The limits of reductionism

If you've been trained in Computer Science, there's a good chance that you see problem solving as primarily about breaking down big problems into lots of small, solvable problems.

(Alternatively, you may have learnt to create solutions to small problems independent of the big problem, which might then be usable when solving the big problem, but either way, it's the same pattern: small used to solve big.)

The drawback with this approach is that it leads to a tendency for reductionism; the idea that the universe is just a big problem waiting to be broken down into ever-smaller problems that need solving. The ideal reductionist position is to prove everything from the theorems of physics (dealing as it does with the fundamental particles of the universe).

But reductionism has a big limitation: it cannot cross the boundaries of a discipline. This limitation comes about as a direct result of the nature of axioms.

Axioms exist in all disciplines. They are bedrock proposition, regarded as self-evidently true without proof. Axioms come in two forms:

  • abbreviative definitions - we could prove this was true, but defining it as an axiom avoids the need to prove it
  • creative definitions - we can't prove this, but require it to be true as a foundation for our discipline

A reductionist believes that we should treat all axioms for a non-base discipline as abbreviative, tracing cause and effect down through laws and theorems and across disciplines until we finally reach the axioms of physics.

But there is one small issue. How can we ever know that our laws and theorems are true? Many widely accepted theories (eg. Newton's Laws of Gravitation) have turned out to be erroneous in small or big ways as time has passed. In fact, a philosophical discipline called Critical Rationalism holds that even if there is a 100% correct theory on some law of nature, we can never know that we've found it. All that we can do is subject our theories to rigorous testing and prefer theories that seem to hold up better.

Now, this has important implications for any system of axioms. If we describe an abbreviative axiom for any discipline, then it only remains abbreviative as long as all underlying axioms remain true. As soon as a single axiom it depends on gets disproved, or as soon as a single new axiom in a "lower-order" discipline is discovered, the axiom ceases to be abbreviative (we know this is true) and instead becomes creative (we need this to be true). This brings the whole reductionist "house of cards" tumbling down.

In other words, the only way that a reductionist approach will ever be possible is if we are 100% sure of every piece of underlying science. And since there's a strong case that we can never be 100% sure of any theory, let alone every theory, reductionism is an experiment doomed to failure.

(Heavily based on material from Popper's The Open Universe, and conversations with Joe Firestone about Critical Rationalism.)