3

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?

6
  • See Popper: Falsifiability. Jan 5, 2023 at 16:20
  • @MauroALLEGRANZA, did read up on Popperian falsifiability, and I tried working out as to how a theory that explains everything is unfalsifiable, but no success! Can you provide me a hint or just, I wish, blurt out the answer.
    – Hudjefa
    Jan 5, 2023 at 16:25
  • A theory that explains everything can have no assumptions. But how does one derive a meaningful conclusion from "no assumptions"?
    – nwr
    Jan 5, 2023 at 18:50
  • 1
    If a theory can "explain" everything then for any A it can "explain" both A and any of its alternatives, whichever happens. But then it cannot explain why it was A that happened and not an alternative, so it explains nothing at all.
    – Conifold
    Jan 5, 2023 at 22:19
  • From @MauroALLEGRANZA's cite (fn omitted): "Popper said that a demarcation criterion was possible, but we have to use the logical possibility of falsifications, which is falsifiability. He cited his encounter with psychoanalysis in the 1910s. It did not matter what observation was presented, psychoanalysis could explain it. Unfortunately, the reason why it could explain everything is that it did not exclude anything also. For Popper, this was a failure, because it meant that it could not make any prediction." Jan 6, 2023 at 4:52

4 Answers 4

1

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:

  • O - some observation we might make. O is the "anything" in the original formulation.
  • H - some hypothesis (or "theory") we might be investigating.
  • P(O) - the prior probability of us seeing O.
  • P(H) - the prior probability of H being true - that is, how strongly we initially believe in H.
  • P(O|H) - the probability of O happening, assuming that H is true. If H is a reasonably complete hypothesis, it should provide an explicit formula for this number (or at least a roadmap for finding such a formula).
  • P(H|O) - the posterior probability of H, given that we observed O. Bayes' theorem provides a formula for this number in terms of the other three probabilities.

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.

23
  • Good post even though much of the math flew past in a dizzy blur. I would say this: P(O/H) = P(~O/H) describes a theory that explains everything. How that affects your calculations is beyond me. Care to expand and elaborate? Danke
    – Hudjefa
    Jan 7, 2023 at 7:11
  • @AgentSmith: P(O|H) + P(~O|H) = 1, as a basic axiom of probability theory (without even getting into the Bayesian weeds). So if your theory has P(O|H) = P(~O|H), then both must be equal to 0.5. A "real" theory could have that for certain values of O, without purporting to "explain everything," but if it has that identity for all values of O, then H boils down to "either the sun will explode tomorrow, or it won't, so it's 50-50." I think it's pretty obvious why that's a problematic H. If you take multiple different values of O that are not independent, you can probably find other problems.
    – Kevin
    Jan 7, 2023 at 21:53
  • My premise is unfalsifiability
    – Hudjefa
    Jan 8, 2023 at 5:36
  • 1
    @AgentSmith see WP on falsifiability which is a logical criterion per Popper: Duhem–Quine thesis says that definitive experimental falsifications are impossible...because an empirical test of the hypothesis requires one or more background assumptions...falsifiability does not have the Duhem problem because it is a logical criterion. Experimental research has the Duhem problem and other problems, such as induction, but, according to Popper, statistical tests, which are only possible when a theory is falsifiable, can still be useful within a critical discussion... Jan 11, 2023 at 16:45
  • 1
    Thus my above point in the statistical context of possible (infinitely) many hypothesis testing and selection problem, for the candidate H it's possible that p(H|O)<p(H) for some rare O (not necessarily many to be able to reject H significantly per Kevin's suggestion above) since other competing H's may explain such O better... Per Popper above it seems the easiest refute to such universal H is simply that it never can explain the necessary background knowledge X which is independent from H necessarily... Jan 11, 2023 at 17:08
1

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.

8
  • I believe you're on the right track, but I'm not as yet clear on the point Popper or whoever said it was trying to convey. Do you have any examples of actual scientific theories/hypotheses that could be used as an exegesis in re the claim as set out in the question's title?
    – Hudjefa
    Jan 5, 2023 at 17:08
  • 1
    @AgentSmith -- Popper's two go-to examples were Freudian psychoanalysis, and Marxist Historicism. In discussions with a psychoanalyst he worked for, he was disappointed to discover the psychoanalyst treated reported symptom A, as confirming a diagnosis, and gave a reason why A would exist.. But when Popper asked if the LACK of A would also confirm the diagnosis, his employer also said yes, and gave a different explanation for why A would not exist. This prediction of ANY POSSIBLE OUTCOME made the diagnosis irrefutable, and useless.
    – Dcleve
    Jan 5, 2023 at 20:16
  • 1
    @AgentSmith -- Popper also volunteered as a Communist party supporter, until he found similar "explains everything" in the way communist theoreticians would claim all events confirmed their "scientific socialism" theories.
    – Dcleve
    Jan 5, 2023 at 20:18
  • 1
    @AgentSmith -- another recent example is string theory, which is shown to have enough free variables (more terms can be added at will, and some were, when observations contradicted early String Theory Multiverse predictions) that no possible observations in our universe can be in conflict with it. This is detailed in two popular physics books, The Trouble with Physics and Not Even Wrong. The authors consider string theory to have stifled physics, because it CANNOT suggest useful confirming OR disconfirming tests or experiments.
    – Dcleve
    Jan 5, 2023 at 20:27
  • 1
    @AgentSmith -- I have a review of The Trouble with Physics here: amazon.com/gp/customer-reviews/R6JY5GBLAV2BV/… and The Cosmic Landscape here: amazon.com/gp/customer-reviews/R3JVQDAK1408BR/…
    – Dcleve
    Jan 5, 2023 at 20:34
1

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.

3
  • Axioms are included in everything. The question talk about "theory that explains everything".
    – Atif
    Jan 7, 2023 at 4:17
  • I agree. The axioms that can be used to build ourselves a theory that proves everything ate problematic. What would such axioms look like?
    – Hudjefa
    Jan 7, 2023 at 5:01
  • Nothing, those axioms would look like nothing; because such theory cannot exist; because it goes against definition of explanation. Its like a natural number between 19 and 20. Such number do not exist, so looks like nothing.
    – Atif
    Jan 7, 2023 at 10:39
1

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.

8
  • I was hopin' for a reason Popper said what he said other than that a theory that explains everything is unfalsifiable.
    – Hudjefa
    Jan 7, 2023 at 8:27
  • This answer has nothing to do with claims regarding the unfalsifiable. To have a theory is to have to have true facts and a theory which doesn't seem false. This quotation is about explanation, and explanation on some views is what makes a truth understandable. Presuming Popper said this, and speculating on his motives, it would be to expose the certainty of logical positivism as being unjustified. Rejection of certainty by confirmation and verification is one way. Rejection of certainty by explanation is another way. The first is truth-conditional. The second is more linguistic.
    – J D
    Jan 8, 2023 at 17:35
  • Have you reflected on what it means to be "a scientific explanation"? plato.stanford.edu/entries/scientific-explanation This is part of the struggle of philosophers at justifying certainty. Consider the propositional attitude of the claim "I am certain scientific theories give me knowledge". How does one justify? One has to show that the knowledge is both true and meaningful. To claim it is false shows it isn't true. To claim it explains nothing shows it is meaningless. Both counterclaims undermine that scientific theories give knowledge certainly.
    – J D
    Jan 8, 2023 at 17:37
  • There are other epistemological routes that justify certainty: among them are faith, divine revelation, and intuition. All of this undergirds the bigger discussion around characterizing epistemological positions. Theologians speak of fideism. Contemporary secular epistemologists speak of fallibilism. The sciences are just one flavor of epistemological method, though many of us in the modern world intuit is the only reliable one.
    – J D
    Jan 8, 2023 at 17:44
  • Popper believed in science, but he wanted to undermine the claims that the logical positivists made about the degree of certainty it brings so that the claims were more realisitic (ironic given that he was undermining the program of realism introduced by Comte).
    – J D
    Jan 8, 2023 at 17:47

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .