Tag Archives: Occam’s Razor

An Atheist’s Flowchart, Part 2: The Unspoken Axioms

In previous posts we have worked our way two layers down into the “flowchart” I have for this argument: we are dealing with my argument via epistemology, and within that argument we are dealing with the idea of god as an axiomatic belief. Today hopefully we will finish that piece, and next week we will take a look at the idea of god as a derived belief. Last week I sketched out the shape of this post, so I’m just going to run down the list of claims and flesh each one out as I go.

The Core Axioms

First, there is a core set of axiomatic beliefs which everybody accepts, and which everybody must accept to participate meaningfully in the world (and therefore in this debate). These are effectively axioms 3, 5, 6, and 7 from my original eight:

  • the existence of reality
  • the existence of causality
  • the reliability of one’s senses
  • the reliability of one’s mind/memory

Without these core beliefs it is functionally impossible to accomplish anything at all. Simply participating in a conversation requires implicit acceptance of all of these things.

The other axioms in my original eight (numbers 1, 2, 4, and 9) are philosophically important for me to able to make this argument (it would be impossible without a belief in formal logic, for example), but I don’t consider them fundamental in the same sense. It is theoretically possible to live your life in a quasi-coherent fashion while rejecting logic in all forms, although you wouldn’t necessarily get very far.

Their Power and Sufficiency

Surprisingly for their simplicity, these core axioms are extremely powerful all on their own, and support a broad set of derived beliefs. For example, you need nothing else in order to build the scientific method and a general set of empirical beliefs (logic and mathematics often helps in formulating precise hypotheses, but are not strictly required).

I will go one step further however, and make a stronger claim: these four axioms are almost or completely sufficient, on their own, to form a coherent worldview. They produce science, and science is capable of describing and explaining an enormous number of things about the world around us, from bed bugs to light bulbs to thunderstorms.

The Complexity of God

I’m going to take a very brief sidebar now to talk about the complexity of God as an axiom. If you’re hip with information theory you can read this considerably more formal explanation from Less Wrong using Solomonoff Induction and Turing Machines. It uses the phrase “a witch did it”, but just substitute in “god did it” and the whole thing still works.

For the rest of us, here’s the straight-forward version: the existence of god is massively complex. Just consider how much it adds to any worldview based on the core axioms. It adds:

  • the existence of something real that is not observable via our otherwise reliable senses
  • the ability for this extra thing to breach the normal contract of cause and effect
  • the existence of a non-physical mind
  • something with the power to create, destroy, or change the observable universe

Not only does this add a lot of pieces to any worldview, it provides very little explanatory power. As empirical science has now explained or debunked any claims of literal miracles, it is generally claimed that god explains human morality, the religious impulse, and… I think that’s it. When you compare the cost (the complexity of what you accept) to the benefit (the things it actually provides and explains), god is a terrible deal.

Putting It All Together

We now have all the pieces and we can put together the argument. The first half is simple: if the core axioms are in fact entirely sufficient on their own, then by Occam’s razor we cannot and should not take any further axioms, including the existence of god. However, if one believes that the core axioms are insufficient (for example, one believes in it is necessary to have an axiomatic source of moral truth) then one might still be tempted to use god in this way.

Occam’s razor also slices away this second tack because god is so ridiculously complex as an explanation. For any problem you propose, the answer “god did it” or “god is the reason” is an objectively worse explanation than any number of choices I can come up with on a moment’s notice (to continue the moral truth example, “human life is intrinsically valuable” is a far simpler axiom that a lot of humanists take and is otherwise just as good). Any way you slice it, god is overly complex and unnecessary as an axiomatic belief.

Therefore you cannot take the existence of god as an axiomatic belief.

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An Atheist’s Flowchart, Part 1: Occam’s Razor and Axiomatic Beliefs

The first pillar of my atheistic treatise is the one I called “via epistemology”. Of the three, it is probably both the strongest and the most applicable to the real religious beliefs commonly held by real people. It is certainly the most logically rigorous, if that means anything.

Axiom vs Derivation

The starting claim for this argument is that every belief we have must fall into one of two categories: it must be either axiomatic, or derived. Axiomatic beliefs are unsupported by anything else, they are effectively taken on faith. Without axiomatic beliefs in which to root our worldview, we end up in a circular trap of nihilistic doubt. Conversely, derived beliefs are not taken on faith; they are instead supported by some other beliefs we already hold. Those beliefs are in turn supported by other beliefs down the chain until you end up either at an axiomatic belief, or a loop.

Of course, the vast majority of day-to-day beliefs are derived: my belief that I will get wet if I go outside is derived from two other beliefs:

  • my belief that it is raining outside, and that it will keep raining for the near future
  • my belief that things, when rained on, get wet

In fact, there are only a handful of common beliefs which need to be axiomatic. These include belief in the existence of reality, causality, and your own senses, and the reliability of your mind and memory. You may notice that this list looks an awful lot like the core set of axioms with which I started this blog; that is not a coincidence.

We now have two possible branches we can follow: someone’s belief in God may fall into either of these two categories. Let us explore both.

God as Axiom, and Occam’s Razor

The first path we will explore is when belief in god is taken on faith, as an axiom in itself. This is probably the path applicable to the most real peoples’ real beliefs, and it is certainly one of the most articulable: it feels deceptively simple and makes an easy fallback whenever a theist is challenged to prove their beliefs.

Unfortunately that simplicity is very deceptive, and simplicity is important.

The number of axioms we accept must be limited or else we can believe in anything, from flying spaghetti monsters to inter-galactic teapots to invisible dragons. Don’t feel like arguing for something? Just claim it as an axiom and you’re done! To avoid this, we put a limiting law on our axioms known as “Occam’s razor”, which goes roughly as “when all other considerations are equal, choose the simplest solution”.

It is important to note here that the simplest solution is not necessarily the one with the fewest axioms. In information-theoretical terms the simplest solution is actually the one encoding the fewest bits of information. Otherwise you could still take as many axioms as you want and glue them together into a single sentence via a lot of “and”s.

Sneak Peek

We’ve covered a lot of ground already in this post and haven’t even really gotten to the core of the argument yet, so I’ll sketch it out now and flesh it out properly next week. In broad strokes:

  • There is a core set of axioms which everybody accepts (regardless of religion) and everybody must accept in order to meaningfully participate in the world.
  • This core set is almost or completely sufficient on its own.
  • The existence of god is massively complex, as axioms go.
  • Even if the core set is insufficient on its own, there are better and simpler alternative axioms which complete it.

Therefore, by Occam’s razor, the existence of god cannot be an axiomatic belief.

Occam’s Razor and Epistemic Explosions

We have started by accepting a single axiom on the validity of axioms, and all of the relevant circularity. We must now be careful though, for we currently have no criteria for which other axioms we accept. In fact in our current state we are allowed to choose any and however many axioms we want. Don’t feel like arguing for a particular proposal? Just take it as an axiom!

This epistemic explosion puts no limits on what we can claim as fundamental truth. As with it’s opposite, epistemic nihilism, there isn’t actually anything philosophically wrong with this. We are still effectively too close to the circular trap to be able to make that kind of judgement. However, like epistemic nihilism, accepting an epistemic explosion just doesn’t seem practical or useful. If we take a nihilistic view then there is nothing more we can say, whereas if we take an explosive view then we can say literally anything. Either way, we’re philosophically finished. Frankly, that kind of view is just boring.

So, we will add a second axiom to our set, based on a fairly well-known principle: Occam’s Razor. A lot of the historical details around Occam’s Razor are rather fuzzy, including who said it first, whether Ockham said it at all, and why the spelling has changed. These questions are not really relevant to the underlying principle though, which is often stated as “entities must not be multiplied beyond necessity” (Wikipedia claims this formulation is due to John Punch).

The razor has many other various formations, but they all basically boil down to “simpler is better”. Or more practically, if you’ve got two possible explanations for a thing that do an equally good job on all points, pick the explanation that only requires a paragraph, not the explanation that requires thirty pages, two diagrams and an appendix. With all that in mind, we can formulate our second axiom:

Axiom 2: The fewer axioms you need, the better.