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.
Hi Mindbuilder, rgb (Robert Brown), Oldberg, and Chris:
Here’s something on induction I serendipitously found 15 minutes ago while Googling Images for something quite different. Maybe you’d care to comment?
———–
Philosophical Terms and Methods
Vocabulary Describing Arguments
Contents
Valid Arguments
Sound Arguments
Persuasive Arguments
Conditionals
Necessary and sufficient conditions
Consistency
Most of the arguments philosophers concern themselves with are–or purport to be–deductive arguments. Mathematical proofs are a good example of deductive argument.
Most of the arguments we employ in everyday life are not deductive arguments but rather inductive arguments. Inductive arguments are arguments which do not attempt to establish a thesis conclusively. Rather, they cite evidence which makes the conclusion somewhat reasonable to believe. The methods Sherlock Holmes employed to catch criminals (and which Holmes misleadingly called “deduction”) were examples of inductive argument. Other examples of inductive argument include: concluding that it won’t snow on June 1st this year, because it hasn’t snowed on June 1st for any of the last 100 years; concluding that your friend is jealous because that’s the best explanation you can come up with of his behavior, and so on.
It’s a controversial and difficult question what qualities make an argument a good inductive argument. Fortunately, we don’t need to concern ourselves with that question here. In this class, we’re concerned only with deductive arguments.
http://www.google.com/imgres?imgurl=http://www.jimpryor.net/teaching/vocab/strawman.png&imgrefurl=http://www.jimpryor.net/teaching/vocab/validity.html&usg=__818E7H5Hn2qcGyFj–R9-uoYQNI=&h=500&w=735&sz=53&hl=en&start=90&sig2=NgvD-VdzzSKpnJTuPXnGpg&zoom=1&tbnid=A8ZjeIINWoW5NM:&tbnh=96&tbnw=141&ei=5_GaT92nIqmhiAKg2-DCDg&prev=/images%3Fq%3Dstrawman%26start%3D84%26um%3D1%26hl%3Den%26client%3Dsafari%26sa%3DN%26rls%3Den%26tbm%3Disch&um=1&itbs=1
PS: In particular, can any of you give me references to places where the issue of the “controversial and difficult question what qualities make an argument a good inductive argument” can be found? TIA.
rogerknights:
A model is a procedure for making inferences. Each time an inference is made, there are many candidates for being made. Logic contains the rules by which the one candidate that is “correct” may be discriminated from the many candidates that are “incorrect.” The problem of how to make this discrimination is called the “problem of induction.”
A solution to this problem is facilitated by the fact that each inference has a unique measure. The measure of an inference is the missing information in it for a deductive conclusion, the so-called “entropy.” It follows that the problem of induction can be solved by optimization. In particular, the correct inference is the one that maximizes the entropy or, depending upon the type of inference, the one that minimizes the entropy under constraints expressing the available information.
The IPCC’s climate models were not built under principles of logical reasoning. Instead, intuitive rules of thumb called “heuristics” were used in the discrimination of the one correct inference from the many incorrect ones. A consequence is for the models to be riddled with logical errors. Among the most serious is that when a maker of governmental policy on CO2 emissions believes the IPCC has provided him/her with information about the outcomes from his/her policy decisions, he/she has no information at all. While there is no basis for making policy, it seems to the policy maker as though there is a solid basis. This error has the capacity for costing us 100 trillion US$.
PS: In particular, can any of you give me references to places where the issue of the “controversial and difficult question what qualities make an argument a good inductive argument” can be found? TIA.
Dear rogerknight, sir,
Please grab Jaynes’ Mobil Lectures. If, at the end of reading it (it is quite readable even to a lay person, not too technical) you do not feel Enlightened, I would be amazed.
As I also noted, you might want to grab my own online draft:
http://www.phy.duke.edu/~rgb/axioms.pdf
which more or less precisely answers your question, with considerable examples and discussion. Polya’s books on inference in mathematics are also highly illuminating — even mathematicians rely almost entirely on heuristics and inference to formulate the theories they later, sometimes, manage to prove deductively. And sometimes they don’t. The Riemann conjecture, the Goldbach conjecture, appear to be true but (so far at least) are not provable. And Godel tells us not to be too surprised if they turn out to be true and not provable, as he proved that true, unprovable theorems exist in any sufficiently complex theory.
Cox’s monograph is also quite excellent, as is Boole’s Investigation into the Laws of Thought. Finally, if you are fairly competent in math, stats, computation or something similarly technical, you might try to tackle MacKay’s online book, but it is not terribly simple and presupposes competence at the level of at least an undergrad major in physical science, math, stats, computation in its contents. Even so, you can probably appreciate parts of it, but the math is heavy going at times. It was intended as a college text for upper-level majors or lower-level grad students, after all.
Hope this helps. Personally, I think all lawyers and many other kinds of scientist or economist or engineer would benefit from understanding Bayesian probability theory and its connection to plausible reasoning along the lines illustrated by Jaynes and in Axioms. Examples in Axioms make it clear how shifty the sands of argumentation really are.
rgb
rgb – The link below is to another well written (abeit quite dated) paper that also speaks to your nicely described parallels & rationales between religions and AGW believers.
http://econot.com/page4.html
Among other points, it hits upon the irony of the virutally complete parallel between the GAIA-ists and the Judeo-Christian “Garden of Eden” in the “Mankind is Evil and must be Redeemed” postulate.
As rgb asks, redemption at what price? Belief in God and the science of an apparently demonstrable robust agregate climate sensitivity is clearly cheaper than giving up our lifestyles to live in caves again.
Apologies to the moderator for being off-topic (sorta).
By an unfortunate accident of timing, Mr. Oldberg made the unfounded – and false – assumption that my background in inductive logic is “next to non-existent” shortly after I had posted a comment explaining in some detail precisely how mathematical induction works. Inferentially, he had not seen my comment. Since my previous posting at WUWT had revealed that I have been Classically trained in logic, as would perhaps have been evident to anyone who had done me the kindness of reading that posting, it was unwise of Mr. Oldberg to make (and still more wise of him to state) an assumption contrary to the evident facts.
However, the present head posting was designed precisely to allow people who are unfamiliar with logic – such as Mr. Oldberg – to appreciate by mathematical reasoning why it is that climate sensitivity to a doubling of CO2 concentration cannot be determined by the methods now used in the climate models.
Notwithstanding my careful explanation of the many unknown and unknowable unknowns that constitute the climate-sensitivity equation, Mr. Oldberg – as though I had not written a word – puzzlingly goes on to accuse me of making what he calls the “error” of assuming that “equilibrium climate sensitivity has a numerical value”.
Of course climate sensitivity has a numerical value: whether Mr. Oldberg likes it or not, it is a real quantity expressed in Kelvin per doubling of CO2 concentration. The point of my head posting, however, was to demonstrate that the IPCC’s methods cannot help us to narrow down the value of that crucial quantity to a small enough interval – whether expressed as a central estimate flanked by error-bars or as a probability distribution – to provide useful information for policymakers. There is no error of logic in my approach.
Mr. Knights makes the puzzling assertion that “most arguments are not deductive but inductive”, though he does not define either term. So, for the sake of dispelling the fog of confusion that seems to surround these elementary concepts in logic, deduction is the inference of a conclusion from stated premises (if any of the premises is unstated, then the logician must be diligent enough to state it). Deductive logic, when done properly, is the appropriate, valid (because internally self-consistent) and sound (because the premises are true) inference of a general conclusion by reasoning from the general to the particular.
Induction, by contrast, is the valid and sound inference of a general conclusion from particular instances. Mr. Knights is quite wrong to state that “inductive arguments do not attempt to establish a thesis conclusively”. Mathematical induction, an instance of which I demonstrated in an earlier comment, is explicitly designed to establish propositions conclusively: and, for instance, as I pointed out in that comment, Andrew Wiles relied upon mathematical induction in conclusively demonstrating Fermat’s Last Theorem. In all species of formal logic, whether deductive or inductive, the intent is to establish the truth of a conclusion by arguing validly (so that the premises logically entail the conclusion) from premises that are true. An argument in which the premises are true and validly entail the conclusion is known as a sound argument, and its conclusion is necessarily true.
It is a matter of great regret that logic is no longer universally taught to the governing class, as it was until my generation in the United Kingdom. The climate scare would never have gotten off the ground if most politicians had had some formal training in how to think.
Monckton of Brenchley (April 27, 2012 at 2:12 pm):
You appear to believe that to know about mathematical induction is to know about inductive logic. This is far from the case.
The possibility of an inductive logic was created by the discovery of a mathematical theory of information. Had you mastered this logic you would know that “information” is the measure of the intersection between two state-spaces, both of them observable. As an equilibrium temperature is not an observable, the rise in the CO2 concentration can provide no information about the rise in the equilibrium temperature. If the equilibrium climate sensitivity has a particular value, though, the rise in the CO2 concentration provides perfect information about the rise in the equilibrium temperature. The apparently perfect information is entirely fabricated.
I was taught logic at a very rigorous school, and I well remember inductive vs deductive logic classes.
As Lord Monckton says, inductive logic is from the particular to the general, while deductive logic is from the general to the particular.
An example of inductive logic would be: “I see a white swan. Therefore, all swans are white.” Inductive logic is fine when first formulating a conjecture, but it is deductive logic that separates the wheat from the chaff; true from false.
Anyone can employ inductive logic to support their conjecture. We see it done here all the time: “There were tornadoes, ergo, global warming.” Inductive logic is for lazy minds.
Smokey (April 27, 2012 at 2:38 pm):
You’ve confused induction with inductive logic. Also, your conclusion that all swans are white does not logically follow from your premise of an observed white swan, for information about the colors of the unobserved swans is missing.
Finally, in examining the method of construction for a model for the presence of logical errors it is necessary to use the inductive as well as the deductive logic. For example,use of the deductive logic alone would not catch your error in concluding that all swans are white.
Terry Oldberg,
I’ve confused nothing; I gave examples. Could my comment [“inductive logic is from the particular to the general, while deductive logic is from the general to the particular”] have been any more simple and straightforward?
I gave two examples of inductive logic, which take a particular fact and extend it in general. Simples. I don’t know why you don’t get it.
An example of inductive logic would be: “I see a white swan. Therefore, all swans are white.” Inductive logic is fine when first formulating a conjecture, but it is deductive logic that separates the wheat from the chaff; true from false.
Sadly, this is not correct. Inductive logic is not concerned with “true versus false — it is concerned with “probably true versus probably false”. Deductive logic is altogether about one thing and one thing only — the consistency of a proposition with a set of assumed truths — the axioms of the theory. Deduction cannot give you the axioms.
Again, you can learn all of this by reading Jaynes’ “Probability Theory, The Logic of Science”, or his Mobil lectures, or a perhaps simpler rendition in my axioms draft.
rgb
Mr. Oldberg wrongly asserts that Smokey has “confused induction with inductive logic”. The process by which the truth of a general conclusion is tested against premises that are particular is called “induction”, and the species of logic that is being deployed is “inductive logic”. The two phrases mean much the same: and, even if they did not, it is poor technique to assert that someone has confused two terms without going on to dispel the confusion by defining the two terms.
Mr. Oldberg’s assertion that “it is necessary to use inductive as well as deductive logic” to establish that a fallacy is a fallacy needs qualification and clarification. The fallacy of inappropriate argument from the particular to the general, i.e. a dicto secundum quid ad dictum simpliciter, is a well-known species of fallacy, as is the fallacy of inappropriate argument from the general to the particular, i.e. a dicto simpliciter ad dictum secundum quid. One can identify these fallacies without recalling which of them is a fallacy of deduction and which a fallacy of induction. Two instances will demonstrate this.
“CO2 causes warming. Warming melts ice. The Arctic ice is melting. Therefore CO2 is causing the global warming that melts the Arctic ice.” Here, all three premises are true if one takes the trend since the satellites were first able to measure polar ice extent reliably. Yet the conclusion is false, because the argument from the particular to the general in this instance is inappropriate, for the obvious reason that there are other causes that may have melted the Arctic ice, and for the still more obvious reason that the Antarctic ice has been growing, indicating that the warming (however caused) is not truly global.
“Global warming intensifies hurricanes. Hurricane Katrina was a bad one. Therefore global warming caused Hurricane Katrina.” Here, neither of the premises is true, and nor is the conclusion, and in any event the argument is invalid because it is an inappropriate argument from the general to the particular. According to the 30-year record of hurricane activity maintained by Dr. Ryan Maue at Florida State University, hurricane activity worldwide is at its least since the satellites began watching; and theory suggests that a reduction in temperature differentials that drive hurricanes will occur if there is warming. Secondly, when Hurricane Katrina made landfall it was not a particularly bad one: it was Category 3 (on a scale of 1-5). The reason why it did so much damage was the failure of the [Democrat] administration in New Orleans to make sure that the Corps of Engineers kept the levees up to strength. Thirdly, as the IPCC itself concedes, one cannot ascribe individual extreme-weather events to global warming: nor is it possible to maintain that there have been more extreme-weather events in the last few years: and even if there had been more extreme weather, it cannot have been caused by global warming because there has not been much of it to write home about for 15 (or, according to a recent report) 20 years.
Mr. Oldberg goes on to define a heuristic, with unfortunate imprecision, as an “intuitive rule of thumb”. In mathematics, however, where precision in the definition of terms is just as important as it is in logic generally, a heuristic is a rigorous and disciplined parallel thought-experiment that illuminates or assists in confirming a result by an empirical method. It is neither “intuitive” (indeed, it can sometimes be counter-intuitive) nor a “rule of thumb”. An example will point the moral and adorn the tale.
Twice in the 2007 Fourth Assessment Report, the IPCC publishes a graph of annual global mean surface temperature anomalies since 1850. Each graph is overlaid by four overlapping least-squares linear-regression trend fits, all ending in 2005 but each commencing at a different date: 150, 100, 50, and 25 years before 2005 respectively. Each successive trend-line has a steeper slope. From this, the IPCC draws the fallacious conclusions a) that the rate of global warming is itself accelerating (an intriguing special instance of ignoratio elenchi by which the start-dates for the trend-lines are arbitrarily chosen to generate the desired result, whereas a different choice of start-points or end-points would produce precisely the opposite result); and b) that we are to blame for the imagined (and imaginary) acceleration in the warming rate (a howling non sequitur). How a supposedly trustworthy intergovernmental body can come up with such noisome garbage, and get away with refusing time and again to correct it (but without being able to defend it, for it is indefensible) beats me.
As a heuristic, one can apply the IPCC’s flagrantly bogus technique to a sine-wave. By definition, a sine-wave has a zero trend, which is why it is useful as a heuristic to illuminate the question whether the IPCC’s technique is acceptable. One can readily choose four overlapping trend-lines each less steep than its predecessor, suggesting that the sine wave exhibits not merely a falling trend, but on an accelerating falling trend. Shifting the entire sine-wave half a cycle to the left or right allows one to choose four more overlapping trend-lines each steeper than its predecessor, suggesting that the sine wave exhibits not merely a rising trend, but an accelerating rising trend. Each of these results is incompatible with the known zero trend for a sine wave, and the two results also contradict one another. Accordingly, since the data are accurate and each trend-line is calculated correctly, these two contradictions demonstrate rigorously that it is the technique of allowing the statistician to select arbitrary start-points and end-points that is defective. Accordingly, the IPCC ought not to have used the bogus technique, and the conclusions it draws by the use of that technique are inappropriate and unustifiable. This is a good example of the power – and the rigor – of the heuristic in mathematics.
Intriguingly, I was demonstrating this heuristic in Brisbane, Australia, a few months ago. Professor Bob Carter, one of the sharpest intellects on the skeptical side of the global warming debate, was sitting in the audience. He almost fell off his chair. He, too, uses the sine-wave as a heuristic to demonstrate the shoddy bogosity of the principal conclusion of the IPCC’s 2007 report. Yet neither of us had been aware that the other had independently developed the same thought-experiment. Great minds … [fools] …
If any readers are having some difficulty visualizing this thought-experiment and would be interested, they should add a comment about it and, if there is enough interest, I shall offer Anthony a posting about it (if he has not carried one already).
Smokey (April 27, 2012 at 4:01 pm):
You’ve swapped terms. It is “induction” that is from the particular to the general not “inductive logic”; inductive logic contains the rules that make an induction valid. Similarly, it is “deduction” that is from the general to the particular and not “deductive logic”; deductive logic contains the rules that make a deduction valid.
Terry Oldberg,
I’m not going to get into a hairsplitting debate over what you believe inductive logic is or isn’t. I’ll just leave you with my handy on-line dictionary definition. The entire definition is:
inductive |inˈdəktiv | adjective
1 characterized by the inference of general laws from particular instances.
I’ll go with Mr. Webster.
Smokey (April 27, 2012 at 5:08 pm):
Webster is right. You were wrong.
Terry Oldberg:
Monckton is right. You were wrong.☺
Smokey (April 27, 2012 at 5:22 pm):
Please clarify.
Mr. Oldberg continues to confuse matters: one hopes that this is not deliberate. He writes that I “appear to believe that to know about mathematical induction is to know about inductive logic. This is far from the case”. Yet, whether Mr. Oldberg likes it or not, mathematical induction is a particularly rigorous and demanding species of inductive logic, which nicely illustrates how it is possible to reach rigorous conclusions by inductive methods.
Mr. Oldberg then sneers – yet again, without the slightest evidence – to the effect that I have not “mastered this logic”. It is very clear, however, that it is he who has not mastered it. For instance, he asserts that, “as an equilibrium temperature is not an observable, the rise in the CO2 concentration can provide no information about the rise in the equilibrium temperature.” Of course it can. We know by experiment that, at certain characteristic wavelengths in the long wave, radiation interacts with CO2 molecules in the atmosphere, causing warming. From these experiments we know that a rise in CO2 concentration will be likely, all other things being equal, to cause some warming. As my head posting here demonstrates, we do not have enough information to determine how much warming will occur: but we do have enough information from the increase in CO2 concentration to know that we should expect some warming. That, whatever else it is, is not “no information”.
Likewise, until recently, the far side of the Moon was not “observable”: however, it was legitimate to infer from the state of the visible face of the Moon that its invisible face was very likely to be composed of regolith pitted with impact craters, with a thermal conductance, an albedo and a mean surface temperature similar to those of the visible face. When we were finally able to have a look, we found – not greatly to our surprise – that the far side of the Moon was not, after all, made of green cheese. It was indeed made of regolith with characteristics very similar to those of the Moon’s visible face. Once again, what we could legitimately infer from the observable face of the Moon about its unobservable face is not “no information”.
Mr. Oldberg goes on to compound his error: “If the equilibrium climate sensitivity has a particular value, though, the rise in the CO2 concentration provides perfect information about the rise in the equilibrium temperature.” Since the climate system (though non-periodic) is deterministic, equilibrium climate sensitivity indeed has a particular value, though, since the climate (though deterministic) is non-periodic and the information to us about its initial state at any chosen starting moment is insufficiently precise, we do not know what that value is. Notwithstanding what Mr. Oldberg and the IPCC claim, knowing the increase in CO2 concentration tells us little about what that value is, except that it is likely to be positive. But that, though it is not “no information”, is not “perfect information” either.
Mr. Oldberg should appreciate that reciting half-understood definitions in information theory is not at all the same thing as understanding – after due thought – what these definitions mean. In the present instance, Mr. Oldberg has deluded himself by failing to stand back and think about what he is saying.
The bottom line remains the bottom line: my head posting was intended to offer a mathematical alternative to the formal, logical approach with which Mr. Oldberg and one or two others continue to have such difficulty. There are too many unknown and unknowable unknowns in the fundamental equation of climate sensitivity, and particularly in the parameters that define the overall feedback gain factor: therefore, the methods deployed in the models relied upon by the IPCC cannot determine climate sensitivity to a sufficient precision to be policy-relevant, and the interval of estimates presented by the IPCC is accordingly guesswork. It is as simple as that, and no amount of inexpert waffle about the intersection of two observable state-spaces will alter that simple and, in my submission, undeniable conclusion.
Monckton of Brenchley (April 27, 2012 at 5:58 pm):
The proof of my assertion is by the definition of the term “information.” Your attempted rebuttal of this assertion is by redefinition of the same term. You should understand that in the mathematical theory of information, the term “information” acquires a precise definition that is identical to the definition I have used but different from the definition you have used in your rebuttal.
Also, in the course of our debate you have repeatedly employed the ad hominem fallacy. For the future, please refrain from muddying the waters by addressing the argument with which you disagree and not the qualities of the person who is making this argument.
Terry Oldberg says:
“Please clarify.”
I was just razzing you. See the smiley? I could also ask you to please clarify how you believe my definition and Webster’s definition are basically any different.
But I’m not asking, because it will lead to nitpicking. I know the difference between inductive and deductive logic. I made an innocent comment giving two examples of inductive logic, as opposed to deductive logic, and you haven’t convinced me that they’re not examples.
I don’t want to argue because I think we’re generally in agreement regarding the “carbon” scare. So feel free to have the last word on this subject. Me and Mr. Webster are on the same page on this. You can join us, or not.
In resonse to Lord Monckton’s suggestion above to provide a comment regarding his clear demonstation about the bogus manipulation (or “impermissable statistical technique”) of a sine wave as the IPCC does (I suspect Dr Kevin Trenberth is the source?), I add his presentation below (please start at the 5:50 minute mark):
RGB: Thanks for the guidance. I hope you are saving these comments of yours for future use elsewhere, so they won’t have been wasted if they go over my head. I will visit and print out material from your links. And thanks also, Terry. I’ll be printing out everybody’s remarks and studying them later.
Christopher Monckton wrote:
That wasn’t me–that (and the rest of the material he took issue with) was from the material I quoted. (I’ve discovered that it’s a help page for students in a course in deductive logic.) I should have used the “blockquote” tag to indent and italicize it, as I usually do, and/or put it in quotation marks. But I thought it was clear enough, because I introduced it this way:
Checking further, I discover that the author of my quoted material is Jim Pryor, an assoc. prof. of philosophy at NYU. Here’s his home page: http://www.jimpryor.net/
Clicking on the “Teaching & Advice” line brings up a pageful of links to course notes for various courses (past and present) of his, at http://www.jimpryor.net/teaching/vocab/validity.html
Clicking on “Intro. to Philosophical Terms & Methods” (near the top of that page) brings up a six-line outline, at http://www.jimpryor.net./teaching/vocab/index.html
Clicking on the second line, “Vocabulary Describing Arguments,” brings up the help-document (or whatever these things are called) that I quoted from.
FWIW, the first link, “What is an Argument?” has this URL: http://www.jimpryor.net./teaching/vocab/argument.html
The second link, “Vocabulary Describing Arguments,” is at http://www.jimpryor.net./teaching/vocab/validity.html
The third link goes to “some Good and Bad Forms of Argument” at http://www.jimpryor.net./teaching/vocab/goodbad.html
4th link, “Analyzing Concepts” (displays the fifth, subsidiary link’s contents too): http://www.jimpryor.net./teaching/vocab/analyses.html
6th link: “A Philosophical Glossary for Beginners”: http://www.jimpryor.net./teaching/vocab/glossary.html
—————-
That doesn’t squarely address the material I quoted, which focused on arguing about fuzzier questions in everyday life, including detection (and espionage analysis, I presume), as the context makes evident:
Lawyers and politicians, and doctors, and detectives, and generals, use this sort of induction, and have to use it, right? So what’s wrong with it? “Let’s you and him fight” about the issue. Or maybe the other participants would like to slug it out–I hope so! I’m a novice and don’t want to muddy things further.
BTW, the reason for my interest in this matter is that I’m planning to launch a counterattack on a critic of my inductive arguments elsewhere online. Here’s an example of what I’m up against. To simplify things, assume there was an enormous, eye-catching scar on a face the witness (“she”) supposedly saw for a lengthy period (several minutes) at close range, and that she was questioned intensively about every detail of what she saw:
I think my inductions in this everyday-situation were quite appropriate. And can anyone give me a rebuttal to his use of “special pleading” in this instance? He’s accused me of it four times, but I strongly suspect he’s talking through his hat.
Monckton of Brenchley says:
April 27, 2012 at 2:12 pm
By an unfortunate accident of timing, Mr. Oldberg made the unfounded – and false – assumption that my background in inductive logic is “next to non-existent” shortly after I had posted a comment explaining in some detail precisely how mathematical induction works.
=====================================================
Christopher, let me make you familiar with two most important commandments of the new internet age: 1. you shall not try writing on everything and 2. if you do, check the internet first.
“Induction” and “mathematical induction” are two different things. A lot of people learn about mathematical induction in the high school and can apply it and at the same time they have no idea about induction. That means, Christopher, that a more or less knowledge of “mathematical induction” does not indicate ANY knowledge of “induction” in the logical sense.
So, if anyone assumes, that your background in inductive logic is next to non-existent, you can not dispute it by mere referring to your knowledge of mathematical induction.
It is not very different, Christopher, from someone claiming he has knowledge of dogs referring to his expert knowledge of hot dogs.
This is what the Stanford Encyclopedia of Philosophy writes about induction: “An inductive logic is a system of evidential support that extends deductive logic to less-than-certain inferences. For valid deductive arguments the premises logically entail the conclusion, where the entailment means that the truth of the premises provides a guarantee of the truth of the conclusion. Similarly, in a good inductive argument the premises should provide some degree of support for the conclusion, where such support means that the truth of the premises indicates with some degree of strength that the conclusion is true.”
I friendly suggest you consider stopping to argue about the issue, because otherwise it will only get worse, exactly like with you arguing about “experimental proofs” that CO2 produces” some warming”.
Mr. Oldberg says: “Proof of my assertion is by the definition of the term “Information”. However, he does not specify what “assertion” he is “proving”, still less how the mere citation of a definition “proves” the “assertion”.
He then complains, justifiably, that I had defined “information” differently from him. Well, here is his original definition: “… the intersection between two state-spaces, both of them unobservable”. And my paraphrase of his phrase: “the intersection of two observable state-spaces.” My mistake. The conclusions he drew from this definition as to the distinction between “no information” and “perfect information” about the effect of CO2 on climate sensitivity were nevertheless manifestly incorrect for the reasons I explained.
He then accuses me of arguing against him ad hominem. Pot calls kettle black: for instance, he had accused me (without adducing evidence, thereby indicating an ad-hom attack) of not having “mastered this logic”, and now whinges that (with evidence, indicating that I was addressing his argument and by definition was not, therefore, arguing ad hom) I demonstratred that he had not “mastered this logic”.
Mr. Knights says that most everyday arguments are inductive rather than deductive logic, and cites an authority for that proposition. However, in logic – which, whether we like it or not, is what we must concern ourselves with when we are looking at scientific questions such as the “how-much-warming” question, one may argue as readily from the general to the particular as from the particular to the general, provided that the logical quantifiers are appropriately deployed and that the fallacies of accident and of converse accident are avoided.
Mr. House, having been defeated in his futile attempt to hijack this thread into a discussion of his unscientific contention that there is no such thing as a greenhouse effect, now seeks to interpose himself – with characteristic sneering illiteracy (the word “friendly” is not an adverb, for instance, and the tenor of Mr. House’s comments throughout has been unfriendly) – into this previously interesting discussion of philosophy and logic. He begins with the contention that one should check the internet before writing something. Useful though the internet is, it is not always a reliable source: consider, for instance, that Wikipedia actually advertises itself as “the encyclopedia that anyone can edit”, which tells one all one needs to know about whether it is likely to prove reliable.
Mr. House cites out of context a textbook definition of the term “inductive logic” that he has found on the internet, but, as will become apparent, he has clearly not thought about the question before making his citation. However, it is good news that he proves able, after all, to look up textbook definitions: for I have made several suggestions that he should enlighten himself as to the existence of the greenhouse effect by consulting any textbook of climatology. His replies have been to the effect that it is for me to educate him, and that, since I have declined to allow this thread to be hijacked by entering into that futile debate, there is no such thing as the greenhouse effect. That is our old friend the argumentum ad ignorantiam, the fallacy of ignorance of the matter of an argument: the greenhouse effect has not, in Mr. House’s opinion been proven; therefore, he fallaciously contends, it is disproved. That will not do.
Mr. House then makes the blindingly obvious observation – which had already been made and disposed of earlier in this thread – that “induction” and “mathematical induction” are different things. He might, perhaps, have noticed that the word “induction” appears twice, indicating that the latter term is a subset of the former. Therefore, to illustrate the process of inductive argument by an instance of mathematical induction is to demonstrate some knowledge of the process of inductive logic, and to demonstrate, contrary to the inadequate and loosely-worded textbook definition of induction that Mr. House cites, that inductive logic can indeed be deployed in the decisive demonstration of a proposition.
Once again, the head posting provided a mathematical argument about a scientific question, precisely so as to make life easier for people, like Mr. House, who have little knowledge of or background in any species of formal logic, Accordingly, Mr. House, having been off topic in repeatedly asserting that there is no greenhouse effect (which was irrelevant to the head posting, since if there were no greenhouse effect the conclusion of that posting would follow a fortiori), now again strays off topic and, as usual, well beyond his competence.
The conclusion of my head posting stands. Given that there are too many unmeasured and unmeasurable, unknown and unknowable unknowns in the fundamental equation of climate sensitivity, there is no scientific basis in the models relied upon by the IPCC for the assertion that climate sensitivity will be dangerous in the least. That is the main point: and no attempts at diversion or misdirection will alter it. “The moving finger writes, and having writ Moves on, nor all thy piety nor wit Shall lure it back to cancel half a line, Nor all thy tears wash out a word of it.”
I am most grateful to Tomazo for having kindly posted in this thread a link to an extract from a recent talk by me that explains the inappropriate statistical technique deployed by the IPCC in reaching the principal conclusion of its 2007 report – the conclusion that the rate of global warming is accelerating and that we are to blame.
Monckton of Brenchley (April 28, 2012 at 12:30 am):
Thanks for taking the time to reply. You’ve misquoted me. In my post of April 27, 2012 at 4:41 pm, 2nd paragraph, I say “…’information’ is the measure of the intersection of two state-spaces, both of them observable.” In your misquote, you’ve dropped the phrase “measure of the” and changed “observable” to “unobservable.” The two changes in it render my argument nonsensical.
In the previously cited post, I state the fact that the “…equilibrium temperature is not an observable” and conclude from the definition of “information” that “…the rise in the CO2 concentration can provide no information about the rise in the equilibrium temperature.”
To clarify, in the literature, Shannon’s measure of the intersection of two state-spaces is often called the “mutual information.” It is the information that one gains about the state in one of the intersecting state-spaces from knowing the state in the other. The mutual information is an example of a mathematical function. If you wish, you can discover the formula for it via a Web search.
An example follows. The example features the state-spaces X and Y. X contains the sequence of states x1, x2… where x1 is the proposition that at time t1 the CO2 concentration lies between 200 and 210 ppm, x2 is the proposition that at time t1, the CO2 concentration lies between 210 and 220 ppm and so forth. Y contains the sequence of states y1, y2… where y1 is the proposition that at time t2 the global average surface temperature lies between 10 and 10.1 Celsius, y2 is the proposition that at time t2 the global average surface temperature lies between 10.1 and 10.2 Celsius and so forth. t2 exceeds t1. By definition, the mutual information is the information that one gains about the state in Y from knowing the state in X. By the symmetry of the mutual information function, the mutual information is also the information that one gains about the state in X from knowing the state in Y.
If Y is redefined such that rather than referencing temperature values this state-space references equilibrium temperature values then the mutual information between X and Y is not defined, for equilibrium temperatures are not observable but both state-spaces on which the mutual information is defined are observable.
In making policy on CO2 emissions, a governmental policy maker needs to have information about the outcomes from his/her policy decision but a policy maker gains no information about the equilibrium temperature at Earth’s surface from knowing the CO2 concentration. This is a message that I wish you would deliver in the course of your various lectures and debates.
Also, in order for policy makers to be provided with information about the outcomes from their policy decisions, global climatology must be restructured such that it provides this information. An essential element of the restructuring will be to identify the statistical population that underlies the IPCC’s inquiry into global warming. Currently, this population is undefined.
If further clarification or amplication would be useful to you, please call on me.
Henry@Monckton
Honestly, I think we need to clear some air here.
I m sure people like me and Greg and others here never meant to say that a greenhouse effect does not exist.
To prove that a GH effect does exist you only have to look at the respective minima here, in RSA,
on a cloudless night and a subsequent cloudy night, during winter, when there is no wind.
The point we argue is whether an increase in CO2 causes more warming or less or whether the effect is more or less neutral.
I have spent a few years investigating and could not find any proof either way.
see comment 968281
(to which I have not have a decent reply)
HenryP says:
April 28, 2012 at 11:39 am
Henry@Monckton
Honestly, I think we need to clear some air here.
“I have spent a few years investigating and could not find any proof either way.
see comment 968281
(to which I have not have a decent reply)”
This is what this article has been trying to explain. There are so many factors involved that an analytical solution may not be possible at present. However, if global warming is supposed to be caused entirely by the increasing CO2 concentration and the warming has stopped while the CO2 continues to increase, then the CO2 is not really causing the warming.
pochas says:
April 28, 2012 at 3:10 pm
However, if global warming is supposed to be caused entirely by the increasing CO2 concentration and the warming has stopped while the CO2 continues to increase, then the CO2 is not really causing the warming.
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Pochas, unfortunately, the warmists do not really say, that CO2 is the only factor influencing the temperature, but they say, that CO2 physically causes warming by trapping radiation. So they can always say, that the warming has stopped for some reasons, but nevertheless CO2 always contributes to warming.
At the same time their basic claim about CO2 falls immediately, if you ask them about IR coming from the Sun.
@Greg House
There is not much IR coming from the sun, its almost all shortwave. Check out the wiki spectral diagram http://upload.wikimedia.org/wikipedia/commons/7/7c/Atmospheric_Transmission.png
Notice that the incoming solar spectrum and the outgoing IR transmitted from earth do not overlap.
Warming caused by CO2 was the original claim. When that was falsified, they did indeed embellish it with an admission of a solar effect and some ad hockery 🙂 about aerosols. We now know much of the alleged warming was due to “adjustments” and there is really no reliable data on the effect of aerosols and the supposed positive feedback from water vapor appears to be absent or quite possibly negative.