Sunday, January 24, 2016

axioms to grind

So many people make decisions through beliefs which are missing satisfactory corroboration. In so doing they adjust how they act and think and—most alarmingly—treat others. Calling them "followers" is more apropos than "believers". Whatever they're called, it's far too simplistic to assume that none of them ever notice the relative suspiciousness of some of their beliefs, on some level, sometimes. They compensate with an an array of strategies, such as contenting themselves with the self-concept of perpetual seeker. Perpetual seekers always openly look for fuzzy beliefs that "speak to them right now" as opposed to beliefs with excellent impersonal accuracy.

Without a doubt, that option wouldn't tempt followers who are more fastidious about their beliefs: they who wish they could detail the sturdy reasoning behind their thinking. Mathematics is the paragon of this formal style. It demands painstaking proofs. The overt exceptions are axioms, which are purposefully accepted as true without proof. Proofs can then build on top of the axioms. Plane geometry is a familiar example.

Axioms generally fall under the principle of parsimony, i.e. few and small, selected with stringent awareness of benefit and cost. The content is centered on universal premises reusable in discrete cases, not on the minutiae of historical facts. It's not rare to work on reducing dependence on axioms by showing that one or more can be proven via the rest or further distilled to essentials. Cursorily proposing more or larger axioms is not the predominant method of reaching reliable, persuasive results.

Followers may opt to equate their most central beliefs to axioms. By analogy, this removes the perceived burden of justifying plausibility. Axioms are invaluable in mathematics, which avoids gaps in arguments whenever possible. Consequently, they can feel more serene about disregarding the realism of the "axioms" in their beliefs, too. And they can retain high standards for ideas beyond those. In words, "All diligent thinking about a topic needs to start with axioms. I start with those, and I can't be expected to reasonably justify why." Axioms impart a respectable-looking loophole.

The tacit error, as usual, is easier to distinguish from outside of the follower's mentality: the discussed beliefs don't mirror the qualities of sensible axioms. People could drive in nails using miscellaneous objects, but not all of those objects qualify as sensible "hand tools". Perhaps the beliefs have inhabited the follower like axioms, because the follower was taught early that the beliefs' accuracy was unquestionable. But in order to properly mimic the axiom category of mathematics, almost all propositions should be left out. If it's quite possible to contemplate a variety of cases without referring to a proposition, and/or it's feasible to estimate/determine a proposition's accuracy through normal means, then a proposition shouldn't be dumped into axioms.

If it is anyway, then its logic withers. It shifts the intellectual status of the beliefs' coherent whole. A system that obliges onlookers, from the start, to adopt an abundance of weighty, uncorroborated propositions isn't a viable axiomatic system. It has a different mathematical analogy: a sequential set of conjectures. Conjectures aren't useless or repugnant, of course; throughout history conjectures have motivated brilliant leaps. Greater candor is the main difference between naming the beliefs axioms or conjectures. Followers shouldn't mislead themselves, or anyone, to depict their beliefs in the image of logically derived proofs which result from "simple" beginnings—little idea dominoes tipping one another. It's worth remembering that tipping over a preliminary domino such as "one or more gods exist" has kept debaters occupied for centuries. So has the next domino, "What are these one or more gods like?"

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