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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 sa

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.

jhbadger 7y ago
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.
- ailideex 7y ago
  > 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.
  - jhbadger 7y ago
    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.

jhbadger 7y ago

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.

ailideex 7y ago
> 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.
- jhbadger 7y ago
  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.