William M. Briggs

Statistician to the Stars!

On The Truth And Knowing Why

aard

Guy walks up to you in the street and says, “If f is some continuous function on the closed interval a to b, and if you take the definite integral of that function from a to x, then the first derivative of that definite integral is the function f(x).”

You say, “Sounds spooky to me. How do you know it’s true?”

“It just is, buddy. I don’t know why it’s true, but it is.”

And he’s right. Not just that his statement is true, which it is, but that he doesn’t have to provide you with an explanation why it’s true. That is, his ignorance of the why does not in any way change the truth of the statement.

Now whether this guy, lacking any convincing tale or other corroborative evidence, succeeds in transmitting this truth is another question. But it just doesn’t matter how he came by his truth: whether he proved it from first principles, whether he heard it as a rumor, whether it was revealed to him in a dream, whether he actually thought it was false but was pretending it was true as a little joke, or whether he just insists it is true.

You might be tempted to accept this because you know the example (the readers of this blog are nothing if not mathematically literate); which is to say, you know how to prove the proposition from first principles. But that would be a mistake. The majority of folks who hear propositions like the above will only be able to judge them on the veracity of the deliverer and will not be able to gauge it in any other way.

Think about it. People are asked to believe that (say) neutrinos have mass, and given the source of the pronouncements on this weighty subject, they accept it. Of course, given the lives of most people, this information, like most highly technical and scientific information, is of no use and will not cause anybody to act differently than if they hadn’t believed the proposition.

The weakest argument in favor of something is, as all know, the argument from authority: though despite what you might have heard, it is not a formal fallacy (and most things you believe are probably based on it!). And anyway, even if it were, if any authority were to say, “X is true because I say so”, the statement is no proof of X’s falsity. X can be true even if every argument you know which asserts it is fallacious.

Occasionally we get lucky and are able, from first principles, to formally prove a proposition asserted by an authority false. In the public arena, this is a daily and even trivial occurrence (listen to NPR for dozens of examples of easily disproved propositions). But this is not so in more advanced fields.

You have to work hard, and maybe for years (and maybe never), to identify formal fallacies in the work of many philosophers, and even when you do, you haven’t proven the contentions of these folks false. Proving anything false still requires formal proof. This proof must begin with a list of axioms all agree upon, and lead through successive propositions using rules of argument also believed by all.

In absence of this disproof, it is always the case that the contentions of anybody might be true, even if all that it is offered is an argument from authority (or revelation).

So if somebody on authority contends that an infinite number of turtles supports the earth, you can disbelieve it, but in order to argue its falsity you’re going to need proof. Sneering isn’t proof. Neither is laughter or haughtiness or insults. Nor are other counter-arguments from authority, i.e. “Most philosophers now believe it is aardvarks and not turtles shouldering the burden.”

That one is easy to disprove (an observation will do it). But other contentions are not. And some might even be true, even if you don’t want them to be.

27 Comments

  1. Matt, are you talking about the distinction between “necessary” truths and “contingent” truths? In counterfactual worlds, necessary truths must hold, but contingent truths might not. AGW is a contingent truth and so requires evidence (which has not been forthcoming). And the existence of God (not necessarily the Christian God)? I’m sure the commentors will debate about whether this is a necessary or contingent truth.

  2. Ye Olde Statisician

    September 11, 2014 at 9:02 am

    judge them on the voracity of the deliverer

    Those deliverers sure are hungry.

  3. judge them on the voracity of the deliverer

    makes perfect sense to me, I would judge one who delivers a ‘truth’ and claims a right to great rewards based upon their discovering said ‘truth’ is more likely to presenting a false ‘truth’ than one who humbly presents a ‘truth’ and disclaims any benefit from the discovery is more likely to be presenting a true ‘truth’.

    Isn’t there a semi-Latin phrase for this, “in typo veritas?”

  4. @YOS,

    Everyone knows that Mr Briggs keyboard is infested with gremlins in the employ of his enemies. 🙂

  5. I’ve always been under the belief that it was Atlas

    (except that brief time Hercules took it)

    Later I learned it was elephants standing on a sea turtle

    But I will bow to the master

  6. MattS

    Mr. Briggs has anomalies?

  7. John B, as the elderly lady said to the cosmologist, “it’s turtles all the way down!”

  8. In the public arena, … (listen to NPR for dozens of examples of easily disproved propositions).

    Can you prove the above claim? I don’t believe you unless you can show me those propositions. Yes, show me those dozens of such easily disproved propositions. And DISPROVE them!

    I have a couple of fun examples from Fox News though. I got them from a junior-looking speaker in a conference. The session organizer, a senior researcher, told him on the spot that his political comments were inappropriate for the professional conference.
    http://www.ritholtz.com/blog/wp-content/uploads/2009/11/best-pie-chart-ever.jpeg
    http://static.businessinsider.com/image/534148976da8116f2975afc1-1200/image.jpg

  9. Sander van der Wal

    September 11, 2014 at 12:18 pm

    If he doesn’t provide you with a proper explanation, a proof, then you are under no obligation to believe him. After all, people are well-known to make lots of false statements, by mistake or deliberately.

  10. Bob Kurland –
    When it comes to cosmology or physics,
    I’m not much further than “a warm summer evening in ancient Greece”.

    I do, however, remember Yertle the Turtle

  11. “So if somebody on authority contends that an infinite number of turtles supports the earth, you can disbelieve it, but in order to argue its falsity you’re going to need proof. ”

    Err… No.
    We are playing with language again.
    They can ‘contend’ all they want – it’s not up to me to deliver proof.
    I don’t feel any duty to ‘argue its falsity’.

    I’m still waiting (15 years so far) for some climate scientist to give me some ‘proof’ of the amount of forcing triggered by CO2. Until that comes why should I do anything?

    If someone ‘contends’ that the moon is made of green cheese. so what? Gimme the evidence… Let’s not even get into Popperist falsification!

  12. Here’s the background for “turtles all the way down”…there’s even a country song on YouTube, but I can’t understand the lyrics..http://en.wikipedia.org/wiki/Turtles_all_the_way_down

  13. Ye Olde Statisician

    September 11, 2014 at 3:26 pm

    But “voracious” is the best typo of all except for one recently received from a friend who told me his son at U. Penn had worked on the device used to detect the Higgs Bosom.

  14. Peter: You may feel no need to argue the falsity, but if you did ever want to do so, you would need proof the theory is wrong. You of course have the right to simply ignore those things that don’t provide sufficient proof for you to believe, but you are just ignoring them or waiting on evidence. It’s not really the same thing as saying the theory is false. I can see where it’s really a very easy thing—no impetus on your part to do anything. Unfortunately, some theories, such as global warming, do have a huge impact on what happens in the world and simply waiting for proof may not be enough, unless you don’t care what happens with it.

  15. Peter,

    I’m still waiting (15 years so far) for some climate scientist to give me some ‘proof’ of the amount of forcing triggered by CO2.

    I think I shall never tire of recalling this post: http://wmbriggs.com/blog/?p=13214 Proof is for metaphysics, not physics, for math and logic. Item 1, no less.

    Climatologists are unlikely to drop even mere evidence in your lap … some searching and reading is required. You could start with this paper for an empirical basis: http://tinyurl.com/bs8rloa [.pdf file] A negative-going brightness temperature difference is observed on the edge of the CO2 v2 band … in accord with the known increase in atmospheric CO2 concentrations between 1970 and 1997.

    Coming up with an actual forcing amount is not a back-of-napkin proposition. For that, it’s models all the way down. Those models are evaluated against observations: http://rtweb.aer.com/docs/alvarado2013.pdf

    The amount of forcing attributable to CO2 works out to ~32 W/m^2 at present levels, which is ~20% of the net greenhouse effect, or just under 7C in terms of temperature. While interesting numbers, they’re not terribly useful when running climate scenarios as explained in this paper: http://tinyurl.com/q2vdn56 [.pdf file].

  16. Sheri,

    You may feel no need to argue the falsity, but if you did ever want to do so, you would need proof the theory is wrong.

    I agree, but original research is expensive. I imagine (this is strictly a WAG) the money spent on refuting AGW is less than the expected cost of mitigation by at least an order of magnitude. Plus, spreading FUD is far cheaper, and thus far has proven rather successful. It doesn’t hurt that the mitigation strategies are economically unpalatable and/or arguably ineffectual, especially when presented to the international community. While the 1st world is all but politically deadlocked on the issue, the 3rd world is more than happy to add its collective middle finger to the mix.

    That latter contingent makes a good point: we got ours, who are we to tell them they can’t have theirs? Terribly short-sided, of course … Africa is ill-suited for graceful adaptation to drought.

  17. Proof may not exist in Science but falsification does. So, for a scientific claim, it is necessary to find a disproof and this is often done by showing discrepancies such as missed predictions. The recent discrepancy between temperature records and the claimed prediction they would rise with rising CO2 concentration shows the current theory is far from complete, in fact, outright wrong. Yet we still have those who toss around things like “AGW” as if it were “proven” while simultaneously remarking on the lack of proof on science.

    If it’s not a scientific claim, Peter is quite correct.

  18. DAV, I agree that AGW has been falsified. So it is “a contingent truth” that has turned out to be a counterfactual.

  19. Bob Kurland

    Thanks, I had looked up the story … I had subtle references to Terry Pratchett’s Discworld series as well as the Big Bang Theory.

    Speaking of the Big Bang Theory, they introduced a ‘game’ called “Counter Factuals” where they ask how the world would change given a current truth no longer applied.

    (Dr. Seuss’s Yertle the Turtle could be described as a modern day secularized version of “The Tower of Babel” story.)

  20. DAV: I read your comment after Brandon’s on “proof”. I agree. I would add my two cents worth:

    In actuality, even math and logic are not “proven” but rather “defined”. We created both and we can redefine them whenever we want. Newton created a whole new math. What it comes down to is “there is no proof in anything, so we need to throw that word out of the discussion entirely”. Henceforth, “proof” is to be replaced with “confidence interval” or “probability”, whichever is appropriate. As DAV noted, falsification can also be used when talking about whether a theory is valid.

    The current AGW theory, if you go with only the “CO2 adds warming” does not yet appear to be falsified. Few disagree with the idea that CO2 is involved in warming the planet and humans do add CO2. However, we cannot prove how this affects climate and whether or not “our” CO2 is a driving force or a minor player. If we say that what we believe to be the earth’s energy balance is still out of balance to the warm side, I’m not sure that has been falsified. How it got that way is still a matter of dispute and whether this is in any way different from the past probably can never be shown without centuries of actual raw data.

  21. Sheri,

    If we say that what we believe to be the earth’s energy balance is still out of balance to the warm side, I’m not sure that has been falsified. How it got that way is still a matter of dispute and whether this is in any way different from the past probably can never be shown without centuries of actual raw data.

    Wanting certainty tantamount to proof is understandable. But even if we had it, do you really think a 50-100 year planning horizon in a matter of public policy on this scale would find any less opposition? I flat out don’t. Not at the national level, and definitely not planet-wide. It’s as unheard of as 400 ppmv CO2 … unless you go back a few million years, give or take.

  22. i don’t know if certainty tantamount to proof would motivate people or not. I do know that scare tactics that cannot be backed up are not effective. I don’t really think humans are capable of planning 100 years in the future, not because they don’t care, but because things change so much. My grandfather died at age 90. In his lifetime, he crossed the ocean on a boat from Denmark. He went from horses to cars. He flew back to Denmark in the early 60’s. He saw two world wars, an atomic bomb, landing on the moon, television and movies, space shuttles, etc. How in the world (and I mean that literally) could humans ever plan 50 or 100 years ahead? It’s just not possible. We might manage to save for retirement. Other than that, I don’t see that it’s possible.

  23. Sheri,

    How in the world (and I mean that literally) could humans ever plan 50 or 100 years ahead?

    The argument for keeping temperature (and thence climate) within current bounds is to reduce the need for such nearly impossible long-range planning. The argument against is that we’ve always been able to adapt to changes. Both arguments have merit in my view, but the skeptic in me wonders about ulterior motives.

  24. The argument for keeping temperature and climate within current bounds rests on the idea that we as human beings control the climate. This runs counter to the belief that we adapt because that belief includes the idea that we do not control the climate. I guess until we get Star Trek’s weather net and absolutely control the climate, there’s little to be agreed upon in all of this. Currently, we are looking at models that are 50 and 100 years out and no way to verify if warming or cooling will occur in those years. I’m not seeing planning as possible. I guess we just deal with it like we always have. Maybe we just can’t be as much in control as we imagine we can.

  25. Sheri,

    The argument for keeping temperature and climate within current bounds rests on the idea that we as human beings control the climate.

    That we affect climate, which is an important distinction that I did not make clear in my previous comment.

    This runs counter to the belief that we adapt because that belief includes the idea that we do not control the climate.

    I don’t see that they’re at all mutually exclusive. As I said previously, both arguments have their merits. They’re also both loaded with political agendas which arguably are not in the best interests — and certainly not wishes — of all.

    Currently, we are looking at models that are 50 and 100 years out and no way to verify if warming or cooling will occur in those years.

    That’s the nature of long-term predictions. There’s some asteroid out there with our name on it … might be a million years off, might be 50 or 100. We might have 10 years warning to prepare for it, maybe less. Those things are sneaky.

    There are far less exotic unpredictables at play here. They are legion, and they’re being feverishly worked on if you’ll allow me a pun.

    I’m not seeing planning as possible.

    And now we’ve gone full circle. The argument is that forward planning is necessary if … and that is a big if … we find that we actually can keep climate within present bounds. Which I personally don’t think is possible; it’s not economically palatable, and economics generally wins in the near term. I see it less as a matter of knowing how, much more a matter of just not being able to execute.

    Adapt it is, methinks. And I’m not the only one … our friend Betts says the focus on modeling these days is on nearer term planning horizons … on the order of a decade. Reliably modeling ENSO et al. 5 or so years in advance would be a big win.

  26. Errata: … less forward planning is necessary if …

  27. Brandon: We are pretty much in agreement. My major disagreement with climate change is the highly improbable notion that we could ever predict climate change accurately, no matter what the causes. Yours seems to be that economically, adapt may be more palatable. In the end, adapt wins simply because there realistically is no way to get billions of humans who have extremely divergent views on life (everything from monks to terrorists to terrorist monks!) and politics to pull together on anything—climate, asteroids, anything. I have always believed that had climate science not been usurped by radical politicians, but rather people had been encouraged to research new energy sources and save energy, it would have had much more effect than a bunch of people jetting around the globe once or twice a year using more fuel than a small town, telling people to conserve or we’re all doomed. Radical agenas only work with force.

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