I was just thinking about how many people believe that it is possible to know something in a objective manner. However, this is not true, not even of perceptions. Everything we can know or express to ourselves inherently has a subjective element, because it is processed through subjective filters.
An example many people use to show that we can have objective knowledge is the mathematical notion that 2+2=4. However, this formulation is in fact subjective in several ways. First, it assumes that the person is using decimal, standard mathematical notation, and agrees on the meaning of each number. For instance, just by switching to quaternary, I could make 2+2=10. Now the person might argue that this is actually the same answer because you can acheive the same result with physical objects. But this is also subjective, because you would first have to agree on what should be defined as an object. With what we consider to be two books, we have to agree that it is the set of pages, ink, ideas, atoms, etc, that we have somehow defined as a book, separately from it's surrounding environment. Also, the idea of counting does not change anything about the books, it simply is part of how we define our perception of them. The idea that the two books are independent entities is part of a limitation in how human beings process reality. Truthfully, we cannot say that anything exists outside of our perception of it. Everything that we can communicate is based on a shared set of assumptions and rules for processing things that we somehow accrue over the course of our lives. Even this communication is entirely subjective, based on my perception of reality, language, and logic.
Even if we assumed that things that we perceive exist outside our perception, we still must acknowledge that we only comprehend something by superimposing a subjective impression onto it, and examining that. For instance, if our understanding is correct, what we call "red" exists in nature, but only as a material that reflects light particles within a certain band of the electromagnetic spectrum. To a being that perceived the electromagnetic spectrum differently, we would be able to explain "red" to them, but they might not understand what that particular perception really means to us, because what "red" means to us has more to do with the subjective impression it makes on us, rather than how light particles respond to it.
So how can anything truly be objective? It can't. Why do some people claim that they can say something objectively, when all knowledge is subjective?
What does this mean?