I think you have them in the right order. Science is by far the best means of gaining knowledge about the world, followed by philosophy which shares a core trait (reason/rationality) with science but lacks the extraordinarily effective method of science. Religion is by far the least effective means of gaining knowledge about the world, so much so that I wouldnt bother mentioning it as a means at all. It actually has a history of the opposite, of preventing and obscuring knowledge about the world.

How do you compare these things in their attempts to seek knowledge about the world? Is science a part of philosophy? Is science an entirely different method of seeking knowledge about the world? Does religion have any meaningful role to play in seeking knowledge about the world?

Without using labels, I imagine humans first began understanding the world through a lot of storytelling and basic intuition, with little data to aid them. From there they began to focus on logic and discovered much, but tried to explain far too much with it, such as why things fall to the ground. Eventually they started to focus on collecting data to fuel their logic, by creating observational tools like telescopes and constructing well measured experiments like Galieo. — Malice

I heard someone say "science is a wholly-owned subsidiary of materialism" and if that's true, it appears to be, then the immaterial world, if such exists, is open to other approaches like religion, philosophy, etc.

Notice that I said "...the immaterial world, if such exists"; it indicates a fundamental problem with our conception of being/existence. The most widely-accepted meaning of existence is that which can be perceived through the senses or instruments. This view of existence, that only the physical exists, is relatively new as evidenced by the fact that religion is older than science. While such a materialistic stance may have its benefits in terms of being amenable to proof, it's possible that there's more to this universe than just that which is perceivable through the senses and their extensions, instruments. After all who's to say that we're in possession of the full complement of senses; maybe there's a sense that we're missing, a sense that allows us to perceive the immaterial. For all we know, we could be like a colony of termites, lacking vision, and thus ignorant of color and shades of illumination. So, existence if defined as limited to the perceivable would lead to termites thinking color doesn't exist.

Perhaps those who're inclined towards religion are people who either intuit or infer the possibility of a hole in materialism.

I heard someone say "science is a wholly-owned subsidiary of materialism" — TheMadFool

There really isn't a concept of materialism in science. It's more of what you can observe and replicate, to ensure only quality objective data gets added to the pool of data that other people have to work with. They try very hard to go beyond the senses, that's why they develop tools to explore the world (e.g. radio astronomy and gravitational waves).

if that's true, it appears to be, then the immaterial world, if such exists, is open to other approaches like religion, philosophy, etc. — TheMadFool

Sure. But also, it doesn't infer that approaches outside of science are any good at it (or bad at it). Science has a way of objectively testing how good it is at something. It's falsifiable, and as such, has predictive power. Philosophy, as I understand it, has some testability in that much of it follows the rules of logic. But so does science, it just has the added benefit of collecting data through tools and experiments, so that you have more to observations to infer from.

The most widely-accepted meaning of existence is that which can be perceived through the senses or instruments. This view of existence, that only the physical exists, is relatively new as evidenced by the fact that religion is older than science. — TheMadFool

From a scientific standpoint, I don't hold this view. Scientific methods don't deny the existence of non-physical things. If you cannot perceive something via your senses or instruments, then it's typically hard to dictate to everyone else that they exist. Religion is often fine with dictating reality to everyone else, even when there is no evidence.

There is an issue with the mind. You cannot detect it via senses or instruments. The best you have is inferring that other humans have minds because you have a mind. But science doesn't dictate that the mind doesn't exist on the grounds of it not being physical.

It simply has limited tools to investigate. We have limited tools to investigate. But it's a part of neurology. Scientists study the brain, such as structures and defects, and correlate it to how people say they feel. For example, they've found that people with a smaller than average hippocampus report feeling depression more.

it's possible that there's more to this universe than just that which is perceivable through the senses and their extensions, instruments. After all who's to say that we're in possession of the full complement of senses; maybe there's a sense that we're missing, a sense that allows us to perceive the immaterial. — TheMadFool

I agree. That's why science doesn't dictate that things we cannot perceive don't exist, that's why there is work being done on string theory and the multiverse. It works with what we can falsify or hope to make falsifiable. Beyond that, we are left to our own personal observations/experiences to explore anything else. We just cannot expect those things to convince anyone else other than ourselves.

How do you compare these things in their attempts to seek knowledge about the world? Is science a part of philosophy? Is science an entirely different method of seeking knowledge about the world? Does religion have any meaningful role to play in seeking knowledge about the world? — Malice

Science as a method is part of philosophy. Actual scientific research, on the other hand, is not. I'd say that all methods of gaining knowledge are part of philosophy, including a possible "religious method". However, unlike the scientific method, a "religious method" has not been established.

Without using labels, I imagine humans first began understanding the world through a lot of storytelling and basic intuition, with little data to aid them. From there they began to focus on logic and discovered much, but tried to explain far too much with it, such as why things fall to the ground. Eventually they started to focus on collecting data to fuel their logic, by creating observational tools like telescopes and constructing well measured experiments like Galieo. — Malice

I don't think it works out quite so neatly. For one, I think our mental machinery only changes very slowly over thousands of years. What has changed the way humans think is primarily the education they received, and the values they lived. The "religious" impulse is still very much there, it just manifests differently. Many of the core questions of philosophy are based on the same search for answers, rather than just predictions, that have led to religions. It's the very structure of our minds that leads us to search for meaning.

Is science a part of philosophy? — Malice

Philosophy has informed science regarding errors of judgement that can be discovered, empirically. Post hoc ergo propter hoc errors are routine in everyday life. One association can wrongly lead a person to conclude that event Y was caused by event X. When Y necessarily follows X, then it seems perfectly reasonable to conclude Y was caused by X (e.g., self-determined actions). However, testing can reveal third variables.

Also, if the consequences to Y select the probability of future occurrence of Y, then the "cause" of Y moves to the event that followed. How could an event that follows a response in time "cause" the action that preceded it? It can't cause the one that preceded it. It increases future probability. It selects the response.

The person at the slot machine receiving a pre-determined schedule of payouts, pulls the lever at a rate consistent with the schedule. This phenomenon isn't learned a priori (as in philosophy), it had to be discovered a posteriori vis-a-vis experimentation that was structured to reduce threats to internal validity (science); many of which were known from philosophy.

Is science an entirely different method of seeking knowledge about the world? — Malice

The process of science allows one to demonstrate the functional or casual relationships between variables. With good experimental control one can predict, verify, and replicate findings in ways not accessible to deductive reasoning.

As regards the definition of philosophy and its demarcation from other fields [...] While it is a contentious position within the field of philosophy to conclude (as I do) that it is never warranted to appeal to faith, it is nevertheless generally accepted that philosophy as an activity characteristically differs from religion as an activity by not appealing to faith to support philosophical positions themselves, even if one of those positions should turn out to be that appeals to faith are sometimes acceptable.

But although philosophy relies only upon reason or evidence to reach its conclusions, not faith, it can also be demarcated from the physical sciences in that philosophy as an activity does not appeal to empirical observation either, even though a philosopher may conclude (as I do) that empirical observation is the correct way to reach conclusions about reality. It is precisely when one transitions from using empirical observation to support some conclusion, to reasoning about why or whether something like empirical observation (or faith, or so on) is the correct thing to appeal to at all, that one transitions from doing science to doing philosophy. — The Codex Quarentis: Metaphilosophy

Is science a part of philosophy? — Malice

That depends on how you define philosophy. The definition of science is easy, peasy: science is the collection of propositions that you can justify using the scientific method. The definition of philosophy is not as straightforward. There is actually no agreement on it.

If you pick epistemology instead of all possible forms of philosophy, the problem becomes easier.

There were science seeks to detect patterns in the physical universe, epistemology seeks to detect patterns in the abstract, Platonic world of knowledge, i.e. in the universe of justifiable beliefs.

Both science and epistemology are empirical, but the universes that they study empirically are different and even non-overlapping. In that sense, science cannot be a part of epistemology.

Is science an entirely different method of seeking knowledge about the world? — Malice

In comparison to epistemology, no. Both science and epistemology are empirical but they observe different universes, i.e. the physical universe in the case of science versus the abstract, Platonic world of justifiable knowledge in the case of epistemology.

Does religion have any meaningful role to play in seeking knowledge about the world? — Malice

There is no generally agreed definition for religion as a whole. However, the ontology and epistemology of religious law are straightforward. Religious law is a formal system that seeks to derive moral advisories from an axiomatic scriptural base. Therefore, since religious law produces syntactic entailments from basic rules using the axiomatic method, it looks much more like mathematics than science or epistemology.

The question whether religious law has a meaningful role to play depends on whether you believe that a formal system of morality is needed or not. I personally believe that moral judgments must syntactically entail from basic rules.

Furthermore, morality does not seek to describe how human behaviour in the world happens to be, but how it should be. It is meaningful in a sense that we actively shape the world. We are not merely passive spectators.

How do you compare these things in their attempts to seek knowledge about the world? Is science a part of philosophy? Is science an entirely different method of seeking knowledge about the world? Does religion have any meaningful role to play in seeking knowledge about the world? — Malice

Knowledge is a justified (true?) belief.

Faith does not lead to knowledge because faith is belief without justification, and sometimes in spite of justifications, or reasoning, that contradict or oppose those beliefs.

Philosophy just asks questions, even asking what knowledge is, and is therefore a mode of skepticism or recognizing our ignorance - which is the antithesis of knowledge.

Science is the only method that leads to knowledge through both empiricism and reasoning. Both are necessary components of proper justification for some belief to qualify as knowledge.

Even reasoning requires some kind of empirical structure. What we think or reason about takes the form of our empirical structures of colors, shapes, sounds, feelings, smells, and tastes. How do you know you are thinking, and how do you know what you are thinking about, if your thoughts or reasoning don't take some form (I think, therefore I am)?

Faith does not lead to knowledge because faith is belief without justification — Harry Hindu

The basic assumptions of any discipline rest on faith.

For example, there is no justification for the scientific method, as it is not justified from underlying premises.

In mathematics, the problem is even more obvious. The axioms must not be justified. The axiomatic method insists that axioms must be speculative, arbitrary beliefs with no justification possible from within mathematics. Otherwise, they are not legitimate axioms.

There is also no justification possible for the axiomatic method itself, if only because logic itself is an axiomatic system that ultimately rests on fourteen arbitrary, speculative beliefs.

Hence, the core pillars of knowledge, i.e. its starting point beliefs, its normative ontology, and its normative epistemology, are always accepted on faith and without possible justification.

Therefore, the idea that faith does not lead to knowledge is contrary to the entire body of existing knowledge. It is, in fact, exactly the other way around. Without faith, there cannot be any knowledge.

Unfortunately, even the most intelligent of us suffers from the myopia of human-chauvinism. We humans tend to think that what we can sense...is what can be known. We also seem to think that humans...particularly modern humans...KNOW a great deal.

But "know a great deal" is an ambiguous term...and is referential. Referring it to "all that is"...shows that it can be VERY LITTLE indeed. We humans may know very little more about the totality of the REALITY of "everything that is"...than does an ant in our backyard.

We really have to shrug off the notion that we are a truly intelligent species. Mind you, we may be...but we may also be something slightly above the level of an amoeba in the grand scheme of things.

Much of what ancient "philosophers" and "scientists" have offered is now considered passe'...for good and compelling reasons. There may come a day...not too distant...where what we suppose to be advanced science and philosophy will be seen as primitive.

In the meantime, it is fun to explore. We should continue to do it. But we should regard it in greater proportionality than I see being done here right now.