Axiom: a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident.
I’ve found when arguing or debating an issue it’s very helpful to be able to identify a difference in axioms, and if one is found to disengage from the argument as politely as possible, declaring that you’ll just have to agree to disagree, because arguing further is just talking past each other.
There are two varieties of axiom clash:
If your axiom is “There is a God” and my axiom is “There is no God,” then we have competing axioms.
If we happen to agree on the axiom “There is a God,” but you hold the axiom “God demands world conversion to religion X by force” and I do not — that is, if one’s position is the absence of a competing axiom — then we have mismatched axioms.
When identifying an axiom clash, I look for the lowest-level axiom logically behind a stated proposition. For instance, “The Bible is the inerrant Word of God” assumes “There is a God,” and since my axiom is “There is no God” then that’s where the competing axiom clash occurs, rather than at the mismatched axiom level of “The Bible is the inerrant Word of God” versus “no, it isn’t.”
Since people hold a large number of propositions in their head as axiomatic, I’ve found it useful to try to find the highest-level competition or mismatch and end the debate there. Sometimes you can identify a principle that your counterpart thinks is axiomatic but isn’t in terms of other lower-level axioms they also hold; in such cases you can sometimes influence their thinking, especially if some or all of the lower-level axioms are ones you share.
Now, obviously it’s not possible to always agree to disagree if one or both parties to the clash decide that the clash is itself intolerable and must be decided by resort to force. Ultimately, we all have to decide whether our axioms are worth dying for if the other party believes their axioms are worth killing for. I believe that some axioms are worth dying for — although I pray it’ll never come to that — even though it means anything up to the level of total war.
I’ll try to identify those propositions I hold as axiomatic as I go forward on this blog, and I think being able to identify one’s own axioms is a necessary tool of philosophy and should be practiced by everyone. If you spot a contradiction among my axioms like I’ve just described, please point it out to me. But if your axioms clash with mine, then it’s probably best if you just say so up front and spare us the argument-at-loggerheads.