William M. Briggs

Statistician to the Stars!

Author: Briggs (page 151 of 543)

Good Ways Of Speaking About Truth

Quid est veritas?” Pilate asked. Famously, his interlocutor did not answer, perhaps because Pilate didn’t give Him the chance. Then Pilate may have been (understandably) addled because the Answer was standing there.

Anyway, Aristotle, under less pressure, had a go at a definition (one that Pilate almost certainly would have known). He said, “To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true.”

That is lovely, understandable, and complete. It—the definition—is called realism, a pleasant and accurate label. Actually, it is called Aristotelian or ‘moderate’ realism to distinguish it between the hyper and over-literal realism of his pal, Plato. That difference makes no difference to us today.

There are other ideas of truth, all of them wrong, which follow two main roads: idealism (everything exists in your head, therefore your head doesn’t exist) and nominalism (what’s in your head doesn’t exist, therefore there is nobody there to think up and fret over nominalism). But we’ll pass these by today, too.

Yesterday, we agreed it was true that ‘all men are mortal’ and that ‘2 + 3 = 5′. It is the nature of men to die and for integers to behave undeviatingly according to certain rules. These are universal truths. There also exist contingent truths, which are propositions that accord with Aristotle’s definition conditionally. Unfortunately, there is only word in English for both, which means universal and contingent truths are often confused—which leads to hurt feelings.

To explain. Universal truths are those which begin with indisputable axioms and lead inexorably and necessarily to certain truths. For example, once we accept, without proof and based on no evidence save introspection, that “For all natural numbers x and y, if x = y, then y = x” and a couple of other similar sounding axioms, it is necessarily true that ‘2 + 3 = 5′. Because we don’t know why or how the axioms can be true—we just know that they are—we don’t know why or how ‘2 + 3 = 5′ is true, except in the weak sense that we say the equation is true because the axioms and intermediate theorems are. But we cannot say why it didn’t turn out that ‘2 + 3 = 7′ (don’t even think of arguing over the symbols).

Contingent truths are those propositions which follow from premises that might themselves not be universally true. For example, if we accept “All cats speak French & Whiskers is a cat” then it follows, i.e. it is contingently true, that “Whiskers speaks French”. Yet nobody but a cat lady would run into the street and claim Whiskers’s linguistic ability were universally true. That’s because the first premise is, according to other well known premises, false. Therefore, on that evidence, the conclusion, while contingently true, is universally false. True and false simultaneously, at least speaking loosely, and therefore something to fight over.

The “Laws” of science are all contingently true. Any one or even all of these Laws may be universally true, but we don’t (possibly yet) know it. If they were universally true, then they would all be in the same epistemic boat as mathematics and logic. We would start with introspection, decide what follows from beliefs we just know are true, and then build theorem upon theorem until we reached the Law of Gravity.

That’s almost how it works, but not quite. Inside the Law of Gravity are several fudge factors, “constants” of the universe which are derived via observation, i.e. which are not deduced from first principles. And (we read) there are one or two other dicey premises which are not entirely convincing. The Law of Gravity, which nobody doubts in practice, cannot be said to be universally true (no pun; nay, not even from me), even though it contingently is.

Because the Laws of science are only, or at least, contingently true the premises which accompany them may be argued over. It is not unscientific to do so. It is prudent. When physicists argue over gravitation, it is clear to everybody that the conclusion is accepted because it is observed to hold in most places, and so discussion centers on the premises which would make the Law hold in all places.

The situation is different in climate science, for example, where the conclusion itself is in doubt (rampant global warming will kill half the population by 2009—oops, I meant 2017), and where the premises are so beloved that they are Not To Be Questioned. The (suitably modified to keep current) doom conclusion is contingently true, but that does not make it truly true, i.e. universally true. Failing to understand that distinction is what leads the weak to shout “Denier!”


Bad Ways Of Speaking About Truth

Easy

It is true that all men are mortal. It is also true that 2 + 3 = 5. Yet it is not “true” that all men are mortal, nor is it “true” that 2 + 3 = 5.

True means true. We learn from David Stove (and by experience) that by supplying scare-quotes “true” means “not true, but believed by so-and-so to be true”; which is to say, “true” means false, or, at best, unknown. Waving your fingers around truth is like becoming the assassin who puts his arm around his victim and calls him friend—as he knifes him in the back.

Yet scare-quotes are not the only, or even the best, way to sabotage logical expressions.

A slier method is to embed a truth conditionally. This example comes from Michael Voris (drop the S.T.B. Mikey, and learn to crack a smile!): “Jesus has risen from the dead, we Catholics believe.” (Voris recognized the mistake.)

This way of phrasing gives comfort to those who don’t want to acknowledge the truth—it is only the curious “belief” of some religious sect—while also releasing the teller from his duty of proclaiming a truth. So much less confrontational, you see.

Saying a truth conditionally is to kill with slow poison, not violence. “P is true, so-and-so believes”, “I believe P”, and “My professor said that P” no more imply P is true than does saying “P is ‘true’.” In other words, it is not an argument for P to say “I believe P”. It is the mere announcement of your mental state at some particular time. Since it is not an argument, there is nothing to refute, for there is no definitive way for me to know your mental state (no, not even with an electric phrenology device, i.e. an fMRI). And then all history suggests there is no point in arguing over somebody beliefs.

Update The main and obvious disadvantage of speaking this way is that it sets you back on your heels, puts you on the defensive immediately, when truth is always an offensive weapon.

Not easy

So much for the easy stuff. Let’s now talk about scientists and academic philosophers and their love of talking about conditional truths (i.e. theories) as if conditional truths were truths Stove (from his Rationality of Induction, p. 117), where he gives us three arguments:

(a) “Hume is a father, therefore Hume is a male parent”,

(b) “All male fathers are parents & Hume is a father, therefore Hume is a male parent”,

(c) “If Hume is a male parent then Hume is a father & Hume is a father, therefore Hume is a male parent”.

The first, (a), is a valid argument, which is to say that its conclusions follows from the accepted premise. Since the conclusion of (a) follows from its premise, we can augment that premise, which is why (b) and (c) are also valid (rule of logic: “if p entails q, then p-and-r entails q, for any r“).

But (b) is an example of the formal fallacy ‘undistributed middle term,’ and (c) is an example of the formal fallacy ‘affirming the consequent’ (look them up). Even so, (b) and (c) are still valid. This means that something is wrong with the formality, i.e. the theory, which declares them invalid. Yet philosophers, like scientists, are loathe to abandon a beautiful theory. This creates a severe difficulty, and even psychic pain, for those who cherish the formality (theory):

[T]he formal logician cannot call (a), (b), or (c) valid, consistently with his professional creed: hence his disapproval of them. But he dares not call them invalid either: hence his unease.

A situation so painful as this one is bound to produce distress signals, even if only half-conscious ones. Some of the commonest of these signals sound as follows. ‘Argument (c) is invalid in propositional logic‘; (b) is not valid in predicate calculus‘; ‘(a) is neither quantificationally valid nor truth-functionally valid.’ You can easily see how suitable such phraseology is to the distressed logician’s situation. A phrase like ‘invalid in propositional logic’, for example, by including the word ‘invalid’, has the effect of setting the desired tone, the tone of disapproval; while at the same time it is admirably non-committal, because after all—as the formal logician himself will hasten to assure you—‘invalid in propositional logic’ no more entails ‘invalid’, than (say) ‘suspected murderer’ entails ‘murderer.’ [p. 122]

The gist: “Arguments are not ‘in’ predicate logic, or ‘in’ any other artefact that logicians may happen to make. Still less is their invalidity or validity ‘in’ anything at all, except the arguments themselves.”

In other words, all arguments have to be evaluated individually.


Dinner With Atheists: A Mini-Play In One Act

SCENE: The monthly meeting of the Madison Atheists Evangelization Society at the I-12 Marriot Courtyard’s Badger Room, a rambunctious group sitting at a table, long side to the audience, like at a celebrity roast. The food has been eaten and cleared away. The CHAIRMAN sits in the middle, the SECRETARY is to his right, the TREASURER to his left. Others fill in.

PLAYERS: CHAIRMAN, SECRETARY, TREASURER, nine other male members, numbered from stage left to right (M1-M9, actors should use their own first names), and LATE GUY (oldest actor) who shows up near the end. The character “ALL” is where the cast should ad lib in the spirit indicated.

——————————————————-

ACT ONLY

Curtain

ALL: murmuring and general pre-meeting chatter; words not loud enough to be distinguished by audience.

SECRETARY: It’s time.

CHAIRMAN: Uh huh. Okay, everybody. Let’s settle in. Before we get started—

M2: —The opening prayer!

ALL: laughter; “God” bless us; calls saying how smart, clever M2 is.

CHAIRMAN: Which “god” should we pray to?

ALL: Thor, Zeus, Gaia, Obama, etc.; laughter; calls saying how smart, clever each other are.

CHAIRMAN: [To calm the group] Okay, let’s try to behave rationally.

M7: I think, therefore I disbelieve!

ALL: laughter; calls saying how smart, clever M7 is.

CHAIRMAN: I want to introduce one of our new members. M-9 [indicates M9, who waves] who used to be part of the Boston group. M9 is working on his Masters in…what was it?

M9: Science eduction.

ALL: applause; hi M9; science rules!; calls saying how smart, clever M9 is.

M1: That’s what’s needed! More science!

ALL: here-heres; calls saying how smart, clever M1 & M9 are.

SECRETARY: We should get going.

CHAIRMAN: Yeah, you’re right. But we can’t praise science too much.

M3: Religious people deny science! They’re deniers!

ALL: religious people are idiots, foolish, irrational; calls saying how smart, clever M3 is.

M6: Religion is nothing but organized child abuse!

ALL: religious people are idiots, irrational, foolish; calls saying how smart, clever M6 is.

M8: [Standing] It sickens me that in this supposedly free country, people are able to teach their children lies and myths as if they were reality.

ALL: calls saying how smart, brave M8 is.

M4: It’s because living by a myth is more comforting than surrendering to reality. They hate reality.

ALL: claps; calls saying how smart, brave M4 is.

M5: They don’t understand how beautiful science and reality are!

ALL: calls saying how smart, clever M5 is.

M2: [Quietly, after a lull] Cancer’s maybe not so pretty.

M7: [Angrily] That’s not the point! It’s that religious people don’t believe evolution created cancer. They’re so ignorant they don’t even know that evolution makes them religious!

ALL: God gene!; sage nods; murmurs of agreement, calls saying how intelligent M7 is.

SECRETARY: [To CHAIRMAN] Maybe we can get started?

CHAIRMAN: Yeah. But he’s right. I can’t believe how willfully stupid religious people are.

ALL: they’re fools, morons, etc.; calls saying how smart CHAIRMAN is.

CHAIRMAN: Sadly true. But let’s do something. TREASURER, how much money do we have in the fund?

M1: [Standing, interrupting] Flying spaghetti monster!

ALL: general uproar, hooting, hollering, joy; calls saying how smart, witty, clever M1 is.

TREASURER: [Who stood during merriment, speaking over crowd; holds paper] We’re actually in the hole. People haven’t been keeping up their promised donations. Somebody’s gotta pay for this meal. I’m not getting stuck again—

M3: [Standing] —We should believe in ourselves, not God!

M6: I believe! I can see you!

ALL: laughter; calls saying how smart, clever M3 and M6 are.

M4: We should really be talking about how intolerant religious people are.

M8: Yeah, they’re always telling us what to do! Religious views don’t belong in a tolerant society.

M5: They oughta be stopped. Like in Canada. We should have a law passed that nobody is allowed to foist their views on other people who don’t want them! Especially children!

ALL: applause; religious people are dopes, etc.; calls saying how smart, clever M4, M5 and M8 are.

[LATE GUY enters stage right, quietly vies for CHAIRMAN’s attention.]

CHAIRMAN: Ah, LATE GUY! You finally made it. We worried you joined a cult!

ALL: hilarity; all religions are cults, etc.; calls saying how smart, clever CHAIRMAN is.

LATE GUY: [Over laughter, trying unsuccessfully to whisper] Uh, yeah, sorry. Um, I was actually never coming. My mom found out about the group and she made me quit. I only showed up because I promised M8 a ride home.

ALL: giggles, some suppressed, some open; M8’s mom not as smart, clever as us, etc.

CHAIRMAN: Oh, that’s right. Your mom still goes to church. Don’t worry. Here. Give her these pamphlets [collects from SECRETARY] which will prove to her how irrationally stupid her faith is. She’ll come around.

ALL: lighter giggles; whispers how all religions irrationally stupid, etc.

LATE GUY: [Trying to disappear] Oh. The hotel guy asked me to tell you you’re time’s up. They need the room for the Madison Young Activists Yoga Alliance. [Author’s note: may be shortened to ‘YaYa.’]

CHAIRMAN: Okay, everybody. That’s it. Next month we build on this meeting’s success and really show why atheism’s an intellectually superior belief system.

ALL: happy applause; calls saying how smart, brave CHAIRMAN and everybody is.

SECRETARY: [Standing] Just a reminder that next month’s meeting is joint with the Unitarian Universalists. They’re giving us a talk on ‘Seeking the Spiritual Path to Atheism.’

CHAIRMAN: Should be good. They told me they got some smart people there.

ALL: people stand to go; self-satisfied jocularity; high fives, chest bumps, etc.

Curtain


Regression To The Mean (And Performance Curses) Simply Explained

I complete this foursome

I complete this foursome

I’ve just read about The Second Term Curse which supposedly besets (of course) second-term presidents.

There is also the infamous Sports Illustrated Curse, which is said to befall athletes soon after they appear on the cover of that magazine. Other examples abound.

Roughly, ceteris paribus, on average, all other things equal, these “curses” more or less work like this:

Everything that isn’t a stick in the mud, or the product of a bureaucracy (or a bureaucrat), or isn’t otherwise ossified exhibits, for a given behavior, a range. Batters coming to the plate have hot and cold streaks. Actors have scintillating and dull performances. Golfers hit over and under par. Presidents please then displease the citizenry.

Now most of the time performance, for this or that person, is middling. Professional golfers don’t shoot birdies constantly and consistently, nor do they hit boogies: they hit par—which is why they call it par. For me, I don’t shoot two or three over par each time, nor do I hit nine or ten; my usual tally hovers around five or six over. I mean per hole.

But suppose I were invited to join this summer’s Internet Philosophers Open, held each July in beautiful downtown Gaylord, Michigan. Further suppose that I, strengthened by the love and support of my dear readers (and a sufficient dose of the water of life), shoot par and therefore win.

Instant celebrity would result. My picture and bio would appear on tens of blogs, I wouldn’t have to pick up the tab on the nineteenth, and I’d probably even get an interview request from the local paper. The Mayor would shake my hand. Discussions about t-shirts imprinted with my image would be had. I’d be the talk of the interwebs for hours.

This publicity would not go unnoticed and thus I’d surely be asked to participate in the Fall Bloggers Classic, which is October in Cleveland (weather permitting). Once there, it’s much more likely I’d “revert” to my average performance and finish +297 ( = 18 * 3 * 5.5 ).

Think of the headlines! “Shame and Ignominy on Full Display”, “Briggs Muffs It”, “Tournament Organizing Committee Under Investigation”, etc., etc. The psychic pain of my fall would be so intense I’d probably take to listening to NPR—and imagining that I enjoyed it.

Theories by the dozen would be propounded about why, after showing so much promise, I failed so badly. Some would place the blame on atmospheric conditions. Others would compare the quality of Polish sausages between the two locales. Many would pore over my writings between the two tournaments searching for clues about my mental state.

Some, none, or even all (in part) of these theories might be right—something caused me crumble—but the smart money before the Fall Classic would have bet on a dismal performance, simply because that was the best evidence and the most likely outcome.

But if people don’t recognize this, and only remember the see-sawing of performances between the two tournaments, they might put the changes down to a curse.

This all works in reverse, too. If you witness an atypically dismal performance, chances are good the next will be better. They have “regressed” (in reverse) to their “mean.” Or if you see somebody displaying their everyday ability, that’s most likely how you’ll see them the next time.

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