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★★★☆☆ Explanations and falsification

The Logic of Scientific Discovery


Karl Popper


I would not advise most people to read Karl Popper's The Logic of Scientific Discovery, but only because David Deutsch's The Fabric of Reality contains a better presentation of Popper's ideas. The following quote is a good place to start to understand the significance of The Logic of Scientific Discovery
The value today of philosophy to physics seems to me to be something like the value of early nation-states to their peoples. It is only a small exaggeration to say that, until the introduction of the post office, the chief service of nation-states was to protect their peoples from other nation-states. The insights of philosophers have occasionally benefited physicists, but generally in a negative fashion—by protecting them from the preconceptions of other philosophers.
--Steven Weinberg
One such preconception was the idea that science is based on inductive logic -- whatever that means -- it is far from clear. I was told this in elementary and high school. This idea, which apparently we owe (at least in part) to Immanuel Kant, is quite, quite wrong. It makes no sense, as Popper clearly explains in his first chapter. Furthermore, as a description of how actual scientists actually think, it utterly fails.

Popper contributes two useful new ideas. The first of these is explanation. Good theories are not just descriptions or generalizations -- they are explanations. The difference is not easy to pin down -- Popper puts some effort into it. Deutsch gives an example I really like, though. Suppose we are asked for an explanation of why a particular copper atom is located where it is: 45 meters above the ground in Trafalgar Square, London. One could imagine an attempted explanation that started with the creation of the copper atom in a supernova and described in minute detail all the forces that pushed and pulled it around until it ended up in that location. This is not really an explanation -- it is just a uselessly detailed description. Suppose, instead, someone tells you that a large group of apes who called themselves "Great Britain" fought a war with another group of apes called "France", and that one of the apes, a male called "Nelson" commanded the British apes that won a battle with the French apes. In memory of this battle the British erected a bronze statue in London and elevated it on a tall column.

As an explanation of how copper atoms move around, the second is obviously more useful. Good explanations -- good theories -- have what I call "fanout" (a term borrowed from electronics). A good explanation explains not just the things it was created to explain, but other things. Newton's Theory of Gravitation was a splendid example. With just a few simple principles: an inverse-square forces between any two masses, Newton explained an apple falling to Earth, the moon falling toward (and thus orbiting) Earth, all of Kepler's planetary laws, and the tides.

A REALLY good theory fans out not just to things we already know, but to the future. This is where Popper's second key idea, falsification comes in. Falsification is the idea with which Popper replaced induction. A good theory makes predictions about the results of experiments (or more generally, future observations). For instance, Newton's theory predicted that two masses should be attracted to each other. Newton's theory could be falsified if there was no such attraction. That was very hard to test, because gravity is such a weak force, but Henry Cavendish eventually managed it -- and in fact, Newton's Theory was right about this. A theory is successful if it "resists falsification".

How do Popper's ideas hold as a description of how scientists really think? Very well! Scientists in my experience don't think explicitly about explanation (a shame, since it is a helpful idea), but their behavior reveals a preference for theories that are good explanations. And they do think quite explicitly about falsification. Scientists try to prove their theories wrong! Yes, they do. First, nothing is more exciting to a scientist than a result that clearly shows that some previously popular theory is wrong. Second, even those scientists seeking to prove their own theory gravitate immediately towards the most implausible predictions they can experimentally test, because they know that those will most effectively convince skeptics.


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