The Dirtiest Word in Critical Thinking: «Proof» and its burden

The Dirtiest Word in Critical Thinking: «Proof» and its burden

by Евгений Волков -
Number of replies: 0

The Dirtiest Word in Critical Thinking

«Proof» and its burden

Posted Feb 09, 2018

When I teach critical thinking, I warn my students about the word ‘proof’ and its variations, explaining that points will be deducted if I see it in their writing. Though it may seem harsh, I’m not being ‘nit-picky.' The issue of “proof” is at the heart of critical thinking. Proof is often described as evidence establishing a fact or the truth of a statement — indicating a level of absolutism. ‘Proof’ and ‘proven’ have infiltrated minds in ways that make people sure of certain phenomena. For example, I wonder how many tubes of a certain toothpaste have been sold based on its advertisement as ‘clinically proven’ to whiten teeth. But, what happens if it doesn’t whiten your teeth? Is that not proof that it doesn’t work? What happens if it whitens teeth in 95 percent of people, is that enough to satisfy the parameters of ‘proven’? The problem with the word, in this example, is that it implies that the toothpaste will work for everyone, not just most people. This phrasing is, I imagine, a product of the marketing team — well, I would hope no self-respecting scientist would use the word ‘proven.’ We are also aware that not everyone who used the toothpaste wound up with whiter teeth — yet, why do so many fall for the ‘clinically proven’ tagline despite the lack of absolute certainty?

People feel safer when they are assured. They also like nice, neat little packages – it either works or it doesn’t (hence the label ‘proof’). People don’t want to hear that something will only work under certain conditions — this does not sell toothpaste. However, this particular burden of proof (pun intended) extends beyond toothpaste. What about a “simple proven treatment” for a serious illness? Proof can be dangerous and educationneeds to address this.

Though no first-hand written legacy of Socrates exists, his student Plato avidly relayed his mentor’s teachings throughout his own works. It is from this that we are provided with the Socratic Method and, at its core, the elenchus, which refers to the procedural refutation of a claim based on in-depth examination. The falsification of a claim through this form of examination often leads to the realization that the original claim requires refinement in order to make it true. Though debate exists over whether the Socratic Method actually leads to the attainment of knowledge or is used simply to make another’s argument look foolish (i.e. the negation of false knowledge), from a scientific perspective, it should be regarded as the former. That is, through the falsification of a claim (which may have been previously accepted as true; e.g. ‘X is Y’), new knowledge is created (e.g. ‘Actually, X is not Y’). For example, the acknowledgment of the fact that the Earth is not flat was just as important as the discovery that Earth is round. Simply, a finding that indicates the truth of a null hypothesis is still a valuable finding and is in itself new knowledge. This latter point is an important point to consider, particularly in the world of publishing research and the tendency to ‘chase statistical significance’.

Over two millennia later, the use of the Socratic Method and the associated falsification process remains an integral function of critical thinking. Perhaps the reason for such focus on falsification is that, according to the logician and philosopher of science, Karl Popper, we simply cannot prove things true—only false. We can only disprove. As a result, we live in a world where lasting certainty does not exist. For example, over the past 10-15 years, consider how many times thoughts regarding the number of planets in our solar system have changed. I grew up with the knowledge of our solar system having nine planets. Currently, we have eight…as well as a number of newly categorized dwarf planets. With respect to knowledge attainment, the best we can do is simply improve upon old theories through further examination.

According to Popper, knowledge is theoretical. That is not to say that there may or may not be something that is knowledge, rather, what we think we know may or may not be the case. Essentially, all that we hold as true is not proven fact, but simply the current best working model for how things are—they are theories and not laws. Important to note in this context is that a theory is not simply an educated guess or hypothesis; rather, an established model of how something works, observed over many repetitions (e.g. gravity).

As in the example above, prior to the Enlightenment, it was widely believed that the Earth was flat. Though it may seem to us silly that this was actually believed (i.e. to the masses anyway, bar some conspiracy theorists), generations from now, people might view one of our near-and-dear beliefs as equally preposterous. The manner in which such beliefs change is through falsification. According to Popper, no amount of consistently occurring outcomes can prove a theory – it simply suggests, at best, that the theory is likely not to be false. On the other hand, in order to falsify or disprove a theory, it only takes one occurrence of an outcome that contradicts the theory to prove its generalizability false. For example, it was traditionally believed that all swans are white. We know this to be false because, one day a black swan (cygnus atratus) was spotted and ‘knowledge’ had to be amended. To reiterate, though a proposition (e.g. there is a black swan) cannot be used to prove a claim true (i.e. all swans are black), it can be used to prove a claim false (i.e. all swans are white).

From Popper’s perspective, knowledge develops based on the process of eliminating falsified theories. Following this process, there may be only one or even a few theories that are still open to falsification; but this does not mean that one of these theories is true; rather, one better fits the problem-situation it was designed to solve. The manner in which theories develop and adapt (i.e. ‘to fit’) is what we perceive as our improved understanding of the universe; and as a result, the problem-situations we face also adapt, develop and become more complex, in line with our theories.

Please note that the premise that nothing can be proved is not to say that reality is entirely subjective or that facts are relative to each and every individual (i.e. it is not a license to propagate previously falsified or evidence-lacking information). For example, yes, gravity is a theory; but, I would not recommend ‘jumping off the Brooklyn Bridge’ (as my father would say during my childhood with reference to conforming to my peers). Again, we cannot prove, but we can disprove; and on top of that, the information we hold as absolute is generally so well corroborated through countless repeated observations, that we must consider the related outcomes as extremely likely, at the very least; albeit, still not provable.

Similar to both Socrates and Popper, we can consider adequate and appropriate investigation and examination as being attempts at refuting and/or falsifying ideas, concepts and theories. To reiterate, though a proposition cannot be used to prove a claim true, it can be used to prove a claim false. Thus, we must strive to conduct critical thinking through rigorous evaluation, in order to develop the most accurate conclusions we can; examining thoroughly any claims of proof. 


Popper was wrong. His epstemology is not tenable, nor do the majority of philosophers of science or scientists themselves actually embrace his approach due to its serious problems. Also, even in the Middle Ages, almost no educated person believed that the Earth was flat, whether it was "widely believed" or not.

Interesting approach, and I am sympathetic to the warnings against proofs. Indeed science proceeds "negatively" at best; we never really know if we are any closer to the truth.

Yet proofs are surely possible in some fields, no? For example, logic and maths.

And in the empirical sciences, proofs are still possible, but most be fairly qualified in terms of what level of evidential support is given, and in what the claims made actually mean.

Many thanks for the comments thus far!

Regardless of whether or not everything Popper said was 'wrong' or 'right', it remains that many sciences (if not most sciences) work on the basis that a significant finding is based on rejecting the null hypothesis rather than confirming the alternative/experimental hypothesis. That is, significant effects are indicated based on 'it is not the case that nothing happened' rather than 'it is the case that the alternative happened'. The point is, science works, to a large extent on the fundaments of falsification. As a result, we must reflect what science actually does in how we report it through language.

Proofs in logic and maths are a little bit trickier. My example within the text regarding gravity is of course based on mathematics and, as I said, I'm not going to test it any further! But it does bring us to the important point of the discrepancy between well-structured problems (e.g. 2+2=?; i.e. problems that have one correct answer) versus ill-structured problems (e.g. Discuss the importance of Daisy Buchanan in the Great Gatsby; i.e. problems that have multiple paths to differing, though equally plausible solutions). When we engage with well-structured problems, such as mathematical proofs, we're going to see the same correct answer over and over again - hence reference to it as a proof. However, from a true falsification standpoint, like theories, these proofs are simply observed over and over to yield the same outcome. All it takes is one occasion for this outcome not to occur for it to be falsified and because no one can see into the future, we cannot be 100% certain that this falsification will not happen. What happens if on one occassion 'modus tollens' is not correct or if gravity does not work? That said, I wouldn't bet on either of these, but nevertheless, scientific rigour would dictate that we take nothing for granted, even if we are 99.9999999999% sure of something.

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