Help with falsifiability!

[woodbine]

Can an unfalsifiable hypothesis be demonstrated to be true, beyond reasonable doubt by evidence, or does the fact that no evidence could falsify it mean that the value of all evidence is negated?

My first thoughts were that evidence would indeed be useless but I hope someone can help confirm or deny it.

[Steve3007]

If a hypothesis is falsifiable this means that it's possible to state how some evidence could be presented (in finite time) to demonstrate that it is not true. So if it is not falsifiable then no such evidence could possibly be found. Example of a falsifiable hypothesis: "all swans are white". Example of an unfalsifiable hypothesis: "there exists at least one black swan".

The first proposition is falsifiable because it's a proposition about every member of a potentially infinite set, so an observation of one member (a finite number) falsifies it. The second proposition is unfalsifiable because it's a proposition about one member of a potentially infinite set, so falsifying it means searching every member of that set for that member; a needle in an infinite haystack. So it would take infinite time to falsify it, which is of course just another way of saying that it's unfalsifiable.

But when you say this:

My first thoughts were that evidence would indeed be useless but I hope someone can help confirm or deny it.

what evidence are you referring to? If a hypothesis is unfalsifiable then there is no evidence to be either useful or useless.

[Terrapin Station]

What we say is that we provisionally verify something in lieu of falsification. Well, or at least that's what we're supposed to say. Lots of scientists are terrible about following through with this basic aspect of science methodology--as if they never really learned of understood it, and they frequently talk about "proof."

Provisional verification is very useful. But science is never supposed to get to "beyond reasonable doubt" or "no evidence could falsify that P." One of the primary points of science was to avoid that sort of dogmatically infallible stance, which is instead characteristic of religions.

At this, though, it can be clear that it would be bizarre for some things to be falsified, but it would never be impossible for anything to be falsified (at least in theory--human psychology makes it more difficult), or we're just not doing science.

[Terrapin Station]

Oh, and of course provisional verification requires evidence, including but not limited to attempts to falsify the claim that didn't succeed.

[Steve3007]

Lots of scientists are terrible about following through with this basic aspect of science methodology--as if they never really learned of understood it, and they frequently talk about "proof."

As I've noted before in conversations with, among others, creation, the word "proof" is used in at least two distinct ways. The context "scientific proof" is the same as the context "the proof of the pudding is in the eating". i.e. it is approximately a synonym for "test". This is completely different from "mathematical proof", which is the elucidation of a tautology. But it seems to me that people often conflate the two meanings without being clear which they're using, which often leads to fallacies of ambiguity.

[Terrapin Station]

Scientists shouldn't be using "proof/proved/etc." period, because it always has a connotation--even if just subconsciously--of "can't be wrong."

Of course, even mathematical or logical proofs are only proofs within the confines of a particular construction (a particular species of mathematics or logic), but it's still near-impossible to get past the "can't be wrong" connotation, so it should just be avoided altogether.

[Steve3007]

Scientists shouldn't be using "proof/proved/etc." period, because it always has a connotation--even if just subconsciously--of "can't be wrong."

Simply to avoid being misunderstood, you may have a point. But the usage of the word "proof" as an approximate synonym for "test" has a good pedigree, as demonstrated by that advice about puddings. So scientists might grumble about not being able to use the word in this sense in the same way that some older people grumble that they can't use "gay" to mean happy any more. But, like it or not, unless they want to be misunderstood, I guess they can't.

Of course, even mathematical or logical proofs are only proofs within the confines of a particular construction (a particular species of mathematics or logic), but it's still near-impossible to get past the "can't be wrong" connotation, so it should just be avoided altogether.

Well, if we can't even use the word "proof" in a mathematical context (for the reasons you give here) doesn't that mean that "proof" has no use at all? If so, isn't that a bit of a waste of a nice, solid little one syllable word?

[Terrapin Station]

Well, if we can't even use the word "proof" in a mathematical context (for the reasons you give here) doesn't that mean that "proof" has no use at all? If so, isn't that a bit of a waste of a nice, solid little one syllable word?

I didn't mean to not use it in a mathematical or logical context (after I posted it, I realized what I wrote might appear to be saying that). I was just saying that it doesn't even really amount to "can't be wrong" (in general) in a mathematics or logical context, but everyone tends to read it that way in those contexts, so the fact that we can use "proof" in ways that don't denote "can't be wrong" isn't a good reason to go ahead and use the term in a scientific context.

[Prof Bulani]

Isn't a hypothesis, by definition, falsifiable? Can you give an example of an unfalsifiable hypothesis? Because I'm pretty sure it wouldn't be a hypothesis.

[Prof Bulani]

Example of an unfalsifiable hypothesis: "there exists at least one black swan

Wouldn't the existence of one black swan allow us to evaluate if this statement is true or false? My understanding of "unfalsifiable" doesn't mean cannot be proven false, but rather cannot be evaluated to be true or false. If a statement can be proven to be either true or false, it's falsifiable.

Terrapin, is that what you meant by falsifiable?

[Steve3007]

I didn't mean to not use it in a mathematical or logical context (after I posted it, I realized what I wrote might appear to be saying that). I was just saying that it doesn't even really amount to "can't be wrong" (in general) in a mathematics or logical context, but everyone tends to read it that way in those contexts, so the fact that we can use "proof" in ways that don't denote "can't be wrong" isn't a good reason to go ahead and use the term in a scientific context.

Fair enough. I do tend to avoid that word in the context of science and confine it to mathematics for pretty much the reasons you've discussed. But if others use it, I try to get them to clarify what they mean by it. They often don't really seem to know what they mean by it. They often seem to intend a vaguely defined combination of the two distinct meanings.

Wouldn't the existence of one black swan allow us to evaluate if this statement is true or false?

It would allow us to evaluate it as true but not as false. As I said, the proposition "there exists at least one black swan" can only be shown to be false by looking at every swan in the Universe to confirm that it is not black.

My understanding of "unfalsifiable" doesn't mean cannot be proven false, but rather cannot be evaluated to be true or false. If a statement can be proven to be either true or false, it's falsifiable.

That's not my understanding. My understanding is that falsification is showing something to be false and verification is showing something to be true. Falsification, as opposed to verification, was preferred by Popper as a solution to the supposed problem of Induction.

The laws of physics tend to be proposed universals; propositions about potentially infinite sets. They leap from the specific to the general, and in so doing they leap from the finite to the potentially infinite/arbitrarily large. Example: We see (a finite number of) objects falling to the ground and planets orbiting the Sun. We come up with a law that claims all objects and planets do something llike this. Even those that we haven't seen yet. Even those that we will never see. We go from the specific to the general. This is the process of Induction.

This is seen as a problem because it does not lead to logical certainty. Popper thought he'd got around this lack of certainty with falsificationism. As far as I understand what he said, I'm not convinced. He seems to me to have simply re-stated the problem. And it's not a problem so long as we accept what we already knew, that science, and empirical observation generally, does not lead to universal statements that are logically certain to be true.

But maybe I've misunderstood Popper. It's been a while since I read or discussed him.

[Steve3007]

Incidentally, it seems to me that proposed universals are not just confined to such things as the laws of physics. Objective propositions generally tend to be proposed universals. It seems to me that this concept of a universal (a proposition that applies to an infinitely/arbitrarily large set) is an inherent part of the concept of objectivity.

E.g: if I make the subjective proposition "I am seeing a table" then I am not proposing a universal truth. I am saying something about my own perceptions. But if I make the objective proposition "there is a table here" - i.e. I propose the existence not just of a sensation but of an object - then I am implicitly proposing that an arbitrarily large number of people will, if suitably situated, see that table.

[Pattern-chaser]

A theory is falsifiable if it meets this simple criterion: if it is false, it can be shown (proven) to be false. And that's all there is to it. Isn't it?

[Steve3007]

Yes, but perhaps best to leave out the word "proven" to avoid confusions due to linguistic ambiguity. See conversation slightly earlier in the topic.

[Wossname]

Steve3007 said

Wouldn't the existence of one black swan allow us to evaluate if this statement is true or false?

It would allow us to evaluate it as true but not as false. As I said, the proposition "there exists at least one black swan" can only be shown to be false by looking at every swan in the Universe to confirm that it is not black.

Yes - “there exists at least one black swan” would be rewritten as “no black swans exist”. This allows the hypothesis to be, in principle, falsified.