We often hear the phrase “that’s OK in theory”, and we all recognise that there is a difference between something we might think is true, and whether or not it really is.
Learning the difference between a thought, an idea or an opinion, and what is actually the case, is part of growing up and it’s a major focus of our education. It is very easy for us to think something is true only to find out that it is not.
There are very many counter-intuitive examples in nature ranging from things that float, things that fly apparently defying gravity, the existence of rainbows, and refraction, right up to more complicated ideas like Einstein’s Theory of Relativity and Quantum Mechanics.
So how do we distinguish between what counts as a theory and what is a fact? In order to manipulate the world we live in, we have to trust our senses to a certain extent even though we are aware that we can be fooled by them. We need some reliable way of finding out when in fact we are being fooled.
Earlier people who studied the external world settled simply for descriptions without trying to understand causes or explain how things came about. But with just descriptions, we just end up with a catalogue, a set of accounts which do no more than describe nature. These are not theories because they do not attempt to explain anything. Where these descriptions did offer an explanation, they provided no evidence. Many of the European writings before the sixteenth century fall into this category.
But from what we observe and measure and manipulate in the world, we try to pull together ideas about how things work. We try to figure out explanations of why things happen the way they do and sometimes we are right and sometimes we are wrong. The question is, how can we tell?
When we take the data we have, whether from sophisticated scientific equipment or just our own impressions and perceptions, and try to build it into an account of how things work, we are constructing a theory. A theory is very different from a simple description because it also has predictive power. We can use what we know to make a prediction about what will happen, and then test it.
Theories allow us to make a statement about what will happen: we call such a statement an hypothesis. Making an hypothesis allows us to construct an experiment to see if it is right or wrong. If it’s wrong, our theory is incorrect and we can improve or reject it. That means our knowledge can grow because we can tell when we are wrong.
By contrast, a description never gets any further than a simple description. It has nothing more to offer.
So for theories, it is the external real world which is the arbiter of what is or is not a fact. By making theories, our knowledge can advance and we can find out more and more about the world.
The post-modernist fallacy
There was, in the 80s and 90s, a philosophical movement that tangled itself up in some very abstruse reasoning. This group of post-modernists saw everything as a “narrative”, including science. Instead of the external world being the arbiter of what is the case, they instead argued that everything is relative, everything is just as valid, everything is just as “true”.
That means, for them, that science is just one story amongst many other equivalent stories. They did not accept that experiments based on theories and hypotheses lead to reliable knowledge about the world. Despite the incontrovertible evidence that technology actually works, they still denied the objectivity of the real world.
The mistake they made was to think that every theory had to contain within itself the proof of its own correctness. This academic abstraction led them into the very dusty corners of academia but there remains a popular misunderstanding about science.
Science is not an opinion, nor is it a belief system. It really doesn’t matter what the scientist believes because it is the experimental evidence that matters. If the theory doesn’t stand up when the evidence is scrutinised by others, the theory falls, regardless of the beliefs of the individual scientists. Scientific knowledge is therefore real knowledge, validated by the external world.
Science isn’t just one more narrative amongst many. It is the method by which we test our theories against the real world and the practical progress demonstrated by this approach is greater than ever before in humanity’s history.
Scientific theories are not all equivalent – some are better than others because they make better predictions about how the real world behaves. So scientific theories will continue to be improved, or rejected. New ones will be proposed and tested, and real knowledge will increase.
What about mathematics?
Some formal systems such as mathematics are based on logical rules in which it is possible to prove something is formally correct. Nature is not like that, which is why we use theories and experiments rather than formal proofs. But mathematics is like that.
So a fact in mathematics is defined by the mathematical system itself. Given the rules of arithmetic, we can be sure about how we add fractions and get the right results. So instead of using theories to test against reality, we produce conjectures and try to prove them within the formal system of mathematics.
But applied mathematics also relates to the real world. We study how the world behaves and draw up laws which are those rules we know from experience to be inviolable. These too are different from simply opinions of descriptions, because we use them to make predictions and test them. We try to explain why they have to be true.