I've been enjoying a conversation with Alex Gregory over at atopian.org. We've been discussing moral relativism, and Alex has been asking whether I'm saying one can rationally deny demonstrated truths within axiomatic systems. Here is my answer to his question, with a little elaboration.
The truths (theorems) within each axiomatic domain exist whether we value them or not. The theorems of Euclidean geometry are true, even if we prefer non-Euclidean geometry.
In many cases, comparable theorems in different axiomatic systems contradict each other. The question is, on what basis should we value each set of axioms and theorems?
My point is that, at best, what we ought to do is subjective. What I ought to do involves a value judgment. Whether I ought to hold an axiom as true depends on how I value it (or its resultant theorems).
This happens in physics. Each scientific theory consists of a set of axioms for modeling the world, and each observation counts as an axiom. A theory is invalidated when it becomes inconsistent, and the predictions of a theory are those axioms that can be added to the system without contradiction.
If we have two scientific theories that are presently indistinguishable (say, because the distinguishing experiments are as yet out of reach), then we might still prefer one theory over another. Sometimes, this selection of axioms is based on aesthetics or taste, and one theory is valued over the other for accidental or historical reasons. For example, if one theory will benefit me, my past works and my department, I have reason to value that theory more than its competitor.
So, let's look at my personal position. I value staying alive, comfort, my ego, my loved ones, peace of mind, etc. Since I view science as vital to survival and peace of mind, I think its axioms are important, and I'm willing to live as if they are true. I accept mainstream ethical values because I see those as conducive to my comfort and my general happiness.
However, a person who has different values (or who is confused or inconsistent) will accept different axioms. For example, a person who thinks that this world is less important than some fictitious afterlife, does not fear death or discomfort. Science does little for these people, and the fact that electronics and pharma science save millions of lives each year is unimpressive to them. Their values allow them to disregard the founding axioms of all scientific systems (logical consistency and regularity) if it delivers them the particular afterlife they seek.
That some primitive screwheads reject science does not imply that science is somehow untrue under its own axioms. It's just a question of whether a man thinks the objective power of science is important.
Now, let's get back to morality. Morality is supposed to guide values, but values are used to select axioms. So how can there be an objective morality? If a person thinks that following axiomatic moral systems is unimportant, on what basis can you logically demonstrate to that person that they are wrong? Their answer to any axiomatic system will be "so what?"
I'll add here that I feel that it is generally better to "game" axiomatic systems, and to do a comparative analysis of them. I think it is morally good to ask why each system is valued the way it is, and whether the method used for assigning value is a consistent one. Is my preferred system appealing to me for biological, social or psychological reasons? Do these values cause me to be blind to defects in my preferred system? Are these values themselves worthy?
I'm still working my way through these questions.
In comparing alternative systems, one will come across systems which actively discourage comparative analysis. Christianity is one such faith-demanding system. While it would be illogical for an outsider like me to pay any heed to such demands, it is significantly harder for Christians to do so, since they presumably value the axioms of their own system to a greater degree. It can be difficult to escape these Jedi mind tricks.
It's also true that social and family bonds act to suppress comparisons. There is an inherent negative value in abandoning the shared axioms of one's family or social group. This doesn't affect me much, and my mother wonders where she went wrong.
I also can't deny that I want to feel that I'm special, and that my formulation of philosophy is right and elite, rather than merely right and mundane. This, too, could potentially sway my judgment in a manner I find distasteful.
Anyway, I think I'm getting closer to understanding the dynamics of selecting axioms, and I plan to write more on this topic.