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Unfalsifiable statements are said to be important in science. An example of such a statement:

All swans are white.

In plain English, that's simply a truthful statement.

So what's the difference between unfalsifiable and true?

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    "All swans are white" is falsifiable by finding a swan that isn't white. It's also false, because we have done so. – user6559 Jun 3 '18 at 7:07
  • So if every known swan was white, the statement would be true, but it would still be falsifiable because there's a chance we might find a swan that isn't white? – David Blomstrom Jun 3 '18 at 7:38
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    According to Popper whose philosophy of science he characterized in terms of "conjectures and refutations" [see a book of his with this title] theories that are in principle unfalsifiable are not science. For a theory to be considered scientific it should be such that it is in principle open to falsification. There are theories that were falsified and yet are scientific and important - such as Newton's theory (that was falsified by Einstein). – Jordan S Jun 7 '18 at 12:51
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    Interesting. It would be really helpful to have a list of examples - scientific theories that are either based on falsifiable/unfalsifiable statements or that were disproved by falsifiable/unfalsifiable statements. Maybe I can make that a separate question; but I'll do some research first. – David Blomstrom Jun 7 '18 at 20:24
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    @DavidBlomstrom, if it is interesting for you, perhaps explore Karl Popper's views on philosophy of science through taking a look also at his "The Logic of Scientific Discovery" and his "The Open Society and its Enemies." – Jordan S Jun 8 '18 at 2:14
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The basic answer has been given several times: a theory is falsifiable if there is some way it could be shown to be false, but not every falsifiable theory has been shown false.

Of course we do not consider every theory to be true until it is shown false. Lots of theories are currently genuinely open questions. For example proton decay. It is not even clear how that could be falsified by experiment, since any amount of very careful searching which reveals no decay could be dismissed as not having looked long enough!

Other theories are accepted as true, although some conceivable evidence could refute them. There may even be well known evidence against them which is just not considered important enough. General Relativity is an accepted theory though, like all serious theories, it has some known problems. It is considered true, and falsifiable.

An important point: "falsifiable" per se is quite vague. Many people believe you can prove evolutionary theory false by showing it contradicts their reading of the Bible. Karl Popper used a more specific notion: "empirically falsifiable." And he noted this is a feature of how you view a theory, not of the theory itself: If you understand a theory in such a way that certain experimental outcomes would make you reject it, then you are taking that theory to be empirically falsifiable.

Some one else, though, might take that very same theory and insist that in the face of any conceivable contrary evidence, they would find some way around the evidence rather than reject the theory. Then they are taking that theory not to be empirically falsifiable.

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A theory is considered true, until it is proven false. The black swan, as mentioned in the comments (also an excellent book: Nassim Nicholas Taleb, The Black Swan), is a great example of this. Until a certain time, saying all swans are white was a true statement, relative to Europeans. It wasnt until Europeans discovered Australia - and black swans - that it was proven false. One can find innumerable observations to support a theory, but it only takes one to disprove it.

Something is unfalsifiable, if it cannot be proven false through measurable or repeatable means. Take the statement "Gravity exists everywhere." While we currently know this to be true and it is entirely possible that it is true, it is impossible to check every location in the universe for gravity. Due to our current understanding of physics, we have to accept it as true, as it is unfalsifiable.

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  • "A theory is considered true" I would add that unsatisfiable statement can't be a part of theory. Therefore something unfalsifiable is not considered true. – rus9384 Jun 3 '18 at 11:16
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    Do you have any references to philosophers who take a similar position about falsifiability? This is a way to strengthen your answer and give the reader another place to look for more information. I edited the answer to add the author and name of the book you linked for clarity. – Frank Hubeny Jun 3 '18 at 21:16
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The OP misunderstands what falsifiability means and how it is used in science and how it relates to truth. Unfalsifiable does not mean true. Quite the contrary! Falsifiable does not mean false!

Falsifiable = able to be proven false = refutable = disprovable

Falsifiable does not mean false. It instead refers to the ability/capacity/capability of a hypothesis/conjecture/theory to be proven false (disproven).

Unfalsifiable = not able to be proven false = irrefutable = not disprovable.

Unfalsifiable does not mean true!

An unfalsifiable proposition means that its 'falsity' cannot be determined, that we cannot know whether or not it is false (and thereby whether it is true), and that we cannot have justification to believe that it is true.

Falsifiability is the one and only necessary and sufficient condition for a theory to be scientific and therefore fall under the purview of science. If a hypothesis is not falsifiable, it cannot be considered scientific, and thereby disqualifies from the realm of science as well as from scientific discourse. A scientific theory must be falsifiable!

The logic of science has an inductive component and a deductive component.

The inductive component of the logic of science is the principle of induction, which is applied to data in order to arrive at natural laws, i.e., inductive generalizations of the descriptive laws of nature.

The deductive component of the logic of science is the falsifiability criterion: the one and only both necessary and sufficient condition for demarcation, i.e., distinguishing science from pseudoscience.

In order to believe as many true things and as few false things as possible, one must have logical criterion that rules out accepting propositions that are false and unfalsifiable, i.e., false and unable to be proven to be so, and instead accept propositions that are true and falsifiable, i.e. true and able to be proven false. Falsifiability refers to the capacity of a proposition to be proven false. If a proposition is in fact false, there must be a way for us to determine this. If a proposition is unfalsifiable, then by definition it cannot be falsified and there can be no way for us to determine the falsity of the proposition.

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I'll make two statements: 1. "There are magical fairies all around me that only I can see. Nobody else can see them, hear them, smell them or feel them. They don't appear on camera, and they cannot be shot, burnt or otherwise damaged". 2. "There's an elephant in my kitchen".

Statement 1 is not falsifiable. You can't prove that I'm lying. The fact that you can't see them, hear them, smell them or feel them is exactly what I predicted, so it's no evidence that they don't exist. But do you believe me? Obviously not. Since it doesn't make any difference to you whether my invisible fairies exist or not, you just don't care about them. That's the problem with unfalsifiable statements: Once we figured out is is not falsifiable, we don't care anymore.

Statement 2 is very easily falsifiable. Just go into the kitchen, and you will know instantly whether I said the truth or whether I lied. You may not believe me when I tell you about the elephant, but once you are in the kitchen and see it, you are 100% convinced, no matter how strongly you disbelieved me.

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