Saturday, May 02, 2015

Why I Don’t Believe: Euclid and Utili-Christians

Why I Don’t Believe: Euclid and Utili-Christians

Here’s the basic article without the graphics:

Why I Don’t Believe: Euclid and Utili-Christians

by Leah Libresco in Patheos

This post is one in a series on why I do not believe in Christianity.  You can check out all previous posts at the series index.

I don’t want to run afoul of the Courtier’s Reply fallacy.  No one should need a Ph.D. in theology to be able to form some basic beliefs about God.  Unfortunately, in writing this post, I seem to have established that you need a background in topology to talk to me about morality.  If parts of this post are unclear, please comment and I’ll try to revise/explain.  It’s the only way I know how to talk, apparently.
The most common pitch I get for why I ought to be a Christian (or at least the most common once my interlocutor realizes that I believe in objective morality) is that Christianity explains morality in a way atheism cannot.
I cannot deny that it’s true, at least with regard to my own atheism.  I do believe that moral behavior is not subjective, even if our understanding of objective morality is flawed.  At the same time, I cannot explain where or how this morality exists, or even give a clear decision-making algorithm that prescribes moral behavior.  On each of these criteria, Christianity offers more than I can, and, to be honest, my own moral beliefs aren’t even that frequently in conflict with those of the Church.
So what’s my objection?  Or my defense?
Er… Well…
Say, would you mind if I started talking about math?
I promise it’ll be relevant in a couple of paragraphs.  (You’ll remember I have a habit of doing this)
Around 300 BC, Euclid wrote The Elements, probably the most important math book ever written.  He formalized geometry into a series of axioms, rules of inference, and theorems that could be derived from the previous two tools.  All of his work stems the five postulates he used to define the structure and language of geometry. They are as follows:
  1. A straight line segment can be drawn joining any two points.
  2. Any straight line segment can be extended indefinitely in a straight line.
  3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.
  4. All right angles are congruent.
  5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.
If you’re like most of the mathematicians of the last 2300 years, the last postulate feels a little clunky.  All the other postulates are simple, while the last one (which essentially states that, if given a line L and a point P not on line L, there is only one line that passes through P and is parallel to L) seems ridiculously convoluted.  Mathematicians struggled for years to find a way to prove that postulate five necessarily followed from the previous four.
They didn’t succeed, and with good reason.  Not does Euclid’s fifth postulate not follow from the previous four, it doesn’t have to be true at all.  Mathematicians can postulate that given a line L and a point P, there are an infinite number of lines parallel to L that pass through point P and end up with hyperbolic geometry.  They can state that no lines are ever parallel and any pair must intersect at exactly one point and end up on the projective plane (the MC Escher drawing at the top of this post is a representation of the projective plane).  These geometries are called non-Euclidean.

And now, back to morality

In mathematics, there must be some definition of what it means for lines to be parallel, but the Euclidean and non-Euclidean are contradictory and equally correct.  The correct definition depends on what you intend to prove.
Now here’s where that takes me with regard to Christian explanations of morality.  I don’t deny that Christianity offers an explanation for the existence of values, but so do many other religions.  I don’t think that these religious explanations are meant to parallel Euclid’s fifth postulate in terms of interchangeability, but that’s often how they’re presented to me.
Christians who urge me to accept Christianity as a way of explaining my moral instincts are asking me to use Christianity as a utilitarian means of resolving uncertainty for the sake of resolving uncertainty.  I might select any of these religious explanations as a way of grounding my moral beliefs,  but without a heuristic for choosing between them, my choice would be far more arbitrary than that of mathematicians choosing a geometry to work in.  Why is the Christian explanation superior to that of the Taoist?  How am I to judge which corresponds to the true explanation?
In the meantime, I prefer to muddle on without an explanation for the mechanics of morality, which isn’t as big a problem as you might expect.
Ptolemy’s Epicycles
A satisfying explanation should do more than just match up precisely to the data observed to date.  Before the Copernican revolution, astronomers believed that all planets orbited the earth.  They were wrong, and more and more the data didn’t make sense, so they kept tweaking the model to make it fit.  Ptolemy introduced a new, powerful tweak to explain retrograde motions.  He added epicycles: extra loops for the planets to spin around as they traveled around the earth.  Over time, he had to add epicycles within epicycles to try to twist his model to fit.

It’s entirely reasonable for scientists and philosophers to be more confident in their facts than their theories, but they too rarely are.  Ptolemy and other astronomers were so determined to have an explanation that they let their model eclipse their data.
I can’t explain why morality exists, any more than scientists have established the ‘why’ of gravity (right now, they’re still working on the how).  A full explanation is not required to discuss morality and ask ethically any more than engineers are incapable of designing buildings until the existence of the Higgs boson and its influence on gravity are definitively established.
Until I find an explanation that can make predictions that go beyond what I already know or until an explanation establishes a causal mechanism that doesn’t operate outside the realm of observation, I’ll be honest and say I don’t find anyone’s explanations satisfactory.
This is the last post in the “Why I Don’t Believe” series.  Check out other linked series here.

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