I attended a forum last week entitled “Is there certainty beyond science?”. As one of the speakers pointed out, perhaps a useful starting question would be, “Is there certainty within science?”, but the title did raise some interesting questions about what we mean by the words “certainty” and “science”.
Certainly (see what I did there?) there seems to be a common assumption that science at least aims to find certainty in the midst of confusion. The general perception is that science rigorously follows a trail of evidence to reach conclusions which can be claimed with a high degree of confidence. And there are even mechanisms to try and assess the degree of uncertainty in a given scientific theorem (although the willingness of adherents to acknowledge that uncertainty may be somewhat hit-and-miss).
What is often missing from the conversation is the impact of methodological assumptions on the usefulness of the conclusions which result from a particular methodology. Let’s look at mathematics as an extreme example.
Maths operates within the ultimate abstraction. It is a realm of pure ideas. This has advantages: because the system is entirely conceptual, the laws can be rigorously defined. This allows us to “prove” mathematical theorems by conclusively demonstrating a logical consistency. But to apply a mathematical concept to anything real, we must project from the abstraction back to the real world, where we cannot rigorously define the laws. Some of the projections are useful: arithmetic operations are easily projected onto everyday objects (so “3 bananas + 4 bananas” can easily be understood as seven actual bananas). Some projections are less straightforward: the relationship between a second-order differential equation and the acceleration of a car under constant force is not quite as intuitive.
Science also operates within an abstraction. The realm of science is limited by its methodological assumptions, such as philosophical naturalism and the regularity of nature. These assumptions are useful in that they allow us to limit the potential interactions that we investigate to those which are amenable to the tools of science. In other words, we limit what we will accept as an explanation of phenomena, and this allows us to define our area of investigation. But in making these assumptions, we have created an abstraction of the real world, and it is this abstraction that we investigate rather than the real world itself. As in the case of mathematics, the conclusions may or may not be readily suited to being projected back into our understanding of the real world.
It is worth noting that any of our abstractions are only definable from outside the system. We say that mathematics operates within a logically consistent and rigorously defined framework, but its logical consistency cannot be proven mathematically. (This isn’t a case of “It hasn’t been done yet”, this is a case of “It’s impossible even in principle”). We make a working assumption of methodological naturalism when we engage in scientific research, but we cannot scientifically demonstrate the validity of such an assumption.
Perhaps more interestingly, this also implies that we cannot fully define the operational parameters of the real world from within the system.