A philosophy paper consists of the reasoned defense of some claim
Your paper must offer an argument. It can’t consist in the mere report of your opinions, nor in a mere report of the opinions of the philosophers we discuss. You have to defend the claims you make. You have to offer reasons to believe them.

So you can’t just say:

My view is that P.
You must say something like:
My view is that P. I believe this because…
or:
I find that the following considerations…provide a convincing argument for P.
Similarly, don’t just say:
Descartes says that Q.
Instead, say something like:
Descartes says that Q; however, the following thought-experiment will show that Q is not true…
or:
Descartes says that Q. I find this claim plausible, for the following reasons…
There are a variety of things a philosophy paper can aim to accomplish. It usually begins by putting some thesis or argument on the table for consideration. Then it goes on to do one or two of the following:
Criticize that argument; or show that certain arguments for the thesis are no good
Defend the argument or thesis against someone else’s criticism
Offer reasons to believe the thesis
Offer counter-examples to the thesis
Contrast the strengths and weaknesses of two opposing views about the thesis
Give examples which help explain the thesis, or which help to make the thesis more plausible
Argue that certain philosophers are committed to the thesis by their other views, though they do not come out and explicitly endorse the thesis
Discuss what consequences the thesis would have, if it were true
Revise the thesis, in the light of some objection
No matter which of these aims you set for yourself, you have to explicitly present reasons for the claims you make. Students often feel that since it’s clear to them that some claim is true, it does not need much argument. But it’s very easy to overestimate the strength of your own position. After all, you already accept it. You should assume that your audience does not already accept your position; and you should treat your paper as an attempt to persuade such an audience. Hence, don’t start with assumptions which your opponents are sure to reject. If you’re to have any chance of persuading people, you have to start from common assumptions you all agree to.

A good philosophy paper is modest and makes a small point; but it makes that point clearly and straightforwardly, and it offers good reasons in support of it
People very often attempt to accomplish too much in a philosophy paper. The usual result of this is a paper that’s hard to read, and which is full of inadequately defended and poorly explained claims. So don’t be over-ambitious. Don’t try to establish any earth-shattering conclusions in your 5-6 page paper. Done properly, philosophy moves at a slow pace.

Originality
The aim of these papers is for you to show that you understand the material and that you’re able to think critically about it. To do this, your paper does have to show some independent thinking.

That doesn’t mean you have to come up with your own theory, or that you have to make a completely original contribution to human thought. There will be plenty of time for that later on. An ideal paper will be clear and straightforward (see below), will be accurate when it attributes views to other philosophers (see below), and will contain thoughtful critical responses to the texts we read. It need not always break completely new ground.

But you should try to come up with your own arguments, or your own way of elaborating or criticizing or defending some argument we looked at in class. Merely summarizing what others have said won’t be enough.

How You’ll Be Graded
You’ll be graded on three basic criteria:

How well do you understand the issues you’re writing about?
How good are the arguments you offer?
Is your writing clear and well-organized?
We do not judge your paper by whether we agree with its conclusion. In fact, we may not agree amongst ourselves about what the correct conclusion is. But we will have no trouble agreeing about whether you do a good job arguing for your conclusion.
More specifically, we’ll be asking questions like these:

Do you clearly state what you’re trying to accomplish in your paper? Is it obvious to the reader what your main thesis is?
Do you offer supporting arguments for the claims you make? Is it obvious to the reader what these arguments are?
Is the structure of your paper clear? For instance, is it clear what parts of your paper are expository, and what parts are your own positive contribution?
Is your prose simple, easy to read, and easy to understand?
Do you illustrate your claims with good examples? Do you explain your central notions? Do you say exactly what you mean?
Do you present other philosophers’ views accurately and charitably?
Comment:    The comments I find myself making on students’ philosophy papers most often are these:
“Explain this claim” or “What do you mean by this?” or “I don’t understand what you’re saying here”
“This passage is unclear (or awkward, or otherwise hard to read)” “Too complicated” “Too hard to follow” “Simplify”
“Why do you think this?” “This needs more support” “Why should we believe this?” “Explain why this is a reason to believe P” “Explain why this follows from what you said before”
“Not really relevant”
“Give an example?”
Try to anticipate these comments and avoid the need for them!

Your paper should do some philosophical work
A kind of complaint that is common in undergraduate philosophy papers goes like this:
Philosopher X assumes A and argues from there to B. B seems unattractive to me. Philosopher X just assumes A and doesn’t give any argument for it. I don’t think A is true. So I can just reject A and thereby avoid B.
This line of thought may very well be correct. And the student may very well be right that Philosopher X should have given more argument for A. But the student hasn’t really philosophically engaged with Philosopher X’s view in an interesting way. He hasn’t really done much philosophical work. It was clear from the outset that Philosopher X was assuming A, and that if you don’t want to make that assumption, you don’t need to accept X’s conclusion. If this is all you do in your paper, it won’t be a strong paper and it will get a mediocre grade, even if it’s well-written.
Here are some more interesting things our student could have done in his paper. He could have argued that B doesn’t really follow from A, after all. Or he could have presented reasons for thinking that A is false. Or he could have argued that assuming A is an illegitimate move to make in a debate about whether B is true. Or something else of that sort. These would be more interesting and satisfying ways of engaging with Philosopher X’s view.

Responding to comments from me or your TA
When you have the opportunity to rewrite a graded paper, keep the following points in mind.
Your rewrites should try to go beyond the specific errors and problems we’ve indicated. If you got below an A-, then your draft was generally difficult to read, it was difficult to see what your argument was and what the structure of your paper was supposed to be, and so on. You can only correct these sorts of failings by rewriting your paper from scratch. (Start with a new, empty window in your word processor.) Use your draft and the comments you received on it to construct a new outline, and write from that.

Keep in mind that when I or your TA grade a rewrite, we may sometimes notice weaknesses in unchanged parts of your paper that we missed the first time around. Or perhaps those weaknesses will have affected our overall impression of the paper, and we just didn’t offer any specific recommendation about fixing them. So this is another reason you should try to improve the whole paper, not just the passages we comment on.

It is possible to improve a paper without improving it enough to raise it to the next grade level. Sometimes that happens. But I hope you’ll all do better than that.

Most often, you won’t have the opportunity to rewrite your papers after they’ve been graded. So you need to teach yourself to write a draft, scrutinize the draft, and revise and rewrite your paper before turning it in to be graded.