, but looks through nature up to God.’”  Deists still needed God to explain the origin of nature, the predictability of the universe, the source of moral laws, and the way to account for the reasonability of reason.
In 1859, everything changed with the publication of Charles Darwin’s On the Origin of Species. The natural world is all there is, and it is always evolving. This view of the cosmos could hardly explain the order of nature or the origin and reliability of reason. Morality and personal rights could be situational, something our founding fathers rejected. And there was one more nagging problem: How does an evolved being with an evolved brain be trusted to reason rightly? Darwin saw the problem. “Darwin confessed ‘the horrid doubt . . . whether the convictions of man’s mind, which has been developed from the mind of the lower animals, are of any value or at all trustworthy. Would any one trust in the convictions of a monkey’s mind, if there are any convictions in such a mind?’”  C. S. Lewis said something similar:
If the solar system was brought about by an accidental collision, then the appearance of organic life on this planet was also an accident, and the whole evolution of Man was an accident too. If so, then all our thought processes are mere accidents—the accidental by-product of the movement of atoms. And this holds for the materialists’ and astronomers’ as well as for anyone else’s [thought processes]. But if their thoughts—i.e., of Materialism and Astronomy—are merely accidental by-products, why should we believe them to be true? I see no reason for believing that one accident would be able to give correct account of all the other accidents. 
There would not have been an America if the evolutionary worldview of Darwin had been around in seventeenth and eighteenth century America. There would not have been any “inalienable rights” since there would not have been a Creator to endow us with rights. The mind could not have been made free since the mind, given evolutionary assumptions, is nothing more than the random firing of electrical impulses among the synapses in the brain. There would not have been any protection of life or liberty since there is no way to account for inviolable moral laws that could have accomplished such a protection.