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Sentences to ponder
[T]he statement "All models are wrong, but some are useful" is itself a model (of an epistemological system, with many competing models) and thus is paradoxical, being true only if it isn't. Moreover, although it asserts directly that some models are useful and indirectly that others are not, the statement tells as [sic] nothing as to which is which, so it is not, itself, useful.
That's from Germany, by the way (original source here). Now ponder it! Even better, the same guy offers (useful) tips on how to cut health care costs.
The original indirect tip is from Seth Roberts.
Posted by Tyler Cowen on July 19, 2008 at 06:49 AM in Philosophy | Permalink
Comments
The conclusion in the second sentence doesn't follow. Even if wrong, "All models are wrong, but some are useful" is useful in pointing out that "truth" is not the standard to which models should be held.
Posted by: conchis at Jul 19, 2008 8:52:13 AM
I first came accross this aphorism in operational research some decades ago. As somebody noted then, the "but" is redundant; the meaning is clearer without it.
Posted by: David Heigham at Jul 19, 2008 9:24:53 AM
"although it asserts directly that some models are useful and indirectly that others are not, the statement tells as [sic] nothing as to which is which, so it is not, itself, useful."
Well, that would be a lot of information to put in one sentence.
Posted by: josh at Jul 19, 2008 9:37:50 AM
While I like the first sentence, I also dispute the author's contention that the statement is not useful. By acknowledging that wrong models are useful, it allows one to search for simpler models that produce useful results. Otherwise, it would be the case that no model is useful.
If we are to accept the author's premise, then by analogy of what "use" is Nash's fixed point theorem. That a fixed point must exist, "tells as [sic] nothing as to which is which, so it is not, itself, useful."
Posted by: Jody at Jul 19, 2008 9:42:10 AM
All generalizations are wrong.
Posted by: at Jul 19, 2008 9:56:02 AM
The opening statement is not a full paradox, since one can consistently assume that it's false: it could be wrong because at least one model is correct. The statement itself just doesn't happen to be one of the models that's correct. However, this particular wrong meta-model is still useful :-).
Posted by: nanoprof at Jul 19, 2008 10:18:07 AM
"All models are wrong, but some are useful"
The same logic applies to....
"All politiicans are wrong, but some are useful"
Posted by: Jay at Jul 19, 2008 11:51:14 AM
Alternative view: "All models are wrong" is not a model; it is a tautology.
Posted by: Andy B at Jul 19, 2008 12:03:03 PM
Aren't the Germans the ones with a transparent dome over their legislative body? How did that get there?
Posted by: Michael F. Martin at Jul 19, 2008 2:23:29 PM
Is mathematics a model? If not, what is it? Is natural language a model?
Posted by: Lee A. Arnold at Jul 19, 2008 2:54:45 PM
we should judge a model by attractiveness, not truthiness.
Posted by: wegwgtr at Jul 19, 2008 4:25:31 PM
"Alternative view: "All models are wrong" is not a model; it is a tautology."
That is correct. Actually the problem is the silly use of the word "wrong", and then pretending "wrong" is identical to "false".
"Is mathematics a model?" No. "If not, what is it?" That's a good question! It's useful for modeling other things though, isn't it? "Is natural language a model?" No, it's a means of communication.
Posted by: KenF at Jul 19, 2008 5:14:28 PM
The original sentence is not a model; it's a generalization, but not a model. (Or, if it is a model, then all general statements count as models, and the sentence is false, since some generalizations are true.)
Posted by: dominic at Jul 19, 2008 6:50:28 PM
George Box is not from Germany, but originally British. For a long time he was in the Statistics Department at the University of Wisconsin-Madison, partly attracted by the presence of the great population geneticist, Sewall Wright, one of the four fathers of the 1930s neo-Darwinian synthesis. Box was married to the daughter of another one, R.A. Fisher. It was the presence of these guys in the late 1950s and early 1960s that attracted strong econometricians to the economics department, such as Arnold Zellner (who would later go to Chicago) and Arthur Goldberger, whom many think should have shared Lawrence Klein's Nobel Prize with him. They would come to dominate the department and turn it away from its institutionalist roots.
Posted by: Barkley Rosser at Jul 19, 2008 8:18:13 PM
KenF, how are you certain that mathematics isn't a model?
Posted by: Lee A. Arnold at Jul 19, 2008 11:33:14 PM
As someone who sees agendas in everything, I'd have to say that it isn't surprising a Ph.D. candidate in Physics is disturbed by the idea that we might be approaching a time when the Google Cloud (which might be best represented by the corporeal giant evil sphere in "The Fifth Element") finally has reached the point where it can provide more bang for the buck than human intuition. I think human intuition has a ways to go and arguments about "method" (that have been going on for centuries) are nothing a clever scientist need fear.
Posted by: themightypuck at Jul 19, 2008 11:36:47 PM
Sorry for the double post, but I also noted that framing his rehash of the "Doc, it hurts when I do this--Don't do that" joke in the context of lowering health care costs puts you on the same page as the "abstinence only" crowd with respect to sex. Hell, people still smoke.
Posted by: themightypuck at Jul 19, 2008 11:46:56 PM
"KenF, how are you certain that mathematics isn't a model?"
Well, I think you'd need to have some idea of what it was a model of, to think that it is a model. And I cannot imagine what mathematics could be a model of. Models are things we create to describe something. I would say that we can create models of mathematical objects (when I draw a right triangle and measure its angles and the lengths of its sides I think it's reasonable to say that you are modeling our abstract mathematical idea of a triangle). But I don't see how mathematical objects are models of something else, in and of themselves. That said, I don't know what mathematical objects are, unfortunately. If you know please tell me.
Posted by: KenF at Jul 19, 2008 11:51:02 PM
Is the Coase theorem a model?
On the one hand, it is not since no one has formulated it in analytic terms.
But on the other hand, if we take a broad definition of the term "model", then I guess almost anything counts as a model.
Posted by: enrique at Jul 20, 2008 3:54:21 AM
Is the Coase theorem a model?
On the one hand, it is not since no one has formulated it in analytic terms.
But on the other hand, if we take a broad definition of the term "model", then I guess almost anything counts as a model.
Posted by: enrique at Jul 20, 2008 3:54:25 AM
"I also noted that framing his rehash of the "Doc, it hurts when I do this--Don't do that" joke in the context of lowering health care costs puts you on the same page as the "abstinence only" crowd with respect to sex. Hell, people still smoke."
themighthypuck,
my larger point was that that sometimes strategies that don't earn a doctor a lot of money (e.g., shouting) are more useful than strategies that do (e.g., giving lots of tests). I was also hoping it was funny - I certainly thought so when hearing the story first.
If you have something more interesting to contribute on the topic, go ahead.
Posted by: LemmusLemmus at Jul 20, 2008 4:45:53 AM
"If you have something more interesting to contribute on the topic, go ahead."
This is a dubious rhetorical device. Nonetheless, I get that I might have missed the joke.
Posted by: themightypuck at Jul 20, 2008 6:08:57 AM
KenF, I believe the Brouwerian or intuitionist starting-point that mathematical OBJECTS are symbolic inventions with their "origin in the perception of a move in time [which] may be described as the falling-apart of a life-moment into two distinct things, one of which gives way to the other, but is retained by memory... a TWOITY..." (Brouwer. "Mathematics, science, and language," 1925.)
I think the evidence is that (1) we could use other symbols, but more importantly that (2) all of mathematics is indeed conceived in, and performed as, a series of pairwise distinctions and operations.
But I don't think a logical consequence of this is that we must accept the intuitionist program for working math: rejection of infinity and the law of the excluded middle and so on.
The wonder is "the unreasonable effectiveness of mathematics," i.e. that some of mathematics applies to physical science (while some does not, or at least not yet.) But there are also counter-indications: givens such as extremum principles, concessions such as complementarity principles, imprecise matchings such as statistics, and of course meta-limitations such as incompleteness.
I take from this the conclusion that mathematics is a MODEL of a only a part of human cognition, and neither this part nor its model match the universe completely.
Posted by: Lee A. Arnold at Jul 20, 2008 12:09:39 PM
The proposition --- "all models are wrong, but some are useful" --- is either a platitude or a paradox.
Why? Because, aside from its uses to describe in popular parlance something like "last year's Camry model", a model as used in the sciences and social sciences or in architecture and engineering is a necessary simplification of the "reality" it is describing. The simplification, usually a drastic one if mathematical or statistical, is purposeful. Imagine, otherwise, an economist trying to analyze the workings of a complex national economy of the United States with 150 million workers, 250 million consumers, millions of business firms, hundreds of thousands of bureaucratic regulators, and -- to boot --- its global linkages with over 150 countries with a population of more than 6 billion people.
In short, no model is "isometric" with the complexities of the world it is both describing and likely to be trying to explain.
.....
Want more proof? Ok, Try a dictionary definition of a model. As with this one from dictionary.com:
"[a] simplified representation of a system or phenomenon, as in the sciences or economics, with any hypotheses required to describe the system or explain the phenomenon, often mathematically,"
......
If, however, we ponder the epistemological implications of the original proposition about models, then it rises above the level of a platitude or paradox. It raises the whole issue of epistemological realism . . . in particular, whether any of our sentences (propositions) formulated in language actually describes the "reality" it is referring to.
Traditionally, epistemological realists claim that we can move beyond our use of language --- including mathematics and mathematical models and theories --- by the use of logic and empiricism . . . or at least, empirical testing in the sciences of theoretical laws or the hypotheses they generate. Logical positivists, for instance, sought to distinguish between meaningful and meaningless propositions by reducing the former to atomistic sense data, which could be subject to the "verification principle". Logic would then, on this view, allow scientists and others to link the empirically verified atomistic propositions into theories for further testing and so on.
...........
The entire logical positivist view --- along with the other forms of epistemological realism --- was shattered by Quine in his seminal paper, "The Two Dogmas of Empiricism" in 1951.
Dogma One: the analytical-synthetic distinction, which goes back to Kant. Analytical statements such as logical propositions are true, on this view, by definition: e.g., all bachelors are unmarried. In effect, Quine argued, unless they're circular, they might in fact be subject to being disproved at some point.
Dogmas Two: The belief that individual propositions are verifiable empirically as facts the way positivists claimed they were. Quine argued, convincingly, that scientific theories aren't tested by one proposition at a time. That's because any failure of a specific proposition or hypothesis entailed by the theory to withstand an empirical test can always be blamed on auxiliary conditions . . . confounders in statistical terms. So what then? Theories stand or fall in holistic terms, and hence a scientific theory isn't replaced until a "better" one in the holistic sense can explain the world more adequately than its replacement and at the same time predict the world better in the future.
In short, Quine stressed that "truth" about the world had to be understood in terms of coherence --- theoretical holism and utility by way of prediction --- rather than by means of "correspondence" theories of truth.
.....
Quine's work inspired, in ways he didn't agree with, by his pupil, Thomas Kuhn and the use of paradigms and "irrational" breaks between one paradigm and normal science and a new revolutionary change to a new paradigm. And yet Kuhn's work, if not a logical outcome, was obviously one inference from Quine's work. (Quine, by the way, also claimed that all scientific theories are under-determined by their evidence.) Donald Davidson, probably even more influential than Quine in analytical philosophy since the late 1950s --- he regarded Quine, his colleague at Harvard, as his mentor --- disputed Kuhn's work and to an extent Quine's by adding a "Third Dogma" of empiricism: "the myth of the paradigm": in effect, so he argued, paradigms don't create unbridgeable theoretical languages with different facts, but instead can be translated from one paradigm to another . . . contrary to what Quine had argued and, more radically, Kuhn would argue.
......
All of which brings us back to the proposition about models: all models are wrong, but some are useful.
The key term here is "useful." It's what pragmatists have all along claimed about our use of science and knowledge and whether they are "true" or not. Truth, for pragmatists in general, is a matter of utility: not correspondence with reality (whatever that might mean) or just coherence, but rather knowledge and science are useful and hence true to the extent they allow us to cope ever more effectively with the complexities of our natural and social worlds.
Quine himself, note in passing, later acknowledged that he was in many ways in the lineage of the great pragmatists of the late 19th and early 20th century (leaving aside Charles Sanders Peirce's differences with William James and John Dewey, and Richard Rorty's interpretations of Dewey). [Peirce always believed that scientific work was self-correcting and at some point in some unspecified period would ultimately be accurate in scientific depictions of "reality". How human scientists would ever know what "ultimate" means or how to recognize it is a puzzle, no?)
And so, in strict pragmatic terms, models are neither true or untrue --- and hence neither true nor wrong if wrong means not fully isometric with the reality they seek to depict in simplified terms --- but useful or not in dealing with the challenges and problems of human communities and individuals within them.
......
Michael Gordon, AKA, the buggy professor: http://www.thebuggyprofessor.org
Posted by: the buggy professor at Jul 20, 2008 12:10:05 PM
Try this one instead:
"All models are fallible".
There is no paradox if by "wrong" one imples "fallible" rather than "false". Utility is orthogonal to the issue.
-KP
Posted by: KP at Jul 20, 2008 11:49:15 PM
