William M. Briggs

Statistician to the Stars!

Page 146 of 541

Russian Roulette And Certainty

An American Classic

An American Classic

Suppose one fine day you pick up your Smith & Wesson 586 ($809 MSRP), a .357 Magnum revolver—which means that thingee in the middle spins around, advancing one round at the time. It has an old-fashioned, manly wooden grip and six inch barrel (not wooden).

You savor it for a moment, considering it is not, or at least not yet, on a list the White House can peruse. Then, as you take out your cleaning rag, a knock comes at the door! The rag and oil can are pushed aside. As you load it, you shout, “Just a minute!”

The hallway seems longer than usual. But as you near the door—the gun comfortably nestled inside your pocket—you begin to relax as you recognize the outline of the man standing at the entrance. It’s your neighbor Fred, a professor down at the college who frequently drops by to try his latest theories out on you.

Fred had been reading Peter Kreeft’s Summa Philosophica and came across this passage:

[S]ometimes we need certainty, e.g. in matters of life or death. If a gun had 100 chambers, then 100 of them must be checked, yielding certain safety, and not just 99, unless you want to play “Russian roulette.”

Fred notices the bulge in your pocket and says, “What a coincidence! Would you, for one million tax free dollars, play Russian roulette with your .357? One chamber with a round, the others a empty, and so forth?”

Since you are not an idiot, you say no. This is because you deduce there is a 1 in 6 chance you’d fail to take the dog for his evening walk, this night or any other.

It is not certain you’d live, nor is it certain you’d die. If it were certain you’d live, every chamber would have to be empty; and for it to be certain you’d die, every chamber would have to be loaded. So much is elementary.

But Fred makes the game more interesting. “Suppose I were to build a machine which is like your gun but could hold N chambers. Only one would be loaded, the rest empty. Same game. How large would N have to be for you to play?”

And that, dear reader, is the question to you. Is an N of 1,000 large enough? That gives you a probability of 999/1,000 of not ceasing upon the morrow. But it’s still a 1 in a 1,000 shot of the wrong kind of haircut. Maybe 10,000?

Besides telling us your N, would you agree with me that no matter how large N gets it is never certain you will survive? And that the phrase practically certain has the same logical relation to certain as practically a virgin has to a virgin?

Do you think you would say N = NA, or N = NaN. I.e., no number? That you would refuse to play? Then I wonder why you strap yourself into your car and drive yourself to your paycheck-issuing location each weekday. There is, after all, a non-zero chance that you will become the subject of a high school drivers training film.

Real examples abound. Flying, skiing, walking along a road, eating donuts, listening to NPR, etc. All which prove you are willing to endanger your life in return for moola or thrills.

Is there a difference between purposely risking your life, as in Russian roulette, and routinely risking it, as in driving to work? If so, what is it?

Epistemology: Peter Kreeft’s Summa Philosophica Part VI

Why did God create us? She is the mystery!

Why did God create us? She is the mystery!

Read Part V.

Remember, we’re doing summaries of summaries here; only bare sketches are possible. Buy his book for more detail.

We are back on familiar stamping groups with Question VI, Epistemology. Directly related to probability and statistics, this stuff. So brighten up! See at least the summary in Article 2.

This is the last of the foundational meaty tough stuff. Next time we we’re on to the more succulent material: ethics.

Article 1: Whether Skepticism is refutable?

Oh, yes. The basic objection is that even the most uncontroversial syllogism must rest on premises that themselves have to be proved. And if those are proved, it is because they rest on still further, more basic premises, which also have to be proved, seemingly ad infinitum. And then even the workings of the syllogism itself—why is it that the conclusion follows—must be proved, etc.

As Aristotle showed, this “backward doubt” terminates in two places: psychologically indubitable immediate sense experience and logically indubitable first principles such as “X is not non-X” in theoretical thinking and “Good is to be done and evil to be avoided” in practical thinking.

Another way, with Pascal, to say “indubitable” is “by faith.” All who claim to be skeptics lie (at least to themselves). “To practice skepticism is to cease to speak, like Cratylus, who would only move his finger.” And even that’s cheating.

Article 2: Whether truth is objective?

Yes. If you think not, tell any professor “Evolution is false.” You will quickly learn not only is there objective truth, but that some truths are sacred.

[I]f all truth were subjective, then that truth also would be subjective. But what is subjective is changeable and uncertain. Therefore if all truth were subjective, it would be changeable and uncertain, and thus that “truth” also—that all truth is changeable and uncertain—would be changeable and uncertain. But what is uncertain may be false, and what is changeable can be changed. Therefore the “truth” that all truth is subjective, is uncertain, and may be false; and it is changeable, and can be changed—and if changed, then changed to “truth is objective.”

What’s true for thee, is true for me, baby, and vicey verso. Truth is “thinking and saying what is” (Aristotle, again). It’s not “what works” or the “coherence of ideas with each other.” And it certainly isn’t idealism. I love this checklist-summary so much, that I can’t resist quoting it all (but still buy the book!):

(1) Is this thing real?

(2) If so, do I, or do we, or can I, or can we, know that this thing is real?

(3) If so, is that knowledge certain rather than merely probable?

(4) If so, can I convince others of that certainty by rational arguments?

(5) If so, does the argument use the scientific method?

A thing can be real without being known.

A thing can be known without being known with certainty.

A certainty can be private rather than demonstrable.

And proof or demonstration may use other methods than the scientific method.

Confusion between (1) and (2) produces philosophical idealism.

Confusion between (2) and (3) produces skepticism or probabilism.

Confusion between (3) and (4) produce subjectivism.

And confusion between (4) and (5) produce scientism

Article 3: Whether we know things-in-themselves?

Yes. Though Kant said we can’t. I’ll only point you to David Stove’s famous contest to identify the worst argument in the world (see Jim Franklin’s page, or this PDF). Here’s the stinker:

We can know things only {as they are related to us; under our forms of perception & understanding; in so far as they fall under our conceptual schemes etc.}

So: We cannot know things as they are in themselves.

Article 4: Whether appearance coincides with reality?

No. We need the distinction of what is “true (in which appearances faithfully coincide with reality) and the false (in which appearances deceive because they fail thus to coincide with reality).”

To ask (1) what a thing is, (2) whether it is, or (3) why it is, is to express the will to know what is true; and this is to assume that there are both true and false, i.e. real and only apparent, answers to those questions, and thus that appearance and reality are not identical.

“In order to judge appearances, we must know something more than appearances.” Which is to say, reality.

Article 5: Whether all ordinary (natural) human knowledge begins with sense experience?

Yes. Though it seems we know tidbits like “X=X, that 2+2=4, and that if it is true that X is, then it is false that X is not” without benefit of sense experience.

On the other hand, “The blind have no innate idea of color, nor the deaf of sounds.” And we “must distinguish the claim that all our knowledge begins with sense experience from the claim that it is limited to it” which is false.

We don’t learn tautologies like X=X “unless we fist experience some things through the senses and only then rise to such principles by abstraction and inductive reasoning. It is not infants but philosophers who formulate such tautologies.”

Article 6: Whether there is a priori knowledge?

Yes. But didn’t we just agree “that all knowledge begins with sense experience, which is another way of saying that all knowledge is a posteriori knowledge”? Maybe a stronger objection:

If there is a process of thinking that leads from a posteriori knowledge of sensed particulars to a priori knowledge of understood universals, it is invalid; for it is invalid to conclude to a universal merely from particulars. “All men are mortal” does not follow from “this man is mortal” or “these men are mortal” or “some men are mortal.”

Yet there “is no contradiction between saying that all our knowledge begins with sense experience and saying that from sense experience we can rise to knowledge that does not depend on sense experience” which is a priori knowledge.

The process is not first of all one of inductive reasoning…but the understanding…of a universal which we find embedded in sensory particulars and which we abstract from those particulars…We can distinguish necessary and essential features of human nature (e.g. mind and body) from contingent and accidental ones (e.g. race and gender), but abstracting the former from the latter…Thus our knowledge that all men are mortal is a priori knowledge, known with certainty even prior to observing everyone die, but it emerges only from abstraction from experience which is a posteriori and empirical.

Stove (again!) shows the difficulty begins with improper use of inductive, which is now unfortunately taken to mean all non-deductive reasoning, instead of solely the type which leads to universals. Not for the first time I recommend his Rationality of Induction.

Article 7: Whether ideas are the immediate object of knowing?

No. Idealism, as we have long agreed, is deader than Marley. Kreeft slips in a joke. “[I]f the objects of our thinking were ideas, all sciences would be subdivisions of psychology. (Perhaps some psychologists would not regard this as a reductio ad absurdum.)”

Another opportunity to push Stove: see his essay “Idealism: A Victorian Horror Story”, reproduced in many places.

Article 8: Whether certain knowledge is possible?

Yes. And if you say no, you say yes, so you must say yes. And if you say maybe, you also say yes. Put up any fight at all and you say yes. Thus, yes.

Examples of certainty? Non-contradiction, whatever comes to be is caused (God does not come to be, therefore is not caused, thus He can be the uncaused first cause). Again, try the “evolution false” gag at your nearest college campus. Or try to write a blog post about which every reader agrees (the temptation is to say it certainly cannot be done).

Article 9: Whether the essential questions of philosophy are “mysteries”?

Yes. Mysteries not in the sense of whodunnits, but are thought puzzles in the sense of nobody knows, or can know, their whys. Not to beat you over the head with Stove, but in Rationality he has a lovely essay explaining that it is senseless to ask how something which is necessarily true is true.

Why is it true that “X=X” (or pick your favorite axiom)? I don’t know, and you don’t either: it’s a mystery. It’s just true. The terms is broader than this, though:

Marcel defines a “mystery” as distinct from a mere “problem,” as “a problem that encroaches upon its own data,” i.e. a question which so involves the very being and life of the questioner that it is impossible, and even undesirable and misleading to have total detachment and objectivity, as is required in the sciences.

Incidentally, many (not all) “problems” in philosophy aren’t. They are called so because the natural conclusion derived from cherished premises is unacceptable, or a conclusion is believed but can’t be derived from acceptable premises.

Article 10: Whether we can have knowledge of mysteries such as God, freedom, immortality, morality, and the meaning (purpose) of life?


[I]f we have no knowledge of [mysteries], how do we know them well enough to know that we have no knowledge of them? For instance, how can we know God so well that we know we cannot know Him at all? Is not such skepticism, like all skepticism, ultimately both self-contradictory and arrogant?

It’s as well to leave off with another shade of faith.

Religious faith is not the same as opinion. For faith, whether true or false, is a human response to a divine revelation, like light reflected in a faithful mirror, and thus its content is in itself most certain, even if not logically provable, for God can neither deceive nor be deceived; while mere opinion rests on the uncertainty of the human mind alone.

Faith is not (always) identical with intellectual belief.

Read Part VII.

The Hypocrisy Fallacy: If You Don’t Do What’s Right, I Don’t Have To Either!

L is for 'Lots of armed body guards.'

L is for ‘Lots of armed body guards.’

We continue our delightful series1 of mistakes in logic, this time highlighting the hypocrisy fallacy. It also has an official Latin name: ad hominem tu quoque, which loosely translated is, “You canting, sanctimonious fraud!”

Suppose an opinionator—intellectual, journalist, television news reader, academic, celebrity, blogger, etc.—were to issue the following prototypical statement:

I think we can all agree that the notorious ax murderer Joe Blogs, who used his last words to state that killing is wrong, is a hypocrite. Therefore, hacking people to pieces with dull axes is okay.

We would be right to wrest from the grip of this man the bottle of which he is obviously too fond. But what if he said this instead?

The Catholic Church acknowledged covering up the crimes of a bunch of misordained molesting male priests who were ‘oriented’ mainly towards post-pubescent young males, therefore we are right to ignore what the Church says about fornication, birth control, self abuse, divorce, and abortion.

This time our man would be rewarded with at least sage nods from his audience, if not a plaque acknowledging his journalistic boldness. He would even be bought drinks when, indeed, he should be cut off, because he is engaging in the same fallacy as before.

A murderer preaching against murder does not make murder right; other men rape, abuse, or fornicate and preaching against these acts does not make these actions allowable, even if you really want to do them.


Because the very pro-abortion former executive director of the National Family Planning & Reproductive Health Association Scott Richard Swirling has pleaded guilty to negotiating on-line to have sex with a man’s 12-year-old daughter, it means that those associated NFPRHA (pronounced nif-pur-Ha!) can’t be trusted in what they say about abortions on demand for pre-teen females.

This one is more difficult because it’s not clear if there is any hypocrisy. But if there were, then we cannot judge the morality of abortions from the actions of its prominent supporters, naughty as they are. Instead we say it is wrong because it is the deliberate killing of an innocent human being whose life is “inconvenient”.

More examples:

If your doctor who is a smoker says smoking is bad for you it is not necessarily true that smoking is good for you. Though smoking does give one a rich, resonant voice (evidence: most radio and screen actors of old). Your author does not smoke. Though if he did, it would (a) be none of your damn business, and (b) no proof that smoking is good for you.

If a celebrity, say Michael Moore, rails against private ownership of firearms yet surrounds himself with firearm-carrying private citizens (and might even himself occasionally sport one), this does not necessarily mean private ownership of firearms is sound. Though guns are obviously the only way to frighten off obtrusive revenooers and other varmints.

If a prominent personage, say Joe “Wakka Wakka” Biden, preaches that sacrifice is good yet gives annually to charity a sum smaller than the amount he spends on hair plugs and tooth whitening, this does not necessarily mean giving to charity is unwise. Because “Though I speak with the tongues of men and of angels, even as President of the Senate, and have not charity, I am become as sounding brass, or a tinkling cymbal.”

Besides our intellectual elite, kindergartners are also especially fond of this fallacy:

“You’re a poopy head!” shouted Tot One.

“You shouldn’t call people names! You’re a poopier head!” retorted Tot Two.

Tot Two is entirely right that one should not call people wounding, scurrilous names; though in calling Tot Two a poopy head Tot One has given some evidence that he (Tot One) is in fact himself a poopy head, because poopy heads use this kind of language. However, this is not proof that Tot Two is not a poopy head, too. Tot Two will instead have to produce independent evidence that he did not steal the cookies out of Tot One’s lunch box.

Your examples?


1Consisting so far of just this present one and this old one.

Thinking About Dying Or Just Saw Bad Art? Pop A Tylenol, Say Researchers

After viewing, take two Tylenol and call me in the morning

At last justice! Psychologists are finally admitting that surrealism is painful. Take that starchitects! In your face performance artists! Swallow bitter pills transgressive painters! Actually, swallow Tylenol, because new research says it’s a cure for the headaches one gets from exposure to MOMA.

Of course, it was already well known Tylenol cures headaches. But not headaches caused by bad art or thoughts of death.

So, for your consideration, the peer-reviewed article “The Common Pain of Surrealism and Death: Acetaminophen Reduces Compensatory Affirmation Following Meaning Threats” by Daniel Randles, Steven Heine and Nathan Santos in the journal Psychological Science.

For their first experiment, 120 college kids either swallowed a couple of Tylenol or 1000 mg of sugar pills, and were asked to jot a few words about either their Final Exits or “dental pain.” Why? Well, “Terror management theorists have argued that thoughts about death produce a unique type of anxiety”. Which is similar to the anxiety caused by surrealism, or by “viewing subliminally presented incongruous word pairs”. However, thinking about the dentist is just like thinking about the dentist.

The kids also filled out two questionnaires. First, the “PANAS,” as in “I have an itchy PANAS.” It asks how much (scale of 1-5) people felt like one of several words in the past week. Words like: distressed, excited, upset, strong. It creates two scores by adding up the positive and negative words. The scores are what make it science.

Second, the “How Much To Let The Prostitute Go,” or HMTLTPG (pronounced hymn-til-pig). Yes. The kids read an arrest report and suggested bail amounts from $0 to $999.

Bails for those in the dentist group were roughly $250-$350 for Tylenol takers and $230-$340 for sugar-pill users. In the think-about-death group they were about $275-$350 for Tylenolians and $375-$500 for sugar highers. Meaning that people fed sugar and asked to think about death are more likely to stick it to prostitutes than everybody else.

In their second attempt at producing something to write about, the researchers gathered another 200-some kids. But this time instead of asking them to think about handing in their dinner pails, they made half of them watch Donald Duck cartoons (“designed to ease participants into the task”) and then a clip from David Lynch’s short film Rabbits. After that, it was on to Snoopy cartoons.

This brings up the question why Bugs Bunny wasn’t used as the easer-intoer, because (as must be well known) moving from ducks to rabbits is more stressful than sticking with rabbits all along, especially when using Snoopy as a closer (dogs chase rabbits, see).

The other group, instead of imaging root canals, got to see four minutes of The Simpsons in between Daffy and Snoopy.

The PANAS reappeared, but no prostitutes. Instead, a rioter from Vancouver who was disappointed by the Canuck’s blowing their chance for Lord Stanley’s Cup was used as the bad guy. Kids were asked to indicate his punishment on a 0 to 200 scale, with 0 meaning the rioter shouldn’t be fined, 100 meaning he should be assessed the normal fine, and 200 meaning double the normal fine.

Fines for those in the “Simpsons” group were roughly 118-128 for Tylenol takers and 120-132 for sugar-pill users. In the David Lynch group they were about 120-132 for Tylenolians and 138-147 for sugar highers. Once again, this meant that people fed sugar and asked to think dismal thoughts were demanded greater pounds of flesh.

Since Psychological Science is a family publication, there was no word on the kids’ PANASes, the main measure and theoretical justification for the study. Actually, in neither study could they get any wee p-values out of the PANASes, so they kept mum on them. They called the lack of statistical significance a “disconnect.”

The researchers put the differences down to Tylenol and brain chemistry. The dorsal anterior cingulate cortex, you see. Tylenol molecules make their way up there (somehow) and switch off the punishment circuitry (or something). At least it wasn’t the amygdala this time.

Yet equally or even more plausible is the explanation that mixing sugar and depressing situations makes one unsociable. After all, the differences between Tylenol and sugar in the happy groups were negligible, and were of the same order as the Tylenoled-up folks in the harrowing-situation groups. If Tylenol was mingling among the synapses, why weren’t the bails and fines in the happy Tylenol groups smaller?

The surliest group in both trials were hopped up on sugar and made to feel bad. Bad mood plus high blood sugar equals Miss Gulch syndrome? The key result seems to be that defense attorneys ought to be careful about sodapop-drinking jurors.

Most plausible is that nothing is going on, and that even though the experiment was said to be blinded, researchers were over-excited in interpreting their findings. Wouldn’t be the first time. Won’t be the last.

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