Is science true? Yes, that is the question. Is it really, really true? Helping to motivate this discussion, we recently assailed upon a little philosophy of math, here, where we remarked and marveled how math can represent both real and non-real things and yet both kinds can teach us about reality.
I thought this was incredible, and so it is! However, I used the Navier-Stokes equations in fluid mechanics as an example and as one commenter stated, even the respected Navier-Stokes equations aren’t true in the hard sense…they neglect many things like radioactive decay. This did not sit well with me, for I like to think what I am doing is true, and caused me to wonder what is truth, and what in science matches this. Let’s combine this discussion with a little science history.
I recently read and discussed with a few friends part of Thomas Kuhn’s famous book The Structure of Scientific Revolutions. Here he presents fields of science as progressing from one paradigm to the next as their ability to describe reality increases. These man made paradigms get exchanged like quantum physics replaced classical mechanics. Which then presents the obvious question … is all I believe in science about to be replaced with a new paradigm?!?!
So what do we have here. We have the realization that most (maybe all) of our equations in the scientific community are not true in the hard sense. Now, combine this with the notion that all we have learned and studied may soon be shown incomplete, half-whitted, or worse … passé. What are we to do? Let’s start by doing two things. First, let’s come to terms with these ideas – there is a good chance, most of what we have learned is not 100% true and may be updated in the future.
Next, let’s be good scientists and define our terms for we are in desperate need of defining true and false. For the purposes of this blog post, I will define a true statement as corresponding to reality. I will then define a false statement as devoid of all truth. With these handy definitions, let’s look back at our test case, the Navier-Stokes equations, and see if they fit our definition of true by asking, do the Navier-Stokes equations correspond to reality? As we know and our commenter pointed out, they don’t. They neglect at least radioactive decay and therefore fail to correspond to reality.
Ok, let’s see if they are false by asking, are the Navier-Stokes equations devoid of all truth? Well, I am a little stuck, but I feel inclined to say no. With this definition, I would say the Navier-Stokes equations are not false. So with these hard definitions of true and false, we get that the Navier-Stokes equations are floating around somewhere in the middle. I propose to define a middle ground in this way, corresponding to some, but not all of reality. Perhaps we can agree this is a good description of most of science at this time. Classical mechanics is not true, quantum mechanics and general relativity do not reconcile, and Plank’s constant isn’t actually 6.6260698*10^-34 J*s, though each certainly corresponds to some, but not all of reality.
This discussion helps me to relieve my anxiety caused by knowing my knowledge is limited and flawed. The anxiety is relieved because this does not mean my knowledge is entirely false. Phew! Our discussion continues to raise more interesting questions, like when can we say something is true, or, is science like Pi where we can get more but never all the terms. Let me know your responses and follow-up questions.