The Logic of Scientific Discovery (1935) [pdf] | Hacker News Reader

The Logic of Scientific Discovery (1935) [pdf]

strangebeautiful.com

35 pointsboshomi6 comments

I think this book receives a lot of criticism from people who do not understand the fundamental point popper was trying to make.

I think the point can be best summarized as:

1. Claims on infinite sets can only be supported by rules of inference valid for the set.

2. We do not have rules of inference for reality.

I was listening to some debate over the weekend where someone claimed science can only tell us what is false and not what is true. But this is a massive misunderstanding of falsifyability as a criteria for demarcation between science and non science.

If we use the word real for what is in the science side of the demarcation line...

Then, without rules of inference (which again we, any claim about what is real can only be said to be true or false if it is backed up by an actual measurement. So if I say all dogs have 4 legs, I can only defend it as true if I test it against the set of all dogs, the first dog that does not have 4 legs though would make further testing less useful, maybe you want to check some more dogs to make sure you are not testing wrong, but once exception to a claim on an infinite set makes the claim invalid. Or as popper would say, it falsifies the claim.

So for any dog, we cannot say for sure if it has 4 legs or if it does not have 4 legs if we don't measure it. We cannot say the claim that it has 4 legs is true or false before we measure it.

So science does not tell us what is false. It tells us that claims about infinite sets of things which are real cannot be said to valid, because we don't have rules of inference, and while they may be valid we should try our best to find exceptions to these claims so that we do not keep on relying on them if they are not valid.

This idea was somewhat more formalized in E.T. Jaynes' posthumous book, Probability Theory: The Logic of Science (2003), with the idea that truth in science is a matter of probability -- confirmatory evidence increases our estimate that the theory is likely correct, but individual exceptions (like the proverbial three-legged dog, or in reality the existence of experimental error and the like doesn't mean we throw out a theory when only a few cases disagree with it).

I think this conflates problems we have with measuring reality with how we should deal with it.

If we know for sure that there is a 3 legged dog then we can say for sure a claim that all dogs have 4 legs is not valid.

Sure, we cannot know if we measured correctly or if some treachery is afoot - but if we could know for sure - then we we would know for sure the claim is not valid.

I don't think popper ever claimed the first time we got an exception to a claim on indefinite sets it should be thrown out.

I guess I left this out of my earlier post, but he also made some other point that if there is no test of our reality we can make that could invalidate it given a specific outcome of the test then our test is not scientific. Does not mean it is wrong, or should be discarded, but it just is not science. Also maybe some things where we can falsify it with test is not science, but definitely if we cannot falsify it - it is not science.

I think the case of the three-legged dog shows the difference between mathematics and science. In maths, finding even one exception to a hypothesis (like claiming that all odd numbers are prime) disproves the hypothesis. But obviously dogs are really 4-legged animals and the fact you can find one that lost one of its legs isn't very scientifically informative. You'd have to show that there is a whole breed of dogs that only has three legs by default for it to be a meaningful observation.

> I think the case of the three-legged dog shows the difference between mathematics and science.

With math we have rules of inference that allow us to know that claims on infinite sets are valid, for science we do not have rules of inference so any claim on an infinite set can become invalid with one more test.

But that just isn't the way science works. That's why a probabilistic way of viewing it makes more sense than simple falsification. No serious theory in science is ever going to be overturned with "just one test". At most, one's estimate of the theory's truth is going to be slightly reduced when a counterexample is found, as every scientific theory is just a model of the world, and obviously can't cover every minor exception. If it turns out that many exceptions are found, then yes, the theory has a problem and needs to be fixed.

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