The Scientific Method and Knowledge

Have you ever had the feeling that you're alone in the world, that nothing exists beyond you? Perhaps you have, especially if you've just seen The Matrix and its ilk. While that assumption may make for an interesting science fiction film (leaving aside crappy sequels), it doesn't do well when you're living in the real world. However, like it or not, the belief (also known as solipsism) that nothing exists beyond you and your thoughts is logically valid. Why, then, are none of us actually solipsists? Well, someone once pointed out that whenever a solipsist stubs his toe, it means he must be subconsciously into self-injury; and wouldn't it be incredibly boring being all alone?

More seriously, the answer lies in making a distinction between two subtly different, but very similar, propositional functions. To refresh your memory, a propositional function is, represented symbolically as p(X), is a proposition regarding a variable. For example, t(X): "The time is X" is a propositional function, as opposed to t: "The time is 5:00", which is simply a proposition. The two propositional functions we want to contrast are:

"X exists", and
"X probably exists".

When they're written like that, you probably don't see how they can be easily conflated. However, I assure you, you do it all the time. In fact, your brain is wired to treat the second proposition ("X probably exists") as the first ("X exists"). This is why people who hallucinate treat their hallucinations as reality, a propensity used to great effect in A Beautiful Mind. John Nash, Russell Crowe's character, believed his college roommate, that roommate's daughter, and his employer were all real precisely because his mind obeyed the rule of thumb "If it very likely exists, then it does exist." This is the rule of thumb science is based on; indeed, it's the rule upon which we base all of our lives.

You see, solipsism points out that the rule of thumb is not, in of itself, logically valid. There's no reason the truth of a given proposition follows from an arbitrarily high, but not absolute, certainty of its truth. Solipsism points this out, and then stops, pointing out that you can't know for certain if your body exists, that you're not a brain floating in a tank somewhere, or hooked up to a computer simulation a la The Matrix, or that you're insane locked up in a sanitarium in eighteenth century England, or dreaming, or that the world and you and everything you remember all sprang into existence thirty seconds ago, or any other highly implausible yet perfectly possible situation you could care to invent. Solipsism is a philosophical dead end: if you subscribe to it, then you can't get anywhere beyond "I think, therefore I am".

The key to getting past it lies in the words "for certain". You can't know for certain, so who cares? You certainly don't, I guarantee, since you're reading this right now. You operate on the assumption that your senses are not lying to you: in effect, you operate on the assumption that if something very probably exists, then it actually does exist. To give a rather exotic example, suppose you're sitting at your computer, and you feel a nudge on your shoulder. You turn around and lo and behold, there is a unicorn standing behind you. It's even pink. Your first instinct is probably disbelief, so you reach out and touch it. It feels real enough. You can smell the horsey sweat on its body (its pink hair is short and coarse), and you can hear it snuffling as it sniffs your hand. It seems real enough; it's certainly not a mirage, that you can see but neither hear nor smell nor feel. So, you're on the verge of concluding it's not an illusion, but just to be sure, you yell for your wife. She enters. Her first reaction? "Oh my gosh. Is that a unicorn?"

What was the line of reasoning you used there? Well, a unicorn standing behind you is wildly implausible, to say the least. Your instinct was that there's a chance your eyes are being deceived, as in the case of a mirage, so you checked it with all your other senses. Because the probability that all of your senses are being deceived simultaneously is exponentially smaller than the probability that one sense is being deceived, that confirms that there seemed to be a real, live unicorn standing there. A unicorn is still way, way out there, so you called your wife. What's the probability that both you and she are being deceived by some optical illusion? Astronomically small. She sees it, too. Congratulations! You've jacked up the probability that there actually is a unicorn standing in your room to levels that appear to you to be very near certainty.

For another example, turn to A Beautiful Mind. When the representative of the Nobel Committee comes to see John Nash, he turns to a student just exiting the classroom and asks, "Do you see this man?" He's just double-checking and making sure that his senses are not, in fact, deceiving him.

So, no human can lay claim to absolute knowledge regarding existence outside that of his own mind. He can only be certain to within an incredibly tiny probability of error that he's right. Science simply formalizes and quantifies the methods that we humans use to figure out the world we live in, using a process called methodological naturalism- i.e., the scientific method:

This process is, essentially, what you went through when you discovered the unicorn behind you in your room. You saw the unicorn, hypothesized that really, it did exist, tested your hypothesis, and noted that your hypothesis had been confirmed. Science also requires repeated testing of a hypothesis if it is initially successful; this permits many people to confirm your hypothesis. There is one rather large detail this summary of the scientific method glosses over. Science requires falsifiability for scientific hypotheses. This permits it to employ the logic described above: the probability of passing the test while still being incorrect becomes impossibly small after subsequent passed tests.

This is probably unclear, so let me illustrate. As we've discussed above, it's impossible to determine if any proposition or statement about the world is absolutely true, as solipsism acknowledges. Therefore, science must make do with trying to determine how probable a given proposition is. This is why it requires falsifiability: the testing in the scientific method does not look for confirmation, but rather seeks to prove the hypothesis wrong. Confirmation, in of itself, tells us nothing if it's not possible to prove the hypothesis wrong. Going back to our pink unicorn hypothesis, is it possible to prove that there's actually no pink unicorn standing behind you? Sure; you could turn around and not see it, or you could see it but not feel it, or you could see it and feel it but not hear it or smell it, or your wife maybe can't see it.

Again, to reiterate, falsifiability is important because when we test our hypothesis, we test the alternative. That is, we assume that it is false and evaluate our results in the light of that assumption. If the results are what we expect if it's false, we consider the original hypothesis disproven; if they're wildly improbable in light of our assumption of falsehood, we do not consider the original hypothesis proven, but rather that the test has provided evidence for it. We test it again, then, to see if it passes; then we test again, and again. The probability that it passes all the tests but is false is like the probability that you see and hear and feel the unicorn, but it's actually not there.

If we can't prove a hypothesis false, then it tells us nothing, like solipsism (which is, incidentally, tautologically true and therefore literally unfalsifiable). What good is something that we can't prove wrong? It doesn't tell us anything because we can't test it and let the probability that it isn't wrong build up until we're pretty certain that it's correct. If there's no chance we can find a result that shows a hypothesis is incorrect, then we can't crank it through our scientific method to get a result. For an example of an unfalsifiable hypothesis is, check out Carl Sagan's invisible dragon in the garage.

For a case study, consider Newtonian physics. With the advent of Sir Isaac Newton's calculus, and with it the power to describe continuously changing quantities, science entered what might be called its golden age. Newton's system of mechanics generated prediction after prediction, all of which could be proven false, and yet weren't. For example, Newton's law of gravitation, in conjunction with his three laws of motion, accurately and with an incredible degree of precision predicted the motion of all of the observed celestial bodies. However, it was quite possible for its predictions to be falsified (although it's difficult to think of a situation where they're wrong, given how correct it is): for example, if Mercury's rate of precession was larger by a few arcseconds per century than Newtonian mechanics predicted, it would be falsified.

Incidentally, that's what happened; toward the end of the nineteenth century, as observations became increasingly precise, several experiments and observations falsified Newtonian predictions. Mercury's precession around the sun was one; another was the famous Michelson-Morley experiment, which detected no evidence of a universal ether through which electromagnetic waves moved. These, along with issues of atomic stability and black box radiation, effectively falsified the classical model of physics which had grown since Newton's publication of the Principia and before.

As an aside, this is why science also insists on quantification, or turning observations into numbers. Using numbers permits science to use the objective language of mathematics to describe its hypotheses and its observations instead of ultimately subjective verbal languages. Mathematics permits science to create models which describe the world and generate predictions; as Galileo said, "Mathematics is the language with which God wrote the universe." So, the goal of science is to use the scientific method to create a model that describes the universe. There are many models out there; some are more accurate than others. Newtonian physics, for example, is such a good approximation of the world on a scale where things aren't too big or too small, and don't move really fast, that though it's been falsified, we still use it to describe things in everyday life. For example, an Earth-crossing asteroid will be moving at a speed of about 30 km/s; if it has a diameter of 300 m, it will impact with a single titanic blast equivalent to about 250,000 Hiroshima bombs all going off at once. To generate that estimate, I used the Newtonian definition of kinetic energy, that KE = (m*v^2)/2. Because the asteroid does not have mass on the order of stars, and it's not moving at any appreciable fraction of c, there's no reason to use the much more precise relativistic descriptions.

Once it's been confirmed, a scientific hypothesis may fall into one of three categories:

A fact is simply an observation; for example, I may hypothesize that if I drop something, it will fall at 9.8 m/s/s. This can be confirmed through testing. A law is a mathematical description that, well, describes observations. For example, Newton's law of gravitation, in a modified form (a = GM/r^2) predicts an object (when you plug in the numbers) that an object will fall at 9.8 m/s/s when it's dropped on the Earth's surface. Note that it makes predictions that can be falsified; for example, I could hypothesize that a = 8pi*GM/r^2, and I would, of course, be wrong. In this case, I'd be wrong by a factor of 1/8pi. Finally, a theory is a hypothesis that postulates a mechanism to generate predictions. For example, Einstein's theory of relativity postulates a mechanism, namely curved spacetime, to describe the phenomenon of gravity. From this mechanism, it generates predictions, which can be tested against observations and falsified. None have so far, which is why relativity is so widely accepted in the scientific community. Do note that the scientific definition of theory is removed from the colloquial definition; a scientific theory is anything but a casual guess, although the two definitions are often equivocated.

So, to recap, science evades the problem of absolute truth by refusing to lay claim to it. Since no truth is absolute beyond your own existence, science doesn't seek absolute truth, but rather to establish that a particular model or approximation is very likely correct. This is formal and mathematical, but analogous to the way in which you would convince yourself of the existence of a startling occurrence, such as a pink unicorn standing behind you. The scientific method formalizes the process you use to discover knowledge into the scientific method (also known as methodological naturalism). The scientific method requires hypotheses to generate predictions which can be tested and proven wrong, and in doing so will weed out inaccurate descriptions of the world. Hypotheses that are tested, retested, tested again, then tested again, etc., and eventually become accepted, fall into three categories: fact, law, and theory. This descriptive power, the ability to weed out hypotheses which are inaccurate and useless, leads science to generate useful descriptions and approximations of the universe around us. These descriptions, in turn, have led to technological advancement, greater wealth, and, in general, the affluence, comfort, and luxury we as a society enjoy. The greatest gift of science, however, is scientia gratia scientae.

For another short introduction to some interesting concepts, check out this essay.

All original material copyright Neal Coleman, 2005-07. All previously copyrighted work copyright their respective owners, and used here under Fair Use provisions of copyright law for the purpose of criticism and analysis. Click here to return to my homepage.