Sometimes people are inclined to describe an area of inquiry, like morality, as subjective. However, it is important to separate out two senses of the word “subjective,” which I will call the metaphysical sense and the epistemological sense.
An area is metaphysically subjective if there actually are no objective criteria for deciding questions in that area of inquiry.
An area is epistemologically subjective if there are objective criteria for deciding questions in that area, but we don’t know what they are.
Every area of inquiry is epistemologically subjective prior to discovering the objectively correct criteria to employ, by definition. For example, logic was epistemologically subjective prior to Aristotle, since no one had explicit rules for how to reason properly or identify logical fallacies. People just reasoned using intuition until the objective logical standards were discovered.
Some areas of inquiry are metaphysically subjective, like astrology. There are no objective criteria for what your horoscope should say, because the field has no basis in reality. If the objective criteria for an area of inquiry are not known, then that may be used as an argument for the position that that area of inquiry is metaphysically subjective – that is, that there are in fact no such criteria. This is the basis for the philosophical position that morality is subjective.
It is critically important that we not rest content with a subjective approach to any legitimate area of inquiry, but rather work to define objective standards for everything we do. In the absence of objective standards, disagreement will proliferate, and skepticism and mysticism will run rampant.
Plato held that in philosophy, we arrive at the truth by means of a process of “dialectic.” Dialectic, for Plato, works as follows:
We begin by having one person put forward an answer to the problem in question on the basis of certain arguments.
Another person then comes along, points out flaws in the first person’s answer, and puts forward his own answer.
Then a third person comes along, criticizes both viewpoints, and puts forward an answer that is better than either of them.
Plato held that, over time, this process leads us closer and closer to the truth. This is illustrated by some of his dialogues.
Plato’s theory assumes that we have a way of rationally evaluating an answer to a philosophical question as plausible or implausible. Plato held that we could see this “intuitively,” but his account of intuition depends on his metaphysics, which most philosophers have rejected.
Another perspective on dialectic comes from David Hume. Hume agrees that it often happens in philosophy that one person puts a position forward, and then another person criticizes it and puts their own position forward. However, according to Hume, the intuitions that this process depends on are subjective products of “habit or custom.” So, while dialectic can arrive at conclusions that better appeal to a given person subjectively, it is not a source of objective truth like Plato thought.
I think the only way to answer Hume once and for all is to present a body of demonstrably true conclusions in philosophy. So long as philosophy is seen as an endless debate, many will be inclined to question whether it has any cognitive status at all. There have been a number of attempts to do this since Hume, and evaluating all of them is beyond my scope here.