By Nathaniel Brookes
Published 10th October 2026
It is often said: “We know this”, "that is correct" – but are you sure it really is? Can any statement be provably true, and does complete certainty exist?
After years of innovations in science, technology, and now AI, humanity seems to have gained ever-increasing information and knowledge; We understand more about the world and ourselves than we have ever have before.
"We know that the sun will rise tomorrow morning" [1]
"It is true that water freezes at 0°C under standard conditions" [2]
"It is a fact that memories are primarily stored in the brain" [3]
"Scientists can prove that is impossible to travel faster than the speed of light" [4]
The foundations and systems of modern life rely on the principles of testing our knowledge and proof. Whether at school, in a courtroom, or in medical and industrial sectors – we depend on knowing what is true and what is not.
"I swear by Almighty God that the evidence I shall give shall be the truth, the whole truth and nothing but the truth."
The oath traditionally used for giving evidence in court [5]
People strongly desire certainty – without it, we wouldn’t be able to live and function normal lives. So, in a changing, uncertain world, how can we really know anything?
Patterns and Predictions
Science may provide a solution to contain this uncertainty.
Even without realising, we are all scientists – through daily observation, our brains analyse patterns from the environment, and combined with prior memories, we make assumptions about the world – these ultimately guide our everyday decisions and allow us to make evidenced predictions.
If patterns repeat often enough, we tend to call them facts. Scientists might refer to them as 'laws' if they appear to be constant, universal truths – e.g. Law of Conservation of Energy
The scientific method involves
(1) Create a hypothesis of how you think the system works
(2) Test it a bunch of times
(3) Form a conclusion(s) about the system based on the results
Stage (3) effectively becomes our understanding of how the system works, which can help us form a working model of the world. [6]
This process can be very useful at providing abstraction from the chaotic world. It also gives us confidence in our assumptions of reality so that we can plan ahead without worrying about every detail.
One Scientific Model to Rule Them All
Advances in scientific models like the discovery of atoms and quantum particles have created the impression that that we know more about the Universe now than we did 100 years ago – so if that’s the case, will we ever get to a point where we know how the world works completely and with certainty?
Some scientists believe so – they think that the entire physical properties of the universe could be described and compressed into a single mathematical function.
The well-know "Theory of Everything" is still being debated today. [7]
As of writing however, this universal model of the world has not been found. Personally, I do not think that we could ever truly model the Universe in this way for a number of reasons...
One critical problem that isn't always mentioned regarding the scientific process is: How many times you should test your hypothesis? – is 10 times good enough? What about 100 times or 1000 or 1 billion? Even if you test for 𝑥 number of times, what happens if you get a different result on the subsequent test? How could you prove that your model will work 100% of the time if you could be disproven?
This Universally Falls Apart
In 1687, Isaac Newton famously published the "Three Laws of Motion", which demonstrated the fundamental physical relationships between force, mass and acceleration. [8] Newtons 'Laws' of motion are great for most everyday applications: they are still widely taught in classrooms, and used in many industry applications from designing rocket engines to controlling drones.
However, it turns out that Isaac Newton made several assumptions in his gravitational modal.
In 1915, Albert Einstein presented his "Theory of General Relativity" which changed our understanding of how gravity works. Einstein proved that the prior assumptions of F=MA were incomplete – gravitational acceleration is not constant, and it behaves differently at very fast speeds.
We now know that Isaac Newton's 'Laws' are not good enough for certain scenarios that require precision such as GPS navigation, where Einstein's model works much better. [9]
The Scientific Method is great for empirical modelling and predicting, but clearly, no scientific model is an exact representation of the real world – It is still a human interpretation of the Universe. Even Einstein's new theory is not good enough – it breaks down completely when observing subatomic particles. [10]
Should Science Always Be Trusted?
It is nice to think that since we are in the ‘Modern Scientific Era’ of humanity, what we know today as facts will remain so forever, but history suggests otherwise. The issue of changing facts is not always as abstract as academic debates over the properties of gravity – they also influence decisions that impact us all.
It was not that long ago, when Asbestos was used to rebuild Britain following the Second World War. The material was known by material scientists to be strong and fireproof, resistant to chemicals, etc. So, a great choice for construction in houses, schools and hospitals. Right?
What they did not consider was the health impact on people. Asbestos fibres cause damage internally, and the material is now classified as a carcinogenic, and banned for use in construction. We now know that the old model for Asbestos was incomplete and based on out-dated assumptions. [11]
In the near future, it's likely our understanding of the risks and benefits of everyday chemicals and materials will change – among other things.
For example, Microplastics and chemical additives are actively used today in polyester clothing, food and drink packaging, and forever chemicals are found in water supplies. Future scientists may soon realise, that these chemicals cause issues or unintended health consequences that we never knew could happen or even thought to ask.
Empirical Reality vs. Formal Systems
So does this mean we cannot know or prove anything with 100% certainty?
– It depends on how many assumptions you are making...
Empirical Reality (Open Knowledge)
The vast majority of what we know in the world is uncertain and cannot be proved since we do not know all the variables that may be involved. This includes seemingly trivial statements such as: “Ice will melt in the sun” – sure we could watch ice melt in the sun for as many times as we like and assume that temperature is an important variable. We could even create a model that says when temperature rises above 0 degrees C, the ice will melt.
However, we cannot prove that ice will always melt in the sun no matter how many times that we test our hypothesis; as the ice experiments are conducted inside the Universe which contains variables that could impact the ice melting which we may not have considered in our model.
The reason we cannot prove statements like this is because we do not know all of the rules of the Universe. The Universe operates as an Empirical Reality.
Formal System (Closed Knowledge)
There are some things that we can be certain of 100%. For example, the mathematical statement: 1 + 1 = 2. This statement is different from the ice statement in that not only is it true, but it can also be proved to be true: [12]
So why are some statements provable and others impossible to prove?
The reason why the mathematical statement can be proved is because it exists in a system where all of the rules are defined: The system of Mathematics. This system is an abstract language (and could also be thought of as a model), the rules are defined in axioms and in the statement: 1 + 1 = 2, there are no unknown variables. Mathematics functions as a Formal System.
Since the mathematical system does not depend on the universe (it is a separate system), it is possible to prove some statements made in its language with 100% certainty.
The core challenge with relying on provable truth from Formal Systems like Mathematics is that these systems break down when applied to the real world...
Models and Uncertainty
Who knows? What is considered definitively true and factual today might be thrown out entirely for new theories of the world in the next 500 years.
Ultimately, what seems true, is the fact that our current models of the world can and likely will change as we learn more and ask more questions.
References
[1] www.schoolsobservatory.org/learn/stargazing/plan/sunrise-set
[2] www.ebsco.com/research-starters/science/freezing-point/
[3] pmc.ncbi.nlm.nih.gov/articles/PMC8611531/
[4] www.livescience.com/can-anything-travel-faster-speed-of-light
[5] www.judiciary.uk/guidance-and-resources/witnesses/
[6] www.unesco.org/en/query-list/s/scientific-method
[7] www.scientificamerican.com/article/a-geometric-theory-of-everything/
[8] www1.grc.nasa.gov/beginners-guide-to-aeronautics/newtons-laws-of-motion/
[9] www.energy.gov/science/doe-explainsrelativity
[10] www.quantamagazine.org/where-do-space-time-and-gravity-come-from-20220504/
[12] en.wikipedia.org/wiki/Proofs_involving_the_addition_of_natural_numbers