Home > Uncategorized > Willard Opens a Can of Worms

Willard Opens a Can of Worms

2011 January 23

In the comments, Willard asks if formal propositions, phrased in a logico-mathematical language, a predicate logic, would improve communication about such questions as “is the Earth warming.” In short, I doubt it.

People have an intuitive sense of what they mean when they use a phrase such as “warming.” This intuition will differ for different people, or even the same person addressing different audiences, leading to confusion. Trying to wring out the ambiguities by reaching for formal logic might work for technical audiences working from a common starting point, but it will only lead to greater confusion amid the general public unused to peculiarities of predicate logic. I count myself among them.

But there is a deeper problem …

There is nothing more dangerous or powerful in the philosophical process than selecting one’s axioms, especially given that they are nearly invariably expressed in sloppy old human language. There is nothing more useless than engaging in philosophical, religious, or social debate with another person whose axioms differ significantly from one’s own.


And that’s the nut, isn’t it? Not all disagreements in “the debate” are based in the science. The guppies feeding on the chum at WUWT, who swim the blogosphere swarming the comments on every global warming article, aren’t really interested in the science. Instead they create a polarized world, an artificial binary division, with two sides which accuse the other of engaging in religious belief. “Man’s impact is too small to matter” is hurled up against “Models and natural history tell us enough to be afraid.” The “climate is always changing” sings out against “we are causing climate change.” In the public-at-large, the positions surrounding global warming incorporate many different axioms, many different world views, many different fundamental beliefs that aren’t going to be changed by formal logic. Don’t get me wrong – I strongly believe that there is such a thing as climate science, that the science is sound, that it is evolving, that it provides a better description of the world as it evolves, and that it might be subject to disruptive discoveries, and that it should be subject to skeptical critiques. But without an agreement on the axioms, there is no way forward in rational discussion.

To see this process in action, just take a look at McKitrick’s paper asking “what ‘is’ is” and Benestad’s response, “Yes, Ross, there is a Santa Claus.” Do you think that these two could ever come to an agreement on the axioms of the proposition “Is the Earth warming?” much less agree on the conclusions. (More fun here, note the additional links in the title.)

However, I don’t think I can dismiss the whole idea of using predicate logic that simply. As I approach statistical analysis, I realize that many problems are posed as propositions with null or alternative propositions. That these propositional statements, these hypotheses, seem to mirror the formalism found in predicate calculus. Indeed, as an outsider to both subjects, there appears to be a great deal of similarity between predicate logic and formal statistical analysis.

But logic is it’s own field of study – one with its own language and symbolism to learn. I’ve got enough on my plate just learning statistical methodology. So while I can see some potential in Willard’s call for predicate logic in structuring claims that can be tested, I don’t see it being much help in developing understanding between those with fundamentally different world views. And if Willard takes a closer look at the how statistical propositions are made, I think he will see a surprising resemblance to predicate logic.

  1. carrot eater
    2011 January 23 at 10:04 am

    Just take the word ‘significant’. To a technical audience, ‘statistically significant’ indicates that some formal test was done. To the layman, it merely means that it seems sort of big or important.

  2. 2011 January 23 at 12:16 pm


    I feel honoured. Now, I must contribute something, ain’t I? Let me think about it.

    I must admit that I share your intuition: my suggestion does not seem plausible. We should not hope for some statistical Jacob’s ladder. Sooner or later, one must get informal.

    My humble suggestion was first and foremost meant to hint at the idea that we should make our basic assumptions more or less explicit: carrot eater provides a nice example. On the same vein, I found this article interesting:


    The only other thing I can add for now (I need to go and only come back tomorrow) is that we could also construct our arguments in some kind of informal logic. For instance, simply stating the scope of “warming” would help. We could also distinguish what we assume must happen (lawlikely) and what our data makes us see (empirically). The interface between the two is never as easy as “Popperian-reborns” would like us to believe:


    Let’s hope these are good worms for our Earth,

    Until tomorrow,


  3. 2011 January 23 at 12:19 pm

    An addendum: the scope of warming I had in mind was related to space and time. It is warming since around 1880, all over the world on average, and most probably until next Ice age. Et cereta. Et cetera.

  4. 2011 January 23 at 2:24 pm

    But Bayesian methods introduce a confusion into the actual meaning of the mathematical concept of “probability” in the real world. Standard or “frequentist” statistics treat probabilities as objective realities; Bayesians treat probabilities as “degrees of belief” based in part on a personal assessment or subjective decision about what to include in the calculation. That’s a tough placebo to swallow for scientists wedded to the “objective” ideal of standard statistics. “Subjective prior beliefs are anathema to the frequentist, who relies instead on a series of ad hoc algorithms that maintain the facade of scientific objectivity,” Diamond and Kaul wrote.

  5. 2011 January 24 at 9:03 am


    Nevertheless, let’s keep in mind that this divide between objectivists and subjectivists is wider in theory than in practice. You can say that theoricians know how to spin a scandal, if only for the sake of keeping the students awake. Pun intended, it also keeps the Whiteboard clean. One writes “Conceptions of probabilities” at the top, then draws two lines. The first is “objective”, the second is “subjective.”

    Here is a good example of how to do that with words:



    I would have to read a bit more to comment on the debate between McKitrick and Benestad. On the face of it, it reminds me of the neverending hurly burly between realists and nominalists. I also note that to rely to an “ontological argument” oftentimes adds some theological zest to a debate, which is not unrelated to another endeavour by McKitrick:


    Any philosopher will tell you never to enter into a debate against a theologian.


    I’ll end up for now by this little correction: I am not suggestion we start talking in first-order predicate logic. As I said earlier, even modal logic would suit me. If you knew my alter ego, you’d recognize there a effort to reach a compromise…

    Of course, informal logic would be alright too. I’ll illustrate what I mean later.

    Bye for now,


  6. 2011 January 28 at 11:55 am

    A little bump to say that while pondering on McKitrick’s argument, I stumbled upon this argument:


    And so it seems that not only we do not know what a global mean temperature exists, but we might not even know what temperature is, if measuring temperature near the ground induces a “bias” in it.

    Let’s also not forget how the word “bias” can lead to mischaracterization.

    Until later,


  7. 2011 January 29 at 6:48 am

    Willard, I’m not sure mt’s discussion is exactly what you have in mind by calling on wider use of formal logic in stating claims – but I think it is an educational practical example. “While they are cordial and patient, conversation is time consuming and pedantic, largely because of idiosyncratic use of standard words and ideas”. Bang! Bullseye on that one. I always feel that I’m translating while reading Pielke Sr. As opposed to say …. Huybers. So it’s not just a matter of being unfamiliar with the language of science in general. And having to unravel Pielke’s double-negative claims so that you can grasp their meaning makes it appear as if they trying to build broad conclusions on very narrow foundations.

    Let me ask you this? Is there a prescriptive case to be made for applying formal logic to climate science – as opposed to descriptive? Mt’s look is descriptive. It points out some places where K&P go wrong – obfuscate rather than clarify. I’m not sure what the prescriptive case would be. The practical method would have been to hand it to a grad student or two and ask if it made any sense.

    If modal logic is the application of qualifiers to claims/statements – aren’t well stated statistical tests in effect modal logic? Is this a case of two languages, two narratives, looking at essentially the same problem space from two perspectives, two histories?

  8. 2011 January 29 at 7:51 am


    Here are some prescriptions that really work:


    They have their limitations and may have gotten a bit old. (Being truthful is more of a condition than a prescription, for example.) But I believe they might look like something you might like. They are good for any kind of conversation.

    Formulating logical claims could be seen as a way to make sure Quantity and Manner is respected. This does not mean that it’s easy. Applying formal statistical tests shows how it can be illuminating, but it also shows that it’s easy to be led astray.

    I readily concede that converting everything into logic won’t solve every communication problem. It would be possible to use these maxims to make sure that your opponents do not escape by obsfuscation. But dealing with argumentum ad nauseam is still an open problem, I believe.

    At the very least, formulating complete reasonings could be seen as a very efficient way to promote scientific arguments. Here is a simple example taken from an Allen’s talk:

    > CO2 keeps inserting itself everywhere we look. If you leave CO2 out nothing makes sense. If you put CO2 in a whole lot of it makes sense. And then you can put the other pieces into the puzzle and make it work. CO2 keeps being the only explanation for a lot of what happened which is validated, that works.

    Secondary source: Confidence in radiative transfer models | Climate Etc.

    This kind of reasoning would need to be spelled out a little more, if only to show that climate sciences proceed by evidential-based reasoning, i.e. inference to the best explanation. That would also show that there is no logical magic bullet: Allen’s reasoning is not a deduction. You can only make it work because you know its context and the way science reasonings are being usually expressed.

    Empirical sciences almost never proceed by formal derivations. Asking for an engineer-level formal derivation is oftentimes meaningless, obviously so when we are targetting a planetary phenomena.

    All this is being covered by what is called informal logic:



    I’ll return later on modalities. Girma’s latest outburst is a very good example.

  9. 2011 January 29 at 9:51 pm

    Here is a ‘kinda’ counterpoint.

    The exponential+sine fit, even bereft of physical underpinnings, is more persuasive to the ‘man-on-the-street’ than any carefully framed statement of climate sensitivity estimates based on complex AOGCMs. It presents a “model” that any one can understand more-or-less intuitively. Link it appropriately to CO2+solar or CO2+amo, and you can even use it to convey some physical science along with the pretty picture of trends.

    Now – as a physical model, is exp+sine “correct”? Probably not. But as a toy model, it can convey more information than the flow chart of some AOGCM. I once posted one to a political forum – it was utterly unpersuasive precisely because of its complexity.

    My ‘blunt skippy’ on AGW is as follows:
    1. Man is adding CO2 to the atmos
    2. CO2 in the atmos is increasing
    3. CO2 is a greenhouse gas
    4. The global T is rising.

    How do we know that 2 and 4 aren’t accidentally related? “Correlation does not prove causation.” Molecular physics give us the fine grained view . Climate modeling gives us the broad view. How do we know that climate modeling is reliable? “Trust me” But public trust in the scientific process is broken (deliberately, intentionally). So I think there might be a need for toy models that provide intuitive insights into sufficient portions of the problem that will bolster confidence that the scientific community isn’t engaged in a fraud.

    Now, I am not really setting out to provide those toy models – I am just a scientifically curious Joe Citizen trying to get a better sense of the magnitudes of the forcing and feedbacks. Ice Age. Holocene. Anthropocene. The little reconstructions done by Tamino (or Schmidt in a recent pub) go a long way towards providing those. As does reading Budyko, Sellers, North, and company.

    Oversimplifying a problem can mask genuine issues which is a problem in itself. But so is pointing the general public at a black box and saying ‘trust me.’ I’m not all that interested in how to bridge that gap for others, but I’m slowly working myself forward.

    Let me try to link this to your informal logic pointer. Note the discussion of the vodka ad. It is stated that This approach to the image allows a more critical assessment of the image because it provides a basis for a critical rejection of the argument it presents. I would add the modal descriptive:
    rarely. People just aren’t that logical. Even those able to explicitly outline the implicit argument of the ad are more likely to react viscerally based on their prior experiences with vodka. Bad party – react negatively. Some fondly remembered urban parties – react positive.

    E=mc^2. Even today, only a small fraction of humanity understands the math underlying that formulation. But they believe in it anyway. Why? Well, there is some 100 years of physical science behind it. But also – it is simple. It links two intuitive concepts – energy and mass – together in a way that is elegant, beautiful, simple.

    I suspect – as far as the public understanding of climate science goes – that we need more toys and fewer supercomputers. But, ultimately, their acceptance or rejection is going to based on non-rational influence that climate scientists have little influence over. Or so I see it.

    So what problem are you trying to solve, Willard? Communication between scientifically literate groups – or between the public and the scientists?

  10. 2011 January 30 at 7:22 pm


    I did not realize that the problem I am trying to describe could be about communicating science. Nobody warned me about that when I started my field research. Girma’s contributions (among many others) inspired me the idea of a system to adjudicate scientific claims. Some kind of formal dialogue to settle scientitic differents, if you will. (The idea of a formal dialoguing system is quite old and has been popularized by Charles Hamblin and many others.)

    Scientifically litterate people do not really need this kind of system, when they communicate between themselves in normal channels. On the other hand, improving the exchanges between the public and scientists is a problem of public relations. (Blaming journalists is tiresome and as constructive as blaming can be.) What I am hinting at lies between the two poles you describe.

    As I see it, scientific debates as practiced in blogs lack the means for the public to follow the debates, the “play by play.” Blog debates are mainly done between scientifically litterate people. These debates are read and judged by the public. But how can they tell who win?

    The only way I see for the public to grasp the issues and to understand what arguments win is to create a game where it would be easy for almost anyone to see. I would even call such a game RHETORICS ™.

    Sure, this game comprises cheap shots: high-sticking, cross checks and hits to the head, as any great game has. (Tone trolling is futile and underestimates the joy of contact sports.) That granted, it should comprise some logic too, be it as informal as can be. Logic is quite powerful. It’s a weapon mighty enough to be one of the hallmark of our civilization.

    If what we do is blog science, there must be a way to argue rationally on blogs, in a way that every single rational argument gets adjudicated and everyone digs it.


    While I ponder on your other interesting thoughts and questions, here is Vaughan Pratt’s answer to “Is the Earth warming?”:


    Vaughan’s story appeals to me. I hope it will appeal to you and your readers too.




  11. 2011 January 31 at 8:47 am

    The game of RHETORICS is one in which I am familiar with in broader, more political contexts which include – now – climate science. It has also included evolution. And discussion of immunization to H1N1 the other year.

    One of the tests I’ve seen mt and Eli propose to help the public distinguish between science and non-science, to help them judge the play-by-play themselves, is coherence. I’ve advanced that argument myself. What they fail to understand is the fact that The Other Team has a coherent narrative as well. It goes something like this:

    Politicians motivated by fame and power (Gore) have joined forces with scientists motivated by fame and greed (Hansen, Jones, Mann) to create a regulatory framework which will effectively enslave the world, choking economies, stifling innovation, and which could lead literally to the starvation and suffering of hundreds of millions. Corrupt scientists gain access to funding from corrupt politicians by providing scientific “evidence” that the politicians need to extend their regulatory control over most forms of economic activity. Evidence of this corruption can be found in c-gate emails which show that ‘inconvenient facts’ are deleted and peer review is suborned to the corrupted pov. Further evidence can be found in the manner in which urban heat is intentionally discounted and that global temperature records are deliberately manipulated to provide the ‘evidentiary basis’ for this expansion of political power. In turn, scientists are given grants and access to new computing facilities. Any who question this arrangement are martyred. Grad students who wish to succeed in the field quickly learn to parrot the party line or their careers are quietly squashed.

    I’m currently reading Anathem where ascetic lovers of knowledge are contemplating methods of bridging multple universes seperated by the light-speed-causal-bubbles . In many worlds, a quantum event can split the causal history, seperating the universe into different, isolated paths. One is tempted to describe the quantum choice of axioms, made at a pre-conscious level, as defining membership in seperate universes between which information cannot flow. But it would be a poor metaphor. Information flows between the two all the time. But the information is cast into a biased framework which builds coherence within its particular realm.

    I freely acknowledge the above is philosophy-babble. (caveat lector: It’s also physics-babble.) But let me give you an example to help clarifiy what I’m discussing. Recently, Dr Bookhagen published a paper describing the role of debris in glacier dynamics. He has also pointed out that some Western Himalayan glaciers are growing while others retreat, with an overall loss of glacier mass. He has also explicitly rejected the “disappear by 2035” claim.

    So how is this new paper received in the “fraud,hoax,corruption” narrative? Thank God someone finally looked at the data and further debunked the IPCC. And in the ‘climate science is science’ narrative? Yet another paper confirming the science findings of the IPCC. Is LOGOS sufficiently puissant to pierce the walls of these tunnels, much less merge narratives or subsume one to the other?

    I’m afraid that this subject is now beyond the game of RHETORICS ™. We are now in the hands of history. Rota Fortuna is a harsh mistress. May God have mercy on our souls.

  12. 2011 February 2 at 9:09 am

    > Is LOGOS sufficiently puissant to pierce the walls of these tunnels, much less merge narratives or subsume one to the other?

    I believe so. A first reason would be that these narratives are part of what “logos”: language, reason, discourse, calculus. A second reason would be that we have evidence that it works.

    While revisiting my first posts of my Neverending Audit, I stumbled upon this very anti-climatic exchange:


    I have abstracted away this exchange hereunder: http://neverendingaudit.tumblr.com/post/3067453775/shame-on-me

    Auditing is powerful when it brings light on an archived subject.

    One source of light can tame an army of cave trolls. But the trolls regenerate, so it’s a neverending quest.

  13. 2011 February 2 at 6:14 pm

    Still revisiting my posts, I stumbled upon an interesting article. Here is a quote that could show a way to argue for your main point that might be more relevant for your own endeavour:

    > Inference can’t be completely automated for most quantities, and we typically can’t make inferences without some modeling assumptions, but the answer won’t be right unless the assumptions are correct, and we can’t ever know that the assumptions are right.

    Source: http://www.iq.harvard.edu/blog/sss/archives/2006/04/a_unified_theor.shtml


    My own main point would be that we need to express those claims and assumptions as clearly and as logically as possible for discussion’s sake. And not more than that, of course.

    I do hope we can agree about that.

  14. 2011 February 2 at 7:00 pm

    Heh! Seeing the way that this data was being handled at CA, the frame that it *had* to be wrapped in by Steve, convinced me that I didn’t really want to work there. It is a shame. Smart guys. Wrong side of The Force.

    But ,,, it helped propel me to open this one. Also almost one year old.

    Happy Blogday, Willard. I enjoy your idiosyncratic scrap-booking of the climate blogs. Almost poetry in all the best ways. Provocative.

    Happy to agree with you on the last point!

  15. 2011 February 21 at 11:52 am

    Since this is my thread, I’ll refer readers to this interesting discussion between Vaughan Pratt and Girma, started on the 2011-02-21 at 00:49 EST:


    Who needs words when one has letters and operators?

  16. 2011 February 22 at 6:06 pm

    Nice tag, Willard. I enjoyed the start of that conversation. It looked like it might go somewhere. But then, but then.

  17. 2011 February 23 at 6:33 pm

    Yup. Logic helps to render explicit gaps in reasoning. And then the discussion becomes tengential.

    Let’s wish Girma the best of luck in his future drive-bys.

    PS: I should return to the existence of global temperatures soon enough. You have my word.

  18. 2011 February 26 at 1:53 pm

    …. it’s all about the axioms …

  19. 2011 February 26 at 10:56 pm
  20. 2011 February 26 at 11:06 pm

    Oh, and this might provide a nice ending to Girma and Vaughan’s conversation:


  21. 2011 April 12 at 10:18 am

    Just a marker, you can make any argument coherent with an infinite number of axioms. Coherence and simplification travel together in models (Somewhere Eli wrote something about levels of models and the tradeoffs between simplicity, reach and coherence). The problem with political argument Ron cites as coherent as it requires lots of things that are implausible, basically that any conspiracy with infinite people involved fails the laugh test.

  22. 2011 April 14 at 4:17 pm


    Eli reminded me of this thread. I just found this answer from Vaughan Pratt:

    > Answer [to Does a Global Temperature Exist?]: no, but no one was claiming otherwise. What is the point of this paper? Global warming is about changes in temperature, a concept that does not require an absolute notion of temperature because additive constants disappear when taking finite differences. This is one good reason why temperature anomalies, or departures from some recent temperature, are always used rather than global temperatures: the latter simply do not exist.

    Source: http://boole.stanford.edu/dotsigs.html#ClimateChange

    I’ll return later to a specific argument in the paper.

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