Seeking Universal Truth
A few weeks ago, I came across a Medium article written by Matthew Prince, titled “Why No One Should Be an Atheist”. In his article, he argues that absence of proof is not the same as proof of absence, and when applied to the question of whether gods or deities exist, atheists cannot be sure that there is no higher intelligent being looking over everyone. Based on that idea, atheist should be considered as agnostic instead. Besides the fact that his article is riddled with holes, since atheism and other religions are fundamentally different beliefs that should not be confused with the act of ‘knowing’, it still raises a rather perplexing question: What do we actually know?
There are many types of truth, and it can be difficult to define the term exactly, but the 'truth' which this article refers to, and the type which many people tend towards when thinking about truth, is universal truth. Although it is difficult to define, there are a few characteristics which are true to universal truths, which includes objectivity and universal applicability, which is not constrained by time or space. Universal truth can be further characterised into different types, the most obvious one being material truth. Material truth is the fundamental reality around us, and whether that reality is, well, real or not.
Take the device you are looking at right this instance, say a phone, for example. This device is indisputably a phone, since it is a description which we give to these types of devices. However, if one delves deeper and ponders further as a reductionist would, he or she will find that the phone is made of constituent parts, such as a screen, a few cameras, the electronics and all the fancy small parts in the phone which makes it a phone. Repeating the process a few times, you will venture to the level of molecules, atoms, nuclei, and fundamental quanta, such as quarks. As we go deeper and deeper, our knowledge of the material which makes up stuff becomes increasingly fuzzier. We would like to think that we know of such particles, their interactions with other particles, and the universal invisible rules which govern them, but time and time again, we have proven ourselves wrong.
The Test of Time
Scientific progress has come a long way, and yet it has always resolved around the same principle, albeit refined through the years. That principle, or process, is known as the scientific method. It sounds complicated, but it is actually a very intuitive process which everyone applies to a certain extent, particularly during problem-solving. The scientific process involves first questioning, which is to come up with a scientific question which you want answered. Through questioning, a hypothesis is formed, which is the scientific term to use for a supposition, a proposed explanation, or even a guess. Subsequently, the hypothesis is tested via conducting experiments and observing the results, which after analysis and interpretation yields a conclusion possibly proving or disproving the hypothesis made. Through the years, the scientific process has been refined by many notable scientists through the addition of many details such as controls, placebos, analysis methods, sampling strategies etc., but the fundamentals of questioning, observing and interpreting have remained.
Although the scientific method has been excellent in producing results and crucial in society’s progress, there are flaws within it which makes it inevitably imperfect. The problem exist in the second and third step: observation and interpretation. As crucial as observation is in noticing certain trends and patterns in our universe, our senses, or the machines we build to assist us in making those observations and measurements might not reflect the universal truth of reality. One simple example is the observation of certain trends and the plotting of graphs to describe those trends. Say, for a certain experiment, you noticed that your values seemingly fit a straight line, also seemingly passing through the origin.
You then decide to draw a straight line of best fit through those points, passing through the origin. Instinctively, it looks and feels correct, but in reality, the values might not be directly proportionate to one another, instead having another relation which binds y and x together. You have only captured a snapshot of that relationship, and even though your observations are accurate, you are merely observing a few points in the grand scheme of things. Then, you might ask, is the solution to increase the range of y and x, such that is encompasses more values, giving you a better understanding of the big picture? It certainly helps, but however large your range of values, the relationship might still differ beyond that range. Hence, as sad as it is, the relationship you discovered is not a universal truth, but just another ‘could be’ of reality.
Resultingly, scientific knowledge is constantly being updated and changed. The things we understand about our universe today could be proved to be wrong tomorrow, which, to many is frustrating, but to others is fascinating. One personal example is the change of the number of ATP molecules produced from 1 molecule of glucose from 36–38 to 30–32, because of the change to the ATP:NADH and ATP:FADH2 ratios. I remember this example especially clearly because I have grown up learning of the 36–38 number, only to be greatly surprised when there was a change to the number, which was added to the new edition of Campbell Biology. At that time, the significant change to a very fundamental process of life during such a modern era came as quite a shock, but now, I can better appreciate scientific progression.
Math and Logic
If it is impossible to obtain material truth and understand the fundamental reality of our universe, are there other forms of universal truth we can seek? If you have already read this chapter’s title, you might guess a form of truth which is closer to the human mind, since it is something that we have created after all, that being logical truth. Logical truth is a statement which is true regardless of the truth and falsity of its constituent propositions. One very straightforward and obvious example of a logical truth is “if p, then p”.
Logical truth can be applied in many ways, with one especially important one being the vast field of mathematics. Mathematics is a form of logic which uses axioms, being assumptions which are taken to be true, to formulate proofs for mathematical theorems.
However, there are a two problems with this concept. Firstly, theorems in mathematics are limited to the term ‘theorem’, because they are proven to be true if and only if the axioms involved are true. However, proving that the axioms are true is an entirely new and greatly complex problem by itself. Moreover, even if the axioms are true, there are still mathematical theorems which have not been proven. In an insightful YouTube video released by the channel Veritasium, Derek Muller described the fatal flaws in Math, which led to the presence of holes in math, which have yet to be, and will probably never be filled.
The content of that video revolves around an extremely famous german mathematician named David Hilbert, who held formalist views in mathematical philosophy, meaning that mathematics and logic can be considered to be statements about the consequences of the manipulation of alphanumeric sequences of symbols, usually as equations using established manipulation rules. Hilbert thoroughly believed that mathematics is complete, consistent and decidable. This means that any theorem in math can be proven/disproven from the given axioms, and must be consistent with everything else. However, over time, brilliant minds such as Kurt Gödel and Alan Turing has published papers with the concept of self-reference which show that mathematics is incomplete and at times undecidable. On top of that, its consistency cannot be proven, hence that leaves another question mark in math.
The collapse of formalism in mathematics came as a surprise to many, because math is intuitively logical. It is a field created and developed by us humans, so the absence of universal truth in this field is appalling. This is the reason why certain conjectures, such as the twin prime conjecture in math, stating that there are an infinite number of primes which differ by 2, a seemingly simple problem, might never be proven true or false by even the greatest minds.
Once we have accepted that universal truths do not exist, we can then better embrace uncertainty in our knowledge of reality. In this case, embracing uncertainty has a positive connotation to it, because although we can never know something with perfect certainty, it doesn’t mean we stop trying. Just like how we measure something, there is always uncertainty, regardless of the instrument used to measure the item. However, we can work towards reducing that uncertainty, perhaps using a vernier caliper or a micrometer screw gauge instead of a normal ruler to measure the item. At this stage of technology, scientists have went to the extent of using electron microscopes to measure the size of things to the smallest detail, reducing the uncertainty to the lowest levels but never completely eliminating it.
It is through this process where scientists from around the world collectively obtain a clearer understanding of the forever unclear reality of our universe. Just like how Alan Turing created modern computers by fighting to show how certain mathematical conjectures are undecidable, in attempting to know more, we create new inventions, methods and ideas which better the lives of humans on Earth. In having better understanding, we have more confidence in dealing with modern problems such as climate change, pandemics, among other pressing issues.
“Perfection is not attainable, but if we chase perfection we can catch excellence.”
Many people fear uncertainty in their lives, but if you look at it in a positive light, the presence of uncertainty means that there can always be room for improvement. We can never be content with our knowledge, nor can we prove that what we know is correct, and that is why we should take steps to improve on it, or to break it down completely, striving for the unattainable perfection. The adoption and application of this mindset is what has driven science far, and what will drive science even further into the future.
Bayesian Reasoning and Credence
So, what does this all mean for the common folk, who are typically not scientist pursuing the reduction of uncertainty? Some might think that there is no objective truth in our universe, since there is no way to prove that what we know is correct, truth is hence subjective and any version of truth can be justified. Conspiracist might be elated at this notion, inventing more and more conspiracy theories more bizarre than the last, and saying that there is no way to prove that it is wrong. What’s even worse is that the uneducated common folk might believe them, creating a more polarised and chaotic community with unproductive information circulating in the population.
If there is no one right answer, then who gets to decide what the right answer is? To that question, I argue that the answer is no one, and everyone. This is where the subjectivity of knowledge and truth comes in. Everyone gets to decide on what their version of their truth is, and nobody has the right to say that you are definitely wrong. To argue on what the right answer is would be unproductive, and so we should change our perspective in order to make progress in this field.
It is my belief that the answer is not as important as the process of finding the answer, just as the destination is not as important as the journey itself, because the process gives meaning to the answer. Because truth is subjective, the journey should be undertaken by the self, and through that discovery can we find an answer which is satisfactory.
So, what might that process be? In a book written by American theoretical physicist Sean Carroll titled ‘The Big Picture: On the Origins of Life, Meaning and the Universe Itself’, Bayesian inference has been suggested. Bayesian inference is a method to update the probability of a hypothesis being true/false as more and more evidence are surfaced. Observe the following example to understand how Bayesian inference and probability works.
In a particular school, the ratio of girls to guys are in the ratio 1:3. You receive a peculiar hand-written message from a student of this school, asking what you think the probability of the person being a girl is. Since you know that girls take up a fourth of the population of students in the school, you are about to guess 0.25. However, you notice that the letter is written in cursive handwriting, and guessing that if 50% of girls write in cursive handwriting while only 20% of guys write in cursive handwriting, you very quickly formulate mathematical equations in your head and solve the question. Here’s how it is done:
Assume that there are 1000 students in the school. Using the gender ratio, you calculate the number of girls in the school to be 250 and the guys to be 750. Next, using the perceived percentages of specific genders who use cursive handwriting, you calculate that 250 X 20% = 50 guys and 750 X 50% = 375 girls use cursive handwriting. With the updated numbers, you calculate the probability of the person who sent you the letter to be a girl to be 375/(375+50) = 0.882 or around 88%. This is an updated value from the original 75% using the evidence given. If you already understand Bayes’ theorem, you can simply plug the values in, quickly calculating what is known as the ‘posterior probability’.
The above example explains Bayesian probability through a mathematical method, which is not always applicable in real life. For one, you will always never know the probability of the prior, or the marginal, leaving them to be an estimate from the self. However, Bayesian reasoning isn’t always applied in the mathematical sense. After all, if one were to do mental calculations every time a new observation is made, he/she would go crazy.
Bayesian reasoning can be very applicable to how people process information in our universe, because it gives a sense of objectivity in the world of subjective truth. Mind you, Bayesian reasoning is largely subjective, for the main reason that much of the probabilities of either event happening is unknown, and mostly guessed based on personal perspective and experience. The ‘prior’ term in Bayes’ theorem commonly refers to a person’s credence towards a particular topic. Credence is subjective because it is related to the person’s beliefs, which depends on how the person is brought up or influenced during the early stages of his/her life. At the point when he/she is able to think independently and make his/her own judgements, adopting Bayesian reasoning allows one to adapt his/her own credences based on personal observations, be it new experiences, things learnt in class, information gathered from science articles or the web, etc. In this case, having a thinking process to fall back on makes the analysis of new information systematic and reliable.
However, there are a few pointers to take note of when adopting Bayesian reasoning, as suggested by Sean Carroll. Firstly, evidence that favours one alternative automatically disfavours others. This is important to keep in mind because it gives objectivity to assigning likelihoods in Bayes’ theorem. Secondly, all evidence matters. This is even more important to reduce the bias in Bayesian reasoning. A common cause of today’s heavily polarised society is the tendency to stay in ‘echo chambers’, where people listen only to others with similar opinions to theirs. To be effective Bayesians, we have to actively watch out for this tendency, and process whatever information which we receive, not shunning any one out entirely, nor just looking for particular pieces of evidence which fit your beliefs.
Bayesian reasoning is beautiful because it caters to subjectivity, but at the same time, no matter what the personal credence is, say 0.001 or 0.999, if there is enough evidence, evidence will win out in the end. If we are to honestly accept all evidence and assign likelihoods accordingly, what results is a consensus of what truth is, which is as close to what universal truth can be.
Consistency of Knowledge
In a world where universal truth is unattainable, we should instead be searching for consistent truth, which is a form of knowledge which is consistent with everyone and everything else. Consensus of knowledge is crucial to societal progress, as we will be able to move on if and only if everyone is on the same page, similar to that of a group project. Riots, large controversies and fake news, a heavily polarised society and even the acceleration of the Covid-19 pandemic are all largely caused by a disparity of beliefs in society. A difference in beliefs are not all negatives all the time, but when it comes to the small or large sources of friction in society, being on the same page is beneficial most of the time.
When it comes to scientific progress, scientific consensus is the goal, as scientists will be able to take certain established facts and develop on them.
“If I have seen further, it is by standing on the shoulder of giants.”
Regardless of whether you are a scientist, or a random layperson living life to the fullest, I suggest adopting Bayesian reasoning to find out the truth for yourself. Go through the process honestly, and you will find your version of the truth to be both satisfactory and well-justified.