Should scientific theories be falsifiable? Many insist that they must be. Others argue that theories are useful even when they are not falsifiable. In a recent blog, Noah Smith argues that if theories make no claims about the physical world, then it should not matter.
A theory is falsifiable if it makes predictions about physical reality that can be tested now or in the future. For example, it took many decades to be able to test some of the predictions of general relativity. However, the theory due to making those predictions was falsifiable. If a theory about the physical reality does not generate any testable predictions, then it is not falsifiable and it is not different that a pure belief.
Noah Smith made the following (strawman) argument:
“I don’t see why we should insist that any theory be testable. After all, most of the things people are doing in math departments aren’t testable, and no one complains about those, do they? I don’t see why it should matter if people are doing math in a math department, a physics department, or an econ department. “
Noah Smith appears to confuse theories and theorems and tries to extend the concept of falsifiability to math ignoring for a moment that this notion was used for theories that make claims about physical reality. Noah Smith also ignores the underdetermination problem: Even if theories are testable, due to them being undetermined by experience, one could construct an indefinite number of theories that are incompatible with each other, but are in accordance with experience. (Ref. 1).
According to Popper progress is made by falsifying old theories and replacing them with new ones. As a result, theories must be falsifiable so that a convergence of the process can take place. This answers the first part of the strawman Smith constructed, i.e. “I don’t see why we should insist that any theory be testable. ”
Let us now move to the second part of the strawman:
“After all, most of the things people are doing in math departments aren’t testable, and no one complains about those, do they?”
Nobody complains because in math departments people are concerned about the language we use do describe theories, not about the theories themselves, like a theory of physics or a theory of economics. Among other things they are concerned with the consistency, complexity, computability, etc of mathematical statements. Only Platonists believe that these mathematical objects exist but that is realism in the sense that these objects are not directly observable. Most scientists view math as abstract constructions or formulas to use. Therefore, what people also do in math departments is to accommodate other scientists but their theories are not of the same kind as theories that make claims about the phenomena, such as the orbit of an object in space or the term structure of interest rates. I hope this answers the second part of the strawman argument made by Smith.
Let us now move to the last part of the strawman argument: ” I don’t see why it should matter if people are doing math in a math department, a physics department, or an econ department. ”
People in a physics department are not doing just math. They use math to formulate a theory about physical reality, they notice the predictions and try to confirm or falsify them in a laboratory. In reality, the ones that come up with the theory and the ones that test it may not belong to the same group and hence the distinction between theoretical and experimental physics. But ultimately, physics is a one subject. As soon as someone comes up with a new and major prediction about the phenomena, some others try to find out if that confirms in the laboratory. Thus, physicists are doing a lot more than math. And economists are doing a lot more than math as they deal with real phenomena that emerge as a result of the interaction of economic agents. Therefore, it makes a difference where math is practiced.
What about string theory? This theory is not falsifiable although it is fairly old but nobody has come up with a prediction that is unique and can be attributed only to that theory. Is it useful? Probably not and some say not at all. Should we fund a non-falsifiable theory? Probably not if after a long period of development time it cannot generate unique predictions. One could come up with an indefinite number of similar theories that make no testable predictions. It is just a waste of time.
Then Smith says: “And it’s cheap and harmless to have people sit around and work on those things. ”
No, it is not. Actually it is a huge waste of resources.
But why Smith’s whole argument is a strawman? It is because he first set up the argument and then he attacked it himself with the obvious answer that he wrote:
“But as soon as people start saying – or even implying – that their theories describe real phenomena, then the ball game changes.”
Agreed. He only had to say that from start to avoid the whole exercise in futility.
Ref 1. Esfeld, Michael, “Hypothetical metaphysics of nature”, in Michael Heidelberger and Gregor Schiemann (eds.): The significance of the hypothetical in the natural sciences. Berlin: de Gruyter 2009, pp. 341–364