By Christopher Monckton of Brenchley
In a previous post, I explained that many of the climate-extremists’ commonest arguments are instances of logical fallacies codified by Aristotle in his Sophistical Refutations 2300 years ago. Not the least of these is the argumentum ad populum, the consensus or head-count fallacy.
The fallacy of reliance upon consensus, particularly when combined with the argumentum ad verecundiam, the fallacy of appealing to the authority or reputation of presumed experts, is more likely than any other to mislead those who have not been Classically trained in mathematical or in formal logic.
To the Classicist, an argument founded upon any of the Aristotelian logical fallacies is defective a priori. Nothing more need be said about it. However, few these days are Classicists. Accordingly, in this post I propose to explain mathematically why there can be no legitimate consensus about the answer to the central scientific question in the climate debate: how much warming will occur by 2100 as a result of our sins of emission?
There can be no consensus because all of the key parameters in the fundamental equation of climate sensitivity are unknown and unknowable. Not one can be directly measured, indirectly inferred, or determined by any theoretical method to a precision sufficient to give us a reliable answer.
The fundamental equation of climate sensitivity determines how much global warming may be expected to occur once the climate has settled back to a presumed pre-existing state of equilibrium after we have perturbed it by doubling the atmospheric concentration of CO2. The simplifying assumption that temperature feedbacks are linear introduces little error, so I shall adopt it. For clarity, I have colored the equation’s principal terms:
Climate sensitivity at CO2 doubling (blue) equals the product of the CO2 forcing (green), the Planck parameter (purple) and the feedback gain factor (red).
The term in green, ΔF2x, is the “radiative forcing” that the IPCC expects to occur in response to a doubling of the concentration of CO2 in the air. Measurement and modeling have established that the relation between a change in CO2 concentration and a corresponding change in the net down-minus-up flux of radiation at the top of the climatically-active region of the atmosphere (the tropopause) is approximately logarithmic. In other words, each additional molecule of CO2 exerts less influence on the net radiative flux, and hence on global temperature, than its predecessors. The returns diminish.
To determine the radiative forcing in response to a CO2 doubling, one multiplies the natural logarithm of 2 by an unknown coefficient. The IPCC’s first and second Assessment Reports set it at 6.3, but the third and fourth reduced it by a hefty 15% to 5.35. The CO2 forcing is now thought to be 5.35 ln 2 = 3.708 Watts per square meter. This value was obtained by inter-comparison between three models: but models cannot reliably determine it. Both of the IPCC’s values for the vital coefficient are guesses.
The term in purple, 
, denominated in Kelvin per Watt per square meter of direct forcing, is the Planck or zero-feedback climate-sensitivity parameter. This is one of the most important quantities in the equation, because both the direct pre-feedback warming and separately the feedback gain factor depend upon it. Yet the literature on it is thin. Recent observations have indicated that the IPCC’s value is a large exaggeration.
The Planck parameter is – in theory – the first differential of the fundamental equation of radiative transfer about 3-5 miles above us, where incoming and outgoing fluxes of radiation are equal by definition. The measured radiative flux is 238 Watts per square meter. The radiative-transfer equation then gives us the theoretical mean atmospheric temperature of 255 Kelvin at that altitude, and its first differential is 255 / (4 x 238), or 0.267 Kelvin per Watt per square meter. This value is increased by a sixth to 0.313 because global temperatures are not uniformly distributed. However, it is also guesswork, and the current Lunar Diviner mission suggests it is a considerable overestimate.
Theory predicts that the Moon’s mean surface temperature should be around 270 Kelvin. However, Diviner has now found the mean lunar equatorial temperature to be 206 K, implying that mean lunar surface temperature is little more than 192 K. If so, the theoretical value of 270 K, and thus the lunar Planck parameter, is a 40% exaggeration.
If the terrestrial Planck parameter were similarly exaggerated, even if all other parameters were held constant the climate sensitivity would – on this ground alone – have to be reduced by more than half, from 3.3 K to just 1.5 K per CO2 doubling. There is evidence that the overestimate may be no more than 20%, in which event climate sensitivity would be at least 2.1 K: still below two-thirds of the IPCC’s current central estimate.
If there were no temperature feedbacks acting to amplify or attenuate the direct warming caused by a CO2 doubling, then the warming would simply be the product of the CO2 radiative forcing and the Planck parameter: thus, using the IPCC’s values, 3.708 x 0.313 = 1.2 K.
But that is not enough to generate the climate crisis the IPCC’s founding document orders it to demonstrate: so the IPCC assumes the existence of several temperature feedbacks – additional forcings fn demonimated in Watts per square meter per Kelvin of the direct warming that triggered them. The IPCC also imagines that these feedbacks are so strongly net-positive that they very nearly triple the direct warming we cause by adding CO2 to the atmosphere.
The term in red in the climate-sensitivity equation is the overall feedback gain factor, which is unitless. It is the reciprocal of (1 minus the product of the Planck parameter and the sum of all temperature feedbacks), and it multiplies the direct warming from CO2 more than 2.8 times.
Remarkably, the IPCC relies upon a single paper, Soden & Held (2006), to establish its central estimates of the values of the principal temperature feedbacks. It did not publish all of these feedback values until its fourth and most recent Assessment Report in 2007.
The values it gives are: Water vapor feedback fH2O = 1.80 ± 0.18; lapse-rate feedback flap = –0.84 ± 0.26; surface albedo feedback falb = 0.26 ± 0.08; cloud feedback fcld = 0.69 ± 0.38 Watts per square meter per Kelvin. There is also an implicit allowance of 0.15 Kelvin for the CO2 feedback and other small feedbacks, giving a net feedback sum of approximately 2.06 Watts per square meter of additional forcing per Kelvin of direct warming.
Note how small the error bars are. Yet even the sign of most of these feedbacks is disputed in the literature, and not one of them can be established definitively either by measurement or by theory, nor even distinguished by any observational method from the direct forcings that triggered them. Accordingly, there is no scientific basis for the assumption that any of these feedbacks is anywhere close to the stated values, still less for the notion that in aggregate they have so drastic an effect as almost to triple the forcing that triggered them.
Multiplying the feedback sum by the Planck parameter gives an implicit central estimate of 0.64 for the closed-loop gain in the climate system as imagined by the IPCC. And that, as any process engineer will tell you, is impossible. In electronic circuits intended to remain stable and not to oscillate, the loop gain is designed not to exceed 0.1. Global temperatures have very probably not departed by more than 3% from the long-run mean over the past 64 million years, and perhaps over the past 750 million years, so that a climate system with a loop gain as high as two-thirds of the value at which violent oscillation sets in is impossible, for no such violent oscillation has been observed or inferred.
Multiplying the 1.2 K direct warming from CO2 by its unrealistically overstated overall feedback gain factor of 2.8 gives an implicit central estimate of the IPCC’s central estimate of 3.3 K for the term in blue, 
, which is the quantity we are looking for: the equilibrium warming in Kelvin in response to a doubling of CO2 concentration.
To sum up: the precise values of the CO2 radiative forcing, the Planck parameter, and all five relevant temperature feedbacks are unmeasured and unmeasurable, unknown and unknowable. The feedbacks are particularly uncertain, and may well be somewhat net-negative rather than strongly net-positive: yet the IPCC’s error-bars suggest, quite falsely, that they are known to an extraordinary precision.
It is the imagined influence of feedbacks on climate sensitivity that is the chief bone of contention between the skeptics and the climate extremists. For instance, Paltridge et al. (2009) find that the water-vapor feedback may not be anything like as strongly positive as the IPCC thinks; Lindzen and Choi (2009, 2011) report that satellite measurements of changes in outgoing radiation in response to changes in sea-surface temperature indicate that the feedback sum is net-negative, implying a climate sensitivity of 0.7 K, or less than a quarter of the IPCC’s central estimate; Spencer and Braswell (2010, 2011) agree with this estimate, on the basis that the cloud feedback is as strongly negative as the IPCC imagines it to be positive; etc., etc.
Since all seven of the key parameters in the climate sensitivity equation are unknown and unknowable, the IPCC and its acolytes are manifestly incorrect in stating or implying that there is – or can possibly be – a consensus about how much global warming a doubling of CO2 concentration will cause.
The difficulties are even greater than this. For the equilibrium climate sensitivity to a CO2 doubling is not the only quantity we need to determine. One must also establish three additional quantities, all of then unmeasured and unmeasurable: the negative forcing from anthropogenic non-greenhouse sources (notably particulate aerosols); the warming that will occur this century as a result of our previous enrichment of the atmosphere with greenhouse gases (the IPCC says 0.6 K); the transient-sensitivity parameter for the 21st century (the IPCC implies 0.4 K per Watt per square meter); and the fraction of total anthropogenic forcings represented by non-CO2 greenhouse gases (the IPCC implies 70%).
Accordingly, the IPCC’s implicit estimate of the warming we shall cause by 2100 as a result of the CO2 we add to the atmosphere this century is just 1.5 K. Even if we were to have emitted no CO2 from 2000-2100, the world would be just 1.5 K cooler by 2100 than it is today. And that is on the assumption that the IPCC has not greatly exaggerated the sensitivity of the global temperature to CO2.
There is a final, insuperable difficulty. The climate is a coupled, non-linear, mathematically-chaotic object, so that even the IPCC admits that the long-term prediction of future climate states is not possible. It attempts to overcome this Lorenz constraint by presenting climate sensitivity as a probability distribution. However, in view of the uncertainty as to the values of any of the relevant parameters, a probability distribution is no less likely to fail than a central estimate flanked by error-bars.
If by this time your head hurts from too much math, consider how much easier it is if one is a Classicist. The Classicist knows that the central argument of the climate extremists – that there is a (carefully-unspecified) consensus among the experts – is an unholy conflation of the argumentum ad populum and the argumentum ad verecundiam. That is enough on its own to demonstrate to him that the climate-extremist argument is unmeritorious. However, you now know the math. The fact that not one of the necessary key parameters can be or has been determined by any method amply confirms that there is no scientific basis for any assumption that climate sensitivity is or will ever be high enough to be dangerous in the least.
Monckton of Brenchley says:
April 24, 2012 at 11:25 am
I had explicitly and repeatedly stated that the fact that adding greenhouse gases such as CO2 to an atmosphere such as ours will cause some warming has been established by oft-repeated experiments and does not require to be sanctified by any headcount among scientists or anyone else.
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To my knowledge, the only experiment you have ever referred to is the one conducted by Tyndall in the 19th century. Now, this experiment has not established, that “greenhouse gases” cause any warming. Neither has this experiment established, that “greenhouse gases” cause any cooling. This is my understanding of the descriptions of that experiment one can easily find on the internet.
Tyndall’s experiment has only established 1 thing: that “greenhouse gases” absorb and re-emit some IR radiation, that is all. It belongs to common knowledge, that the IR radiation comes from the Sun, too, so from Tyndall’s experiment alone it is impossible to conclude on either net warming or net cooling.
In the moment it looks like you either lack proper knowledge of the issue or you use a false premise to support your claim.
Second, there is a clear indication (but not a proof) that it is probably impossible to prove “greenhouse gasses warming” experimentally. Otherwise AlGore would not have staged a fake recently, that was debunked by Anthony Watts. They would have demonstrated something genuine.
Nevertheless, we can clear the matter once and for all. Please, present clear, distinct references and links to who when and where and how experimentally physically measured (not calculated on the statistical basis) how much increase in physical temperature how much “greenhouse gasses” produce. Physics, please, no speculations.
The assumption that because a model is complex its output must be right is a fallacy that Aristotle would have pounced upon if there had been computers in his day. The greater the complexity of the model, the more likely it is – all other things being equal – to produce incorrect output.
A simpler way to say this (“occam’s razor”) Computers make very fast, very accurate mistakes.
Lord Monckton is going a long way to redeem himself for supporting Thatcher.
[SNIP: Insulting, abusive and obnoxious in the same old way, get snipped in the same old way. -REP]
[Agree. Further references to Peter Hadfield, who will not engage in a face to face debate in a neutral venue will be deleted. Take the ad hominems elsewhere. ~dbs, mod.]
[I overstepped in this case. Although Peter Hadfield has never challenged Lord Monckton to a debate, that is not saying he will not debate. My apologies for giving that impression. He is still free to issue a debate challenge. ~dbs, mod.]
Arkay says: A minor quibble, but facts are important…
While argumentum ad populum and argumentum ad verecundiam are indeed logical fallacies, they are not amongst the 13 logical fallacies described by Aristotle in ‘On Sophistical Refutations’.
(3) that which depends upon ignorance of what ‘refutation’ is:
It would seem to me that #3 presented here fits the above two fallacies quite well. Specifically, the idea of argument by head count or expertise fits. A claim of expertise is an ignorance of what is, or is not, refutation, because experts (and crowds) have often been shown to be wrong, and therefore cannot be relied on as proof or refutation. “Other fallacies occur because the terms ‘proof’ or ‘refutation’ have not been defined, and because something is left out in their definition. .Define for my why your claim of “expertise” means that what you say is always, absolutely true?
There is a way, of course, where it can be true. Simply claim to be god, and provide proof of same. A claim of “expertise” that settles all doubt simply because you say so, is essentially a claim to be god. After all, if you are god, whatever you want to be true, you simply make it true. If you are not god (and I think that can be reliably demonstrated), than a simple claim of expertise is not close enough to godhood to claim infallibility, which is what you must claim under the idea that your expertise proves what you say is true.
Proof that you are not god:
I think I can say that I can find a witness that sometime, somewhere, someone heard you express dislike of something. Subsequent to that, the disliked thing continued to exist. If you were god, you could have changed it, and you would have based on your expression of dislike. You did not. Therefore you are not god.
*If you were god, you could and would change disliked things into liked things.
*You were heard to express dislike of something, and a wish that it would change.
*It did not.
*Conclusion, you are not god.
Old story.
There once was a man named Phil.
Phil claimed to be god.
Some people believed him.
One day, Phil and his followers were walking down the street, and a lightning bolt struck Phil.
All his followers looked up, and they said…
“There’s something bigger than Phil.”
And, of course, you must believe me because…
I AM GOD
No, really, I am!
Stop looking at me like that!
Your still looking at me like that!
Drat, I’m not god.
And it was such a nice dream for a second there.
i hate logic 🙁
Monckton of Brenchley says:
No it doesn’t. The energy balance arguments referred to constrain the average of T^4, not the average of T, on the surface. The 270 Kelvin number is obtained as the fourth root of the average of T^4 on the surface. By Holder’s Inequality, it will be greater or equal to the average of T. Only for a fairly uniform temperature distribution does one expect this upper bound to provide a reasonably good estimate of the average temperature. The moon is an airless body with a very broad temperature distribution and hence it is expected that the average temperature will be considerably less than the constraint provided by this inequality.
That is because most modeling simulations and all empirical estimates of climate sensitivity do not try or are not able to divide up the contribution of each feedback. What Soden and Held did is went through the myriad of models and computed these individual contributions, which are useful for understanding the magnitude of the various feedbacks making up the climate sensitivity and how they differ from one model to another. However, this is basically irrelevant to the issue of estimating the overall climate sensitivity.
Paltridge et al. results for the change in water vapor use data that has known artifacts in measuring what they want to measure and which contradicts nearly all other measurements, be they other reanalyses incorporating radiosonde data, satellite analyses, and shorter-term relationships between temperature and water vapor from all data sets that are not subject to the same sort of artifacts that longer term trends are. The chances of that paper being correct are essentially nil. See, for example, Dessler and Davis (2010) http://geotest.tamu.edu/userfiles/216/Dessler10.pdf
The first version of Lindzen and Choi’s paper was so bad that even Roy Spencer pointed out its many flaws. It is doubtful that the 2nd version will fare much better (except that it may not attract quite as much rebuttal this time around just because of the obscurity of where it was published and the fatigue of climate scientists in having to waste time on this stuff).
Monckton of Brenchley says:
April 24, 2012 at 11:25 am
“And so to a troll, skulking under the pseudonym “Major9985″, who unfairly complains that what he calls “comments that speak the truth are not allowed” at WUWT.”
I tried to post a comment under my name Michael Whittemore [SNIP: Not everything happens in the time frame or at the pace you would like. This topic is exhausted. Drop it. -REP]
You go on to say that the consensus on anthropogenic climate change ‘does not require to be sanctified by any headcount among scientists”. There are a lot of people that don’t believe in anthropogenic climate change. The “head count” is to try and reassure the public that it is real.
“In short, we may see perhaps 1 Celsius degree of warming this century as a result of our activities”
You get this 1 Celsius warming from “unmeasured and unmeasurable, unknown and unknowable” climate sensitivity?
Vince Causey says:
April 24, 2012 at 2:00 pm
“I assume you believe in your analogy”
Vince, it wasn’t my analogy, it was PeterGeorge posting April 24, 2012 at 12:07 pm. I was commenting on how bad an analogy it was, to wit:
“Horrible analogy. Your scenario holds a one time event to happen at an expected time and place. The results of the prediction will be well known at that time with no further threat to worry about. Once and done with people going back to their normal lives. NCCDs (natural climate change deniers) want to permanently change the way we live, redistribute wealth and seek the creation of a world government to keep the rest of us in line.”
tomwys says:
April 24, 2012 at 12:27 pm
Forget the analogy, PeterGeorge! Scientists don’t just present the “…claim of authorities.” They publish material, give justification, make data available (not all do this, I’m afraid), and give enough information, peer reviewed or otherwise, so that the decision to remain in NYC will NOT be made in a vacuum, given the modicum of education available to both of us.
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Climate scientists have done all that. By golly, they’ve even spent billions of our tax dollars doing it. But most of us who frequent WUWT don’t believe them. And we’re probably right and they’re probably wrong.
But it would be really different in the Chicken Little (rock falling from the sky) case, wouldn’t it. We – no I’ll be more modest, I would believe the Chicken Littles. And it DOES have something to do with authority – a legitimate kind of earned authority that comes from being right a lot, being able to reliably demonstrate key facts, knowledgeable people being free and able to disagree and debate until there is convergence, and so on.
But, critically, it is a heuristic authority; few people believe or argue that scientists CANNOT be wrong. And it is only a fallacy to argue from authority in absolute terms. Any statement like: “Authority says its true, so it MUST be true” is false, just as Lord Monckton reminds us, and for the reason he cites. But a statement like: “These people have been right nearly 100% of the time on a huge number of claims, so they’re probably right this time” is not false. It’s a perfectly valid heuristic argument.
People can and do disagree on appropriate heuristics in different cases. Hence, I’m afraid I can’t agree that the argument from consensus used in the climate debate can be simply dismissed on the grounds of argumentum ad verecundiam (argument from authority).
Putting it bluntly, if Drs. Lindzen, Christie, Spencer, Michaels, Lord Monckton, Anthony Watts, and the Idso and Pielke families published a joint paper in which they claimed compelling evidence that the temperature sensitivity to a CO2 doubling was at least 3C, I would believe that they were probably right even before reading the paper. I admit it. And its presumptuous, but I think most WUWT would too. And like it or not, there is nothing wrong with that heuristic reasoning.
PeterGeorge
There’s something wrong with heuristic reasoning. This is that it is ILLOGICAL.
major9985 says:
April 24, 2012 at 7:50 pm
You go on to say that the consensus on anthropogenic climate change ‘does not require to be sanctified by any headcount among scientists”. There are a lot of people that don’t believe in anthropogenic climate change. The “head count” is to try and reassure the public that it is real.
—————————————–
“Reassure”!?! If you want to “reassure” us poor, ignorant folk how about getting Mann to release the info he’s hiding and has been fighting tooth and nail to keep hidden for years. (Thank you, whoever released the Climategate stuff.)
The “head count” among a select few is not to reassure us dolts. It is to dupe the public into agreeing to whatever policy or regulation or installation of a political power to fix the problem until, when we wake up, it will be to late to stop those pushing for the “change you can believe in”.
These fallacies don’t make things false. It’s a “take it for what it’s worth” situation. As in, take it for what its worth that a senator named Al Gore raises a call to alarm.
RE
John Coleman says:
@ur momisugly April 23, 2012 at 7:20 pm
Yes. Agree fully. I have often found myself dumfounded by the ignorant cultist’ prostetations that ‘Monckton isn’t a scientist’. Well, all I can say is, I spent many years training in the company of some publicly celebrated scientists at more than one of the commonly-regarded ‘elite’ universities. And what I can tell you is, Monckton is most certainly a scientist and a highly accomplished thinker. As this article so eloquently demostrates.
RE
Greg House says:
@ur momisugly April 24, 2012 at 2:49 pm
You must be a lawyer. You are splendidly articulate in appearing almost-knowledgable yet saying practically nothing of any substance. I bet you read a lot of crime novels.
Monckton of Brenchley,
This notion of effective radiating altitude is nonphysical and apparently some fabrication of james hansen from back in the 90s or even 80s. Gases emit and absorb in a characteristic spectrum while liquids and solids emit and absorb in a continuum. A gas could emit/absorb in a continuum only when it is optically opaque over the whole continuum. The outgoing radiation from Earth comes from many altitudes and from the surface. Probably none of the radiation is actually emitted from the characteristic altitude as it will have been absorbed and reradiated many times at those wavelengths where molecules absorb and emit radiation. Where they don’t, it is coming from the surface or from the cloud tops and solids and liquids present in the atmosphere.
Stefan’s law was originally determined through experiment but was later found to derive from Planck’s law which deals with emission intensities by wavelength or frequency. It turns out Stefan’s law is the integration of Planck’s equation over all frequencies and all angles outward from a surface.
cba says:
It is not “nonphysical”. It is a simplification, as any such notion must be that takes a complicated process with both wavelength dependence and probability distributions and reduces it to a single number.
Monckton of Brenchley,
There is a way to determine an average sensitivity that includes existing feedbacks and doesn’t require lots of modeling or assumptions.
After albedo reflections, Earth receives about 239 W/m^2 averaged over its surface which is captured by the surface or atmosphere and must be shed for balance. Surface temperature averages around 288.2K and varies by small amounts permitting us to approximate differences in power as linear. The average emission according to Stefan’s law is around 391w/m^2 since at these wavelengths, emissivity is almost 1.0. 391-239 = ~ 151 W/m^2 which must be trapped by the atmosphere. Analysis of ghg components indicate all major ghgs trap about 110 W/m^2 with the balance being clouds. particuates. Note that there is both absorption and emission going on with the absorption not being as temperature dependent as emission. If we compare a blackbody emitting 239 W/m^2 to Earth, we find that it would have a temperature of around 33 deg C less than Earth, around 255 K. Consequently, we can say that 151 W/m^2 of atmospheric trapping has led to 33 deg C of temperature increase. We can also say that 391 W/m^2 of radiated surface temperature has led to 239 W/m^2 escaping, around 61%. 33/151 = ~ 0.22 deg C per W/m^2 sensitivity. The 61% escape fraction indicates that for 1 W/m^2 increase in atmospheric absorption means for a simple case that 1/0.61 = 1.6 W/m^2 additional power must be radiated from the surface for 1 W/m^2 additional to escape. Stefan’s law shows that for our surface radiator, there must be a 0.29 deg C rise in temperature to emit 1.6 W/m^2additional. Note that the difference between 0.29 – no feedbacks and 0.22 W/m^2 sensitivity with all feedbacks shows us a negative net feedback at work.
Also note that this 0.22 deg C/W/m^2 includes all existing feedbacks and it is an average value over all the W/m^2 currently present. It doesn’t include added feedbacks due to the 0.22 deg C rise which contribute additional W/m^2. One must go to the absolute humidity tables and radiation effects of water vapor to gain insight into the most important feedback – which turns out to be miniscule with results that are less than a simple black body example.
I have a Calculus book. I wasn’t even sure what calculus was a few years ago. With nothing more than having this physical manifestation of a persons thoughts, knowledge and experience, typeset onto 984 pages, I was able to learn what calculus was. I am nearly an expert now on calculus, and I intend on becoming an calculus expert, a mathematician (for my own satisfaction).
Just over 2 years ago I wanted to get up to speed on climate science, to see what I could find out there on the internet, having armed myself with enough math abilities to handle whatever math would be thrown my way, differential equations and all that.
So when I read that one has to listen to a “consensus”, I say B.S. I want to see the math, like what Lord Monckton does here. I don’t need to defer to a higher authority, or any authority. Show me the math.
For others who think that they should be doing something about global warming / climate change, may I suggest that the most effective thing you could do is, study math.
There’s something wrong with heuristic reasoning. This is that it is ILLOGICAL.
And sadly, as Hume showed so very long ago, all reasoning about things that exist is heuristic.
Bummer, eh?
rgb
rgbatduke (April 25, 2012 at 5:59 am ):
Thanks for the thoughful reply and for giving me the opportunity to amplify.
Hume addressed the so-called “problem of induction” – the problem of how to extend logic from the deductive branch that was described by Aristotle and through its inductive branch. Hume attempted a proof that this problem had no solution.
In the construction of model, the builder of this model is repeatedly faced with the necessity for selecting the inferences that will be made by this model. In each instance in which an inference is made there are candidates a, b,… for being made. The builder must select the one inference that is correct from among the many candidates, but how?
Currently and in virtually every case, model builders make the selection using the intuitive rules of thumb that I call “heuristics.” As you point out, if Hume’s proof is correct we are forced to do so. However, in each case in which a particular heuristic selects a particular candidate for being made as the one correct inference a different heuristic identifies a different candidate as the one correct inference. In this way, the method of heuristics violates Aristotle’s law of non-contradiction. Thus, if Hume’s proof is correct, science lacks a basis in logic.
In the period between 1963 and 1975, the engineer, lawyer and theoretical physicist Ronald Christensen exploited a weakness in Hume’s proof and solved the problem of induction. The weakness was that Hume’s proof did not deal with the possibility of selecting the one correct inference by optimization. In particular, the one correct inference is the optimal inference.
Optimization is facilitated by the fact that the measure of an inference exists and is unique. The unique measure of an inference is the missing information in it for a deductive conclusion, the so-called “entropy.” That an inference has a unique measure and that this measure is its entropy is of colossal philosophical and scientific importance.
By 1975, the team that I then managed for the Electric Power Research Institute was using Christensen’s ideas in employing logic rather than heuristics in selecting the inferences that would be made by models that were the product of scientific studies. By 1980, Christensen and his colleagues were using these ideas in meteorological studies. Early in the 1980s, Christensen published a voluminous description of his work. the “Entropy Minimax Sourcebook.” Academic philosophers and statisticians ignored it. Thus, the situation came to pass in which academia continues to award PhD degrees to illogical scientists while prestigious journals continue to publish their illogical and often pseudo-scientific works.
Andrew says:
April 25, 2012 at 5:03 am
You must be a lawyer.
=================================
Andrew, the whole AGW thing needs a sort of lawyer approach to catch the AGW proponents (both radical and moderate) lying. Dealing with them, you should first ask the question, whether their premises are true. Of course, not everyone consciously misleads others, some of them are good people, who themselves have been misled by the liars.
In my previous posting on this thread I asked Lord Monckton to present scientific evidence concerning the core issue. It doesn’t look like his scientific answer is going to come soon.
My guess is, that warmists produce an enormous amount of papers and postings on the blogs to obfuscate the simple truth: they have nothing real in the hand on the core issues and are selling speculations based on speculations as scientific facts.
You do not need to wait for the Lord Monckton’s answer, you can do some research yourself and I can predict the outcome: zero evidences. And the whole thing is certainly not about me being a lawyer or not.
cba says:
You are pretty much just repeating back to Monckton an argument that he loves to make which is, of course, completely wrong. That number does not include feedbacks because it considers everything, including changes in water vapor, clouds, etc., to be forcings not feedbacks. (And, it ignores changes in ice-albedo because the 33 C number assumes albedo doesn’t change.)
As for the strength of the water vapor feedback, I would trust those who actually calculate it to those who “look at absolute humidity tables and radiation effects” to conclude something totally at odds with the calculations.
Oh, and the reason that it is smaller than the no-feedback value is because the one feedback that it includes (as you roughly describe) is the one odd-man-out feedback, i.e., the lapse rate feedback which is the one feedback known to be negative. (The reason that the lapse rate feedback is included is it is different in nature than the other feedbacks. It is not really a feedback on the process … but rather just a correction to account for the fact that the mid- and upper-troposphere where most of the radiation escapes to space from warms faster than the surface so the surface doesn’t have to warm as much to restore radiative balance.)
One should not allow some of the comments here to divert attention away from the fact that the arguments from consensus and from appeal to authority or reputation are logical fallacies. Any argument founded upon any of these fallacies is not a valid argument and cannot, therefore, be a sound argument. That is why the assertion that one should believe the climate-extremist notions on the ground that there is a consensus among the experts and those opposing it are cads, and bounders in the pay of Big Oil is altogether without merit, and is intellectually feeble-minded. And that is why, in every opinion poll, members of the public are expressing increasing skepticism. They have seen the savage, persistent and often childish attacks of the climate extremists on those of us who dare to raise legitimate scientific and economic doubts; they have seen the extremists, time and again, take refuge behind their mantra of a consensus of experts, and they don’t buy it any more. They are right not to do so.
In the Aristotelian canon the fallacies of consensus and of appeal to authority or reputation are categorized, along with the argumentum ad hominem, as special instances of the red-herring fallacy, which the medieval schoolmen would later label ignoratio elenchi, the fallacy of fundamental ignorance of the proper method of examining the validity of an argument. The reason why the consensus, reputation, and ad-hom fallacies are fallacies is precisely that each of them introduces to the argument a matter that is extraneous to it and, because it is extraneous, cannot tell us anything either about the logical self-consistency of the argument or about whether the premises are true.
Hank Henry says: “These fallacies don’t make things false.” No, they don’t: but they don’t make things true either. A sound argument is one in which the premises validly entail the conclusion and the premises are true, whereupon the conclusion is necessarily true. A fallacious argument is invalid: therefore, the argument itself tells us nothing about whether its conclusion is true or false.
Peter George says it is reasonable to rely upon a consensus of people who have been right nearly 100% of the time. Yet climate scientists have not been right nearly 100% of the time, or the long-range weather forecasts of no snow by 2010 (followed by the second-coldest, second-snowiest winter since 1659 in central England) or of a “barbecue summer” (followed by the wettest, coldest summer in living memory) would not be so much of a joke that the Met Office has had to abandon its former practice of issuing them. Even if climate scientists had been right nearly 100% of the time, the question whether they were right on other matters is extraneous to the argument that because we are adding CO2 to the atmosphere there will be dangerous warming. Therefore, like it or not, the argument from consensus is a fallacy, and, however many attempts are made to dress it up with sprigs of parsley, it remains a fallacy, and that is that.
Mr. Whittemore, a.k.a. Major9985, says the “headcount” among the supposed experts is “to try to reassure the public that [climate change] is real”. But the attempts to reassure the public of a dubious proposition by the use of an ancient logical fallacy are not, in fact, inspiring in the public a confidence that the supposed experts are correct. And it is intellectual dishonesty of the worst kind to deploy what one knows to be a fallacious argument on the ground that one hopes the public will not realize that it is fallacious.
Mr. Whittemore goes on, in that sneering tone of his, to say, “You get this 1 Celsius of warming [per CO2 doubling] from unmeasured and unmeasurable, unknown and unknowable climate sensitivity?” No, I advanced the estimate of 1 Celsius of warming per CO2 doubling on the basis of the 3.1 Watts per square meter of radiative forcing from all anthropogenic greenhouse gases since 1750, less 1.1 Watts per square meter of negative non-greenhouse forcings, compared with just 0.9 Celsius of warming since 1750, of which perhaps less than half was anthropogenic. In short, rather than trying to model climate sensitivity using the seven unknown and unknowable unknowns, I approximated it by using measurements and observations from the real world. It is the IPCC that attempts to derive its 3.3 Celsius of warming per CO2 doubling from the use of unmeasured and unmeasurable parameters. It is wrong to do so, and still more wrong to claim a high confidence for its prediction.
Joel Shore says theory does not predict that the global mean surface temperature of the Moon is 270 K. Yes it does: which is why he will find this value explicitly stated in NASA’s lunar fact-sheet. The 255 K characteristic-emission temperature of the Earth is calculated by a similar method, and may, therefore, be similarly exaggerated. Mr. Shore makes the mistake of assuming that, thanks to the Holder inequality as applied to the non-uniform latitudinal distribution of temperatures, the true mean temperature of a planetary body will be less than the theoretically-predicted mean temperature. However, as the IPCC itself makes clear, the terrestrial value of the Planck parameter – and consequently of the characteristic-emission temperature – is approximately one-sixth higher than the theoretically-determined value, precisely to allow for the latitudinal distribution of temperatures. Yet the measured lunar temperature is very considerably lower than that which theory predicts, and the same may well be the case on Earth. Like it or not, the Diviner mission has cast a legitimate doubt upon the terrestrial value of the Planck parameter, which has probably been exaggerated, taking climate sensitivity with it.
Mr. Shore then makes the bizarre suggestion that the values of individual temperature feedbacks are irrelevant to the issue of climate sensitivity. This, too, is simply wrong. The IPCC assigns almost two-thirds of all CO2-driven warming to temperature feedbacks, so their collective value is unquestionably essential to the determination of climate sensitivity: and that collective value cannot be reliably determined, not least because the true values of the individual feedbacks that constitute the feedback sum cannot be reliably determined, nor readily distinguished from the contributions of other feedbacks, or from the forcings that triggered them. This is a highly relevant consideration.
Mr. Shore also attacks Professor Lindzen’s papers of 2009 and 2011 demonstrating a net-negative feedback and a climate sensitivity of just 0.7 Celsius per CO2 doubling. He says the first version of the paper was “bad”. Yet the statistical infelicities of the paper were not in fact bad enough to change the result. As the ocean surface warms or cools, the satellites can measure the corresponding changes in outgoing radiation from the Earth to see how much of it is being trapped as the official theory predicts. The results seem to show that most of the radiation is escaping to space much as usual, so that climate sensitivity is low. That is, no doubt, an inconvenient result, but – as far as I know – the second version of Professor Lindzen’s paper has not been seriously challenged in the climatological literature. It is one of a growing body of papers that establish, by a variety of empirical rather than numerical methods, that climate sensitivity is low.
Mr. House challenges me to prove the existence of the greenhouse effect. He may care to refer to any elementary textbook of climatology. However, he is – as usual – off topic. For it is my contention in the head posting that there is no scientific basis for the official conclusion that, as a result of our enhancement of the greenhouse effect, catastrophic global warming will be likely. If there were no greenhouse effect, then my conclusion would be true a fortiori.
Brendan H says that, in a logical argument “the premises and the argument need not be explicit”. In logic it is a requirement that each premise and the conclusion they entail be made explicit.A mere declarative statement, such as “There’s a CONSENSUS!”, may be either a premise or a conclusion, but on its own it is simply a statement and no argument exists.
Son of Mulder says the first differential of the Stefan-Boltzmann equation, from which the Planck parameter is derived, is a non-linear feedback. Some months ago I discussed the Planck Parameter with Professor Roe, who shares my own opinion that the Planck parameter is better understood as an essential ingredient in the reference-frame for determining both zero-feedback direct warming and the post-feedback indirect warming that the direct warming is thought to trigger. If so, it should be expressed in Kelvin per Watt per square meter, rather than in Watts per square meter per Kelvin. Again, however, the question whether feedbacks are linear or non-linear is not relevant to the argument in my head posting. If some of the feedbacks are non-linear, then in addition to the seven unknowable unknowns on the right-hand side of the climate-sensitivity equation there are several additional unknowable unknowns in the shape of the non-linearities in the feedbacks, from which my conclusion that no reliable conclusion as to climate sensitivity can be drawn from an equation in multiple unknowable unknowns manifestly follows a fortiori.
CBA deploys a beautifully simple demonstration of low climate sensitivity based on the observation that the total forcing from the presence as opposed to absence of all greenhouse gases in the atmosphere is about 110 Watts per square meter, and that the corresponding increase in temperature, after very nearly all feedbacks have acted, is only 33 Celsius degrees. However, the usual suspects have seen how dangerous that argument is to their notion that climate sensitivity is high, so they are now maintaining that the 110 Watts per square meter, though plainly described as Watts per square meter (i.e. as forcings) rather than as Watts per square meter per Kelvin (i.e. as feedbacks) nevertheless include feedbacks. They don’t, of course: but this moving of the goalposts on their part, knowing that the average Minister or journalist will not have a clue what they are on about, is exactly how they have kept this long-dead scare going at official level when everyone else has long since seen through the nonsense.
Gary Mount has it right: he has just taught himself calculus (no mean feat, that) and recommends that those who want to Save The Planet should study math first.
In recent weeks, thanks to Anthony’s courtesy, I have now advanced three fatal arguments against taking any action about “global warming”: first, that even if it were going to happen at the officially-predicted rate (which it is not), it would be at least an order of magnitude more cost-effective to do nothing about it now and to adapt to any adverse consequences of warming later; secondly, that most of the arguments most frequently deployed by the climate extremists are instances of logical fallacies that would have been recognized as such at once by an educated man in any previous generation from the Middle Ages until half a century ago; and thirdly, that there are too many unknowable unknowns in the climate-sensitivity equation to allow anyone to maintain that there is a serious likelihood of a future warming rate significantly higher than what we have seen globally over the past 150 years. Two of these arguments rely upon math; the other relies upon logic. All I am asking for is a degree of intellectual honesty, mathematical rigor and logical analysis in addressing the climate question that has been absent among the climate extremists until now. “The road to the truth,” said the father of the scientific method, “is long and hard: but that is the road we must follow.”
Monckton of Brenchley: “Brendan H says that, in a logical argument “the premises and the argument need not be explicit”. In logic it is a requirement that each premise and the conclusion they entail be made explicit.”
As I said, in practice, in informal situations, it is unlikely that writers or speakers will fully explicate their argument, and even less so as a syllogism.
“A mere declarative statement, such as “There’s a CONSENSUS!”, may be either a premise or a conclusion, but on its own it is simply a statement and no argument exists.”
In the context of the comment, the claim was almost immediately followed by a reference to the consensus argument. Even the not-so-alert reader would have linked the two. However, I am happy to accept that you do not consider the above-expressed claim of consensus to be a logical fallacy.
Presumably, you are also happy to accept that the claims made about logic by a person who is Classically trained in logic are about as good as the next person’s.
In the period between 1963 and 1975, the engineer, lawyer and theoretical physicist Ronald Christensen exploited a weakness in Hume’s proof and solved the problem of induction. The weakness was that Hume’s proof did not deal with the possibility of selecting the one correct inference by optimization. In particular, the one correct inference is the optimal inference.
By which time he was already decades late. The problem of induction was solved by physicist Richard Cox in a set of papers in the 40s, and solved (indirectly) at a slightly later date by Claude Shannon’s information theory. The two different approaches were shown to be more or less equivalent and to form the “logic” of science by E. T. Jaynes in “The Mobil Lectures” in the mid-50’s. Those lectures were turned into a book that Jaynes never quite finished but that was published posthumously as “Probability Theory: The Logic of Science”. The draft of this book and the Mobil lectures themselves are both available online, although the book is well worthwhile to anyone who cares to learn the mathematically precise basis of scientific inference. Cox’s work is available in a monograph entitled “The Algebra of Probable Inference” that is again a must for the shelves of any thoughtful person interested in this general topic.
Both Cox and Jaynes acknowledge, however, that the true master of this was none other than John Maynard Keynes, who wrote a lovely book on probability theory back in the 1921. Keynes introduced the principle of indifference, which eventually became the maximum entropy principle used by all of the rest (originally championed by Jaynes, IIRC), which was further advanced by Jefferies in 1939.
This is still hardly complete, but it is close. It is also important to note that “the correct inference” is not the optimal inference. All the correct theory (and science) can do is make things more or less plausible, given the evidence and the rest of the (Bayesian) network of plausible evidence supported belief. In my book Axioms (which I’m still working on, sigh) I try to reduce the idea to a pithy little sound bite: It is best to believe the most that which you can doubt the least given the evidence and the network of best evidence-supported belief.
Even this isn’t quite adequate — in order for science to function as a system of improving knowledge, that is, an optimizing algorithm, it has to be quite tolerant of error. That is one of many reasons why “correct inference” is an ill defined concept, let alone term. One can argue that x or y is the best inference to make from the data, given this or that, but because Bayesian reasoning depends on the priors and we don’t KNOW the priors, but are trying to optimize on a varying multivariate surface with lots of complexity, in many cases there is not “best” inference.
If you are interested, you can grab http://www.phy.duke.edu/~rgb/axioms.php to take a look at the first 1/3 or so of the book in draft form, but it includes most of this part of it.
rgb
rgbatduke (April 25 at 12:02 pm):
Thanks for taking the time to reply. It sounds as though you are unaware of some of the history.
Though Shannon contributed to solving the problem of induction, he didn’t complete the job. Among the unfinished business that was left in Shannon’s wake was a method for the assignment of numerical values to probabilities. Maximum likelihood estimation doesn’t work as it overestimates the amount of information in the data causing the model building process to blow up. Christensen solved this problem with the application of the principle of entropy maximization which he called “maximum entropy expectation.”
Though Jaynes’s posthumously published book is subtitled “The logic of science,” Jaynes seems to have been unaware of two necessary components of a solution to the problem of induction. One is maximum entropy expectation. The other is entropy minimization. In the absence of entropy minimization, the logic fails to converge to the classical logic in the limit that the missing information is reduced to nil. In his written works, Jaynes seems to have applied only entropy maximization. I’ve read many of these works but not all.
Many people contributed to solving the problem of induction. There is strong evidence that person who finished the job is Christensen. In one of his published works, Christensen reports that the year of this invention was 1963. Eleven years later, while managing a program of theoretical research for the Electric Power Research Institute, I conducted a worldwide search for persons with the ability to construct a model from the available information using information theory. A single person exhibited this ability. This person was Ron Christensen.
Regarding the question of the identity of the prior probability density function, in the absence of available information, the prior PDF must be uninformative. It is generally true that uninformative prior PDFs are of infinite number. In this circumstance, the model builder has no option but to select one of them by the method of heuristics. Historically, the uniform prior has been popular model builders. According to IPCC AR4, a flat prior PDF has been popular among climatologists seeking to extract posterior PDFs for the equilibrium climate sensitivity from observational data. The associated procedure is illogical from its violation of non-contradiction. No logical procedure for the extraction of a posterior PDF for the equilibrium climate sensitivity from observational data is a possibility.
There is an exception to the rule that uninformative prior PDFs are of infinite number. This exception is the basis for maximum entropy expectation. As the associated uninformative prior PDF is unique, violation of non-contradiction is avoided.
Tom in Florida says:
April 24, 2012 at 7:53 pm
Vince Causey says:
April 24, 2012 at 2:00 pm
“I assume you believe in your analogy”
Vince, it wasn’t my analogy, it was PeterGeorge posting April 24, 2012 at 12:07 pm. I was commenting on how bad an analogy it was, to wit:
“Horrible analogy. Your scenario holds a one time event to happen at an expected time and place. The results of the prediction will be well known at that time with no further threat to worry about. Once and done with people going back to their normal lives. NCCDs (natural climate change deniers) want to permanently change the way we live, redistribute wealth and seek the creation of a world government to keep the rest of us in line.”
Yes, my apologies. I didn’t take time to see that you were in fact quoting PeterGeorge.