2005 : WHAT DO YOU BELIEVE IS TRUE EVEN THOUGH YOU CANNOT PROVE IT?

I believe that scientific theories are a means of going—somewhat mysteriously—beyond what we are able to observe of the physical world, penetrating into the structure of nature. The "theoretical" parts of scientific theories—the parts that speak in seemingly non-observational terms—aren't, I believe, ultimately translatable into observations or aren't just algorithmic black boxes into which we feed our observations and churn out our predictions. I believe the theoretical parts have descriptive content and are true (or false) in the same prosaic way that the observational parts of theories are true (or false). They're true if and only if they correspond to reality.

I also believe that my belief about scientific theories isn't itself scientific. Science itself doesn't decide how it is to be interpreted, whether realistically or not.

That the penetration into unobservable nature is accomplished by way of abstract mathematics is a large part of what makes it mystifying—mystifying enough to be coherently if unpersuasively (at least to me) denied by scientific anti-realists. It's difficult to explain exactly how science manages to do what it is that I believe it does—notoriously difficult when trying to explain how quantum mechanics, in particular, describes unobserved reality. The unobservable aspects of nature that yield themselves to our knowledge must be both mathematically expressible and connected to our observations in requisite ways. The seventeenth-century titans, men like Galileo and Newton, figured out how to do this, how to wed mathematics to empiricism. It wasn't a priori obvious that it was going to work. It wasn't a priori obvious that it was going to get us so much farther into nature's secrets than the Aristotelian teleological methodology it was supplanting. A lot of assumptions about the mathematical nature of the world and its fundamental correspondence to our cognitive modes (a correspondence they saw as reflective of God's friendly intentions toward us) were made by them in order to justify their methodology.

I also believe that since not all of the properties of nature are mathematically expressible—why should they be? it takes a very special sort of property to be so expressible—that there are aspects of nature that we will never get to by way of our science. I believe that our scientific theories—just like our formalized mathematical systems (as proved by Gödel)—must be forever incomplete. The very fact of consciousness itself (an aspect of the material world we happen to know about, but not because it was revealed to us by way of science) demonstrates, I believe, the necessary incompleteness of scientific theories.