It is true that science is based on axiomatic thinking. It started when Euclid laid down the foundations for Geometry (Euclid probably was more of an encyclopedic writer - the mathematics was done by other people). This inductive and deductive reasoning, along with
data from Brahe and theories of Kepler, was subsequently used thousands of years later with extraordinary success by Newton in his Magnus Opus, The Principia, to explain and predict the orbits of the planets. Science in its modern form was born.
You have turned upside down the reason this method is used to derive scientific truths. We use the method not to prove some
preconceived notion the way religion does. Instead, we lay down axioms as to how the world works. Notice this is based on observation, not by imposing our will on what is there and asking the Pope if this is what God says. We measure a lot of land, and notice that the hypotenuse is a square root. That is what Euclid did. Then, through some magic which
we don't quite know how or why it should work, using inductive and deductive reasoning, we are able to predict new phenomena that is nowhere to be seen in the axioms themselves. You are correct, that in some way it is circular reasoning in that we point to its own "atoms of assumptions" and means of arriving at truths in this mechanical form. But all methods of reasoning does this - it is called scaffolding. Religion does it too.
The biggest difference between science and other forms of inquiry is that religion is basically a small subject of philosophy. Because this philosophy is accessible to the general population, it is by definition, "popular". People think that science has some sort of war
only with religion. In fact, modern scientists think very little of
any philosophy when it comes to understanding the natural world [mind you, I mean philosophy in modern terms. In the old days, all subjects including Physics was a "Natural Philosophy" That is why a PhD is a Doctorate of Philosophy].
That science has chosen to distance itself from the other traditional forms of inquiry is not a conceit. It is because like its daughter subject of religion, philosophy in general is an endless "chase your tail endeavor" with no possible resolution. Religion feeds itself to the past. Science is a seed that gives birth to new insight and information, constantly pushing forward to the future. Imagine trying to discover the semiconductor that allows you to type on here with the methods of religion. How could it? It is stuck endlessly in the past, frozen in time.
Your argument is that science is also this "endless circular reasoning". However, there is a big difference. Science puts men on the moon, creates cure for cancer, gives us the semiconductor, the combustion engine, graphene, plastic, and the list goes on and on. All philosophy, and by extension religion, gives, is the KKK, Scientology, praying five times a day making sure you face east, 30,000 denominations of Christianity arguing which version of Jesus is correct, oppression of women, and on and on.
All science says is, I don't know and I learn by observing and applying mathematical principles to my observation. That anything I can do on this side of the universe I can give you instructions on how to duplicate and get the same result on your side of the universe. Pope, Allah, etc not included. That's it!
I will say this though. I do read philosophy, and I find science dismissal of much of philosophy to be detrimental. For example, even within science there are people that will tell you, don't philosophize about quantum mechanics - just compute. This to me is also wrong, and impotent and sterile thinking. In this thread and elsewhere, I have also stated that religion has a place in a humans life and that it can help us build a better life through encouraging hard-won ancient wisdom through
humanity's' psychological adolescence. Many scientist think this is wrong and that all religion should be abolished from our thinking. But I don't agree from a practical point of view.
