You Cannot Prove Anything (To Someone Else)

“You cannot teach a man anything, you can only help him find it within himself.” – Galileo Galilei

If you have ever tried to prove something to another person, you might notice just how difficult it can be. Some people may agree with every point you state, whereas other people might appear to be intentionally arguing with you for the sake of arguing. If you believe all humans – or at least all those of a particular sex – should think the same way, then you might readily conclude they should all reach the same conclusions. Or perhaps you think that everyone is logical in some way, so it should be theoretically possible to show another person the correct line of reasoning and have them come to the correct conclusion. For some of us, nothing can be more frustrating than dealing with a person who simply “doesn’t get it”, someone who doesn’t understand our logic no matter how many ways we try to explain ourselves. This problem is no accident of course.

As it just so happens, it isn’t possible to prove anything. By “prove”, I mean more than presenting some logical argument that is acceptable to a single person. I mean establishing something as fact in such a way that in every time and place, that “proof” remains completely valid in and of itself. This implies that there are no assumptions necessary for the proof, and thus observant people may note that we are excluding here any proof of mathematics – all of which rely on axioms (assumptions and definitions). Such a “universal proof” could, in theory, be presented to every single person on earth and be accepted and understood so long as each person had the mental capacity capable of understanding speech.

A “universal proof” has many enticing features that we lead us to seek such a myth. It would seem to allow us to definitively answer key questions about life and the universe for all time. Furthermore, it would imply that everything in the universe has its own universal proof. This is because universal proofs could build upon each other to create even more universal proofs. Universal proofs for simple things could be combined to make universal proofs for more complex things. Universal proofs for complex things would imply the possibility of universal proofs for simple things. Or so it would seem at first.

Moreover, if universal proofs are even possible, it suggests that there are less logically-robust proofs that still hint at the components of some universal proof. It would seem then that the only thing necessary to find such universal proof is to deeply examine common “proofs” and arguments in search of the superior logic to which they allude.

If it turns out that this “superior logic”, these flawless arguments, these definitive facts don’t exist, then there can be no hope of ever finding a “universal proof” – a perfect argument that always works. On top of that, even if definite truths do exist, it does not imply that human reasoning could ever flawlessly assemble them in a manner to derive universal proof.

Notably, the assembly of universal proofs is a mechanism for discovering the answers to key questions in life. That is a powerful yet enticing delusion. Enticing as it is, it is a good reason to look deeper into philosophy. The objective becomes this: find the flawless arguments so that universal proofs can be made. That is exactly what I tried to do as a young college student, and that is how I ended up becoming an epistemologist.


Begin with the question, “How do I prove something to someone beyond the shadow of a doubt?” How can I prove something to someone in a way that they can’t argue with? In order to do this, I must find something to which all humans appeal. I must find some fact, some truth, some argument so universal that other human beings – if they are to be honest – must agree.

To find such an amazing fact, I considered basic arguments, but I knew people would come up with contrary arguments. I wanted something that even the cleverest of critics would not deny. This meant appealing to something all humans knew in common.

After all of my analyses, I had come upon very interesting conclusions, but I found myself unable to convey them for a number of reasons.

As it turns out, there are a number of reasons why human beings are unable to prove an idea to each other beyond a shadow of a doubt, much less in a way that would make such a proof “universal”.

Why Not?

When trying to understand anything, it is first required that you have some point of reference. Consider “motion” for example. What is “motion”. We can observe at one moment a thing being at a particular place but then it appears that this object is no longer at the place we recall it being. Our mind tells us the thing should be at a different location. This discrepancy is called “motion”, and we blame the discrepancy on “time”. We don’t know what “time” is, only what it does in relation to other things we observe. There are all sorts of ideas about time, but all of these are merely allusions to some common points of reference, which all stem from what we call “experience”.

If our experiences are different, then that means anything related to those experiences will also be different. Perhaps the easiest examples of this can be seen in culture. Certain customs and mannerisms that are obvious in one culture are completely bizarre and weird (out-of-the-ordinary) in another. And yet, such customs may have similar labels, hiding their true nature. The way in which business proceeds in one culture may be quite different from that of another, but both may be labeled “business”.

There are differences in experience among individuals as well. If we are to believe chemistry and biology, then we must conclude that mind of each and every person in this universe is unique. This is because the atoms and molecules in one person’s brain haven’t the tiniest likelihood of aligning themselves the exact same way as in another person’s brain. The atoms and molecules – and thus the cells and their components – are always moving around and thus never sitting it exactly the same location. Atoms naturally move, but contributing to that is the motion of the entire body when the person decides to move.

Considering also the possibilities of diseases, brain damage, and other biological and chemical problems that could arise to affect human memory and thinking capacity, it is unreasonable to believe – from a standpoint of chemistry and biology – that the mind of a human being – if influenced by chemical and biological laws – could ever maintain exact correspondence with the mind of another human being. Therefore, there will be some discrepancy in the precision of the formulation.

Still, it could be supposed that these problems are unlikely or minimal, and I shall discuss that shortly.

Supposing chemistry and biology are ignored, there still remains the fact that humans have misunderstandings, miscommunications, and differences in overall experiences based on where they go, what they do, and the ways in which other people interact with them.

It might be possible to make experiences similar by keeping a pair of twins in a tightly-controlled environment. But even in such a scenario, both twins cannot occupy the exact same space in time and thus, will not have identical observations of the things they experience. The things they notice about some event may be different. Moreover, both twins will not necessarily agree to do the same things, thereby resulting in one having an experience a particular way in which the other does not. Attempting to force them to do the same things will result in the experience of force being applied unevenly to one as to another, which too results in a new and unique experience. And finally, supposing both everything in such a contrived experiment did result in a very similar vocabulary, the correlation in ideas would be indistinguishable from mere coincidence, and therefore, it would not prove that humans could relate their ideas in a manner necessary that would make it possible to find a “universal proof”.

Can’t We Talk To Each Other?

If the problems preventing exact correlation of human person are viewed in the most extreme cases, then human communication is impossible. In fact, the human mind can come very close to this. Consider two people that speak radically different languages. Neither can understand each other through words alone because their vocabularies are different. Their vocabularies are based on the association of ideas within their society and culture. In such a case, what allows humans to overcome this barrier is the fact that a limited set of mechanisms and experiences are available to both of them. For example, all humans are physical and must communicate by physical means – sounds, text, carving, and so forth. The sounds and text used for communication are limited to what humans can produce. If a human uses a language that is expressed with syllables and letters or characters of some sort (for writing), then it is easier to overcome the communication barrier with humans using languages with similar dependencies or features.

The problems in their extreme cases are not certainly not the case for two humans communicating in the same language, and yet, if these problems persist at even their most minimal realistic forms, then humans cannot prove something to each other, and “universal proof” cannot be found.

Sadly, the problems do persist in reality in their most minimal forms, but they aren’t generally noticeable. How so? The answer to this is, incidentally, also one of the problems with human communication: Human reflection on life.

Here, “human reflection on life” simply refers to the fact that humans think about everything (life, the world around them, and how everything fits together) and the fact that all of these thoughts come together to form a unique view of the cosmos and the things in it. Everyone holds onto some views, but as they progress through life, these views are changed, “improved” upon, refined, and result in some synthesized form that is the conclusion of the human reasoning applied to them. As this occurs, the final forms of these ideas deviate from what other people believe, even if those other people have nearly identical experiences.

The differences are either minimal or are hidden such that, most of the time, people don’t notice how their ideas differ until some obvious conflict arises.

The differences may be hidden because the underlying logic is assumed to be true and assumed to be held by everyone. This means one person thinks that everyone holds to a certain belief for the same reasons they do, even though this isn’t necessarily true. Many people may share a belief that sounds similar but in actuality is very different. For example, consider rain. Everyone knows rain falls from the sky, but exactly what constitutes the “sky”. What are the particulars of this belief? Some people may only classify elevations of several thousand feet to be the sky. Some people may believe water does not need to fall from such a “sky” at all to be considered rain. In general, people don’t debate the definition of rain because the discrepancies in belief are never noticed behind the facade of (what we might call) “collective understanding”.

At first, such discrepancies may seem trivial to resolve. After all, if people agreed on some specific, written definition, then they could always appeal to that written definition in the case of an argument. However, like all ideas, each and every word – as well as the very formulation of the definition – is understood subjectively. The fine details start to become important because we don’t have any way of measuring exactly how important they really are, and therefore, any neglegence in understanding them could potentially result in a major miscommunication. This seems unlikely to some people, so let us consider the example of rain.

Exactly what is considered “sky”? Air is part of the sky, but at what elevation? At what elevation could it rain? There is certainly a range of elevations because precipitation is possible whenever it becomes cold. We could agree on the scientific definition – precipitation – but this wouldn’t help us clarify what we mean by “tropical rain storm” yet it would include the tiniest and briefest moments of precipitation, which only some people might call “rain”. What constitutes “rainfall” depends on a general idea, not a specific one.

Abstract ideas can be more specific, more exact, making them easier to understand and convey. Everyone can be taught what a circle is. However, abstract ideas are ideas that have only been modeled after reality, not necessarily found in reality in their purest of forms – at least not in all settings. We understand what a “circle” is, but how many of us have called many things “circles” even though such things are not authentic (“perfect”) circles? We know what “one” means, but in a barrel of apples, which apple constitutes the “oneness” that all must share? Two larger apples certainly amount to more mass than two smaller ones, possibly even three smaller apples. This is reality, and it indicates that the abstract “one” applied to a broad variety of items is not truly the “fair”, “universal”, “perfect” “one” to which the abstract idea (of “oneness”) hails.

Since even basic things are not “perfect”, there is some room for human choice in regards to what a person considers as meeting the criteria of a definition. For example, one person may consider round fruit to be apples based on their biological features (seeds, juices, skin) and origin (from an apple tree). Another person may consider something round to be an “apple” as long as it takes on the familiar apple shape. Finally, a third person may require that apples be red, green, or golden yellow and not purple or blue. Consequently, when any of these three people speak with each other about “apples”, all of them will have different ideas. One person might speak of apples turning blue – a statement to which another person objects!

If the discrepancies remain fairly minimal, it is possible to at least stimulate the mind of a listener (or reader) into thinking about things a particular way. However, to say that an idea is “conveyed” is a misnomer. An idea cannot be conveyed at all. It can only be rediscovered by the audience in their own way, in their own mind, with their own logical analysis, with their own personal vocabulary shaped by the many unique experiences they have had in life.

As Galileo said, “You cannot teach a man anything, you can only help him find it within himself.”


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