My friend and I got into an argument around Kant's categorical imperative. Eventually, ignoring all of that rigmarole, he argued that a priori knowledge was subjective. Things like 4 > 3 don't have to be, they just are. To this effect, does this affect the existence of a priori knowledge, and using that knowledge, can we confirm the existence of the objective?
Yes, and yes.
Anything subjective must be based on some objective cause that allows for that subjectivity to even exist. Whether or not subjectivity is able to know completely the objective is of no consequence. All that matters is that subjectivity is still able to deduce the existence of its own cause.
A priori knowledge is generally accepted in academic philosophy; the vast majority of academic philosophers accept it as being true.
Depending on how one values and follows academic consensus, then, a priori knowledge is indeed a logical inference and thus a respectable stance.
I guess I kind of what to know what you mean by “the objective?”
If you’re referring to objective knowledge, on one hand all human interaction with the world must be done through the perception of the individual. Perception is limited to the (at most) five senses of the individual. Scientific method can’t. E used to prove such things as the color one individual percisves as red is equal to the color another individual perceives as red.
On the other hand, there is “meta-knowledge” in this circumstance that is objectively true, that being the existence of a classification system of the perceived world by individuals, which has been agreed upon by the collective.
While this isn’t an example of a-priori knowledge, I would say it’s an example of objective truth. The knowledge being, not that red exists a certain way in reality, but that the human collective have agreed to classify certain parts about reality as red. The objective knowledge/truth is the existence of a classification system that allows for individuals to comprehend/communicate and become “the collective.” One individual objectively knows what another human is communicating because of this classification system.
I’m not sure this answers what you are looking for, but I would hope that this provides an avenue for discussion that objectivity surely exists.