Too bad there isn’t a dunce cap smiley. I guess this will have to do :o.
Falsifiability is a concept I kind of understand, but not completely. My understanding is that a hypothesis or theory should be able to be tested to see if it holds up under conditions that might contradict it. Is that accurate?
I’ve heard that if something isn’t falsifiable then it isn’t scientific, is that true?
What about tautologies? Are they, or can they be scientific?
Here’s an analogy that I thought of. It’s simplistic and mathematical, but it’s the best I can think of.
Pretend it’s thousands of years in the past (or it’s the present but everybody is an idiot :D).
I gather people around and make a profound statement, “One item plus one item equals two items.”
To demonstrate I take one stick and place it next to another.
Now to test my hypothesis somebody takes a bowl of water and pours it into another bowl. There’s now there’s a bowl with twice as much water, instead of two bowls of water.
That act is falsifying my hypothesis, and in this case also proving it false, right?
So then I narrow my statement, “One solid item plus one solid item equals two solid items.”
Is this falsifiable?
If it is, then do I have to narrow it down some more until there are no tests that contradict what I’m saying in order for it to then become a valid theory?
“Falsifiable” technically means that it is possible that a specific data point, if found, nukes the hypothesis.
In practice, every single piece of discernable data is subject to interpretation. Such is life. But restricting ourselves to ideal situations, the hypothesis that “Cannibalism is not practiced in the United States” is falsifiable if (ignoring the vagaries of getting everyone to agree that Incident X did indeed constitute cannibalism) one single instance of cannibalism can be shown to have taken place in the United States.
Falsifiability can rely upon aggregate and statistical findings. “Children are smaller than adults” is falsifiable and yet comes out looking like a valid hypothesis if we restrict ourselves to sample sizes of adequate sizes, demand that they be random, and take the average (mean) of populations so defined. (The possibility that one child might be larger than one adult notwithstanding). The “specific data point” that would falsify the hypothesis would be a study with randomly selected children and adults, decent size sample size, in which on average the children were larger than the adults.
A non-falsifiable hypothesis is one where you can’t explain what result would blow your hypothesis out of the water. You’re setting out to do research; you have a hypothesis; you had better be able to identify a result that would capsize you were you to find it. It looks good. It keeps you honest. Yes, in real life many of the things worthy of study are subject to interpretation on all levels, but it’s still a good attitude to embrace when doing research.
Part of the deal lies in making sure you define your terms rigorously.
That’s the issue with most word problems. Words are slippery and often (well, always) don’t mean the same thing to various people. The obvious example are all the proofs concerning God. You can try to prove there is a god or there is not a god, but if the other person doesn’t accept your definition of god then the entire exercise is meaningless before you start.
Nobody, you seem not to realize it but 1 + 1 = 2 is not a tautology. It requires proof itself. When Russell and Whitehead set out to put math onto a rigorous logical basis in their Principia Mathematica they took hundreds of pages to lay out a foundation before being able to do a proof that 1 + 1 = 2. And despite all that Godel later proved that their system could never be complete because it was always possible to find theorems that could not be proved within it.
At its most basic, falsifiability presents an issue in a way that the person making the claim can be shown to be wrong that everybody who understands the subject will agree upon. The details of how that claim is proved can be exceedingly complex. But if you’re making a claim that I can’t show is wrong no matter what I do - and all religious claims fall into this category - it is not falsifiable. It can be disagreed with, mocked, scorned, ignored, or countered. But it’s not falsifiable. If you add “and therefore it is not science” most people will agree with you. But whether falsifiability and science must be connected is a philosophical issue that has been debated for decades. Are philosophical issues ever falsifiable? Down the rabbit hole we go.
Math is not science. It’s a set of logical rules with truth/false values derived from postulates in that system. It’s an entirely different thing from what the OP is getting at.
I’d suggest reading the wikipedia article first, and then maybe asking questions about what you don’t understand. It’s a pretty comprehensive article, giving the history and criticisms of it.
But it does have some strong intuitive appeal wrt science. If I make a hypothesis that cannot be proved wrong, how can we know that it’s true? But a key thing to keep in mind is that inability to disprove something might arise from the nature of the hypothesis or from the limits of our technology.
As far as falsifying the principle that one solid item plus one solid item equals two solid items, you could take two ice cubes and press them together until they fuse (although the surfaces in contact would temporarily be liquid). You could press a knife against another solid object to end up with three solid objects. These processes seem as fair as pouring one bowl of water into another.
“One solid item plus one solid item equals two solid items” is a falsifiable statement. If someone can find a solid item and a solid item, put them together, and have something other than two solid items your statement would have been proven false.
An example of a non-falsifiable statement is “There is no Santa Claus.” Nobody can present you with an example of “not Santa” which proves Santa does not exist. The best someone can do is refute specific qualities of Santa Claus, like “A man named Santa will visit the homes of all Christian children and leave presents on Christmas eve night.” Someone can present you with a case in which a Christian family was not visited by a man named Santa who left presents, which would prove your statement false. You would then have to revise your terms and descriptions of Santa to meet this new bit of evidence.
To answer the OP in part, math is not a science. It deals exclusively with tautologies, none of which are (presumably) falsifiable. Actually, the statement that the Peano axioms of arithmetic are consistent is a scientific statement since it could be falsifiable. The statement that they are complete is also falsifiable and has been refuted. So it was a scientific claim until Goedel and now we can say it is simply false.
I don’t understand the problem with 1 + 1 = 2. Generally, we define 1 = succ(0), 2 =succ(1) (that’s successor) and + by x + 1 = succ(x) (and x + succ(y) = succ(x + y), although the second clause is not involved here), from which the proof is immediate. What were Russell and Whitehead doing that required hundreds of pages (almost entirely unread) to prove it? It is of course necessary to define your terms precisely. Notice that is not adding sticks to sticks or apples to oranges, but numbers to numbers.
It sounds to me like it’s just a bad analogy that’s messing things up. As far as I’m concerned, pouring one bowl of water into another does not disprove 1+1=2.
1/2 bowl of water + 1/2 bowl of water = 1 bowl of water.
Now we multiply both sides by 2/bowl of water.
And reduce.
1 + 1 = 2.
Substitute any fractions and any unit of measurement in there and you still have something true.
In any event, I wouldn’t worry about falsifiability so much. You’ve got the idea of falsifiable down - it’s all about being able to design some experiment or make some observation that would prove the idea true or false. “We live in the Matrix” is a great non-falsifiable statement - if we did live in the Matrix, there would be no measurement or observation we could make that wouldn’t be a product of the Matrix designed to convince us we weren’t in the Matrix.
Is this “not science?” Maybe, but I feel like that’s an inflammatory statement that is more emotional than meaningful. Instead, I’d say that a non-falsifiable hypothesis is not subject to the scientific method, which would require experiments, tests, observations, predictions - something - which with to test it. If no test can be done, you can’t complete the scientific method.
First, my math example was meant to be used an an analogy because I couldn’t think of a good scientific example.
Second, for something to be falsifiable, do you have to be able to do the test or just come up with a situation, test, or condition that the hypothesis or theory could possibly fail under, even if you can’t do the test or create the conditions?
Something is falsifiable if everybody agrees on a test that will disprove the hypothesis. It doesn’t matter if the test is currently experimentally possible.
People here keep confusing the concept of falsifiability with individual experimental results. They’re not the same. One is a concept, the other is a specific.
“There is no Santa Claus” can be proven false by presenting Santa Claus. “There is a Santa Claus” is non-falsifiable, though, because no matter how many examples we have of Santa not showing up, one could always say that he is still in hiding.
Except, as a final philosophical point, humans are allowed to reason statistically, meaning that we can come to preliminary judgements based on incomplete evidence and sound statistical reasoning. Therefore, if some hypothesis would challenge a number of well-tested concepts (such as wind resistance, the top speed of a running reindeer, whether ruminants can fly, etc.), and has never been experimentally verified, we can be justified in concluding it’s very likely false and proceeding accordingly.
True enough. Falsifiability depends as much on the presentation as the statement itself. “Santa Claus exists” is reasonably falsifiable statement if we take Santa Claus to have all the conventional trappings. But there is a problem if we tell a believer that we have checked satellite photography of the North Pole and find no workshop, and the believer responds that the workshop is invisible or somewhere else. Eventually, the goalposts are liable to be shifted into something like “the spirit of Santa Claus exists in everybody”, which is of course unfalsifiable and in the category of “not even wrong”.
So as a practical matter, a statement like “Santa Claus exists” has to be made much more specific before we can talk about falsifiability and speculate about shock waves shed by hypersonic reindeer.
If you have a hypothesis, then it should be “falsifiable.” To find out if your hypothesis is falsifiable, you simply need to answer the following question: could some type of evidence our outcome prove your hypothesis wrong? If your answer is “Yes,” then your hypothesis is falsifiable and you should proceed with the experiments. If your answer is “No,” you have made an error. Or maybe you’re just a crackpot.
Here’s an example. There are many conspiracy theorists who believe the World Trade Center was not destroyed by aircraft crashing into it. They believe the buildings were wired with explosives, and that the government was behind the attacks. :rolleyes: When you argue with these people, you will soon learn that no amount of evidence will dissuade them; regardless of the preponderance of evidence to the contrary, they continue to believe the buildings were wired with explosives. No evidence, no matter how convincing, will convince them they are wrong. Therefore, their theory that the buildings were wired with explosives is *not *falsifiable (according to them), which is an automatic indication that their theory is wrong.
I’ll ignore your example, because as already pointed out, it’s not very helpful.
The problem with falsifiability that seems to cause many people to stumble is that it only requires a theoretical possibiltiy that your theory* can be disproven. If you actually devise a test that refutes your theory, you revise that theory. After you’ve done all the tests, the refined theory should hold up.
The best I can think of is the counterexample for a non-falsifiable theory are the closed loop ones (which are also logical fallacies therefore). E.g. “Christian scientists”: When you are ill, you pray and get better. If you don’t get better, you didn’t pray enough. So there’s no way to break the preconception ever.
Theory in the scientific, not the laymen, definition: a hypothesis that has been tested and refined until it’s valid.
Hopefully this isn’t a tangent. I remember reading somewhere that it’s important that you are able to devise a test that hasn’t been performed yet. It’s somehow cheating to only include data from past experiments that were performed without the theory in mind. Why is this so?
