The Enlightenment
The renaissance and the protestant reformation opened the way to a reinterpretation of what Christians meant by God and a return to many pre-Roman, fundamentally Jewish values of early Christianity. By the time of Sir Isaac Newton, God is more firmly, or once again, revealed to be a divine architect or engineer who has designed His Universe mathematically, governed by the Laws of physics. Using mathematics Newton reveals that bodies are somehow attracted to each other at a distance by invisible forces that are proportional to their mass and decrease by the square of the distance separating them.
This is contrary to ‘common’ experience and understanding, where things need to be in physical contact to be pushed or pulled. Newton was criticised for hypothesising such an 'occult' invisible force but famously replied that on the contrary it was 'inferred from the phenomena (empirically derived), and afterwards rendered general by induction'... 'hypotheses non fingo' (I contrive no hypotheses). This gravitational force is be made apparent by the power of mathematics using data derived from direct observation; it is; it needs no further explanation.
Newton was an experimental physicist in the area of optics, but he derived his Laws of Motion, and demonstrated the existence of gravity, mathematically using pure reason, from Kepler’s Laws of planetary motion; in turn derived from the direct observations of Tyco Brahe.
A century passed in which Newton’s contribution was built upon and he was confirmed to be the most important figure in the history of Science to that time. Newton's concept that what appears to be so (when thoroughly analysed) must be so; even when contrary to conventional wisdom; became a central pillar in the philosophy of science.
By the application of these methods navigation and mechanics was revolutionised, astronomy became a true and important science, many natural events became predictable and new machines became possible. The World was opened to accelerated European exploration and discovery. Natural Philosophers were inspired to discover many additional Laws of nature and it became increasingly obvious that much that had been inexplicable and mystical had a natural explanation.
The age of empires brought with it another profound social change. Old laws were no longer adequate to deal with the governance of far flung empires or rapid technological and social change. A judiciary alone, traditionally administered by the upper classes or the Church, was incompetent to manage new social structures. An active legislature became more necessary and increasingly involved in law making. Old laws were re-examined codified and revised. The law was no longer handed down from God, or even administered in the name of God, but was secular and obviously man-made.
So by the time David Hume sat down to write he could show that there was neither any need to hypothesise a God to explain natural phenomena nor any sound argument for the existence of a God. But he did not assert that this proves that there is not a God.
He destroyed each conventional argument for God’s existence in turn. I will not reiterate these here - you can read Hume for yourself or if you would like a more contemporary version of the same arguments, read Richard Dawkins’ The God Delusion.
More devastatingly Hume questioned the evidence the Bible itself presents for belief: miracles and their sub-group, apparitions.
Hume uses two methods to dismiss miracles. First using logic: by defining a miracle as an event that is contrary to the Laws of nature; then by defining such a Law as something derived from consistent observation. Thus, a priori, a miracle is something contrary to observation.
But this purely logical dismissal is unsatisfying to those who believe in miracles. Moving to the a posteriori (evidential) Hume then points out that people are easily deceived and may exaggerate or be untruthful. People may mistakenly think that unusual but perfectly natural events; such as remissions from cancer or Alzheimer’s are miraculous.
Grand miracles like raising the dead; parting the seas; defying gravity; and so on; that deny natural laws would, if proven, destroy the validity of the relevant natural Law, which would then become nothing more than a generalisation. But these laws stand because there has been no convincing or substantiated evidence that this has ever happened. When laws held to be valid by natural philosophers (scientists) appear to have been broken this has always led, upon investigation, to reveal some additional natural law or principle at work. Scientific Laws are not absolute. Like a mirage, the closer you get to refuting them the less of a law they become.
This became a foundation of ‘scientific method’ and has later been refined by various empirical philosophers. I discuss this in more detail elsewhere.