A hierarchy of truth

Photo by Zulnureen Shariff on Unsplash

I first started thinking more deeply about what it means for something to be true after hearing a, now infamous, conversation between Sam Harris and Jordan Peterson. They disagreed over whether truth should be defined purely on its correspondence to an objective reality, Harris's point of view, or just on its utility. In the second case, Peterson argued that truth should just be defined on its provision of evolutionary fitness to its believers, which could — but does not have to — correspond to an objective reality. Initially, it seemed odd that someone could claim that truth wasn't directly related to reality. There are surely many useless facts that are nonetheless true and many things that are useful to believe, but don't really exist. However, looking into how we know things of the world, it becomes harder to be sure we have enough of a grasp an objective reality to be able to start pinning truth onto it.

As I discussed at length in a previous post, we make sense of the world through intuitions — implicit models embedded in the structure of our brains — and the explicit models that we build from them. These models comprise the intellectual achievements of science and mathematics, along with the everyday concepts we use to function in the world. When we speak of truths, we are usually referring to statements that are consistent within one of our models. But, beyond their ability to make good predictions, there is no guarantee that our models do correspond to reality. Understanding this starts to give Peterson's view more credence.

If we take a step back from our models of the world, however, we can see that we are continuously confronted with a pure form of truth that is wholly undeniable — our raw conscious experience. This is our one window into an objective reality, from which we must infer all other understanding.

Harris and Peterson are far from the first to have this discussion. Their views are widely explored in academic philosophy, and roughly map on to the correspondence and pragmatic theories of truth. But, as truth statements are always made in relation to a particular interpretation of the world, I want to argue that we can nullify disagreements like Harris and Peterson's by thinking of truths as coming in a hierarchy.

Type 1: the truth of undeniable conscious experience

It is impossible to deny that there are conscious experiences in the present moment. This was stated by Descartes in his famous maxim, I think therefore I am. The truth of everything else can be plausibly denied, but not this.

A major aspect of our experience of the present is the information received through our senses. The experience of this raw sensorial input, before its interpretation, is what I call Type 1 truth. Given this input, our brains make use of our internal models to cluster it into representations that allow us to interpret the world — we see the pattern of colour and light that makes up a tree and interpret it as a single entity.

It is easy to mistake these representations with the conscious experience of them, but they are always reliant on a subjective framing of the world, so cannot be undeniable Type 1 truth. This is evident when our senses deceive us — we thought we saw a tiger in the bush, but it was just a striped succulent. There is an error in our interpretation of the world, not in our conscious experience of it. In the normal flow of life it is difficult to spot the difference between our conscious experiences and our interpretations. But, it is both possible and instructive, being the explicit goal of many forms of meditation.

The other crucial part of our conscious experience is thought. When investigated more closely, the raw components of thought can actually be seen to be mentally generated sensory experiences. Our brains represent their inner workings in a way that they automatically understand. Emotions, for example, are experienced directly in the body — anxiety is evident as your legs turn to jelly, or anger as a flame stoked in your chest. Alternatively, more mundane thoughts may consist of a mental experience of a visual image or imagined sound. Even a purely conceptual thought is usually experienced in the form of language spoken in the head, with other subtle bodily sensations accompanying it.

All that we can be sure of is therefore presented to us right now, at this very moment, through sensorial experience. However, in this influx of information, we notice patterns that we can exploit to make predictions about the behaviour of our environment. These patterns can be distilled into fundamental ideas about how the world works, which can be used to construct new statements about the world...

Type 2: truths based on axioms.

The models we have of the world, built up from axiomatic assumptions via logical reasoning, give us a great depth of understanding. Assuming we have selected the appropriate axioms, we can find true statements that work together to build self consistent and complex models. These truths, which only exist within the frameworks of our models of the world, are what I call Type 2 truths.

The axioms that are used to build our models are arrived at through our intuitions — the fundamental ideas inferred from Type 1 truth. Some of these axioms are so intuitive that it seems crazy to doubt them. Others are on shakier ground, but can provide a framework for thinking about the world that is not easily dismissed. To address the difference in the solidity of axioms, Type 2 truths are best split further into two categories.

Type 2a): truths deduced from axioms that no one doubts.

As humans, we share a large set of fundamental intuitions that are so widely held and seem so obvious that we don't doubt them. If someone told you that if you were given two grapes, followed by three, you would end up with the same number as if you were given three grapes, followed by two, you would be rather nonplussed. This, however, is one of the core logical axioms of mathematics.

Photo by Maja Petric on Unsplash

The axioms of science are similarly self-evident — we assume that the laws of physics are fixed. This ensures that any well designed experiment will produce the same understanding if it is repeated at any time or point in the universe.

Fundamental axioms, such as these, allow us to build hugely complex and intricate models that possess extraordinary predictive power over the world. But, the fact that science has been so astronomically successful has drawn many people into believing that scientific truths correspond to an objective reality. Although it doesn’t make a lot of sense to doubt them in most contexts, even a complete scientific theory cannot be epistemologically free of all doubt. Instead the real basis for Type 2 truths is their predictive power.

Put differently, we can only understand the world through the limited capacities of our brains. The models we build are such that they provide a working interface to our brain, via our intuitions, rather than corresponding directly to an objective reality.

Applying this view to mathematics allows us to reduce it to a series of tautological statements, which follow from the axioms that are immediately evident to our intuitions. This was the opinion that Bertrand Russell started to converge on later in life, after his initial attempt to map out the base of mathematics with Alfred North Whitehead in the Principia Mathematica. Even hardcore mathematical realists cannot deny that the hope of basing all of reality on a rigorous footing was killed off by Gödel’s incompleteness theorem. Reducing all truth statements to tautological statements is known as the deflationary theory of truth and is rather alarming at first glance, but surprisingly difficult to refute.

Holding a deflationary view of mathematics does not diminish its achievements though. Instead, it gives it a different position in the strata of knowledge from that of a supreme reality. Mathematics becomes the way in which we can map logical truths onto our inbuilt intuitions. But, this does confound any attempt to think of mathematics as fundamental outside of conscious experience, which is required to infer its axioms.

Overall, the key to Type 2a) truths — the reason they seem like they should provide an objective view of reality — is the universal acceptance of the axioms behind them, not the fact that they are undoubtable. However, the fact that these models do not seem to contradict themselves points to something deep in our widely held fundamental intuitions. We can therefore retain a sense of wonder at the fact that the models we build from such universal axioms seem to work so well for explaining the world. After all, science and mathematics transcend cultural —presumably even interplanetary — boundaries.

Taking this back to Harris and Peterson's discussion, it is unarguable that science and mathematics are useful, so therefore correspond to a pragmatic view of truth. But, the profound consistency that they demonstrate makes them our best tools for inferring the properties of an objective reality. They are the results of a shared axiomatic language that everyone can agree upon, going beyond Type 1 truth, which is necessarily impossible to communicate.

Not all the axioms of our bodies of knowledge are so watertight, however. There are many that are not universally accepted, but can still provide great utility when behaving as if they are true. This brings us to the next and final category.

Type 2b): truths deduced from disputable axioms

When trying to make sense of the world, it is often easier to take a complicated and disputable axiom as given, rather than trying to define everything from first principles. The truths we infer from axioms that are not universally held are what I will call Type 2b) truths. Their value is purely based on their utility — the ability of one to achieve one’s goals when making rational decisions under the assumption that they are true. As pointed out by Bret Weinstein, you might believe that a porcupine can throw its quills. While this is not the case, the fact that you give it a wide berth would help you to evade its tail, which can swing around surprisingly quickly.

Religious truths fall into this category. They are typically derived from axioms based on faith, defined in the founding stories of a religion. For example, the 'truth' that one must behave morally in this life to proceed to heaven in the next. These sorts of truths can convey various psychological and sociological advantages to believers, while being based on axioms that are completely culturally dependent. 

Art can also elucidate truth in a culturally dependent manner. It directly taps into our emotional intuitions to convey something that is not initially obvious. Analogous to how science allows us to discover unintuitive truths about the nature of gravity, but operating in a different realm of experience. A moving piece of music, for example, can convey emotions fundamental to the human condition that cannot be got at through scientific argument. A powerful novel can let us experience the life of another with an understanding beyond that accessible through rational thought.

From these examples, you can see that there is great utility and importance in Type 2b) truths. However, the axioms from which they are derived are perpetually open to debate in a way that Type 2a) truths are not. Crucially, Type 2b) truths lack consistency, as contradictory axioms can be useful in some situations but not in others. Type 2b) truths are therefore unreliable as a way of gaining knowledge of an objective reality, but are still invaluable to human flourishing. Without them, we would be unable to operate efficiently in the world, and would be robbed of much of what makes life fulfilling. But, in their inherent inconsistency there is a huge potential for dangerous confusion, just consider all the lives lost in religious wars.

If we hold Type 2b) truths lightly, however, we can obtain their utility without thinking they correspond to an objective truth. The invocation of a deity, for example, allows us to reason about the world in a way that is intuitive to us — personifying abstract concepts gives us ways to make use of our emotional intuitions to relate to them. Behaving with the compassion of Jesus is not something that comes immediately from logical argument, but can convey significant benefits. While bearing in mind that we are dealing with Type 2b) truths, rather than an indisputable reality, we can gain this advantage without taking the biblical story literally. 

Photo by Peter Nicola on Unsplash

The value of a hierarchy of truth

Many truths are therefore dependent on the models and intuitions we have of the world, their validity depending on the feasibility of their axioms. This allows us to resolve Harris and Peterson's disagreement by seeing that they were really pointing to different levels in the truth hierarchy.

Although we can only be sure of Type 1 truths, the sheer power and consistency of Type 2a) truths allow us to understand what we can about a greater objective reality, given the tools of understanding provided to us by evolution. But, we can still take advantage of the murkier world of Type 2b) truths. We don't have to reduce art or religion to a rational and logical pursuit, we can allow it to invoke profound non-conceptual or emotional insights, while maintaining that they may only be relevant to a particular view of the world.

This way of thinking can help to tease apart and identify the differences in the way people see the world. Much disagreement boils down to statements of Type 2b) truths with misaligned axioms. As many people don’t find the above distinctions clear, they operate under a pretence that all truth claims are referring to an objective reality, without thinking deeply about the axioms that led them to the truths they hold. This is as true for scientific materialists as it is for religious fanatics. 

After reading this, I hope you will take some time to investigate the fundamental axioms that make up your personal view of the world. You may realise that many of your beliefs are Type 2b) truths — they may provide great utility, but can never be held on an undeniably firm foundation, and will often be held differently by others. Although Type 2a) truths can be given a higher status, they are so tied up in the workings of the human mind they can never indisputably represent an objective reality.

Ultimately, the only thing we can be sure of is our immediate conscious experience, not the way we interpret it. Remembering this, and taking time to investigate it, is one of the most enlightening things we can do.