The idea of counting postulates is attractive, but it harbours a problem which reminds me of a story. There once was an editor assigned to review an article. The editor was conscientious and raised 15 questions. But his boss thought this was too many and would only permit five questions. Now the editor cared about his points, so he kept them by generous application of the conjunctive: “and”.
We could come up formal requirements to avoid anything as crude as the editor’s behaviour. But, I think we’d still find that each postulate encapsulates many concepts, and that a fair comparison between competing theories should consider the relative complexity of the concepts as well. So, we are still far away from assigning each theory a numerical complexity score.
A more serious problem is that a postulate count differs from what we usually mean by complexity, which generally reflects in some sense the heterogeneity and volume of considerations that go into applying a theory. Ptolemy’s and Newton’s model of the solar system give similar results. It’s true that Ptolemy’s theory is more complex in its expression. But even if its expression were simpler, I’d still label Newton’s theory simpler, since the Ptolemaic theory requires many more steps to apply.
The idea of counting postulates is attractive, but it harbours a problem...
...we’d still find that each postulate encapsulates many concepts, and that a fair comparison between competing theories should consider the relative complexity of the concepts as well.
Yes, I agree. A simple postulate count is not sufficient. That’s why I said complexity is *related* to it rather than the number itself. If you want a mathematical formalization of Occam’s Razor, you should read up on Solomonoff’s Inductive Inference.
To address your point about the “complexity” of the “Many Worlds” interpretation of quantum field theory (QFT): The size of the universe is not a postulate of the QFT or General Relativity. One could derive what a universe containing only two particles would look like using QFT or GR. It’s not a fault of the theory that the universe actually contains ~ 10^80 particles†.
People used to think the solar system was the extent of the universe. Just over a century ago, the Milky Way Galaxy was thought to be the extent of the universe. Then it grew by a factor of over 100 Billion when we found that there were that many galaxies. That doesn’t mean that our theories got 100 Billion times more complex.
† Now we know that the observable universe may only be a tiny fraction of the universe at large which may be infinite. In-fact, there are several different types of multiverse that could exist simultaneously.
The idea of counting postulates is attractive, but it harbours a problem which reminds me of a story. There once was an editor assigned to review an article. The editor was conscientious and raised 15 questions. But his boss thought this was too many and would only permit five questions. Now the editor cared about his points, so he kept them by generous application of the conjunctive: “and”.
We could come up formal requirements to avoid anything as crude as the editor’s behaviour. But, I think we’d still find that each postulate encapsulates many concepts, and that a fair comparison between competing theories should consider the relative complexity of the concepts as well. So, we are still far away from assigning each theory a numerical complexity score.
A more serious problem is that a postulate count differs from what we usually mean by complexity, which generally reflects in some sense the heterogeneity and volume of considerations that go into applying a theory. Ptolemy’s and Newton’s model of the solar system give similar results. It’s true that Ptolemy’s theory is more complex in its expression. But even if its expression were simpler, I’d still label Newton’s theory simpler, since the Ptolemaic theory requires many more steps to apply.
Yes, I agree. A simple postulate count is not sufficient. That’s why I said complexity is *related* to it rather than the number itself. If you want a mathematical formalization of Occam’s Razor, you should read up on Solomonoff’s Inductive Inference.
To address your point about the “complexity” of the “Many Worlds” interpretation of quantum field theory (QFT): The size of the universe is not a postulate of the QFT or General Relativity. One could derive what a universe containing only two particles would look like using QFT or GR. It’s not a fault of the theory that the universe actually contains ~ 10^80 particles†.
People used to think the solar system was the extent of the universe. Just over a century ago, the Milky Way Galaxy was thought to be the extent of the universe. Then it grew by a factor of over 100 Billion when we found that there were that many galaxies. That doesn’t mean that our theories got 100 Billion times more complex.
† Now we know that the observable universe may only be a tiny fraction of the universe at large which may be infinite. In-fact, there are several different types of multiverse that could exist simultaneously.