There are various other definitions of philosophical naturalism, but the common core is the rejection of the need or cogency of supernatural explanations for natural things and events.

Some naturalists have been deists, e.g. by prefering the second of the given definitions, and by holding there is or may be a god, but his existence is not necessary to explain anything in natural reality.

This Philosophical Dictionary has been written from a point of view that is naturalistic, indeed in both senses of 'naturalism' given. 

One important reason for this position is that so extra-ordinarily much that has been explained and achieved by science, including the enormous amount of scientific technology that is currently involved in the lives and possibilities of everybody who is alife, is completely lacking from all holy religious books, religious texts, communications by religious prophets, etc.

If there is a benevolent, allpowerful, omniscient deity (or deities), then why did he in his goodness and wisdom not supply a cure for cancer, spina biffida, polio, leprosy, or any of the other awful medical ills that have afflicted mankind for so many centuries and have produced so much human pain and misery? And if there is a god, why is there no decent physics, chemistry, bio-chemistry or mathematics to be found in any of the statements attributed to him?

Another important reason for this position, that is related to the previous point, comes in two moves.

First, all the religious believers agree on one thing: That all religions except their own are mistaken, and therefore believe in something that is, properly speaking, fiction or fantasy. Why not extend that position to all religions instead of all but one: All religion - until proved otherwise, by a logically valid argument with true premises - is (at best) fantasy, inspired by fear, wishful thinking or would be false authorities? 

Second, why assume more than is necessary to explain nature? Nearly all men have agreed that there is a natural reality, made up of living and dead things, and that they are part of this natural reality. And the last several centuries have shown, and proved this in so far this is possibly by a working technology based on scientific understanding, that the only truly succesful schemes of explanation, that work experimentally regardless of one's faith, if any, are scientific, and in terms of hypotheses of natural things only.

A third important reason for naturalism is that it neither denies what most men agree on (natural reality) nor affirms what most men disagree about (religion): It seems one needs to assume natural reality and some principles of natural and logical explanation to explain anything at all; it seems that natural science, based on logic, guessing and experiments is by far the most succesful method of trying to know and understand; and it seems nothing else is really needed or useful to explain things and to invent working technologies.

A fourth important reason for naturalism is that so much of so many religions is evidently false and outdated, when compared with modern science, and when allowing for the ignorance of the original religious founders, who usually lived many hundreds and sometimes several thousands years ago, and that so much of what so many religious people have done to other people in the name of their religion was immoral, totalitarian or cruel.