How do you make the distinction between philosophy and religion? Are there some philosophies/religions that are hard to categorize as being one or the other?
Taking the latter part first: yes, there are definitely religions/philosophies which have proven difficult to categorize. The government of Australia, if I understand correctly, is currently trying to decide if Buddhism qualifies as a religion; the government of the US has decided that Scientology counts as a religion for tax purposes, while the government of Germany has decided the opposite. In Norway, the second-largest "faith/life-view" organization (after the state Lutheran church) is the Humanist-Ethical Society (i.e., a group of atheists) which qualifies as a "religion" for many purposes (including tax status.)
The fact that this confusion exists in practice shows that there isn't any clear, reliable indicator one can point to. The obvious candidates (such as the belief in a deity, or a soteriological path, or the presence of rituals or dogma) break down when you actually try to apply them in practice: exceptions abound.
So, that being the case, I would turn the question around: why does it matter? What benefit would be gained by drawing such a distinction? If we could answer that, perhaps we'd have a clearer way to finding an appropriate criterion.
The terms are not synonyms. You should note that religion always refers to a specific set of beliefs, i.e. Christianity, Islam, Buddhism, etc. The term philosophy can be used in two senses: In the general sense it refers to:
In a narrower sense, you can use the word to refer to a specific set of philosophical theories, such as stoic philosophy or Kantian philosophy. It would be these narrower subsets of philosophy which might be considered parallel to a particular set of religious beliefs.
With that cleared up...
How do you make the distinction between philosophy and religion?
Answer: philosophy in general is the rational investigation of truth, whereas religion often makes the same kind of truth claims but doesn't claim to base it on reason or rationality, but instead it is based on other things like faith. The key difference is that they are different epistemological positions — philosophy has a system of logical principles in place to arrive at conclusions whereas many religions (such as Christianity) allow for other sources of knowledge (i.e. faith).
Are there some philosophies/religions that are hard to categorize as being one or the other?
Answer: In principle, it could be a problem to categorize them but in practice it is not very difficult. Why? Because virtually all religions with even a modest following carry with it a set of traditions and rituals which philosophies do not. Put simply, religions have practices and philosophies do not. Theoretically, you could have what might be considered a religion without any practices, but it's not very common.
Thomas Aquinas makes the distinction that philosophy is based on human reason alone, but religion also includes some kind of divine revelation.
One of my favorite statements of Wittgenstein's is this. "At the foundation of well-founded belief lies belief that is not founded" (§253, On Certainty). So, you can believe whatever you can believe. –An experience. –A scientific belief. See: it is of the system in which we claim knowledge of this or that. (I believe this or that statement, but I know my beliefs.) If this were not the case, we'd never know anything. (For me), philosophy is the "system builder." (And Charles Sanders Peirce would seem to agree, as he called science inquiry, and the system that puts everything together philosophical rather than scientific.) But, this makes sense. Think of the scientific use of the word "energy." Physics, chemistry, biology, geology all have their own form of energy, but it is not science that connects them (well, it's actually language), but it seems it is the job of philosophy to systematize. For example, we call physics and chemistry sciences, and yet, they fundamentally see different aspects in the same thing. There is no atom in chemistry. –Only molecules. The differences between the points of views of chemistry and physics really helps show the discontinuity of the modern sciences. It is a wonder of the world to listen to a particle physicist discuss atomic theory with a chemist.
What connects the seemingly infinite divide between our scientific facts is an holistic view (one that philosophy provides). Now the reason I brought up science as opposed to religion is that religion also can fit into this holistic view. That is, it can sit beside chemistry, perhaps between chemistry and biology, or physics and biology. (And there is no contradiction.) There isn't a contradiction because philosophy is what gives us the whole. That is, philosophy lets us put incommensurable systems under a whole system. I say philosophy, but really it could be your parents, or teachers, or friends who glue different points of view onto the same whole. In that, I would say that philosophy uses religion, as it uses chemistry or physics.
I think the two are difficult to disentangle easily. For example:
Buddhism is often taken to be more philosophical rather than a religion, but I think this comes from viewing religion from a Christian perspective. Also Byran Magee (British philosopher) remarks in his autobiography that Kants philosophical thought can be seen as a rationalisation of the pietist tradition he was brought up in.
Acharya Sen, an expert on indian medieval literature and hinduism points out that hinduism includes the lokyata/carvaka tradition which was empirical & scientific. He also writes that rational inquiry is an investigation into the impersonal side of Brahman.
Pythagoras is said to have declared the universe is number and geometry in mystical reverie, this is still current today in the popular imagination, for example the Higgs boson referred to as the 'God' particle, and physicists and mathematicians seen as the high priests of a technocratic world (look at how they are referred to within science fiction).
David Wallace an american novelist writes that human beings are worshipful beings, they have no choice in this - what they do get is the choice of what to worship.
I suggest you read this first "What are some methods of defining things?" to understand one of my logical framework working on this post.
WHAT IS WISDOM?
Wisdom has working area, it's within relativity. Wisdom is about act properly, respond relevantly. Practically, we are responding something through relevant approach. It's relevant respond, it's correct respond, it's appropriate respond.
But what is act properly? What is correct respond? What is appropriate respond?
By knowledge we can know possibilities to make an adjustment (mentally or practically) to further know our priorities. It's wisdom.
And this understanding can be used as comparison to "what philosophy is".
WHAT IS PHILOSOPHY?
We will unpack "what philosophy is" through understanding "what wisdom is". Further we will see whether there is continuation in between "what wisdom is" and "what philosophy is".
WHAT IS RELIGION?
I am not defining religion for all religions, but i am focusing to one of consistencies on some religions to capture the problem area in this post for further proper comparison.
Some religion are strongly related to spiritualism, mysticism (or if you deny it, then i must assert that this discussion related to religion is limited to this term).
From this point of view, we could assert that there is intersection in between philosophy and religion.