Sunday, December 6, 2009


What makes a theory "scientific"? Probably the most widely accepted notion is that it should be falsifiable, i.e., there should be some way, at least in principle, to disprove the theory. This sounds reasonable, but unfortunately it is logically possible - and looking increasingly likely - that the true underlying "theory of everything" is not falsifiable.

What if the theory predicts, for example, the existence of many different universes, unable to communicate with one another? This is a perfectly reasonable possibility, yet we could never disprove it. These "multiverse" theories even have explanatory value in helping us understand why our universe has the particular constants of nature necessary for life (because each universe has a different, random set of constants, so eventually the ones suitable for life will crop up).

Falsifiability is also a very tricky criterion to use in discriminating science from pseudoscience. For a theory to be falsifiable there have to be two "possible" universes, one in which the theory is true and one where it isn't. So we need to know what kind of universes are "possible"; but once we decide this then we don't need falsifiability anymore, since we will already know which theories are possible.

To me it seems that there is a very simple criterion for which universes can exist, namely reducibility to mathematics. As I have argued in another post, any possible universe must be founded on mathematics because only mathematical objects can actually be defined. This implies (as a trivial consequence) that the only "scientific" theories are those compatible with reduction to mathematics.

This criterion immediately rules out any theories involving gods or "supernatural" beings. One can argue at length over the hypothetical characteristics of these entities, but one thing their supporters will never agree to is that they might have a rigorous mathematical basis - because that would defeat the entire psychological purpose of believing in them.

The criterion may seem simplistic and reductive, but it does cast a clear light upon the issues - and one which happens to build upon, rather than shrugging off, the mathematical foundation we have discovered in our own universe.

My criterion is also more honest, I believe, since generally when scientists argue that certain things are "non-scientific" what they really mean is that those things could not possibly exist. For example, if "spirits" could exist and influence events, then those spirits could be studied by science and would not be "unscientific". To say they are "unscientific" is pointless - for that is the exact reason why believers want to believe in them; what one really means by "unscientific" is that they could not possibly exist.

Of course, to believe that only mathematical entities can exist is a belief; we can never prove this. However, it is a belief which matches our discoveries about our own universe, and which makes logical sense, and this is more than one can say about its numerous competing belief systems.

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