What exactly do you mean by "subjective", and what exactly do you define "knowledge" to mean?
True knowledge is, well, 100% knowing something. I think the definition of "know" makes it impossible to have perfect knowledge, because it presupposes you as external to that thing. If you really, really "knew" something, you would have to
be that thing. All you really know is that you exist in some way (not necessarily as you perceive yourself to).
Non-subjective knowledge in this sense is impossible in my opinion--you would be what people call god--thus I think knowledge is ultimately subjective. Even as I write this, I can only think with some large percentage of belief that what I am writing is English and that in the last 10 minutes my mind hasn't rearranged itself such that what comes out to you is random babbling. Do I
know what the difference between "hello" and "hhsfkjdf" is? In everyday terms, yes, I "know," but if you want to start treating knowledge as a science, then not really, no. I only think I know, and act on that belief.
Say tomorrow you roll out of bed and stop signs are all blue for you. Uh oh, what do you do? Do you
know now that they won't be, or do you just have a strong hunch? Will you
know that they were red before? You can't know that they won't be blue tomorrow, because you would be able to see into the future. You wouldn't know that they weren't red before. Life and consciousness would be fundamentally different things, which is a whole other tangent. Tell me that knowledge is not subjective.
Depends on exactly what your standard of proof is.
This reminds me of an anecdote about G.E. Moore, I think it was, that said to an audience, "look, I don't need to *prove* to you that there are windows behind those curtains over there. I see curtains, and I know there are windows. So stop with all this skeptical nonsense." And someone pulled back the curtains, behind which there was a wall.
True proof doesn't exist. Even when you prove, "look, the stop sign exists. You just broke your nose running into it, stupid," you are presupposing a lot of things and everything that comes out of your mouth as "proof" is ultimately based on some presupposition. We have to settle with a fluid, subjective notion of knowledge and proof that simply states (and I'm writing this off the top of my head, so bear with me), "this is consistent enough to be agreed upon by a certain critical mass of conscious entities, whom we presuppose to exist and interpret the world somewhat consistently, such that we can use it for inductive purposes for the indefinite future." There are more presuppositions necessary in that statement, but I won't write them all out. For example, I have to presuppose the meanings of the words and letters that I just wrote down.
So, can you prove, without presuppositions, that you weren't just blinked into existence 2 seconds ago? You have to set up lots of conditions and presuppositions. Biology "proves" things with the scientific method because most all biologists take as given certain criteria, like the existence of their nosehairs. But philosophy is putting knowledge itself to the test, and while I feel the study of knowledge is fascinating and useful, I think it is ultimately subjective because you can't reduce it down to something absolute and self-defining. Especially when you ask questions like, "what is the aim of science?" You don't
know and you can't call something
wrong.