The title of the question - A Theory That Explains Everything Explains Nothing - is said to be a quotation attributed to philosopher of science Karl Popper, but there's no consensus on whether he actually uttered/wrote those words. Googling didn't help.
I've often encountered the sentence online - in videos, podcasts, and forums - and I would like to know whether this statement is true/false and why?
I think it may help to put this in terms of Bayesian probability. Bayesian probability is an interpretation of mathematical probabilities as representing our degree of certainty - a high probability means we believe something is very likely to be true, and a low probability means we believe it is likely to be false. A probability is called "prior" or "posterior" relative to some observation - the prior is what you believed before you made the observation, and the posterior is the adjusted probability after taking the observation into account. Initial priors are selected arbitrarily, but should reflect our actual beliefs for the system to work as intended. Once we have a posterior, it becomes our new prior going forward.
In that context, we can lay this out in terms of Bayes' theorem. We have:
The most straightforward way of describing the theorem is that the posterior probability is equal to the prior, multiplied by the ratio P(O|H) / P(O). In other words, if P(O|H) > P(O) (if the hypothesis says that O is more likely than we initially think it is), then seeing O increases our confidence that H is true, whereas if P(O|H) < P(O) (if the hypothesis says that O is less likely than we initially think), then seeing O decreases our confidence in H.
If H "explains" everything, then the probability of H should always increase with every possible observation (it is compatible with everything). For that to be true, we must have P(O|H) > P(O), for all possible values of O and all possible choices of P(O). So it should work for Not O as well as O. P(Not O|H) > P(Not O). But when we add the inequalities, we get P(O|H) + P(Not O|H) > P(O) + P(Not O) - and that's impossible, because both sides must sum to exactly 1 (the sum of P(X) and P(Not X) is always 1).
OK, but what if we weaken the condition, and say that P(O|H) ≥ P(O) for all O, instead of requiring a strict inequality? That would imply that we never become less confident in H, but our confidence might hit a ceiling at some point. The problem is that the above argument still works (with slight modifications) as long as the strict inequality is true for any O, and the loose inequality is true for Not O. So that leaves us with P(O|H) = P(O) for all possible O. But that means that H says nothing of consequence about any choice of O, because it does not change the probability which we assign to O. QED.
In the context of Popper I'd conjecture that this refers to the ability to make a prediction for any event. Like if you'd understood and are able to explain something you'd be able to offer a prediction how things would work.
This however would naturally be exclusionary so if you'd say the answer to 2+2 is 4 or even in the range of 3 to 5, then if the answer turns out to be 2 or 10 you'd be wrong. Or in other words you could not explain that within your theory. (and that's ok.)
On the other hand a pseudoscience could get any kind of output and come up with an explanation for that. And while that might sounds more potent at first, what it really means is that you'd have no idea how things work, because without the ability to make a limited prediction your theory would essentially be worthless as it doesn't explain anything. Seriously you couldn't use that for any application or as the starting point for any thought.
First we have to understand what explanation is.
A thing can only be explained in terms of simpler things, all the way to axioms. Axioms themselves cannot be explained, they have to be taken as they are.
There cannot be infinite regression in understanding because you cannot get out of an infinite well. You have to start at some point. You cannot forever move the point of start backward.
If you have doubt about axioms check them by comparing them with reality. Thats the basic test for truth.
A theory that "explains" everything (see I put the word: explain in quotes because no theory can do that because of the existence of axioms and non-existence of infinite regression) don't explain anything because it attempts to explain axioms. Nothing can explain axioms. Axioms can only be verified against reality. There is nothing more fundamental than them to compare them to. Also, axioms don't explain each other, because they are the building blocks and thus not made from building blocks themselves.
There is a constant leitmotif in philosophy, one of a struggle between skepticism and certainty of belief. The evolution of 21st century epistemology from the episteme of the Ancient Greeks has been exemplified by a metaphorical Sturm und Drang of thinkers who wage contentious campaigns to make certain claims (think Descartes) or declare the act of claiming itself pointless (think Nietzsche). One particular period in history that reflects a drive towards epistemological certainty was that of the logical positivists, who armed with the formal sciences, set out to show that the ambiguity that inheres in scientific practice and theory could be carved out rendering epistemological science as reliable as an apparatus of Newtonian mechanics. They did so by declaring war on metaphysics and tried to show using the gains in mathematical and logical theory during the end of the 19th and start of the 20th century, that science could be reduced or explained formally with Ramsey sentences, deductive-nomological reasoning, and other clever arguments. But unfortunately, they bumped into a series of challenges that didn't readily dissolve. Carnap for instance hewed mightily to belief in the the analytic-synthetic dichotomy grasping at the disembodied and transcendent logic that Kant himself argued for in his Introduction to Logic.
Enter a series of developments and personae dramatis that doomed the project so that the engineers themselves conceded defeat. Karl Popper took confirmation and verification to task. Quine attacked the analytic-synthetic distinction. Kuhn argued that scientific theories were sociological artifacts with political dimensions. By the 1960's logical positivism was well past moribund. Theory-ladenness and underdetermination of theory helped to bring the coup de grace. Let's analogize.
Let points be our facts of a theory, and let various claims regarding the relationships, the building blocks of a theory, be represented by curves that connect the dots. In any locus, one can pick three points, and draw a curve. In fact, we say that three points underdetermine a curve, because given three points, there are an infinite number of curves that connect them. A theory, then in our analogy, is putting all of the curves together in such a way to have a polynomial. This mathematical practice is less known that linear regression, and is aptly called polynomial regression. So the methods provides that the same points can determine different polynomials, and unfortunate there is no objective property inherent in the points that determines the polynomial, unlike 2 points determining a line, 3 a circle, etc. There is no one true polynomial.
Thus if one asks, which polynomial is represented by these points, and one has a method that says all of these polynomials fits, then in essence, one really hasn't determined anything. Thus the more points the method of regression fits, the more polynomials are feasible, and the less that is actually said about which one polynomial. An imperfect analogy, certainly.
So, likewise, when scientific facts determine more and more theories under the "scientific method", the less and less the scientific theory that combines various theories says. According to SEP, this is the underdetermination of theory by data. Or in other words, a theory that explains everything explains nothing (a clever dialetheism with all the hallmarks of a koan). For opponents of scientific realism, this is evidence there is no one true reality, and theories are merely instruments selected from preference and bias.
