Tag Archives: Axioms

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.

The Ninth Axiom

At the very beginning of this blog, I laid out a set of eight axioms with which I was to derive my philosophy. Since they were spread out across several posts, I will collect them here for convenience:

Axiom 1: Axioms are valid starting points.

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

Axiom 3: There is some underlying consistent reality that is made up of things.

Axiom 4: I (or the thing that I think of as “me”) exist in some form in that reality.

Axiom 5: Things in reality interact, forming temporal and causal relationships.

Axiom 6: My senses provide me with information that is functionally determined by the underlying reality.

Axiom 7: My memory is usually a reliable and valid guide to my past experiences.

Axiom 8: Logic is a valid form of reasoning.

Although I would probably word them differently now, and there are certainly quibbles to be had, I still think the general intent of these eight form a solid foundation for truth-seeking and philosophy.

However, they are incomplete in terms of actually determining how to live your life. I sort of already came to this conclusion in my previous post based on the Charles Taylor essay, but I want to draw some more explicit conclusions from that:

  • My core eight axioms provide sufficient grounding for determining reality and truth, but not for values or decisions.
  • I currently live my life by a so-far-unexpressed set of values which includes truth, consistency, and something akin to secular-humanist values (though that needs much more elaboration).
  • Arguing one set of value axioms over another is impossible as long as they are all reasonably simple and compatible with the core eight.
  • Adhering rigidly to any single declarable value seems to be a recipe for disaster.

With all that said, I present my ninth axiom:

Axiom 9: I value truth and beauty, not necessarily in that order.

The wonderful thing about “beauty” is that it is deliberately vague. Music can be beautiful and I value that. Human life is beautiful, and I do value that. There is beauty in some efficiencies, and I value that. Truth, though sometimes harsh, is always beautiful. The right lie may also be considered beautiful.

The beauty of beauty is its pragmatism. Plus, who can resist the implicit quark-naming joke?

Building Reality, Part Two: The Mind

Five axioms down, three to go. I’ve titled these three “The Mind” because they’re more to do with that kind of concept, but I don’t mean to imply that the mind is necessarily distinct from metaphysics (which was the title I gave the previous three axioms). As I mentioned in the discussion of axiom #4, that’s not true by definition.

Axiom 6: My senses provide me with information that is functionally determined by the underlying reality.

Reliability of the senses is a big question in empiricism, philosophy of science, etc. This axiom doesn’t go quite that far; all it gives us is the fact that our senses are somehow determined by the underlying reality. Maybe we only have access to a subset of reality, or maybe there’s some random transform in place between reality and what we sense. Regardless, we have some sort of access, however mediated or probabilistic.

Axiom 7: My memory is usually a reliable and valid guide to my past experiences.

Reliability of memory is another big question in a lot of disciplines, and there are obviously cases where it doesn’t hold. Amnesia and memory implantation both seem to be real phenomena after all. As with reliability of the senses, I’ve chosen to split the difference. We assume our memory is usually reliable, for some definition of “usually”.

Axiom 8: Logic is a valid form of reasoning.

This one is kind of cheating since I’m explicitly leaving the definition of “logic” so vague. I am intending it here to include forms such as propositional and predicate logic, and all the other weird mental constructs without which it’s hard to make sense of things like mathematics. Perhaps this would be better phrased as something more to do with thought processes in general than pure logic. Hmm…

Regardless, we now have our eight core axioms from which we can start to build up an understanding of the world. I expect to revisit these occasionally as I think up better wordings, or discover missing concepts, but as per axiom #2 I hope not to add to them unless absolutely necessary. Let’s at least see how far we get with just these eight!

Building Reality, Part One: Metaphysics

We now have two relatively basic axioms that let us pull ourselves up by our bootstraps without falling into a nihilistic or explosive view. However, that’s about all they do on their own, so beside these we will lay out a bare handful more axioms that will let us really get going. While several of these axioms may be hard to articulate, none of them should be controversial.

Axiom 3: There is some underlying consistent reality that is made up of things.

There are a couple of different ideas wrapped up in this, most importantly those of existence, consistency, and divisibility. Consistency is hard to define at this level, but is something like “follows unchanging rules”. It should be easy to understand though; if reality isn’t consistent then there’s no way to make sense of anything. It is also worth noting that the “things” which make up reality in this axiom are intentionally vague. They could be atoms, quarks, Platonic ideals, Cartesian egos… What kind of things they are doesn’t really matter at this point.

Axiom 4: I (or the thing that I think of as “me”) exist in some form in that reality.

This one is more straight-forward, it gives us a reference point to work from, although it tells us nothing at all about that reference point. The key here is that the self is part of or contained in reality, not separate from it. It isn’t necessarily a fundamental “thing” in the third axiom’s sense, but it does belong to reality. This is purely definitional: reality is all the things that actually exist, so the self is either one of those things or made up of them.

Axiom 5: Things in reality interact, forming temporal and causal relationships.

This one just works in the concepts of time and causality. Nothing tricky, though lots to argue about if you feel like it. Importantly, this axiom makes causality a property of things in reality, not reality itself. There is no commitment here to the peculiar idea that reality itself must have a cause. Something about the wording of this one still bugs me, but I haven’t been able to pin it down.

These three axioms give us some metaphysical meat to work with, but we need a just a little bit more. I have three more axioms planned for the next post, at which point we’ll hopefully be able to move beyond this low-level mucking about.

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.

An Axiom is an Axiom is an Axiom is an…

In my previous post, I discussed the so-called circular trap and how it does not really seem escapable. I also mentioned that that wouldn’t stop me – I’m basically going to ignore it because otherwise nothing can be discussed. Onwards.

This, of course, leaves us with the question of where to start if we want to move beyond the circular trap. I’m a logician at heart, so I’m going to start with an axiom. And since the circular trap is still fresh in our minds, the axiom I’m going to start with is intentionally circular. In fact, it is:

Axiom 1: Axioms are valid starting points.

Nice and circular, and generally implied whenever somebody reasons from axioms in any situation. Because of this, and because of its extremely tight circularity, I tend to regard this axiom as the beating heart of the circular trap, so it seems like a reasonable starting point. This is where I plant my flag, flying proudly unsupported by anything but itself.

Of course, this axiom on its own doesn’t really get us much in the way of practical consequences. We’re going to have to add a few more axioms to our collection before we can coherently think about all the things we want to think about. But the validity of all the other axioms we use will rest on the validity of this axiom, so I shall leave them for the next post.