The Dependence Tree

Introduction: The Rise and Fall of the Statement Calculus

A great deal of modern epistemology has treated the study of truth and belief as a study of statements. In its purest form this amounts to a reductionism, a calculus where belief in a statement can only be justified by other statements. This leads to the problem of infinite regression, as the need for justifying statements never terminates. Nevertheless, attempts have been made to use this sort of epistemology to build a foundation for science and mathematics. The idea was to define a set of foundational axioms from which everything else could be logically deduced. This was discredited by Gödel’s incompleteness theorems.

Over time, epistemology has progressively moved past this classical statement orientation onto other approaches. One such approach is the notion of ‘epistemic dependence’. This refers to the fact that knowledge depends on, say, properly functioning memory. This concept contrasts with the statement calculus in one crucial way: a dependence is not the same thing as a premise. A premise is a logical proposition, reducible in principle to a statement. There may be an implicit premise in believing my eyes, but my eyes themselves are not a logical proposition.

Why does this matter? Because dependence does not inherently lead to infinite regression or require an arbitrary starting point. Whereas a methodology that insists on reducing dependence to premises will inherit that dead end. The following discussion explains how the principle of epistemic dependence gives us the keys to the kingdom: a fundamental and universal epistemology.

The Law of Dependence: The Great Fallacy of C. S. Lewis

In his apologetic classic Mere Christianity, C. S. Lewis famously made the following claim about God: “When you argue against Him you are arguing against the very power that makes you able to argue at all: it is like cutting off the branch you are sitting on.” In this well known quote, Lewis simultaneously did two things. First, he helped popularize the most apt and hilarious metaphor for a fatal epistemological fallacy. Second, he committed that fallacy himself.

To understand this, we need a more involved metaphor. Suppose a scientist tries to determine whether human eyesight is valid. He takes a human eyeball to the laboratory and puts it under the scalpel. This gives him some clues but isn’t enough. He puts it under the microscope. This is more revealing but still not enough. Then he realizes the lens is dirty, cleans it, and finally finds what he’s looking for. “Hmmm”, he says, “the evidence appears conclusive that the human eye is completely incapable of providing accurate information.”

The fallacy here is self-explanatory: if his conclusion were true, the evidence it was based on would be invalid, because it depended on the validity of his eyesight. His case is therefore fatally contradictory. But what if he drew the opposite conclusion, that the eye does provide accurate information? That would just be a more subtle form of the same fallacy. Because if the eye is validated by the results, it logically follows that it was not yet validated prior. But the experiment still depends on the eye being valid, because if it’s not, then the results are meaningless and he has proven nothing. The entire experiment is self-contradictory.

And that’s exactly what Lewis did. He may have used theology rather than science, but the contradiction is the same. He uses God to validate reason. But that means that reason is not necessarily valid before establishing God’s existence, making it impossible to do that in the first place. Thomas Aquinas’ five proofs go out the window. (It’s actually even worse than that: how can anything at all logically follow from reason not being valid?!) You can’t use anything resulting from reason to validate reason, theological or otherwise. The necessary presumption of reason’s validity is INESCAPABLE.

However, this creates a chicken and egg problem. If God did create us then He probably is the power that enables us to argue. Is that out of the question now? No. That would be like saying biochemistry cannot enable us to see. These objective realities do not cease to be possible just because of our epistemic position. Like methodology, epistemology does not translate to ontology. In fact, their relationship can be mutually paradoxical: ontologically, God is the source of our reason; epistemologically, our reason is the source of God.

Lewis made an ontological assertion that God is the power behind our reason. But he erroneously translated that into an epistemological argument. In doing so, he sawed off the branch he was sitting on by falsely accusing atheists of doing the same thing, because he now had the chicken and the egg the wrong way around.

It turns out that this distinction between epistemology and ontology corresponds to a fundamental distinction within epistemology. Consider the fallacy of our mad vivisectionist. It’s not a fallacy because of what we know, but because of what he knows: that he’s trying to evaluate the very instrument he’s using to evaluate. It doesn’t actually matter here what the truth about the eye is, let alone the vantage point of educated observers coloured by worldview and metaphysics. What matters is the dependence on the eye from his perspective. In epistemology this orientation is called ‘internalism’.

In contrast, ‘externalism’ judges an individual’s belief from the outside. That is, it does proceed from the vantage point of educated observers coloured by worldview and metaphysics, judging individuals who may not agree with those premises. So unlike internalism, externalism does not turn ontology on its head. It rather proceeds from ontology. Lewis’ epistemological critique of atheism was externalist, and because he failed to recognize the limit of that approach, we can say that he committed an externalist fallacy.

And with all of that, we can finally get to the point. How many times have I used the word ‘depend’? This is about ‘epistemic dependence’, specifically internalist dependence. And the fallacy we have identified from that dependence reveals a law:

It is logically impossible for a perspective that depends on the validity of x to evaluate the validity of x.

This ‘Law of Dependence’ is, in fact, an absolute and universal law of epistemology. That’s because it’s internalist, and so is not tied to any ontology. So all our petty differences over God and materialism and metaphysics are irrelevant. The Law of Dependence is not just true for 21st century science. It’s true for the medieval church. It’s true for a brain in a vat. It’s true for the rabbits in Watership Down. The only question now is: how is it actually useful?

The Dependence Tree: A Fundamental Epistemology

With our internalist understanding of epistemic dependence and the law it imposes on epistemology, we can now return to the difference between a dependence and a premise. A premise is a proposition used to justify other propositions. But this begs the question as to what premise justifies that premise ad infinitum. Unless we accept ultimate circularity (coherentism), we are forced to choose some propositions to assume as true.

The magic of internalist dependence is that it doesn’t give us a choice as to where the buck stops. Because, whether we like it or not, everything we believe about the world ultimately traces back to, and can be traced no further back than, one ultimate dependence. That dependence is the immediate experience of our feelings and perceptions, which we call phenomenology. As a premise, you can call it arbitrary. But as an internalist dependence, it is incontrovertibly the very bottom of the tree. Don’t believe me? Check your externalism.

Ergo, we have a fundamental and universally valid conception of epistemology as a tree, not of premise/conclusion statements with an arbitrary foundation, but dependence relationships with an inescapable foundation, which is the individual experience we call phenomenology, on which depends the shared experience of society, on which depends our sciences, and for those so inclined, religion. That is, the Dependence Tree.

So what’s the point? The principle point of knowing a law is not breaking it, and calling out those who do, like C. S. Lewis. The Dependence Tree perspective systematically enforces the law of dependence, keeping it firmly in the spotlight. And because it’s universal, no one is exempt. You can’t deconstruct it away as ‘western’ or ‘secular’. It will cut through any ontology you try to throw at it, making it the ultimate weapon against epistemological fraud.

But the potential of the Dependence Tree is not just destructive. It has implications for moving past the pathetic stalemate of moral epistemology, where the perceived choices are religion, nihilism and the utilitarianism that gave us Covid. I have already used it to show that suffering is not an arbitrary basis of right and wrong. But to really appreciate the potential of the Dependence Tree, let’s take a look at where we are.

Conclusion: The Tower of Babel

There is a certain relativity that must be accepted, because my dependence tree, or at least its fruit, is not the same as yours. We live in a forest of dependence trees, each with a finite view. But we refuse to accept that because we’re still trying to build the Tower of Babel. Screw justified belief, we want the truth goddammit! And how is that working out?

As the fingerprints of money changing pimps grow ever more visible, even science must now grapple with institutional distrust. While educated social elites remain complacent in self-superiority, many ordinary people have become so disillusioned they can barely tell what’s real. As the consensus breaks down, we turn to mutually antagonistic political narratives, from the mainstream to the rebellious, resulting in a social media propaganda war. We can’t even trust each other’s information sources, because we can’t agree which sources serve which bad guys. And just when we need it the most, enter AI.

But the breakdown of societal consensus gets worse, because popular dissent does not stop at politics but extends all the way down to basic ontology. We’re now at a point of mass rebellion against views still largely taken for granted in academia, including positions as foundational as materialism. So we’re back to fighting over religion and metaphysics, and the deeper our divisions go, the less common ground there is to resolve them.

It doesn’t have to be this way. The Dependence Tree is not only something we can agree on, but something we must agree on, because its reality is undebatable. And it forces us to acknowledge the primacy of human experience, first individual and then collective. If we can find the humility to accept that internalism must have the final say, that the objective stands on the shoulders of the subjective, that ALL knowledge stands on human experience, and embrace the relativity of belief justification, then we can all stand on a common ground, which is the true structure of epistemology itself, knowing which way is up. And then we might find that it’s not that difficult to start converging again.