Tag Archives: Epistemology

An Atheist’s Flowchart, Part 3: Proof of God and Russel’s Teapot

In the first part of this series we covered the difference between axiomatic and derived beliefs and Occam’s razor. In the second part I made an argument that belief in any sort of traditional god cannot be axiomatic. In this post I will make the argument that belief in god cannot be derived either; the conclusion, following from both points, is that one cannot and should not believe in god. This will complete my first angle of atheist approach, the one I called epistemic.

In order for a belief in god to be derived, it must be naturally supported by some other beliefs which may themselves be derived or axiomatic. Either way, if you follow the chain of beliefs-supporting-beliefs back far enough you must end at an axiomatic belief at some point. Let us then consider the ways we might go about proving the existence of god.


The first and most obvious way to prove the existence of god is via empiricism: if there were observable, empirical evidence whose only reasonable explanation was the existence of god, then that would be sufficient. However, there is none. God does not regularly perform otherwise-inexplicable miracles on live television; there is no scientific experiment which suggests that god exists; no claims to see god, or hear his voice, or sense his presence, have ever been substantiated.

As an empiricist I must be consistent: if such evidence were ever to appear then I would happily change my mind on this whole point and consider myself to be mistaken. Until that point, the absence of evidence is, in fact, evidence of absence.

Russel’s Teapot

I’m now going to take a brief sidebar to elaborate on that last point since the burden of proof in this situation seems to be a common source of confusion. Succinctly put, the burden of proof in this case does in fact fall on the person making the argument for the existence of god (i.e. not on me). This can be seen most easily via a common analogy known as Russel’s Teapot. More formally, claiming that something is true because it has not been proven false is a fallacy: the argument from ignorance.

Of course, the opposite is also a fallacy: I cannot claim something is false simply because it has not yet been proven true. However this does not prevent absence of evidence from being evidence of absence in all cases. Per Irving Copi:

In some circumstances it can be safely assumed that if a certain event had occurred, evidence of it could be discovered by qualified investigators. In such circumstances it is perfectly reasonable to take the absence of proof of its occurrence as positive proof of its non-occurrence.


The other common approaches to prove the existence of god are via logic, the most popular of which are the many different ontological arguments. It would be counter-productive to try and enumerate and disprove all the various formulations of these arguments; suffice it to say that all of the more popular ones have been specifically debunked by philosophers and logicians at some point already. But more importantly, all of these arguments start with additional axioms beyond the core set. Even the full set of nine in which I believe do not provide for any of them.

As with the empiric approach, I must be consistent: if a logical argument were presented to me for the existence of god, whose only axioms were the nine in which I believe, then I would change my mind. But I do not believe that is likely to happen.

In fact, if you take a broad enough view, these two points are equivalent: since empiricism is effectively built into my axioms, my rejections of both the empirical and logical attempts to prove god are the same: none of the arguments presented are sufficiently supported based on my axioms.

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.

The Scientific Method

All of this wandering around thinking about rationality, empiricism, truth and knowledge now finally culminates in the scientific method. This is, of course, not the be-all and end-all of truth or knowledge, but it is one of the most useful tools we have for probabilistically determining the shape of reality.

If you’re not familiar with the scientific method (really?) it goes something like this:

  1. Have a question.
  2. Take a guess.
  3. Find something that your guess predicts.
  4. Measure it.
  5. If your measurement doesn’t match your predication, go back to 2. If it does match your prediction, go back to 3.

You will note, of course, that the scientific method never stops. It is an endless loop of trying out new ideas and finding ways to verify or disprove them. Every successfully predicted measurement is another step on the way towards statistical certainty, but of course like any empirical practice we can never get all the way there.

It is also relatively important that your guess (step 2) must be capable of making predictions (step 3). Every so often someone will claim to have solved a great complicated scientific problem by the means of some mysterious new substance. When asked about this substance, they are incapable of predicting its properties other than that it makes their theory magically work. These ideas do not fit in the scientific method – if it doesn’t generate predictions, it’s not science.

Truth and Knowledge


While empiricism gives us some probabilistic, mediated access to reality, our senses are frequently consistent with each other. However, we have no way of knowing if this input represents what is or simply some high-level abstract interpretation of a transformed version of what is. Both of these could be called “true” however in normal speech, so I will borrow the Buddhist doctrine of Two Truths. In very brief summary:

Absolute Truth: The underlying reality of what is.

Relative Truth: What we consistently and reliably interpret of what we sense.

Absolute truth might, for example, be nothing more than atoms interacting according to physical laws. Regardless, it is exactly the reality accepted in axiom #3. Relative truth is the world that we construct from empiricism, with tables and chairs and clouds and cats and dogs. Even if, fundamentally, there is nothing that is a dog in the underlying reality, the existence of dogs is still a relative truth, a practical concept useful for navigating the world.


The definition of knowledge is another big problem in philosophy, and is more-or-less the defining question of epistemology. Based on our axioms so far and the previous two posts, I use the following three definitions of knowledge:

True Knowledge: This is the definition of knowledge that pedants like to trot out when arguing for epistemic scepticism. “True” knowledge is knowledge of absolute truth (see above) which is impossible because of the circular trap. We have no way of knowing that the axioms we have taken are correct, thus no way of knowing anything else which we might derive from them. However, this meaning is almost never used in non-philosophical debate.

Strong Knowledge: Strong knowledge is knowledge based on “inviolate empiricism”; facts like gravity1 that consistent across a truly enormous number of observations (all relative truths, of course). Logical derivations from axioms (and from inviolate empiricism) also qualifies of course: knowledge of algebra is strong knowledge. This usage occurs outside of philosophy debates, but mostly in scientific and other formal contexts.

Weak Knowledge: Weak knowledge is knowledge based on probabilistic empiricism. It is reasonable, for example, for me to say that I “know” certain things about Shakespeare, but the chain of actual facts and observations between myself and him is quite long and tenuous. Nonetheless, I say I know these facts because they are still far and away the most probable explanation of all the various things I have experienced. This is the most common usage of knowledge in informal conversation.

(1) Yes, I know, quantum theory and relativity etc etc. What goes up must still come down.

Empiricism and Probability

We have a set of tools now for operating on truths, but we lack the raw materials to operate on. Fortunately there is another common epistemic view.

Empiricism is the view that knowledge of reality comes from the senses. As I mentioned in my brief discussion of axiom #6, we are not assuming quite this much, though we are taking at least a partially empirical view. Our senses provide some sort of access to reality, although that access may be mediated, transformed, inconsistent, etc. Due to this caveat, we cannot simply make knowledge-claims based on our senses: “I see _ therefore I know that _.” could be perfectly wrong.

However, we can say “I see _ therefore I know that something in reality is causing me to see _”. This is somewhat more accurate though less useful. More importantly, we can appeal to the consistency of reality (axiom #3), the partial consistency of memory (axiom #7), and the validity of logic (axiom #8) to make probabilistic empirical claims, such as the following:

I see _, and I have many memories of seeing the same _, therefore it is probable that I will continue to see _.

Of course sight is not the only possible sense here; one can make similar claims using hearing, smell, touch, etc. By adding an appeal to causality (axiom #5) one can also make probabilistic claims about correlation:

I see X and have a memory of just seeing Y. I have many memories of seeing X shortly after seeing Y, and no memories of not seeing X after seeing Y. Therefore it is probable that if I again see Y, I will shortly see X.

(I use X and Y instead of _ above because I have two blanks to fill in that I wish to distinguish between). Just like any probabilistic claim, the more samples you have (in this case memories) the stronger the claim.

It is these probabilistic claims that we can use as raw materials, feeding them into our rational tools to produce an understanding of reality. Of course we cannot use this to achieve whatever constitutes “real” truth with any certainty, but strong probabilities are better than nothing. With rationalism and empiricism in hand we will use the next post to delve more deeply into the concepts of truth and knowledge.

Rationalism and Certainty

The question of what constitutes or defines knowledge is another big problem in philosophy, and on its own forms what is called epistemology. I leave aside (for now) the central epistemic questions in order to discuss certain common perspectives; I will return to the broader questions in a few days.

Rationalism is, loosely defined, the view that knowledge and truth come from reason, logic, etc. By taking axiom #8 we are inherently taking what is at least a partly rational view, although there is somewhat more to it than that. However, on its own this axiom gives us a whole slew of tools in the category of what I shall call “logical systems”. These include propositional and predicate logic, algebra, set theory, probability and all the other systems that are strictly abstract (despite possible practical applications).

The critical point is that these systems are only tools. While they do produce internal “truths” (such as the statement that two plus two is four), all of these internal truths are at root truths by definition. Even the weirder, hard-to-prove theorems do eventually fall out of starting definitions; that’s how we define a proof. More interestingly, these tools give us methods of “lossless” operation on existing truths. The logical form of modus ponens takes two truths and produces a third truth of the same strength; no certainty is lost in the deduction.

These tools are extremely powerful, but like all tools they are useless on their own; they require raw materials to operate on. There are perhaps certain interesting facts that can be derived from our core set of eight axioms, but I would be very surprised if you could get very far (I have not even bothered to try). Instead, we need some other system to generate facts for us to operate on. Next time I will look at where we can get raw materials to feed our rational tools.

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!