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

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.

Non-Euclidean Geometry represented in crochet



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.

Epicycles within epicycles.  Yikes!

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.

About Leah Libresco

Leah Anthony Libresco graduated from Yale in 2011. She works as a statistician for a school in Washington D.C. by day, and by night writes for Patheos about theology, philosophy, and math at www.patheos.com/blogs/unequallyyoked. She was received into the Catholic Church in November 2012."

  • http://www.blogger.com/profile/11174257204278139704 Charles

    I couldn't agree with you more, nor have I agreed with a post of yours more. However I will once again point out that the religious folks would say that you are zeroing in on the one aspect of religion that makes it 'not science' in that it is not an observable testable quality, and complaining that you can't observe it or test for it.I have made the leap to accept that there may be true things that cannot be understand via the scientific method, but this does not answer your question anymore than your acceptance that objective morality may never be understood as a closed system akin to the way geometry is. I can say that I used to not even accept this much and I changed my mind due to overly 'scientific' folks making obviously bizarre claims about things such as the possibility for so-called 'strong AI' – I can elaborate on this but do not have the time right now.

  • A Philosopher

    Why do you think Christianity explains morality in a way atheism cannot? My experience has been that Christian explanations of morality either (a) are philosophically unhelpful, or (b) have obvious atheist analogs.

  • http://www.blogger.com/profile/04746612189094458441 Lukas

    I think you are either misunderstanding the argument made by theists. The theistic claim is not simply that atheists need a better 'why' regarding morality. The theistic claim is that an atheistic metaphysics is incompatible with morality. Richard Rorty, an atheist, acknoweldges this:Anybody who thinks that there are well-grounded theoretical answers to the question "Why not be cruel?" … is still, in his heart, a theologian or a metaphysician. He believes in an order beyond time and change which both determines the point of human existence and establishes a hierarchy of responsibilities.-Richard Rorty

  • Anonymous

    If you think that multiple (or all?) religions can explain your moral instincts equally well, I understand not being able to choose between them. However, they all have a common thread of the supernatural in them. Why choose atheism over a general, nondescript theism or deism? I know what I'm describing would not be particularly useful or descriptive, but it still might be closer to true than atheism, and might change how you view other philosophical issues.

  • spec

    "I do believe that moral behavior is not subjective, even if our understanding of objective morality is flawed."This doesn't make any sense to me. Saying person A should do B in situation C is neither a retrodiction/description/prediction of past/present/future states of affairs, nor is it a claim about logically necessary implications of hypothetical possible states of affairs. So if claims are 'objectively true' by virtue of accurately representing what they refer to, how is a moral 'should' claim objective at all? And like Philosopher said, you never expounded upon exactly what in Christian theology or apologetics successfully gets around this faulty wishful thinking. You can't say "oh we can't prove why strawberry is superior to vanilla ice cream, but we might in the future with more to go on" or claim the existence of furiously sleeping green ideas as an axiom of reality without incontrovertibly committing a category error. Same dealio with prescriptive morality.It's possible you mean "moral behavior" to refer to the existence of unselfish, altruistic, empathic acts by human beings, instead the proposed objective truth of moral ought claims. There actually are scientific and other theories that expound on why humans cooperate and have the capacity to feel and behave for each other.… "the Euclidean and non-Euclidean are contradictory and equally correct."Some clarification needed imo. That's like saying primes and composites are contradictory and equally correct. Prime and composite numbers are just two different types of numbers we can talk about, their simultaneous existence is not contradictory (rather, their attributes are different), and they are not 'correct' because they aren't even statements (the axioms designed to describe them are)."I have made the leap to accept that there may be true things that cannot be understand via the scientific method" [Charles]Could you elaborate? I've come to similar conclusions about how-it-feels type facts of phenomenological, first-hand subjective experience (not through any illogical "leap" mind you), but otherwise the world is intelligible with guarantees only if one uses logic, reason, and empirical evidence.Lukas: You're acting as if there is only a single theist claim. There's more than one believer in the world.

  • http://www.blogger.com/profile/00232551422932887547 Alex Binz

    @spec: For a statement to be "objective" it need not be descriptive nor necessary. The simplest meaning of "objective" relies on the distinction between objective and subjective, between object and subject. "Objective morality" is simply morality that is not predicated on the person ("subject") but on the things external to the person ("object": namely, the act itself, the circumstances of the act, and the intention behind the act). This resolves the apparent category error you point out.You write: "There actually are scientific and other theories that expound on why humans cooperate and have the capacity to feel and behave for each other."In point of fact, there are theories that expound on HOW humans developed the capacity to cooperate and empathize. This is no more an foundation for 'objective morality' than an explanation of the history of chess would be a foundation for chess strategy. Christians don't dispute that altruism is beneficial to society. But that statement (and thus, any theory of the development of altruism) does not demonstrate how a moral standard is objective — that is, how it might transcend subjective perception and conduct.Your explanation doesn't explain morality: it presupposes morality. Altruism developed because it benefits the community, and is therefore good. But why is it good to benefit the community? This explanation is tautological: it assumes that 'the greatest good for the greatest number' is an objective standard, and derives all other standards from this root.

  • Tawanda

    Well I might not know as much as a professor, or have a degree in anything (yet) but I do have an experience
    Its a long story! and I’m not going to tell it, but long story short you ought to be a born again christian to live life to the fullest, get salvation, and find your personal meaning in this life from God, He made the way (on the cross) so he can have a relationship with you, And he can live in your heart anytime you choose to accept him. something that was almost impossible happend to me that changed me it wasn’t random, I had faith for this and it followed. If you want to find the truth, you have to find someone/something that is the same yesterday, today, and forever. and just ask God to make himself real to you :)
    wouldn’t hurt?


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