William M. Briggs

Statistician to the Stars!

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Aristotle On Non-Contradiction: Why UN Chief Ban Ki Moon’s Views On Free Speech Are Invalid

The simplest version The Philosopher gave is this:

It is impossible to hold the same thing to be and not to be.

If something is a “Quantum Superposition” it cannot also simultaneously be “Not a Quantum Superposition”. If something is a “House” it cannot also simultaneously be “Not a House.” That is to say, somebody cannot think that a thing is a “Quantum Superposition” or “House” and also think simultaneously that is it “Not a Quantum Superposition” or “Not a House.” Somebody may certainly claim to hold both beliefs simultaneously, but they are either confused about the word simultaneously, or they are lying or switching between beliefs temporally. It is plausible, or at least intelligible, to say that at this instant I think “House” and at the next instant I think “Not a House“, and that I may oscillate between these views, but I may not hold both at the same time.

Another example: UN chief Ban Ki Moon said yesterday, “Freedoms of expression should be and must be guaranteed and protected,” but then he also said, “When some people use this freedom of expression to provoke or humiliate some others’ values and beliefs, then this cannot be protected in such a way.” So he is either deluded (or thinks his audience is), or he is lying or he changed his mind and settled on the position that speech should be regulated by the UN. Time will tell.

Dispute this? Then forget all of mathematics for a start, which depends fundamentally on this principle. Aristotle goes on to say (Metaphysics Book 4, Article 4):

There are some people who, as we have said, both maintain that the same thing can be and not be and say that it is possible to hold this view. This is the view of many who study nature. We have assumed here that it is impossible for the same thing to be and not to be at the same time, and on the basis of this we have shown that of all principles this is the least open to question.

But this principle is one which is not provable: it is one that just is true, or we believe is true, based on no evidence except our introspection.

Some people, through their lack of education, expect this principle, too, to be proved; for it does show a lack of education not to know of what things we ought to seek proof and of what we ought not.

Note to moderns: this is not an ad hominem, but an observation. Here is the kicker:

For it is altogether impossible for there to be proofs of everything; if there were, one would go on to infinity, so that even so one would end up without a proof; and if there are some things of which one should not seek proof, these people cannot name any first principle which has that characteristic more than this.

If you don’t have a ground, then down you must go and forever, as each turtle supports the weight of those above it. You will never have anything to say that anybody should ever believe, and this by your own admission. Every valid argument, on the other hand, is a chain, anchored to a immovable base of truth.

Now, if you are one of the Moons of the world and believe (based on what principle?) the law of non-contradiction false, but do not wish to defend this view, then Aristotle says you are “no better than a vegetable” and shame on you. But if you do try a defense, then Aristotle asks you to “say something that has meaning both for [yourself] and for someone else. For this [you] must do if [you are] to say anything at all.” But in doing this while you are “trying to do away with reason, [you are] also accepting it.” And obviously, if you say Non-contradiction is false, you have “conceded that something is true quite independently of the process of proof.”

Aristotle then goes on to destroy the not-non-contradiction position, adding in the end that

if all contradictory assertions made about the same thing are true [a necessary implication is non-contradiction is false], all things will clearly be one. A trireme, a wall, and a man will all be the same thing, if it is possible to assert or to deny anything of everything…For if anyone thinks that man is not a trireme, according to their theory he clearly is not one; but in this case he also will be a trireme, if the contradictory statement is true.

There is of course more, much more. Best to go to the original.

What Do Philosophical Proofs Prove? — Guest Post by DAV

Note about civility: we are all, or should be, ladies and gentlemen here. Non-gentlemanly comments will henceforth be censored. Arguments, however, are more than welcome. —Briggs

There have been some recent posts which I believe have reached unwarranted conclusions.

First though, space is short here so I must resort to shortcuts. I don’t wish to get into arguments over definitions. It’s the concepts and not the words used to describe them that is important. The following are provided to move the discussion along:

  • Reality: that outside of ourselves. If you are inclined to believe reality is only in your mind then posting arguments here seems to put you in the curious position of convincing yourself to come around to your own point of view. Sounds like a family fight which should remain private. Concepts are real in the sense that they can exist in other minds as well as our own. However, I will limit real to mean outside of our collective minds.
  • Proof: Suffice it that, here, I mainly use the word to mean existing in reality.
  • Validity: proof of reality.

Let’s consider mathematical proofs. Theorems are proved in math through logical deduction. That is, they are shown to be logically true and can be traced back to the starting assumptions (axioms). Mathematical theorems exist only in the framework of mathematics. They can be used as simplifications in other problems by analogy. This doesn’t mean they exist in reality. Confusing these simplifications with reality can lead to problems such as over-confidence.

The scientific method sidesteps the concept of proof in the mathematical sense. This doesn’t mean science doesn’t employ logical deduction. Scientific results are not logical deductions. Science relies on consistency with observations: information that comes to us from outside of ourselves. Observations are generally taken as fact. In science, the only thing that can be proven with certainty is inconsistency with observations. Theories that fail to predict future results are in need of modification and are rejected as is. Science provides ideas which are testable, that is, verifiable against observation. In short, science comes up with ideas that seem to work and, whenever possible, eliminates those that don’t.

But, you might ask, what about theories that can neither be proven nor disproven to exist in reality? There are a number of these — the Theories of Everything, for example. Presumably, their status is temporary and hopefully they can be tested in the future. Until then, their validity remains an open question.

There are those theories that seem to be forever excluded from testing for validity, for example, the existence or non-existence of God. It’s been mentioned that God cannot be sensed. This precludes using any observation to test whether theism should be preferred over atheism.

Lately, we have seen claims that God has been “proven”. Well, in the logical deduction sense, yes indeed.

Logical consistency is expected for otherwise it would constitute disproof. I’m fairly certain atheism is also logically consistent given its assumptions. If not then why hasn’t its disproof been widely circulated?

The deductive proof is insufficient when it comes to the question: is it real? It accomplished nothing beyond non-elimination toward a validity test. In the common person’s mind, “proved the existence of God” means “proved God is real.” In this case, at least, the deductive proof is the analog of p-value. It provides a misleading answer.

Has God been “proven” by logical argument? My take: in the sense of “shown to be real”, not at all — to claim otherwise is unwarranted. At best what can be said is that the concept of God is not illogical. On the other hand, the concept of no God is not illogical either.


As always, reasonably and well written guest editorials are welcome.

NASA Faked Moon Landing—Academic Psychologists Swoon, Tie It To Climate Change

One day a terrific psychological study is going to be written on the madness and mass lunacy which arose after climate change swam into the public’s ken. I don’t mean the actions and thoughts of the man-in-the-street, which were and are no different in this area than they were and are in any political matterhe . No: the real curiosity is what happened to academia, inside departments which haven’t anything to do with climatology.

There, surrounded by people eager to agree with each other and fueled by infinite estimates of their own intelligence, great hoards of degreed non-experts, people who couldn’t derive the Omega equation if you threatened to remove their tenure and who think Vorticity is a town in Spain, lectured all of mankind on why The End Was Near, Unless…

Unless they, the non-experts, were hearkened to, esteemed, feted, moneyed, and just plain listened to, dammit.

The cornerstone of this future pathological report may well be the peer-reviewed Psychological Science paper “NASA faked the moon landing—Therefore (Climate) Science is a Hoax: An Anatomy of the Motivated Rejection of Science” by Stephan Lewandowsky, Klaus Oberauer, and Gilles Gignac, perhaps the completest, most representative work of its odd era.

Everything that could have been done wrong, was done wrong. Every bias that could have been manifested, was manifested. Every fallacy pertinent to the matter at hand was made. The conclusions, regurgitated from unnecessarily complicated statistical procedures, did not follow from the evidence gathered, which itself was suspect. In its way, then, the paper is a jewel, a gift to the future, a fundamental text to how easy it is to fool oneself.

Consider that its errors are not far to seek1. Take the opening sentence: “Although nearly all domain experts agree that human CO2 emissions are altering the world’s climate, segments of the public remain unconvinced by the scientific evidence.” Isn’t that gorgeous? I count at least seven mistakes, and we are only at the very beginning!

  • Mistake 1: Lewandowsky is not a domain expert, and by his argument is not qualified to speak on matters climatic, yet speak he does.
  • Mistake 2: His opinion about how to consider the science of climate change is therefore no more valuable than any other non-domain expert’s (about the physics), but he considers by this act of publishing that it is.
  • Mistake 3: He conflates voting with truth. His fallacy is to suppose that because the majority of domain experts say X, X is therefore true.
  • Mistake 4: He conflates numbers with weight of evidence. His fallacy is to suppose the minority of domain experts who do not agree with the majority are not to be listened to because they are only a minority.
  • Mistake 5: He confuses physics with economics, a vulgar but common error. It may be true that, say, temperatures will rise by 0.5o C in the next five decades, but it does not follow that any theory of what will happen because of this temperature rise is true, nor is it true that anybody’s suggestion to combat the adverse consequences of what will happen is therefore worthy of consideration.
  • Mistake 6: Since Lewandowsky committed this howler, and is obviously unaware of it, he cannot see it in the people he interviews, who often make a similar error. That is, when a civilian is asked, “Do you believe in climate change?” he often answers “No,” but the mistake is to assume he is answering the question as stated, when in reality he has answered the modified question, “Do you believe in climate change and should the government regulate, rule, tax, control, mandate, penalize, etc., etc. to combat this change?” Such an elementary mistake by a psychologist shows us just how far the madness has progressed.
  • Mistake 7: Lewandowsky, because he is not a domain expert, misunderstood the basic physics. There are no domain experts who do not agree that mankind changes the climate. The only matters in question are: how much? where? when? with what certainty can we know? Notice the absence of “What can be done?” because this requires expertise in human behavior, and that expertise is what is suspiciously missing in this paper.

My dears, I emphasize that this was merely the opening sentence, and that much worse was to come. But before that, there was one more error, more grievous than any other, embedded in his starting sentence. This is Lewandowsky’s befuddlement that any non-domain expert could deign to question “the scientific evidence” (when much of what is “science” is instead politics). He assumes that any who do so, even in the admitted presence of disagreement over what “the” science is, suffers from a psychological flaw. Science has spoken, thinks he, and therefore nothing remains to be said. An actual instance of doublethink, and really quite marvelous when you consider the economy of words used to express it.

Now, the rest of Lewdandowsky’s work is more mundane. He commits the freshman mistake of only seeking evidence for his beliefs, and for none that would contradict him (and of which there is plenty); he says things like “Another common attribute of the contemporary rejection of science is its reliance on the internet” and then uses the internet himself in his “science”; he questions the influence of Steven McIntyre of Climateaudit forgetting that McIntyre is a domain expert and he, Lewandowsky is not.

He admits confirmation bias by calling dividing his sample into “pro-science” and “skeptic”, when the point in question is what the science says. He builds “latent variable” models to “prove” what he already believed, and biased himself to confirm; latent variable analysis being a lovely technique to give desirable results. He amusingly assures his audience of his “theoretical results”: not theories of climate, but psychological (academics do love a theory). He can’t help himself but use the ugly term denial, an appalling word one would have thought a psychologist would have understood was inappropriate.

As I said, a book could be written, and probably will be written on everything that has gone wrong with this paper.


Thanks to K.A. Rodgers who alerted me to the precious topic. Thanks too to John Moore for keeping me sharp.

1We haven’t time here to list and review each error: we leave that to genuine psychologists.

Update At Lewandowsky’s site, he puts up this puzzler: “Quick, consider the following: all polar bears are animals. Some animals are white. Therefore, some polar bears are white. Is this conclusion logically implied or not?” After you answer, “Yes”, he writes, “There is a 75% chance you might endorse this conclusion despite it being logically false.”

This is typical of the “gotcha” questions academics tease civilians with to prove that they, the academics, are smarter than the rest of us and therefore needed. Lewandowsky’s goes straight downhill after “Quick.” Of course people are going to say yes because every damn polar bear is white. They are not answering the question, which was absurdly required to be answered quickly, but instead recalling what they know to be true: polar bears are white.

To get at the true psychology, Lewandowsky should have instead asked, “Take your time and consider the following: all polar bears are animals. Some animals are white. Therefore, some polar bears are white. Is this conclusion logically implied or not? I am not asking whether polar bears are white—we know they are—but whether this logical argument is valid.” Not everybody will get this right, but we’ll at least be able to better estimate the actual percentage of folks who can’t.

As Joseph Epstein observed about speedy answers required by academics:

Only years later did I realize that quickness of response–on which 95 percent of education is based–is beside the point, and is required only of politicians, emergency-room physicians, lawyers in courtrooms, and salesmen. Serious intellectual effort requires slow, usually painstaking thought, often with wrong roads taken along the way to the right destination, if one is lucky enough to arrive there. One of the hallmarks of the modern educational system, which is essentially an examination system, is that so much of it is based on quick response solely. Give 6 reasons for the decline of Athens, 8 for the emergence of the Renaissance, 12 for the importance of the French Revolution. You have 20 minutes in which to do so.

Obama On Way Out? Romeny Hasn’t A Chance? Last Day of Presidential Voting Study

Today is the last day to participate in the voting study. If you have not already done so, please click below. And please send this to people you know, especially those of a different political orientation.

Please take a moment to register who you think will win the presidency. This is a statistical study of how good people are at predicting presidential races.

The results will be posted after the election. This is a self-funded study, so please be honest, please vote just once. This survey takes about one minute to complete and is completely anonymous.


The study closes midnight 16 September 2012.

Help spread this study. Click on the Twitter or Facebook links below, or email the study to one of your friends. Post it on internet forums. We want both progressives and conservatives to take part. See this webpage after the election for the results. Thank you!

College Essays For Sale—By Professors

At last college professors have found a way to supplement their income, and perhaps to steal back some of the tuition dollars that traditionally head right to the pocket of deans.

The new method is this: assign essays, threaten to use Turnitin, software (which did not exist in pre-Biden days) which exposes plagiarism and thus encourages original writing, and then hope the kiddies find their way to UnemployedProfessors.com, a site which sells original essays written by professors to students who are too busy acquiring “social knowledge”, as one school put it.

Incidentally, besides checking for cheating, Turnitin also automatically grades papers, relieving professors of that dull duty, too.

“Unemployed” Professors is unabashed in its description. Step 1 of the process is to “Get a lame-ass project from your Professor,” an acknowledgement that much of college life is mere time filling. Step 2 is to enter the project into the site. Step 3 is “PARTY!”, which by coincidence is also Step 5.

They will write essays, lab reports, even dissertations. They will do math, physics, and statistics homework. They will write computer programs and then claim that, as they write your resume, that you know how to write computer programs. The student is left only one chore: clicking the payment button. Burdens!

The site has a blog which tells prospective clients why its services are superior to its many competitors. It has such entries as “Don’t Hate Da Playa; Hate Da Game” and “How to Sleep with Your Professor.”

It should be obvious that we have Reached The End. There is nowhere left to descend to. Some thought the nadir was in the student riots of the 1960s. Some pointed to the open enrollment policies of the 1970s. Others posited the creation of “Studies” degrees (Gender studies, Black studies, etc.) in the 1990s. But the end was not yet.

It must now be clear that when professors both assign and perform the work (while automatically grading it), and charge for both, we have bottomed out.

Therefore, it is time to admit that classical “liberal” education is finished.

The solution is obvious. Beginning in 2016 (to allow everybody now in time to finish), every high school graduate is to be automatically awarded, by our most beneficent government, a diploma stating that he or she has completed college. The diplomas shall all read “Harvard”, so that nobody can be accused of class bias. The student must only foot the printing and shipping and handling charges of their degree.

Think of the vast savings! Upwards of a quarter-million dollars per student, all of which can be left in their and in their parents’ pockets, to be spent on less moribund areas of our economy.

The majority of our children will be satisfied with their well deserved degrees. And kids who still want to learn what a quark is, or how to titrate, or why Socrates is mortal, or how Constantinople derived its name, or what a div, grad, and curl are, can enroll in the one- to two-year trade schools which teach these subjects, schools which will be created from the remnants of the old colleges and universities, institutions which will not award “degrees”, but will issue letters swearing their students know the material.

And what of the mass of then truly unemployed professors of “Theory”, “Studies” and the like? Ship them to, say, Egypt and Libya and make them members of its bureaucracy. What better punishment for their recent ill behavior?

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