Though a deeply devout young man in his teens, Hamilton eventually settled comfortably into the deism and religious skepticism so common among the revolutionary generation. In a nutshell, deism was religion rationalized. Deists accepted that there was a God, but they gave him a much more limited role in the maintenance of the universe than more orthodox Christians.
According to the deist view of things, God was like a gigantic watch maker who made the universe, started it up, and then stepped back to let it run all by itself. Thus there were no miracles or any other manifestations of divine intervention. These were simply archaic superstitions that had long since served their purpose and had no place in a more rational, enlightened age.
As well as being a deist, Hamilton was also deeply distrustful of organized religion, seeing it as a potential source of tyranny. The established Church of England had been a staunch defender of what many Americans regarded as British tyranny in the colonies, so it was only natural that Hamilton should be suspicious of any kind of organized religion.
What really worried Hamilton most of all, however, was religious fanaticism, which he saw as a real and present danger to the stability and good order of society. He knew only too well how the most abominable crimes had often been carried out throughout history in the name of God.
As a considered response to such dangers, he proposed a free market in religion in which people would choose whichever faith was right for them, thus ensuring that widespread tolerance would become the order of the day. This, he hoped, would diminish the power and influence of religious fanaticism, thus allowing different faiths to rub alongside each other with the bare minimum of friction and mutual animosity.