What are the relationships of Science to Philosophy and Religion?
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Philosophy and religion are subjective. You can argue your way to truth. It’s not provable via concrete proof; rather, it has to do with logic. It’s easier for people to interlace their emotions and biases in these subjects than in science (even though sometimes results are ambiguous and slightly open to interpretation).
You can also consider science as working against philosophy and religion. Evolution seems to be counter to ideas of creationism. (I don’t agree with this.) However, professionals in these arenas are sometimes at odds.
Science strives to explain reality
Philosophy strives to explain Truth (note the capital T)
And Religion strives to explain the way things should be (mostly how people should think and behave).
Of course there will be topics where the three areas have conflicting beliefs, but it is through careful and rational argument that scientists/philosophers/theologians come to any conclusions.