It is often the case that the most fundamental concepts in science are the ones that are the most misunderstood, and that is certainly true with the concept of “proof.” Many people accept the misconception that science is capable of providing proof, and I often hear people make claims like, “science has proved X” or “a fact is something that science has proved.” In reality, however, science is inherently incapable of proving anything. Upon hearing that, many people then jump to the opposite extreme and claim that since science can’t prove anything, it is unreliable and should not be trusted. That position is also incorrect.

The reality is that science deals in probabilities, not proofs. The reasons for that range from the philosophical to the practical, but if you really want to understand the nature of science, then it is very important that you understand the concept of proof. Therefore, I am going to go over some of the reasons why science doesn’t prove anything, then I am going to explain why that is actually a good thing and should not make you question the reliability of science. As I will elaborate on, the best way to think about science is that it tells us what is most likely true given the current evidence. As such, it is an extremely useful tool, and it is far better than the alternatives, but it’s certainly not perfect.

Definition of “proof”
I think that it is important to define “proof” at the outset. When we say that science can’t prove anything, what we mean is that it cannot show anything to be absolutely, certainly, and unequivocally true. For example, we are very, very certain that the earth is orbiting the sun (heliocentrism) but we can never actually be 100% sure that it is. In contrast, mathematics can provide proofs. Mathematics consists of laws, rules, and theorems which are absolutely true. The uncertainty only enters when you apply the laws of math to observations in the physical universe, which in many ways, is all that science is.

Let me illustrate what I mean with the following example:

• Premise 1: The sum of the angles of any triangle = 180 degrees
• Premise 2: For triangle ABC, angle A = 90 degrees
• Premise 3: For triangle ABC, angle B = 45 degrees
• Conclusion: Therefore, for triangle ABC, angle C = 45 degrees

In both philosophy and math, we would refer to that as a logical proof. In other words, if those premises are true, then the conclusion must be true. That qualifier is really important though. You can work out the math using variables and demonstrate that for any triangle the sum of the angles must equal 180 degrees, but as soon as you start plugging actual measurements into the formula, you introduce bias and error. In other words, if premises 2 and 3 are true, then we can be absolutely certain that the conclusion is correct, but as I’ll explain, we can never actually be absolutely certain about premises 2 and 3, which means that we can never be absolutely certain about the conclusion. Thus, absolute proofs are unattainable in the real world.

The original Matrix movie was actually a brilliant portrayal of the brain in a vat argument.

Are we brains in vats? The philosophical problem of proof
The most esoteric reason that science can’t prove anything comes from the philosophical arguments about knowledge. You have no doubt heard of these arguments via Descartes’ famous statement, “Cogito ergo sum” (“I think, therefore I am”). Descartes was concerned with what we could actually be certain of, and he correctly realized that almost everything that we think we know is based on observations, and observations are notoriously faulty and untrustworthy. We cannot, for example, ever be 100% certain that we are not hallucinating, or, as Descartes argued, that there is not some evil demon projecting a reality onto our senses. Similarly, I have personally had numerous dreams where, in the dream, I contemplated whether or not I was dreaming, and I incorrectly arrived at the conclusion that I was awake. Therefore, I can never be 100% certain that I am not dreaming.

Perhaps the most famous of these arguments is the brain in a vat argument. This is the concept on which the Matrix movies were based, and it argues that we cannot be certain that we actually exist in our perceived physical form and are not actually just brains in vats living is some form of virtual-reality environment.

After considering arguments like these, Descartes realized that the only thing that he could be certain of was that he was thinking, which meant that there must be something doing the thinking, therefore he must exist in some form. That is what is meant by, “I think, therefore I am” (or perhaps more correctly, “I am thinking, therefore I must exist”).

I went through all of that to make two important points. First, science is completely dependent on observations, but since we can never be 100% sure that our observations accurately represent reality, we can never be 100% sure of the results that are based on our observations. In other words, even though all of our observations tell us that the moon orbits the earth, we can’t actually be certain that the moon and earth even exist and aren’t simply part of the Matrix environment.

Second, you should not misconstrue this conceptual uncertainty with a practical uncertainty. I (and the vast majority of philosophers) don’t actually think that we are brains in vats or that we are currently dreaming, but we acknowledge that as a possibility which we cannot rule out. In other words, science implicitly relies on the assumption that we are actually in a physical universe, and it would be absurd to make a statement like, “science says that the moon revolves around the earth, but I can’t be sure that I am not a brain in a vat, so I am going to reject that science and impose my own view of reality.” Similarly, if you show me a triangle and tell me that you measured angle A as 90 degrees and angle B as 45 degrees, I’m going to accept that angle C is 45 degrees unless I have a really good reason not to (like looking at the triangle and seeing that it is asymmetrical). Nevertheless, I acknowledge the possibility that your measurements were inaccurate, that an evil demon is projecting a triangle that doesn’t actually exist, etc. Again, I would need actual evidence to convince me that those are happening, but at the same time, I cannot definitively state that they are not.

Practical reasons: Inductive logic
Now that we have the philosophy out of the way, let’s talk about the practical reasons why science doesn’t prove anything. Even if we could be absolutely certain that we aren’t brains in vats, we still could not use science to actually prove anything, and one of the key reasons for this is the types of logic that are used in science. Science involves both deductive and inductive logic, with deductive logic typically being used for specific experiments and testing theories/hypotheses, and inductive logic being used to form general conclusions, hypotheses, and theories. This is important because inductive and deductive logic differ in both the certainty and the scope of their conclusions. Deductive arguments end in a focused conclusion that must be true as long as the premises are true and no logical fallacies have been committed (my triangle example earlier was deductive logic). In contrast, inductive arguments end in a general conclusion that is probably true. Importantly, science is really big on explaining things and making generalizations, because a result that is only applicable to the experiment that produced it is not very useful. Therefore, science relies heavily on inductive logic to form its theories and hypotheses.

For example, atomic theory states that all matter is made of atoms. We arrived at that general conclusion via numerous observations which consistently showed that matter is made of atoms (i.e., we went from a series a specific observations to the general theory). Now that we have the theory in place, we can test it with deductive logic. We can, for example, take a piece of matter, do an experiment to see if it is made of atoms, and use deductive logic to reach our conclusion about that piece of matter. That is a deductive process, and it is a good way to test a theory (all that it would take to discredit atomic theory is to find one piece of matter that was not made of atoms). Thus science involves a seamless transition from inductive to deductive logic and vice versa, but because of the inductive steps, the overarching conclusions always have a degree of uncertainty.

Practical reasons: Statistics
At this point, you may be thinking, “okay, theories and general explanations can’t be proved, but since individual experiments often use deductive logic, surely they provide proof.” In an ideal world, that would be true, but in reality, it is problematic. Consider the following example from a drug trial.

• Premise 1: The only difference between the treatment and control groups was the medication that they received
• Premise 2: The treatment group did better than the control group
• Conclusion: Therefore the drug worked in this trial

Can you spot the problem? Don’t feel bad if you can’t, because it’s not obvious. If all of those premises are true, then the conclusion would be true, but the problem is that we can never actually be certain that the premises are true. In fact, premise 1 is almost certainly false. Unless you are working with clones and each of them is treated by an automated computer program and lives in an identical, sterile isolation chamber, there are going to be differences in your groups. You can minimize these by controlling all of the factors that you can, randomizing your samples, and using very large sample sizes, but you can never actually have truly identical samples. So a properly conducted experiment will have a premise 1 that is as true as possible, but because it is never possible for it to be 100% true, you can never be 100% certain of the conclusion.

The second problem is, of course, that the deductive argument only applies to the specific results of that experiment, and we want to generalize to the entire population (i.e., we want to know if the drug works for most people, rather than simply if it worked for the individuals in our experiment). To do this, we need statistics, because they allow us to gauge how likely it is that our results are representative of the entire population, rather than just being representative of the samples that we collected.

However, statistical tests invariably operate off of probabilities. Indeed, if you read scientific papers, you will never see a statement like, “our experiment proved X.” Rather, you’ll see things like, “these results suggest X (P = 0.002)” or “our results are consistent with X.” I have previously explained what these statistics mean in detail, so I won’t do so here, but the point is that essentially all scientific conclusions are based on probabilities of one form or another. For example, classical frequentist statistics use P values which represent the probability of getting an effect that is equal to or greater than the one that you observed if the thing that you are testing actually has no effect. Other probabilities may involve comparing different models and discussing which is the most likely, using prior knowledge to construct a probability, etc. The point is that statistical tests always involve probabilities. To put this another way, statistics can show you that there is only a 0.0000000000000000000000000000…1% probability of a result arising by chance, but they can never actually prove that a result is real and representative of the general population.

Can science disprove something?
In this section, I want to shift topics slightly, because it is right around here that I usually hear people say things like, “science can’t prove anything, but it can disprove things.” That is only partially correct. Based on the philosophical arguments that I presented earlier, it obviously isn’t true in the strictest sense of the word. Even if we assume that the universe is real, however, it’s still problematic because of the arguments I presented in the section on statistics.

So where does this idea come from? It stems from the work of Karl Popper and the notion of falsification, and it deals specifically with theories and hypotheses. In science, theories are not educated guesses. Rather, they are very general conceptual frameworks that are used to explain facts and observations, and they have usually been rigorously tested. Hypotheses are also explanations, but they tend to be more limited in their scope, and they usually have not been as rigorously tested. As I explained earlier, both of these are based on inductive logic, and Popper was deeply troubled by that because he realized that there were few (if any) instances in which a test could actually confirm an inductive conclusion. Think back to atomic theory again. If we do an experiment and confirm that a given item is made of atoms, would that confirm the general theory that all matter is made of atoms? Of course not. It would suggest that the theory is likely correct, because the theory makes accurate predictions (as does evolution, btw), but it would not demonstrate that all matter everywhere is made of atoms.

That experiment would, however, run this risk of falsifying atomic theory. In other words, if it had turned out that the matter was not made of atoms, that would discredit the theory that all matter is made of atoms. Popper argued strongly (and largely correctly) that this notion of falsification should be one of the hallmarks of science. In other words, it should be possible to discredit any scientific concept if that concept is actually wrong.

So that is what people mean when they say, “science can’t prove anything, but it can disprove things.” It would be much better and more accurate to state, “science generally can’t confirm hypotheses and theories, but it can falsify them,” but the core idea is essentially correct.

It’s good that science can’t prove anything
Finally, I want to talk about why it is actually good that science cannot prove anything. Science is an inherently skeptical process. Scientists are trained to recognize and acknowledge the limitations of their experiments and conclusions, and this forces them to be open-minded. Because science cannot prove anything, there is nothing in science that is so sacred that it cannot be challenged. To be clear, “extraordinary claims require extraordinary evidence,” so if you want to say that atomic theory is wrong, the earth doesn’t revolve around the sun, evolution isn’t correct, etc. you are going to need some incredibly strong evidence, but if you can provide that evidence, then you can overthrow those concepts.

This is a stark contrast to religion (and to many forms of pseudoscience). To be clear, I am not attacking religion or religious people, I’m just pointing out a difference in how science and religion operate. Every religion that I have ever examined has a set of core principles that cannot be challenged, and members of those religions are absolutely convinced that their core concepts are absolutely true. In reality, of course, most major religions can’t simultaneously be true, yet their followers insist that their religion provides absolute truth, and it is the others which are wrong. Pseudoscientists make similar arguments. I have, for example, frequently encountered anti-vaccers who proudly proclaim that nothing will ever convince them that they are wrong.

This type of dogmatic and unquestioning thinking is what science avoids by never proving anything. If you admit that you can never prove anything, then you have just admitted that you could be wrong about anything and everything. Once you accept that, you realize that you have to be open-minded about any new evidence.

To be 100% clear, being open-minded does not mean being willing to accept something without evidence. Opponents of science often use arguments like the one that I just made to insist that we should be open to their unsubstantiated and easily discredited views, but that is not at all what it means. Being open-minded means that you are willing to accept new evidence as it arises. For example, if several epidemiological studies are published saying that vaccines cause autism, I will carefully examine those papers, and if they were done properly, had large enough sample sizes, etc. I will reject my current understanding and accept that autism is probably caused by vaccines. In the mean-time, however, I am under no obligation to seriously consider blogs, Youtube videos, anecdotes, and other sources of baseless speculation. That’s how the burden of proof works. If you can provide actual evidence for a position, then I have to consider that evidence, but if you don’t provide the evidence, then I don’t have to seriously consider your position.

Note: To be clear, I am not suggesting that all scientists are open-minded. Scientists are human and are prone to the same flaws and biases as everyone else, but the system itself is inherently skeptical, and it has a long history of self-correction.

Summary
In short, we can never be 100% that our perception of reality is accurate, and scientific experiments are virtually impossible to totally and completely control. Further, science often uses inductive logic, and it relies on probabilities to draw conclusions. All of this prevents science from ever proving anything with absolute certainty. That does not, however, mean that science is untrustworthy, or that you can reject it whenever you like. Science tells us what is most likely true given the current evidence, but it is a skeptical process that always acknowledges the possibility of being wrong. Thus, it is technically possible that gravity isn’t true, the sun moves around the earth, vaccines don’t work, etc., but that doesn’t mean that you should assume that those ideas are correct. Similarly, it is also technically possible that I could win the lottery, but that doesn’t make buying a lottery ticket a good investment. Even so, it is technically possible that scientific conclusions are wrong, but it is ludicrous to believe that they wrong unless you have strong scientific evidence that discredits them.

On a side note, when you hear some claim that, “Scientists say that there are no absolutes” what the scientists actually mean is that we don’t know if there are any absolutes (or to put it another way, science cannot provide absolutes). So there may be absolutes, but we aren’t able to confirm them (at least as far as we know).

Note: you also should not use Galileo/Columbus or the fact that “science has been wrong in the past” as the basis for rejecting scientific evidence.