As a Latter-day Saint, I believe the restored gospel has truth. I also believe, though, that my understanding of the gospel is incomplete and inaccurate and has non-truth, ideas that are myths and folk-lore. As a follower of Jesus Christ, I am always attempting to distinguish truth from error and to refine my religious beliefs to be closer to a true understanding of God.
I also believe in science. I believe that science is a good and proper approach to the universe, to the cosmos. Scientists do not know everything about the cosmos, and they are continually forming hypotheses and conducting tests and making observations about the cosmos, to give them evidence to accept their hypotheses as fact, or to modify or discard their hypotheses when their ideas conflict with truth.
Both religion and science are trying to obtain truth. Scientists have an advantage in that they can observe and test the cosmos to obtain truth, while religionists can only form hypotheses but can not test those hypotheses in the same way that scientists can test their hypotheses. Does this mean that only scientists can gain truth? Not necessarily.
Religion concerns data that is based on faith. Science concerns data that is based on physical elements. The relationships between religion and science can be represented by two circles that intersect, as shown in the following diagram.
Let Set A in the diagram be religion and Set B be science. As the diagram illustrates, the blue area is the domain of religion that can not be observed and tested by science. This is the domain of god and of spirit. Scientists have no instruments that can measure energy that may radiate from this domain. I believe, and this is merely my personal belief, that the domain of religion involves matter, for Joseph Smith said that all spirit is matter but matter that is more refined and pure, that can not be observed by present-day scientists. The brown area represents the domain of science, the domain of the cosmos. The red area represents the domain of religion and science, the domain that can be discussed by both religionists and scientists. This is the domain that is involved in the science vs. religion aspect of our lives. Of course, the size and positions of the two sets is continually changing, such that the red intersection between the two domains is always changing.
I think it is foolish for scientists to speculate about the blue area, the domain of religion, because those scientists can not make measurements about the blue area, and thus are limited to philosophical discussions of that domain. It is fine for scientists to become philosophers in this regard, but they must remember they are not being scientists when they talk about the domain of religion.
I think it is foolish for religionists to speculate about the brown area, the domain of science. Religion is based on faith and on inspiration from God. If God gives no information about the domain of science, then religionists have no basis for their speculations about that domain.
But, the red area is interesting, because it is the domain of both religion and science. This illustrates to me the importance of science in interpreting religious statements about the red area. Science is a "filter" that can be placed on religious statements about the cosmos, including this earth.
Let me illustrate this with comments about the Book of Mormon. I grew up with a belief that the Book of Mormon is scripture, the word of God given to ancient inhabitants of the Western Hemisphere. I was taught and believed that the Nephites and Lamanites were the ancestors of all the native Americans. I believed that the Nephites and Lamanites lived everywhere on the North and South American continents. I believed that all artifacts of ancient peoples in the Western Hemisphere were from Book of Mormon peoples. Because my beliefs about ancient peoples of the Western Hemisphere were beliefs about peoples, customs, languages, and geography of real people, these beliefs were also subject to scientific scrutiny, thus placing these beliefs in the red area of the diagram given above.
As I've grown older, I've "passed" my beliefs through the "filter" of science, and this has caused my beliefs to drastically change. From science, I've learned that there were many people living in the Western Hemisphere prior to the migrations described in the Book of Mormon. I've learned that many, if not most, of the tribes of Native Americans have DNA that goes back to Siberia not to the near-east. I've learned that the artifacts and languages of ancient Native Americans currently known by scientists appear to have come from non-Book of Mormon people. Does this mean that I now believe the Book of Mormon to be false? No, of course not. My basic belief in the Book of Mormon is based on faith, that is, my belief in the book is in the blue area. I do believe that some of my ideas about the Book of Mormon are being disproved by scientists, and this is OK, because those ideas are in the red area.
I now believe, thanks to science, that the Book of Mormon people were a relatively small group of people, compared with the set of all people who have lived in the Western Hemisphere. Because they were a small group of people, their artifacts are limited in location, and I'm not surprised to learn that scientists have not found any of the artifacts or DNA of those people.
To summarize, I believe that the intersection between religion and science is relatively small and that the science vs. religion argument only applies to a small part of both religion and science. I encourage all of us to learn more of God through our faith and repentance and through obedience to his commandments. I encourage all of us to study science, to not consider science as a threat to religion, for it is through science that we gain most of our knowledge about the cosmos. I encourage all of us to use science as a "filter" on religious ideas that pertain to the physical cosmos so we can identify and remove false ideas from our religious beliefs and thus come closer to finding truth. Truth is truth and can not contradict itself. Truth in religion must agree with truth in science. Eventually, I believe the diagram shown above will be replaced by a diagram having just one circle that is red. When that happens, religionists will know all truth, and scientists will know all truth, and those two paradigms will be the same.