William M. Briggs

Statistician to the Stars!

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Summary Against Modern Thought: The Last Movement

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.

Previous post.

Recall that the First Way has already been done. Meaning we already have one proof for God’s existence. This is the second, and the good news is that most of our terminology has already been introduced. A lot to do today, but the good news is that this is the last of Chapter 13! But these proofs are all we have. We don’t yet know anything about God except that He’s the Unmoved Mover, the Unchanging Changer. What can that mean? That’s coming.

Chapter 13: Arguments in proof of God’s existence

18 Again, if any two things are found accidentallyi united in a certain subject, and one of them is to be found without the other, it is probable that the latter can be found without the former: thus if white and musical are found in Socrates, and musical without white is found in Plato, it is probable that it is possible to find white without musical in some subject.

Accordingly if mover and moved be united together in some subject accidentally, and it be found that a certain thing is moved without its being a mover, it is probable that a mover is to be found that is not moved. Nor can one urge against this the case of two things one of which depends on the other; because those in question are united not per se but accidentally.

If, however, the aforesaid proposition is true in itself, again there follows something impossible or unfitting. For the mover must needs be moved either by the same kind of movement or by another kind. If by the same kind, it follows that whatever causes alteration must itself be altered, and furthermore that the healer must be healed, that the teacher must be taught, and in respect of the same science. But this is impossible: for the teacher must needs have science, while the learner must needs not have it, and thus the same will be both possessed and not possessed by the same, which is impossible.ii

And if it be moved by another kind of movement, so that, to wit, that which causes alteration be moved in respect of place, and that which moves in respect of place be increased, and so on, it will follow that we cannot go on indefinitely, since the genera and species of movement are finite in number.iii And thus there will be some first mover that is not moved by another. Unless, perchance, someone say that a recurrence takes place, in this way, that when all the genera and species of movement have been exhausted, a return must be made to the first; for instance, if that which moves in respect of place be altered, and that which causes alteration be increased, then again that which is increased be moved in respect of place. But the consequence of this will be the same as before; namely, that which moves by one kind of movement is itself moved by the same kind, not immediately indeed but mediately.iv It remains therefore that we must needs postulate some first mover that is not moved by anything outside itself.

19 Since however, given that there is a first mover that is not moved by anything outside itself,v it does not follow that it is absolutely immovable, Aristotle proceeds further, saying that this may happen in two ways. First, so that this first mover is absolutely immovable. And if this be granted, our point is established, namely that there is a first immovable mover. Secondly, that this first mover is moved by itself. And this seems probable: because what is of itself is always prior to what is of another: wherefore also in things moved, it is logical that what is moved first is moved by itself and not by another.

20 But, if this be granted, the same consequence follows.[18] For it cannot be said that the whole of that which moves itself is moved by its whole self, because then the absurd consequences mentioned above would follow, namely that a person might teach and be taught at the same time, and in like manner as to other kinds of movement; and again that a thing would be at the same time in act and in potentiality, since a mover, as such, is in act, while that which is moved is in potentiality.vi It remains, therefore, that one part thereof is mover only, and the other part moved. And thus we have the same conclusion as before, namely that there is something that moves and is itself immovable.

21 And it cannot be said that both parts are moved, so that one is moved by the other; nor that one part moves both itself and the other; nor that the whole moves a part; nor that part moves the whole, since the above absurdities would follow, namely that something would both move and be moved by the same kind of movement, and that it would be at the same time in potentiality and in act, and moreover that the whole would move itself not primarily but by reason of its part. It remains, therefore, that in that which moves itself, one part must be immovable, and must move the other part.

22 Since, however, in those things among us which move themselves, namely animals, the part which moves, namely the soul, though immovable of itself, is nevertheless moved accidentally, he goes on to show that in the first mover, the part which moves is not moved neither of itself nor accidentally.[19]vii

23 For in those things which among us move themselves, namely animals, since they are corruptible, the part which moves is moved accidentally. Now those corruptible things which move themselves must needs be reducible to some first self-mover that is everlasting. Therefore that which moves itself must have a mover, which is moved neither of itself nor accidentally.

24 It is clear that, in accordance with his hypothesis, some self-mover must be everlasting. For if, as he supposes, movement is everlasting, the production of these self-movers that are subject to generation and corruption must be everlasting. But no one of these self-movers, since it does not always exist, can be the cause of this everlastingness. Nor can all of them together, both because they would be infinite, and because they do not exist all together. It follows therefore that there must be an everlasting self-mover, that causes the everlastingness of generation in these lower self-movers. And thus its mover is not moved, neither of itself nor accidentally.

Again, we observe that in self-movers some begin to be moved anew on account of some movement whereby the animal is not moved by itself, for instance by the digestion of food or a change in the atmosphere: by which movement the mover that moves itself is moved accidentally. Whence we may gather that no self-mover, whose mover is moved per se or accidentally, is always moved. But the first self-mover is always in motion, else movement could not be everlasting, since every other movement is caused by the movement of the first self-mover. It follows therefore that the first self-mover is moved by a mover who is not moved, neither per se nor accidentally…viii

30 The Philosopher proceeds in a different way in 2 Metaph. to show that it is impossible to proceed to infinity in efficient causes, and that we must come to one first cause, and this we call God. This is how he proceeds. In all efficient causes following in order, the first is the cause of the intermediate cause, and the intermediate is the cause of the ultimate, whether the intermediate be one or several. Now if the cause be removed, that which it causes is removed. Therefore if we remove the first the intermediate cannot be a cause. But if we go on to infinity in efficient causes, no cause will be first. Therefore all the others which are intermediate will be removed. Now this is clearly false. Therefore we must suppose the existence of a first efficient cause: and this is God.ix

31 Another reason can be drawn from the words of Aristotle. For in 2 Metaph.[22] he shows that those things which excel as true excel as beings: and in 4 Metaph.[23] he shows that there is something supremely true, from the fact that we see that of two false things one is falser than the other, wherefore it follows that one also is truer than the other. Now this is by reason of approximation to that which is simply and supremely true. Wherefore we may further conclude that there is something that is supremely being. And this we call God.x

32 Another argument in support of this conclusion is adduced by Damascene[24] from the government of things: and the same reasoning is indicated by the Commentator in 2 Phys.[25] It runs as follows. It is impossible for contrary and discordant things to accord in one order always or frequently except by someone’s governance, whereby each and all are made to tend to a definite end. Now we see that in the world things of different natures accord in one order, not seldom and fortuitously, but always or for the most part. Therefore it follows that there is someone by whose providence the world is governed. And this we God.xi


iA circle can be accidentally red or yellow and still be a circle, etc. A thing is not defined by its accidents.

iiAquinas created this argument in ignorance of our modern educational system, of course. But he’s still right.

iiiYou can change quantity, mass, color, place, and the like, but there are not an infinite number of changeable qualities.

ivDon’t loose sight of the main example, the stone moved by the stick moved by the arm moved by the muscles, etc., all in the here and now. This movement cannot be circularly caused.

vWe’re starting to hone in on (but have not reached) the idea that there can be only one Unmoved Mover, and not an assemblage of them. Not gods, but God.

viYou cannot potentially and actually be in Cleveland simultaneously. Aquinas is speaking ontologically, not epistemologically. And this reminds me that we have to, sometime soon, introduce Jaki’s criticisms of complementarity.

viiWe’ll also do this more later. But, for now, the soul of the animal is its form. Things are composed of forms and substances or matter. Clay, a substance, can be in the form of an ashtray (eek!) or (say) a model car. Speaking loosely, and later correctly, the soul animates the substance. The souls of plants are lesser than the souls of animals, which in turn are lesser than the souls of men. Like I said, this is only a crude introduction. Let’s stick here to the argument of movement, else we will be arguing that of which we have incomplete information.

viiiYou may feel buried after these last two paragraphs. Slow reading is in order. Again, Aquinas is leading us to why there can be only one Unmoved Mover. There’s no getting around that this last proof is rather dry—I even leave out some discussion about movement of heavenly bodies—but it dots all the Js and crosses all the Xs.

ixHere it is in a compact form! This is the elevator proof. Pretty, too.

xI don’t think Aquinas expected this snippet to be convincing in itself, but included it as an augment to main argument. Here’s a good article from Swinburne on the argument from the beauty of design, and another by Williams on beauty.

xiAnd this sketch is cruder still. It’s doubtful that it, in this telegraphic form, would convince any moderns. I’m not expert enough in Medieval history to know why Aquinas included it, which audience he had in mind.

Hooray! We are finally done with Chapter 13! But not entirely done with motion.

[18] 8 Phys., l.c.
[19] 8 Phys. vi.
[22] D. 1a. i. 5.
[23] D. 3. iv. 27, 28.
[24] De Fide Orth. i. 3.
[25] Text 75.

Readers: Pick Your Theme Song

It’s summer and everybody’s on vacation, except, it seems, Yours Truly. And whoever is left is over at Anthony’s place fighting the Kaya wars. (My side? Take a look at the guy who introduces Pielke Jr in this video. Would you believe any equation/identity introduced from a man who purposely spikes his hair? Fashion tip: Never do that.)

So with all this inactivity on our hands, it’s about time we settled on theme songs, which is to say, leitmotifs. A tune or snippet of a melody that, when heard, tells listeners Briggs has done it again.

Long ago, it had been suggested to me that this offering by Mac Davis would fit best:

But that was then. And since this is now a more humble and self-effacing self speaking to you, something softer and more enlightened is in order.

Note carefully: a theme song is not your favorite pop song. If it were, I might nominate Where Oh Where Are You Tonight? (apologies for not linking to a better version, but the rights holders keep having YouTube delete the good ones).

No, a theme song tells people who are you, what you are about, and what you are going to do. It should accomplish this task in as few as notes as possible.

Yet must brevity be all? The most memorable television theme songs used to last a full minute; now they are five to ten seconds. But that’s because production companies have to make a profit. Ideally, Yours Truly would, too, but we can’t have everything.

There is no end to this post. I don’t have a candidate replacement in mind. I’ll work on it.

Meanwhile, I’d like to hear your theme songs, especially those of regular contributors. If any are at their computers, that is.

Note that links to YouTube are sometimes quarantined by WordPress. Best to cut and paste the URL directly. If yours seems lost, don’t worry, I’ll un-quarantine it in time.

Disbelief In Free Will Causes Disbelief In Free Will

"I have no choice but to love thee, Theory."

“I have no choice but to love thee, Theory.”

Never was the West’s wholesale flight from philosophy and a classic education more evident than in the title of this peer-reviewed paper: Prosocial Benefits of Feeling Free: Disbelief in Free Will Increases Aggression and Reduces Helpfulness.

How could we have forgotten that it is impossible—not unlikely, impossible—to “disbelieve in free will”? Answer: scientism, the curious belief that science and only science is fit to answer all questions. In order to believe you must have free will because to believe is an act of will, and to believe in one proposition is to disbelieve in its contrary; therefore, in order to disbelieve you must have free will.

The paper appears in Personality and Social Psychology Bulletin and it’s by Roy Baumeister, E.J. Masicampo, and C. Nathan DeWall.

The abstract begins with the words, “Laypersons’ belief in free will may foster a sense of thoughtful reflection and willingness to exert energy, thereby promoting helpfulness and reducing aggression, and so disbelief in free will may make behavior more reliant on selfish, automatic impulses and therefore less socially desirable.”

Laypersons. Laypersons are those unfortunate souls who are not trained in the Ways of Science and who cling to superstitions like they are rational beings.

To paraphrase the abstract: since people believe they can make free choices, the free choices they make are better than the free choices they make when they disbelieve they can make free choices.

Preposterous isn’t in it. Yet there it is. And here is more. The opening words, worth paying attention to:

Belief in free will seems widespread and intuitive. Almost every person every day has the subjective impression of making a choice in which more than one outcome is possible. The most influential religious beliefs in Western culture give prominent emphasis to doctrines of free will, assuming that human individuals can freely choose whether to perform virtuous or sinful actions and even stating that eternal judgment of individual souls rests on the choices they make. Likewise, the legal system allocates guilt and punishment differentially based on whether the rule breaker could have acted differently such that perceived reductions in the capacity for free choice (including external pressures, lack of awareness, mental illness, or intense emotion) constitute valid reasons for reduced punishment or even acquittal.

We could spend a week on this. Almost every person? Phffag. Every person. And why pick on religion, why single out jurisprudence? I’ll tell you why, because these are the areas, religion and the common law, which intellectuals are most keen on dismantling. Now that’s a judgement of psychology and not philosophy, but it’s not made lightly. Here are the authors’ next words:

Intellectuals and scientists, however, seem rather less uniformly comfortable with the idea of free will than the general public. Many scientists regard the belief in free will as untenable if not downright absurd…Although not explicitly siding with them, Wegner (2002) summarized the opposition to free will as embodying the assumption that only “bad scientists” could believe such a thing.

Do the authors consider themselves good scientists?

How in the holy heckfire do you congratulate yourself for believing you cannot believe! The only possible answer is insanity. Scientists are driven mad by love of their pure and perfect theories. They have become Pygmalion.

Authors: “To be sure, the impossibility of free will cannot be proven either empirically or conceptually.”

The reason it cannot be proven impossible is that it exists. You cannot prove that which exists does not exist, though you might conduce somebody a few slices short of a loaf to believe that which exists does not—you might even convince them that what does not or cannot exist does, like bigfoot or Utopia.

The rest of the paper is given over to “experiments” where groups of college kiddies are exposed to the researchers’ particularities and then the kiddies fill out questionnaires. The questionnaires are given numerical answers and technologically sounding names. This is what makes it science. There are statistics and wee p-values. None of this is of the slightest interest.

The end the paper with this:

The broader implication is that many people in Western culture share a belief in human freedom of action and that, moreover, human society benefits from such a belief. (Indeed, we suspect that most cultures will have found beliefs in free will to be socially beneficial and hence will tend to favor and promote those beliefs.)

I despair, I despair.


Thanks to Mangan (@Mangan150) where I first learned of this paper.

Rename “Global Warming” Contest


Andrew Jackson (‏@yodacomplex) reminded me of the screwy history of the thing that was Global Warming. The phrase has undergone many revisions, examples of which are:

  • Climate Change,
  • Climate Cataclysm,
  • Climate Chaos,
  • Climate Disruption.

Readers will have noticed the evident Anglo-Saxon preference for alliteration. If only the atmosphere would have cooperated with any of these terms, we’d at least have had a more interesting topic of conversation than The Consensus.

Consensus of what? Apparently that things are worse than we thought. I’ve pointed this out before, but if the same scientists, year after year, step to the microphone and announce “It’s worse than we thought” then the following two facts must hold: (1) these scientists are extraordinarily prone to error—can’t they ever get a prediction right?—and (2) therefore admitting membership in The Consensus is a political and not a scientific act.

Skip it. What’s true is that The Consensus was able to stir and heighten fear—even panic! even syndromes!—using the phrase “Global Warming.” Why no less than the very model of sober propriety, himself, Mr Al Gore, was made nervous enough to make a movie—and then make millions selling carbon indulgences.

Never mind. Familiarity bred its contempt and took the edge off Global Warming, but then so did the lack of global warming. So The Consensus switched to Climate Change. This was a winner in the limited sense that the climate always changes, so at least scientists wouldn’t be embarrassed by frequent flubbed forecasts. Fear rose.

But it never soared to the same heights as before. Hence quickly followed the other monikers. Yet honesty compels us to admit they were poor performers. The glory days of Global Warming are but a dim memory. People stopped caring.

This has had the effect of casting a pall over a once happy group of environmentalists. Before, Greenpeace operatives would chase you down the street, bean you over the head with their white three-ring binders, while cheerfully but adamantly delivering a “Do you have a minute to save the environment!” It was never a question, it was a mini-sermon. Whereas now they stand sullenly, offering only a weak grin and a view of their t-shirts, hoping this will be enough to enchant you into a conversation. Pathetic.

Think of all those who have devoted their lives to assuring us that the End Was Nigh! How sad, how bereft they must be! Christian charity, common human decency, requires us to take pity on these newly created intellectual vagabonds. It is our duty to cheer them, to show them hope is not lost. After all, we wouldn’t want them to all move to Belgium just so they could use that country’s generous disposal services.

Hence this New Contest to rename Global Warming. Let’s put the macabre back in meteorology! Let’s cause flesh to creep over climatology! Come on, gang: let’s get that sky falling again!


All entries must be made in the comment box below by 23:59:59 EDT 23 July 2014. One week, ladies and gentlemen.

I will be asking my pal Gav Schmidt (via Twitter) to be a judge. He might accept, too, since this contest is for his benefit. But upon his refusal or non-answer, I become the sole judge and jury.

Entries will judged on brevity, power to instill terror, memorability, and originality. The words of all entries must begin with capital letters (so I can find them).

Winners (there may be more than one) will be announced in a separate post and in this one. The winners, besides receiving the approbation due to them, will be invited to write a 300- to 400-word essay on What I Learned From Global Warming which will appear on this site. I will be in touch with the winners to arrange the details (so please use the right email when you register your entry).

Candidate #1

My entry, probably unbeatable, especially if I am to be the judge:

Apoplectic Apocalyptic Anthropogenic Atmospheric Aneurysm

Update I don’t want to single anybody out, but don’t forget the spirit of this contest. We’re here to help our sad brothers and sisters. That means a name like (I’m making this up) “Climate Silliness”, accurate as it might be, isn’t going to instill fear and panic.

On Truly Random Numbers

Don Knuth. The equations below are beautiful because of him.

Don Knuth. The equations below are beautiful because of him.

Party trick for you. I’m thinking of a number between 1 and 4. Can you guess it?

Two? Nope. Three? Nope. And not one or four either.

I know what the number is, you don’t. That makes it, to you, truly random. To me, it’s completely known and as non-random as you can get. Here, then, is one instance of a truly random number.

The number, incidentally, was e, the base of the so-called natural logarithm. It’s a number that creeps in everywhere and is approximately equal to 2.718282, which is certainly between 1 and 4, but it’s exactly equal to:

e = \sum_0^\infty \frac{1}{n!}  .

The sum all the way out to infinity means it’s going to take forever and a day, literally, to know each and every digit of e, but the only thing stopping me from this knowledge is laziness. If I set at it, I could make pretty good progress, though I’d always be infinitely far away from complete understanding.

Now I came across a curious and fun little book by Donald Knuth, everybody’s Great Uncle in computer science, called Things a Computer Scientist Rarely Talks About whose dust flap started with the words, “How does a computer scientist understand infinity? What can probability theory teach us about free will? Can mathematical notions be used to enhance one’s personal understanding of the Bible?” Intriguing, no?

Knuth, the creator of TeX and author of The Art of Computer Programming among many, many other things, is Lutheran and devout. He had the idea to “randomly” sample every book of the Bible at the chapter 3, verse 16 mark, and to investigate in depth what he found there. Boy, howdy, did he mean everything. No exegete was as thorough; in this very limited and curious sense, anyway. He wrote 3:16 to describe what he learned. Things is a series of lectures he gave in 1999 about the writing of 3:16 (a book about a book).

It was Knuth’s use of the word random that was of interest. He, an expert in so-called random algorithms, sometimes meant random as a synonym of uniform, other times for unbiased, and still others for unknown.

“I decided that one interesting way to choose a fairly random verse out of each book of the Bible would be to look at chapter 3, verse 16.” “It’s important that if you’re working with a random sample, you mustn’t right rig the data.” “True randomization clearly leads to a better sample than the result of a fixed deterministic choice…The other reason was that when you roll dice there’s a temptation to cheat.” “If I were an astronomer, I would love to look at random points in the sky.” “…I thin I would base it somehow on the digits of pi (π), because π has now been calculated to billions of digits and they seem to be quite random.”

Are they? Like e, π is one of those numbers that crop up in unexpected places. But what can Knuth mean by “quite random”? What can a degrees of randomness mean? In principle, and using this formula we can calculate every single digit of π:

\pi = \sum_{k = 0}^{\infty}\left[ \frac{1}{16^k} \left( \frac{4}{8k + 1} - \frac{2}{8k + 4} - \frac{1}{8k + 5} - \frac{1}{8k + 6} \right) \right] .

The remarkable thing about this equation is that we can figure the n-th digit of π without having to compute any digit which came before. All it takes is time, just like in calculating the digits of e.

Since we have a formula, we cannot say that the digits of π are unknown or unpredictable. There they all are: laid bare in a simple equation. I mean, it would be incorrect to say that the digits are “random” except in the sense that before we calculate them, we don’t know them. They are perfectly predictable, though it will take infinite time to get to them all.

Here Knuth seems to mean, as many mean, random as a synonym for transcendental. Loosely, a transcendental number is one which goes on forever not repeating exactly its digits, like e or π; mathematicians say these numbers aren’t algebraic, meaning that they cannot be explicitly and completely solved for. But it does not mean, as we have seen, that formulas for them do not exist. Clearly some formulas do exist.

As in coin flips, we might try to harvest “random” numbers from nature, but here random is a synonym for unpredictable by me because some thing or things caused these outcomes. And this holds for quantum mechanical outcomes, where some thing or things still causes the events, but (in some instances) we are barred from discovering what.

We’re full circle. The only definition of random that sticks is unknown.

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