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Non-Overlapping Magisteria (NOMA) is a philosophical world view that places religion and science in separate domains of questioning ("magisteria") in order to avoid one contradicting the other. NOMA hopes to provide an end to the conflict thesis between science and religion by establishing a demarcation.
Stephen Jay Gould popularized the designation "NOMA" in his book Rocks of Ages (1999). Gould hoped that the concept could provide a way to eliminate the conflict between science and religion by suggesting that both contribute to different areas of human existence and give meaning to life in different ways. He saw the two "magisteria" as so different that they could not inform, comment on or criticize each other: science based on methodological naturalism offers no insight into issues of what is morally right or wrong. Gould claimed that although science automatically assumes a lack of supernatural causation in its methods, it does not make any definite statements about the existence of the supernatural.
The idea is not entirely new; the twelfth-century Muslim philosopher Averroes used a similar concept. To fend off the fierce religious dogmatic criticism of Aristotelian schools, he proposed that science and Islam presented two different types of truth, one pertaining to nature, and one to the supernatural. Later thinkers, including Thomas Aquinas, vehemently rejected this concept.
The topic was revisited by Barbara Herrnstein Smith in her book Natural Reflections (2010) and by Stanley Fish in a review of the same. Smith discusses how both religion and science seek what she calls "underneath-it-all status", but states that one should not view the two as competing.
As with everything, just because it's the middle ground doesn't make it true.
The proposal is that science and religion describe entirely different things; science describes what is known and religion gives answers to what cannot be known. Moreover, people with faith may argue that science is a good explanation of what things like evolution and gravity are, but religion provides the answer for why they exist. Provided one isn't a biblical literalist or an antitheist, this may be an attractive position. An advocate of NOMA can be confident that their religious beliefs cannot be affected by the materialism of science, and in theory, science can be confident that supernatural entities cannot mess around with its work regarding the understanding of reality.
NOMA may help unite Metaphysical naturalists together with those who believe in religion and science against fundamentalists. Non-Overlapping Magisteria may have helped reconcile the Roman Catholic Church to evolution though this is disputed. 
Criticisms of NOMA
“”Science and religion are incompatible. Simply completely irreconcilably incompatible. And I can give you the bottom line message in case anyone needs to leave, and that is that; science and religion are incompatible in the same sense that the serious pursuit of knowledge about reality is incompatible with bullshit.
Problems with empirical investigation
In practice, NOMA is sometimes used as an excuse to try to make religious doctrines totally immune from examination. Religious individuals often feel that statements concerning empirical reality - such as the theory of evolution - that conflict with literal readings of religious work are overstepping the "bounds" proposed by NOMA. This is a little strange, because according to the doctrine, religion should never have made statements about reality that science could look at in the first place. Still, this often leads to NOMA being more of a "one-way street" in the sense that science is not allowed to examine miracles or prayer, but religion is still allowed to make claims about the material universe that would otherwise fall under the purview of science.
Where science has looked at the specific claims made and adhered to by Biblical literalists, such as the views regarding the origin of life, cosmology and so on, it has easily disproved the versions seen in the Bible. When such research has been done, NOMA-like views have been used to justify ignoring evidence that doesn't fit the religious worldview - this is the basic stance taken by Answers in Genesis and Creation Ministries International when dismissing hard evidence. Regarding the famously negative prayer studies it is often questioned whether religious persons would maintain their NOMA stance should the result have been positive; if NOMA says that science can't disprove religious ideas, then it certainly can't provide evidence for them.
Problems with ethics
Treating "sacred texts" that are clearly flawed in their understanding of the physical universe as unquestionable guides to morality is clearly inconsistent. Ethics without Religion avoids problems with Bronze Age and Iron Age religious texts. Advocates of NOMA - particularly religious ones - don't afford the same protection to scientific methods to be free from religious input, as such views are still allowed to comment on policies relating to scientific ethics, and essentially having a say on what science can and can't study legally. Issues such as stem cell research show a potential conflict.
One moral universal is that preventing harm is morally good while causing harm is morally bad. Science can make a large input in many fields into how harm is caused and how harm can be prevented. Therefore science is inevitably relevant to ethics.
The system itself has met with some resistance and harsh criticisms from figures such as Richard Dawkins (who suggests that Gould was straining to be apologetic when he proposed it), PZ Myers, Jerry Coyne and numerous other from the new atheist movement. These critics propose that questions such as the existence of God can be tested just like any other material hypothesis and that, in principle, even things that are "outside our universe" are still within the grasp of human understanding and the scientific method.
This is because most proposed gods' alleged effects on the material world are, of course, material, and can be studied much in the same way that all science really just detects real-world cause and effect relationships. In this sense, critics reject the "non-overlapping" aspect of the two magisteria and conclude that if the two genuinely didn't overlap, supernatural entities would have no effect on the real world and thus their existence, or not, is a moot point.
- Debate:Is Non-overlapping magisteria merely political correctness?
- Escape hatch
- Theistic evolution
- Templeton Foundation
- Clergy Letter Project
- Separate Spheres ideology
- Stephen Jay Gould. Non-Overlapping Magisteria. Natural History 106 (March 1997): 16-22
- Ursula Goodenough. The Holes in Gould's Semipermeable Membrane Between Science and Religion. American Scientist, vol. 87, no. 3, 1997.
- Must There Be a Bottom Line? Stanley Fish, New York Times Opinionator Blog
- Evolution and the Pope
- See Victor Stenger's God: The Failed Hypothesis for a comprehensive examination of this approach.
- The Fear of Religion, Thomas Nagel, The New Republic