On an Axiomatic Approach Towards Interpreting Truth
Some of my musings about the indeterminacy of truth and the complexity of attempting to understand it
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.
— American Declaration of Independence
What is the truth? You would be hard pressed to find a question more ambiguous and cryptic than that. And yet, it’s a question that we humans have tried to answer for thousands of years. Debate about the nature and accessibility of our universe’s truth(s) has existed since at least Socratic times in Ancient Greece and has, since then, been an area of philosophy populated with various interpretations and beliefs about reality over the centuries. Today, the quest to discover truth has taken many forms, with modern science being a reflection of the pragmatist belief that a true proposition is a hypothesis that is verifiable by the scientific method. That is, if I make the statement “an atom is the smallest, indivisible unit of matter” and it is consistent with any scientific inquiry that I undertake (usually in the form of experimentation), then that statement is true.
However, this notion of truth clearly is not absolute — at least not temporally. If there’s one thing science has shown us, it’s that our understanding of the reality of the world we live in is constantly changing and that our collection of true statements changes with every new discovery. For example, while it was indeed once believed that the atom was the smallest, indivisible unit of matter, we now know that this is not the case, because we have experimentally observed the existence of smaller units within an atom. So the statement “an atom is the smallest, indivisible unit of matter” is no longer verifiable by the scientific method and therefore is not considered true anymore. Consequently, many philosophers who fall in the historical relativism camp believe that the truth is always relative to its historical context and that there is no constant truth.
Most people today happily embrace this pragmatic, contextual interpretation of the truth and choose to live their lives accordingly. After all, this scientific notion of truth affords us the flexibility to change our collection of truths as and when new scientific discoveries are made and lets us avoid asking deep existential questions about the nature of truth because we can simply point to experimental evidence to justify the veracity of our beliefs. However, a key failing of this view of truth is that it only accounts for those beliefs that are testable and correspond to certain physical manifestations. This brings me to what I believe is a huge issue with complete reliance on scientifically derived truth: science doesn’t tell us why certain fundamental truths are true. We can easily accept tautologies such as “if I flip a coin, it will land on either heads or tails” and scientifically derived results without much trouble but we are left to fend for ourselves when it comes to interpreting base scientific truths.
This issue of interpretation is famously illustrated by what the theory of quantum physics tells us about the physical world that we inhabit. In particular, a key result of quantum physics, and one of the most tested results at that, is that the behavior of a microscopic particle is inherently random. In the popular Schrödinger’s Cat thought experiment, a cat is locked in a box along with an unstable radioactive isotope, which would kill the cat if it decays. And since quantum physics tells us that the behavior of the radioactive atoms is intrinsically random, until we open the box, we have no way of knowing whether or not the isotope has decayed and so there is no way of knowing whether the cat is alive or dead. So from the pragmatist approach of only accepting a belief as truth when it is scientifically verified, there does not exist any truth about whether or not the cat is alive until the box is opened. Understandably, this profound statement caused a great deal of panic and opened a huge can of worms because it says that no matter how much information we have, science can’t tell us whether the cat is alive or dead before we open the box. Indeed, even if we abandon hope in a scientific answer and turn to religion, God himself would be unable to tell us what was going on because quantum physics tells us that God plays dice to determine the outcome of the poor cat. So clearly, science offers no help when it comes to interpreting this inherent randomness of the universe and understanding why it is so.
There are two kinds of true statements in science (and in fact, in any system of logic): axiomatic truths and derived truths. That is, every discipline of science necessarily must start with a set of accepted truths and then every discovered result is of the form “if this is true, then that must be true”. Typically, an experimentally observed result that is not explained by some other established scientific truth is simply accepted as an axiom (or a postulate). In the case of the randomness of quantum physics described above, since science cannot tell us why it exists, we are forced to accept it as an axiom. A key point to note is that since every truth is either an axiom or derived from another truth, it must be the case that every truth is either an axiom or can be derived from an axiom. So in the scientific world, this makes the problem of interpretation considerably easier because instead of struggling to understand every single result discovered, it is sufficient to question and attempt to understand just the axioms.
“science doesn’t tell us why certain fundamental truths are true”
A simpler way of restating the inability of science to help with interpreting fundamental truths is that science cannot prove its own axioms. Stated this way, it is obvious: every scientific truth is derived from the axioms and so any attempt to use a known scientific truth to prove that an axiom is true would be circular and therefore impossible. So to reason why the axioms are true, we must venture outside science. This is my simple and clear reason for why we cannot completely rely on pragmatism to learn the truths of our universe. The ancient debate about the nature of truth must continue ad infinitum because any system of knowledge that we have must necessarily contain axioms that cannot be analyzed from within the system itself.
Interestingly, this understanding of the nature of scientific inquiry and truth shows us that it can be helpful to frame our own lives and beliefs in this axiomatic perspective. By identifying which of our beliefs we consider to be fundamentally true and which of them are derived from some other belief, we can establish an internal set of axioms. This way, complex moral dilemmas and ethical questions reduce to investigating and questioning fundamental axioms or beliefs instead of having to question and interpret ill-defined and shaky secondary beliefs. Indeed, an axiomatic framework of ethics is exactly how the legal system functions — the constitution establishes fundamental, ‘self-evident’ rights for a nation’s citizens, from which laws are derived. Of course, issues can arise in the translation of logic from axioms to secondary statements that are consistent with them, and this is usually where modern law works — ensuring that the laws that we follow are just and true relative to the foundational axioms.
So what we see is that when a certain belief of ours gets called into question, there are two important steps to carry out to establish the veracity of that belief. The first step is to understand and define your core set of axioms and to be confident that they are true within the framework of your internal belief system and that they are consistent with your moral compass. Then, from the belief that is being called into question, work backwards to tie it back to one or more axioms. If this step fails, then that belief is inconsistent with your truth, so either the truth needs to be redefined or that belief must be let go of. Alternatively, if you are able to connect the belief to one or more axioms, then it must either be accepted as true or the axiom that it is derived from must be reclassified as being false. Thus, what we have is a procedure using which we can clearly understand if a certain belief is true or false and determine if we need to reevaluate our central tenets and convictions. Of course, carrying out this procedure in practice is no simple task — redefining your foundational beliefs sounds incredibly intimidating. But the important point is that this procedure eliminates a lot of uncertainty surrounding the burden of handling ethical and personal dilemmas. I like to think of it as channeling your inner stubborn child: for every statement that is presented to you as being true, ask why and when you get a logical answer, ask why again, and on and on until you arrive at a statement that has no rational answer and you must make the subjective decision of either accepting or rejecting it. As for establishing your core principles, it is again helpful to draw an analogy to science — just as scientific axioms are established based on experimental evidence, our own personal axioms are established based on personal or collective experiential evidence.
References
- Baghramian, Maria, and J. Adam Carter. “Relativism.” Edited by Edward N. Zalta, Stanford Encyclopedia of Philosophy, Stanford University, 15 Sept. 2020, plato.stanford.edu/entries/relativism/.
- Capps, John. “The Pragmatic Theory of Truth.” Edited by Edward N. Zalta, Stanford Encyclopedia of Philosophy, Stanford University, 21 Mar. 2019, plato.stanford.edu/entries/truth-pragmatic/.
- Glanzberg, Michael. “Truth.” Edited by Edward N. Zalta, Stanford Encyclopedia of Philosophy, Stanford University, 16 Aug. 2018, plato.stanford.edu/entries/truth/.
- Hintikka, Jaakko. “Time, Truth, and Knowledge in Ancient Greek Philosophy.” American Philosophical Quarterly, vol. 4, no. 1, 1967, pp. 1–14. JSTOR, www.jstor.org/stable/20009222. Accessed 7 Jan. 2021.