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Consider this statement: There exist black swans.

It is (practically) not falsifiable, since we can't search the whole world to conclude there are no black swans. However, it is provable, and I guess we can all agree that it's a scientific fact. Can we conclude that falsifiablity is not necessary for being scientific?

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    This question has multiple duplicates with answers, e.g. Why should science be falsifiable? This is aside from the fact that it is unasnwerable as phrased because it is controversial how to demarcate science from non-science, or even whether such demarcation is either needed or possible. – Conifold Apr 18 '18 at 4:57
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    But is falsifiable in principle : thus it is an empirical statement that can be "tested" (search for a black swan). – Mauro ALLEGRANZA Apr 18 '18 at 5:55
  • Ha, just had this on WB.SE! – SK19 May 10 '18 at 22:28
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This argument is based on an assumption that science deals in eternal absolutes. That luxury is generally the preserve of, well, philosophy.

Science deals with hypotheses and experiments. I can test the hypothesis that there exists black swans. And, by luck, I can confirm it readily (as I did last weekend).

Now, if I try to confirm the hypothesis that there exist green swans, I cannot do so so readily. However, assuming my grant money comes through, I can set out on a series of expeditions to look for this elusive creature. As my fruitless search expands, I may not be able to prove categorically that no green swan exists anywhere (my grant money doesn't stretch to searching Jupiter). I can, though, make strong statements about their existence within the bounds of my experimental scope.

And it's this latter point that is key. It's why, for example, people say that Einstein proved Newton wrong. He didn't. He showed the bounds within which Newtonian mechanics apply and the adjustments one need to make to extend the bounds.

And it's why, even when my best seller There are no green swans is reaching its 30th edition, one is discovered in the depths of the Amazon jungle, I will rejoice. Apart from making a great sequel, our knowledge has progressed. Our original understanding was limited and we can now correct our hypothesis.

Some people find this lack of absolutes unsatisfying. Personally, I think it's a swanderful.

  • "That luxury is generally the preserve of, well, philosophy." and mathematics and theoretical computer science. – SK19 May 10 '18 at 22:28
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It might be useful to consider the statement, "No more than 0.01% of swans are black". If we randomly pick 50,000 swans and none of them are black, we can be ~99% confident that we would have falsified the statement had it been false. Now, the statement isn't technically the same as saying "no swans are black", but it's almost as good in practice.

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Well, it is not even provable, there might very well exists a rare case of black swan due to a genetic mutation, disease, etc.. As long as you can't check right now every entity that could falsify your statement, or prove that it is physically impossible that a swan might be black, it can exists one case where it is true.

Basicaly it's all about maths quantifiers:

  1. ∃ swan, swan∈(black swans) <=> There exists at least one black swan => You have to find one case of black swan to prove it

  2. ∀ swan, swan∈(black swans) <=> All swans are black => You have to prove that every swans are black, so you can either check on every ewisting swan, or prove that it is physically impossible that a swan might not be black

  3. !(∃ swan, swan∈(black swans)) <=> There doesnt exists at least one black swan <=> ∀ swan, swan∉(black swans) => You have to prove that there doesn't exists any swan that is black, by the same method than on #2.

  4. !(∀ swan, swan∈(black swans)) <=> Not all swans are black <=> ∃ swan, swan∉(black swans) => You have to find one case of swan which is not black to prove it

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