On September 23, 1846, the planet Neptune was discovered. But the person who discovered it, Alexis Bouvard, died on June 7 1843.
More accurately, Bouvard discovered the absence of the planet Uranus (don't worry, I'm not going to make any puns).
You see, there was this theory called "Physics" which states that the celestial bodies exert these invisible forces on everything. This force is called "gravity" and, if you know the mass and distance between two objects you can figure out how much force they exert on each other.
Based on this you cam predict where the planets are going. But, back in fall of 1846, those predictions said Uranus would be in one place when it was really in another place. Clearly the theory of "Physics" had been falsified and had to be dumped. Or . . .
. . . there could be another planet that we didn't know about!!!
Bouvard chose the latter option and Urbain Le Verrier followed this advice and used the theory of "Physics" to predict the location of this hypothetical eighth planet, and finally, Johann Galle pointed a telescope in the direction of the hypothetical planet and, sure enough, he found a planet.
Fast forward to the year 1934 and the philosopher Karl Popper publishes his book The Logic of Scientific Discovery. Popper argued that a theory is only scientific if it can be falsified. If it makes inaccurate predictions and provides a way of covering explaining those inaccuracies, then it is not falsifiable and is thus pseudo-science. Therefore, this "physics" thing is nothing but a "metaphysical research program."
He didn't say that about physics exactly. In fact, he make a bit of a cover-up explanation about their being different levels of "scientificness". The specific sentence where we encounter the "metaphysical research program" bit is "Darwinism is not a testable scientific theory, but a metaphysical research program." He later recanted on this, thus showing that his "falsifiability" theory was not falsifiable.
Popper was also a strong supporter of Milton Friedman, and supported his belief that right-wing economic policies would inevitably result in freedom. And he had another theory that said that any attempt to make the world a better place will inevitably result in totalitarianism.
These theories were shaken when Milton Friedman became Augusto Pinochet's economic advisor and all of the privatization completely failed to introduce freedom to Pinochet's totalitarian regime. Furthermore, it was people trying to make a better place who ultimately overthrew Pinochet and ended totalitarianism rather than creating it. And yet people still pretend that these theories are legitimate.
Somewhere between Bouvard's discoveries and Popper's nincompoopery, a man named Pierre Duhem came up with a theory that nothing in physics could be scientifically tested. This was because you can't have a completely controlled experiment. The predictions are based on both the theory itself and the controls. So, in the case of neptune, what was really being tested was "Newtonian mechanics is true and there are seven planets and telescopes work the way we think they do and I'm not hallucinating". If any one of those assumptions was incorrect, the experiment would turn out wrong.
The fact that Duhem only applied this to physics was because he was part of the positivist school that insisted on putting arbitrary separation between different sciences. This was rectified by Willard Quine tho adapted the theory to include all of science, including math. This idea that no theory can be conclusively proved or disproved because you can't have a completely controlled experiment is called the "Quine-Duhem Thesis".
For example, Andrew Wiles had a proof of Fermat's Last Theorem that had a hole, but then he corrected the hole and got a legitimate proof. This would mean, according to Popper's "falsifiability" theory, that mathematics is a pseudo-science.
In a sense the Quine-Duhem Thesis is related to Gödel's Incompleteness Theorem and the Heisenberg Uncertainty Principle. All of these things state that we can't know everything about the universe because we are part of said universe. And they all prevent things from being certain that the things we take for granted are true.
Unfortunately, in many scientists ignore the Quine-Duhem thesis and still hold to Popper's "falsifiability" theory.
Why? Part of it is the same reason that Popper himself came to his theory. It's a quick way to shout down opponents, provided you ignore that it could just as easily be applied to your own views. So Popper used his theory to argue against Marxism, specifically historical materialism, and (temporarily) Darwinism, as well as some legitimate targets like Freudianism and Platonism. Modern scientists can use falsifiability as a quick way to shout down Intelligent Design, homeopathic medicine, magic, chi, ESP and all sorts of other things.
Of course, Intelligent Design advocates use the same arguments against evolution. All the "Oh yeah?! Well how do you explain the eye?! Oh yeah?! Well how do you explain wings?!" BS is just using Popper against legitimate science.
Also, some scientists like to use it against other scientists. Big bang theory, string theory and global warming all get shouted down as pseudo-science even as scientists do research in those fields.
But there's another issue with the Quine-Duhem thesis. If nothing can be conclusively proved or disproved then how are you supposed to figure out what's true and what isn't? Quine and Duhem never satisfactorily answered that. And they had their own issues, with Duhem trying to reconcile science with the Catholic church and Quine being a bit of a right-wing douchebag. But most importantly, this theory would seem to give way to post-modernism.
Ultimately, post-modernism and Popperism are equally useful (not at all). Post-modernism holds that all scientific theories are equally legitimate while Popperism holds that all scientific theories are equally illegitimate.
In fact Alan Sokal and Jean Bricmont in their book Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science, inspiration for the Post-Modernism Generator, devoted a chapter to Popper's falsifiability theory.
Either way we would seem to end up in a state of permanent uncertainty. Either everything is true or everything is false.
But, come on, the sky is clearly blue. I mean, just look at it!
Sure you could be hallucinating and all the people who concur that the sky is, in fact blue, could be lying, and the optics involved in the atmosphere used to show that the sky is blue could be based on a mistaken theory. But, come on!
But like people use Popper's falsification theory selectively to things they disagree with, people use the Quine-Duhem thesis and similar uncertainty-type things selectively to argue the legitimacy of certain things.
For instance, Bill Maher, made a documentary called Religulous that made fun of religious extremism. Many people assumed he was an atheist, but in an interview on the Daily Show, he said he's an agnostic and considers atheists to be as crazy as religious fundamentalists, not because of their beliefs themselves, but because they're certain about those beliefs.
You see, because nobody can prove conclusively whether God does or does not exist, we must remain perpetually uncertain. But by the Quine-Duhem thesis, we can't prove conclusively whether the sky is or isn't blue. So by Maher's standards, people who are certain that the sky is blue are just as crazy as people who are certain that the sky is yellow. But most people are pretty certain that the sky is, in fact, blue.
This also comes up with the evolution vs. intelligent design issue. If neither theories are legitimate science according to Popper, why not teach them both? After all, they're both just theories, right?
Some people even rehash Popper's other theory about "making the world a better place resulting in totalitarianism", changing it to "certainty resulting in totalitarianism. Man it must suck to live in the totalitarian United States where we're ruled over by a ruthless dictator who's absolutely certain that the sky is blue.
In order to get any meaningful scientific theory, you have to use the dialectical notion of "quantitative changes resulting in qualitative changes".
The existence of God, the blueness of the sky, the alien conspiracy to assassinate JFK, the labor theory of value, the inherent unluckiness in the number 13 and natural selection are all theories that can be scientifically tested. All of them have some evidence in their favor and some evidence at their expense. All of the falsifying results can themselves be falsified, so by Popper's standards, they're all illegitimate.
But to argue that there was an alien conspiracy to assassinate JFK requires so much straining that there's no reason to consider it true. On the other hand there is so much evidence to suggest that the sky is blue, that we can be certain that it is true.
The non-existence of God may not be as blindingly obvious as the blueness of the sky, but there is still sufficient evidence to consider it a fact. In The God Delusion, Richard Dawkins pointed out that the idea of the entire universe spontaneously coming into existence, improbable as it is, is far less improbable than a sentient being capable of creating the entire universe spontaneously coming into existence.
This is a strong argument for the non-existence of God, but it is not conclusive, as Dawkins himself admits (the chapter is called "Why There Almost Certainly is No God". For instance, if there was archaeological evidence for all the crazy shit in the bible, the burning bush, the chick coming out of the dude's rib, the parting of the red sea, etc. that would be sufficient to overturn Dawkins's argument.
However, no such evidence exists. In fact every attempt to communicate with this allegedly existent sentient being has failed. maybe God does exist and just chose not to speak to anyone, but it's much more likely the guy just doesn't exist. So even if you're not completely certain, it's certainly significantly less crazy than all the shit that goes on in Religulous.
This doesn't mean we can't be agnostic about anything. There are enough issues, for instance, with string theory. Mainly there are the issues with the curvature of the universe, which is negative in most string theory models but positive under relativity. Also, all of string theory's new predictions require a lot of money to test. Opponents of string theory claim that these predictions don't exist, but that's not really true.
The issue is that string theory concerns the relation between general relativity, which studies objects with large mass, and quantum mechanics, which studies objects with large charge. Since there aren't a lot of objects with large mass and large charge you need a lot of energy to test the new predictions in not only string theory, but all the potential replacement theories.
Nonetheless, string theory does make all of the tested predictions that general relativity makes and all of the tested predictions that quantum mechanics makes. Furthermore, it provides a means of explaining the incongruity between general relativity and quantum mechanics, which the standard models of each cannot do. This is strong evidence in string theory's favor.
If mathematicians find a way to reconcile the curvature issue or physicists get the money to do the necessary experiments and get the right results that could provide sufficient evidence to be certain of string theory. If mathematicians show that the curvature issue can't be reconciled or physicists do experiments that go against the predictions of string theory, that could provide sufficient evidence.
For now, string theory is in a blurry region where the Demarcation Problem doesn't have any clear answers. On this matter, we have to remain agnostic and uncertain (but I personally lean in favor of the theory).
But with most theories you'll encounter, there is either sufficient evidence either for or against that it's okay to be certain of it's truth or falsehood. Despite the Quine-Duhem Thesis. Despite Gödels Incompleteness Theorem. Despite the Heisenberg Uncertainty Principle.
With a little bit of dialectics we can go to sleep safe and sound in the knowledge that, when we wake up, the sky will be blue.