Lemma 3: science does not know everything

This is less of a lemma and more of a clarification. An exercise in filtering the mud out of the water.

There is a common argument when one attempts to apply science to certain subjects. It runs something like this: "Science does not know everything. Science does not address X. Therefore X is somehow 'outside' science."

One step at a time then ...

Science does not know everything.

This is true enough. But not necessarily in the way that it is typically intended.

It is true in the sense that the universe contains a lot of stuff and it is highly unlikely that the human race will ever have the resources or technology to observe and catalogue and model every single bit of it.

It is true in the sense that existing scientific models explicitly exclude the possibility of knowing 'everything'. On the macro scale, general relativity tells us that there are parts of the universe that are unobservable. We can never 'see' them. They can never have any effect on us. (That's a slightly heavyweight wiki article ... if anybody wants to volunteer to paraphrase it in layman's terms they are more than welcome). At the other extreme of scale, Heisenberg suggests that we can only know a limited amount about the position and momentum of a particle.

And we've already mentioned incompleteness theory.

(Of course, it is more than possible that the current models of relativity and quantum mechanics are wrong and that we can know more than they suggest. As I've already said, science is always wrong. That's why it works.)

But this statement is true in a more abstract and arguably much more important sense. It is true almost by definition. Science does not strictly know anything at all. It does not even claim to. It claims to provide us with useful models that help us advance in the Real World. A claim I defy anybody to refute (unless they're living naked under a bush and communing with The Internet via herbal telepathy).

A better statement would be "Science can model anything."

If there is something that we can observe and attempt to understand then the scientific method can address it. If something can be defined, then we can attempt to model it. If it can be observed, then we can compare our models with the observation. Essentially, if something exists, then it can be approached with the scientific method.

Have we accidentally addressed the third part of the argument here? Apologies for jumping the gun. Back to the second part.

Science does not address X.
This can be interpreted in two ways. The first and simplest is "there is no current scientific model relating to X". This may well be true. This does not mean, however, that a scientific model of X cannot be formed.

The second interpretation is broader and more nebulous and, I think, is what is most typically intended: "X contains some peculiar quality that differentiates it from the usual subjects of science".

This is the meaning used by people who make claims of supernatural abilities such as telepathy. It assumes that 'science' is a finite set of things: theories and test tubes and computers and boffins in laboratories. But, if you'll excuse me hammering the nail in with yet another nail, science is not a finite and complete explanation of everything. Science is a method.

If X contains some quality, however peculiar, then that quality can be expressed and modelled and compared with observation. That quality can be added to the list of things that the scientific method has addressed.

So ... nothing is a priori 'outside' of science. You can, if you wish, apply the scientific method to absolutely anything at all. The response to the original assertion is:

"Science can be applied to anything. If X exists, then science can be applied to it. Therefore nothing that exists is 'outside' science."

Or, expressed in an even more controversial direction:

"If the scientific model is somehow inapplicable to X, then X does not usefully exist."