Most of us understand the power of knowledge, but rarely scrutinize our means to derive truth. I want to start with the absolute basics to help build some skepticism and release ourselves from dogmatic convictions we’ve gained in our lifetime and generations.
What we believe is true can be doubted to a regression to the fundamental beliefs we built them on – otherwise known as axioms. These axioms are the underlying framework on which our entire understanding of knowledge is built on, and we rarely confront it – perhaps because they themselves cannot be deemed true with an absolute certainty. So a certain amount of “faith” is required before we build our models of truth.
This may seem ludicrous at first – almost childish – to ask “why do you think that?” ad infinitum, but is often a necessary process to break down dogmas that get in the way of an accurate model of the truth – as Silicon Valley tycoons often call it, “thinking in first principles”. As Rene Descartes traced his knowledge back, he found the only thing beyond doubt was the famous dictum I think; therefore I am. Interestingly, the only thing we can truly know is the existence of our own consciousness – not anyone else’s (see p-zombie).
Think of the implications! Everything you believe and hold on to so dearly may in fact be a figment of your imagination. Our moral code, legal frameworks, free will, science – perhaps even what we experience as reality is no more than a simulation.
Okay, perhaps it is not so ground shattering until you truly try to devolve an idea to its core yourself.
Limitations of the Scientific Method
Let us take science as an example. Assume that we do not doubt our perception’s capacity to empirically model our environment (although the limitations, even at a higher level, are obvious). We still understand that science is based on the principle of induction. The idea that the future can be predicted based on our experience of past events.
Many of you may have heard of the thought experiment of the “black swan”. We cannot safely say, after seeing any number of white swans that “all swans are white” except perhaps if we can, without a doubt, see all swans in the universe and see they are all white. Seeing a single black swan would refute that statement.
The universe is under no obligation to abide by its past behavior.
The idea is not to discredit science with this example – but to simply point out its inherent flaws and fallibility. The scientific method has built unprecedented understanding of our world – but to replace one dogma for another, as the stakes of modernity become increasingly higher, we should understand the process as well as it’s results.
Just as we create thousands of new laws to cover all the nuances of reality, we find that no set of numerable axioms are “enough” to encapsulate truth.
Gödel, with his incompleteness theorem, proved that:
First incompleteness theorem
Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F.
And
Second incompleteness theorem
For any consistent system F within which a certain amount of elementary arithmetic can be carried out, the consistency of F cannot be proved in F itself.
So long as a set of finite axioms are consistent (do not contradict), there will always be a statement that cannot be decidable (proven true or false).
This may not seem relevant beyond formal mathematics, but it implies that within a given set of assumptions, there will always be a true statement that cannot be proven within that set.
As computers and coded in arithmetic with defined axioms they are limited by Gödels theorem – a ground breaking idea in mathematics and computation theory. We truly cannot reduce the universe to a Theory of Everything – atleast not without knowing it.
We have now shown (proven) that both the scientific process and computers, saviors of modernity, are fallible – just like the countless religions and political dogmas before. The Sorcratic paradox seems to be the only truth here; “The only thing I know is that I know nothing” – consistent with the pattern of Godel’s self-referential insights.
Mental Models, and Their Limitations
Assuming no quantum mechanics or voodoo applies to the brain; the same physical laws of the universe applied to the neural structure of the brain – composed of atoms at various velocities and positions. Consider that, on a pool table, knowing every minute detail – from the angle at which the billiard ball is hit, the friction of the felt, the air resistance, etc – you can accurately predict the behavior of each ball the moment you hit it. The same principles could apply to the mind – composed of physical material – just as predictable; entirely deterministic. Even applying randomness, you have effectively voided any sense of volition as merely an illusion. Now the human mind, as the likes of Robert Penrose posit, may be above such rigid physical laws (think, again, Gödels theorem – if there was something that is truly irreducible, it may as well be consciousness – we’ll talk about determinism and free will/consciousness at a later point, in depth).
Think about your right-wing uncle, your schizophrenic father, your drug addicted friend – all of whom justify their beliefs due to their undying beliefs. Try convincing them otherwise – it is near impossible. Each one is hampered by a myriad of chemical imbalances, disallowing them to think outside of their current paradigm. The schizophrenic, perhaps through overactive dopamine faculties, will twist every attempt to discredit their understanding as one that further proves their paranoia (“someone is out to get me, you telling me there is not is evidence of that”). Humans were born with an innate tendency to form strong belief systems so that we aren’t vacuous skeptics, incapable of moving forward with an action due to excessive doubt. Our ancestors who could not make up their mind simply exited the gene pool.
These exaggerated examples are not meant to be shown as aberrations or anomalies, but simply make clear the underlying limitations of our cognition. What sets us apart from them is our ability to think critically, not just of the axioms themselves, but as an agent capable of harboring them.
Case in point, the less you know, the increasing confidence in your own knowledge – famously known as the Dunning-Kruger effect. You simply cannot know what you do not know – and absence of evidence is not evidence of absence (tie this back to the problem of induction and you will begin to see a pattern). We form patterns from countless experience and form a distorted render of causal effects we over-fit in uncharted territories.
Why are we discussing this? Because by breaking down our fundamental axioms, the feeling of knowing the ball must fall down when it is up, or that you are in control of your mind, you liberate yourself from holding loyalty to any belief. Axioms should be formed and nullified when needed, as to build a model of reality that is beneficial. Although we will discuss free will at a later point, I argue that (at least it is pragmatic to think so), our ability to recursively identify our thoughts, and to moderate them, renders our closest [simulation] to true free will.
The Universe that Doesn’t Want to Be Modeled (Completely)
Keep in mind that a logically consistent set of axioms cannot be complete; a set with contradicting axioms can.
The idea of truth and falsehood as being mutually exclusive is ingrained in us as a fundamental fact of logic (by now, it should become obvious what I am saying). But the ‘law of exclusive middles’, the idea that a statement can either be true or false, is victim to the same scrutiny.
What is true here and now, may not be true in a different point in space-time, in other words, every ‘law’ we make (no matter how accurate) should come with a timestamp and geo-location (and a few disclaimers). Each instance of the universe, by definition, is unique. That’s what makes life so beautiful – as we skillfully make our best approximation of reality to help navigate it, always bounded by it’s inherent limitations. Neither logic nor faith can independently guide us, but the careful intertwining of both. The folklore and archetypes of our history are symbolic of patterns of life, not prophecies; history rhymes, not repeats. The papers of scientific reviews are a probabilistic model, limited by the biases, contexts, and understanding of the experimenter and the specimen (subset of the universe) under its observation – not a precise simulation.
In Laplace’s thought experiment, a demon, if it knew with infinite precision the location and momentum of every particle – it can accurately predict the universe, and reduce it to its fundamental laws. We cannot simulate the universe with our computational models as it would need to be as big as the universe or larger (and by doing so, we paradoxically increase the boundaries of the universe). The demon is part of the universe it is trying to model, and cannot do so without referencing itself; such same self-reference was actually the building blocks for Godel’s theorem.
In other words, the complex system of the natural world is fundamentally irreducible, yet, we know that there are parts of it that are reducible as we clearly can find some level of order – our job is to model such “pockets” but understand our limitations. There is no panacea; no master key nor a Theory of Everything. Oddly enough, it is the blind spots, the “black swans” in our models that maintain the spice to life. We can only hope to find some periodicity in this chaotic system so that we can exploit it to our desires.
Laplace’s demon, turns out, is no more than a thought experiment, and that leaves us just enough room to squeeze in our superstitions and speculations (even free will).
So far our best bet is that of pragmatism. To empirically and inductively form probabilities and, even still, not take them too seriously.