William M. Briggs

Statistician to the Stars!

Page 2 of 419

On The Truth And Knowing Why


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.

More On Randomness

Anything could be at the end of this lane!

Anything could be at the end of this lane!

I took this picture yesterday (using my mom’s phone: mine can’t offload photos) at the start of the cul de sac, at the bottom of which lies the first job I ever had: washing dishes in a nursing home (in which my uncle now resides).

Who could have guessed I would have moved from there to where I am now?

Certainly not one of my old teachers, who was shocked when told by my parents of my career (such as it is). The teacher was cornered in the back of a grocery store. This same teacher would have taken in stride news that I was just coming up for parole.

This highlights one of the shades of meaning of random. It’s when an event was not just unpredictable, but that it happened almost against the evidence. “That was random,” we say.

This usage acknowledges random is a measure of information, which at least removes some of the mysticism the words has in scientific and mathematical contexts. But maybe not all. We sometimes almost have the idea Nature is working against our desires, though Her actions in this regard are weak.

Mysticism? Did you know that in classic statistical formula if some numbers aren’t imbued—nobody knows how—with randomness, the formula won’t work?

Oh, the formulas will still spit out answers, of course, but you won’t be allowed to use those answers. It’s kind of like sitting down to a feast and discovering the witch doctor didn’t give his prior blessing to the animals cooked, and therefore nobody is allowed to eat.

It’s not just frequentists who believe in magic, but most Bayesians, too. Whenever you hear somebody say, “X is randomly distributed normally” (or some other thing), you have heard an incantation. There is nothing in the world that makes a number “randomly normal” (or whatever). It’s only that our understanding might be quantified by a normal (or whatever).

How X knows it’s supposed to be normal (or whatever) is never specified either. It’s here that the Deadly Sin of Reification mixes with the mysticism of randomness. The formulas become realer than reality, and it’s the power of mysticism which does the deed. But again, nobody knows how. It’s a question which is never asked.

When I’m done with this mini-vacation, I’ll set out more specifically all the shades of meaning of random.

Up North At The Lake, With No Phone, Computer, TV

Another day at the office.

Chris doesn’t have a computer. And he doesn’t want one. He’s my age and works at the Dobleski Marina as a mechanic. He has a house, family, couple of cars, and of course lives near the lake.

The shop has a few dozen men, and one day the boss switched to a new company to handle everybody’s benefits. This required the men to go on line with their “pass codes” and enter information. One by one the men came into the office to do so.

The first started pecking around with one finger, asking for help with the mouse. The boss asked, “What’s the matter. Don’t you know how to use a computer?”

“Nope. Don’t have one.”

Same thing with Chris—and with about a third of the men. No computer, no internet access at home. Why? They see no need for it. Chris said, “It’s a waste of time.” Costs too much, too.

“My boss said, ‘Why don’t you have the internet. It’s great!’ and he proceeded to show me some thing that took an hour to get it to work. Why do I need that?”

Chris also doesn’t have cable television. He had it once, but the company started raising the rates, raised them some more, and then raised them again. Chris called it quits. Said TV is a waste of time anyway. But to please his daughter he bought an antenna. He now gets five channels, and sometimes six if the weather is just right.

You probably already know, but Chris doesn’t have a smart phone, either. And he isn’t alone. Many people up here just don’t see the need.

Now the lake Chris lives on is a big one and the town is one with a lot of rich folks from down south who have summer mansions, in which they spend a week or four a year. These people aren’t any different than anybody else and like to play, but having orders of magnitude more money than most, their toys are shinier—and most of them float.

It’s Chris’s job to fix these toys. Last week, he had to fetch a 59-foot beauty from point A and drive it to point B, about thirty-some miles away. He drove the work boat over to get it (and towed it back), and took along Mitch who spends most of his days inside. Mitch is a detailer.

Now the person who owned that big boat also drives from A to B every now and then. That trip, a popular route, is the reason he bought the boat, and is why he pays for its docking and maintenance. Since the maintenance is expert, it isn’t cheap. Would you know how to fix the motor of one of these things?

The men at the marina are outside most of the summer, and even into the fall and part of the winter. They try to get the inside work done before January, because the building which houses the boats isn’t heated. And boy can it get cold up here, with plenty of snow.

Another fellow bought a fancy new boat and thought something was funny with it, so he called the marina to have somebody take a look at it. Chris was dispatched. Back out onto the lake, the sun shining, the wind just so. Tigers on the radio.

The man was waiting. He said, “My boat smells like water.”

Chris knew enough not to laugh and tried to get the man to explain more carefully what he meant. Well, he meant what he said. When he went below decks, he thought he smelled water.

Now it was costing plenty for Chris to come down and inspect the boat, and to give the man the feeling that he was getting something for his money, Chris told him that boats tend to smell that way, but if he liked he could run his dehumidifier once in a while.

This advice greatly cheered the man, who paid the hefty fee, and Chris got back into the work boat heading north. The sun was still shining.

Chris is gratefully these rich folk want to play in his back yard. If they weren’t there, the 59-foot boats wouldn’t be there, a source of beauty would go missing, and far fewer people up north could make a living. And although Yours Truly didn’t talk with any, it’s a good bet these rich folks are glad people like Chris are around, too.

The names have all been changed, but the story hasn’t.

Comprehensive List Of Catholic Dogmas Refuted By Science













































In other light reading, see also the leaflet: Famous Jewish Sports Legends.

Summary Against Modern Thought: God Is Not A Body. Update

This may be proved in three ways. The first...

This may be proved in three ways. The first…

See the first post in this series for an explanation and guide of our tour of Summa Contra Gentiles. All posts are under the category SAMT.

Previous post.

Update I haven’t any idea how I did it, but I somehow turned off comments on this post. They are now restored.

The conception of what God is went downhill after Aquinas. And, dear atheist reader, shouldn’t you know what it is you claim to reject? New Atheists in particular have been shockingly Would it surprise you to learn that the Church rejects the same gods, or same weakened conception of God, you reject? This chapter, which is broken over multiple posts, shows that God is not a physical body, that God is not a creature.

Chapter 20: That God is not a body

1 FROM the foregoing we are also able to prove that God is not a body.

2 For since every body is a continuous substance, it is composite and has parts. Now God is not composite, as we have shown.[1] Therefore He is not a body.

3 Further. Every quantitative substance is somehow in potentiality: for that which is continuous is potentially divisible to infinity; and number can be infinitely augmented.i Now every body is a quantitative substance. Therefore every body is in potentiality. But God is not in potentiality, but is pure act, as shown above.[2]ii Therefore God is not a body.

4 Again. If God were a body, He would needs be a physical body, for a mathematical body does not exist by itself, as the Philosopher proves,[3] since dimensions are accidents.iii Now He is not a physical body; for He is immovable, as we have proved,[4] and every physical body is movable. Therefore God is not a body.

5 Moreover. Every body is finite, which is proved in regard both to spherical and to rectilinear bodies in 1 Coeli et Mundi.[5] Now we are able by our intellect and imagination to soar above any finite body. Wherefore, if God were a body, our intellect and imagination would be able to think of something greater than God: and thus God would not exceed our intellect: which is inadmissible. Therefore He is not a body.iv

6 Furthermore. Intellective knowledge is more certain than sensitive. Now among natural things we find some that are objects of sense: therefore there are also some that are objects of intellect. But the order of powers is according to the order of objects, in the same way as their distinction. Therefore above all sensible objects there is an intelligible object existing in natural things. But every body that exists among things is sensible. Therefore above all bodies it is possible to find something more excellent. Wherefore if God were a body, He would not be the first and supreme being.v

7 Again. A living thing is more excellent than any body devoid of life. Now the life of a living body is more excellent than that body, since thereby it excels all other bodies. Therefore that which is excelled by nothing, is not a body. But such is God. Therefore He is not a body.vi

8 Moreover. We find the philosophers proving the same conclusion by arguments[6] based on the eternity of movement, as follows. In all everlasting movement the first mover must needs not be moved, neither per se nor accidentally, as we have proved above.[7] Now the body of the heavens is moved in a circle with an everlasting movement. Therefore its first mover is not moved, neither per se nor accidentally. Now no body causes local movement unless itself be moved, because moved and mover must be simultaneous; and thus the body that causes movement must be itself moved, in order to be simultaneous with the body that is moved. Moreover no power in a body causes movement except it be moved accidentally; since, when the body is moved, the power of that body is moved accidentally. Therefore the first mover of the heavens is neither a body nor a power residing in a body. Now that to which the movement of the heavens is ultimately reduced as to the first immovable mover, is God. Therefore God is not a body.vii


iWho knew St Thomas was familiar with analysis! (The first argument above I left uncommented, it being obviously sound.)

iiDon’t forget to review what these terms mean, particularly act and potential. Don’t assume you know how St Thomas and Aristotle meant them.

iiiFrom The Philosopher, lovely as always (yes, but was this peer-reviewed?):

A question connected with these is whether numbers and bodies and planes and points are substances of a kind, or not. If they are not, it baffles us to say what being is and what the substances of things are. For modifications and movements and relations and dispositions and ratios do not seem to indicate the substance of anything; for all are predicated of a subject, and none is a ‘this’…

But if this is admitted, that lines and points are substance more than bodies, but we do not see to what sort of bodies these could belong (for they cannot be in perceptible bodies), there can be no substance. Further, these are all evidently divisions of body, one in breadth, another in depth, another in length…

iv(Heaven and Earth.) St Anselm, anyone? Don’t let’s forget that Contra Gentiles came before Summa Theologica in Aquina’s thinking. See 2c here.

vAs a sound argument, this bullet is shaky, assuming what it seeks to prove, it seems to me, at the end, in much the same way as the ontological argument fails. But, the first premise is certainly true: “Intellective knowledge is more certain than sensitive.” One can mistake cold for hot, but not that you know. This is why many also say mathematical knowledge is supreme.

viThis one is too telegraphic, maybe. We have “Therefore that which is excelled by nothing, is not a body”, which we can grant. But angels are not bodies, and we haven’t yet shown that these are lesser than God. Certainly, this argument is weak. But. If, as he does, St Thomas offers two dozen arguments for a proposition, and one or two fail, this does not imply the others fail, which (as shown) they do not. Do not be intellectually lazy and ponder only that which is admitted to fail. And anyway, like the ontological argument, much can be learned from the failures of these arguments.

viiIf you key in on the heavens moving circularly bit, you’ll be missing the point. This argument, which does not for a mote rely on that contention, is really no different than the proof of God’s existence because in order for anything to move—here and now—we need a first unmoved mover. Go back and read Chapter 13, as St Thomas himself commands in the footnotes.

[1] Ch. xviii.
[2] Ch. xvi.
[3] 2 Metaph. v. [This is a typo; it should be 3 Metaph. v.]
[4] Ch. xiii.
[5] Ch. v. seqq.
[6] 7 and 8 Phys. See above, ch. xiii.
[7] Ch. xiii.

[6] 7 and 8 Phys. See above, ch. xiii.

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