In a recent post (Gravity or Fairies?) I posed the fundamental puzzle of philosophy of science:
How can we justify belief in theories positing the existence of unobservable things?
More specifically, how can we rationally infer from things we observe with our senses the existence of things we cannot observe with our senses—like electrons, magnetic fields, gravity, the distant past, etc.?
In fact, how can we justify thinking that a particular theory is probably true, on the basis of what we’ve observed, when infinitely many other theories are also consistent with that evidence?
My own view is that there is a two-part answer to this puzzle:
First, there are the principles of hypothetical reasoning (which can be explained and justified with Bayes’ Theorem—a theorem of the probability calculus). In a nutshell, the more a theory would lead us to expect the evidence we observe, the more that evidence supports that theory.
But this by itself doesn’t solve the problem. The other part of the solution is The Principle of Simplicity:
All else being equal, the simpler a theory is the more likely it is to be true.
There is no question that scientists favour simpler theories over more complex theories. This is universally agreed to among scientists and philosophers of science. It is also clear that we do this in everyday life as well.
The Principle of Simplicity is a generalization of ‘Occam’s Razor:’ “Do not multiply entities beyond necessity.” If we need to posit the existence of something (like electrons) to explain something we observe (like electrical phenomena), we should not posit the existence of more things than are necessary to do the job. Occam’s Razor is universally agreed to; it’s treated as almost an axiom of reasoning among scientists and philosophers of science.
But we all also favour theories which are simpler in other ways as well.
It’s puzzling why a simpler theory would be more likely to be true than a complex theory. So many take the Principle of Simplicity to be just a pragmatic matter: stick with the simplest theory you can until the evidence forces you to go to a more complex theory. It is a pragmatic matter, not that simpler theories are actually more probable.
That weaker version of the Principle explains why we favour simpler theories. Except it doesn’t explain why we actually tend to think simpler theories are more likely to be true. And so we actually think some of our theories are probably true, even though there are many more complex theories equally consistent with our evidence. The only way to justify belief that our theories are actually probably true seems to be the stronger version of the Principle: Simpler theories have a higher probability to begin with than more complex theories.
So the Theory of Gravity is more likely to be true than the Theory of Fairies (see Gravity or Fairies?) because it is simpler. The gravity theory posits the existence of just one force—gravity—and the concept of that force is extremely simple (everything is attracted to everything else proportional to their masses and inversely proportional to their distance apart). The fairy theory posits the existence of uncountable fairies pulling everything toward everything else. And the concept of a fairy is complex. (They have wings, personalities, etc.)
So it is more likely that there really is such a thing as gravity than that there are all these invisible fairies pulling on everything. This is explained by the Principle of Simplicity, an extremely important and powerful principle of reasoning.
I even think this principle supports belief in God: It is the simplest overall point of view to suppose that everything that exists has one ultimate cause. It is simplest to think this thing as unlimited power than only limited power. And unlimited power entails all the other basic characteristics of God. So the concept of God is actually an extremely simple concept. So belief in God provides the simplest explanation of the existence of everything else. So it is most likely to be true. Oxford philosopher Richard Swinburne has convinced me of this.