William M. Briggs

Statistician to the Stars!

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Summary Against Modern Thought: God Is Not In A Genus

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.

We know God’s essence and existence are the same thing. God necessarily exists; existence necessarily exists. We know God is not made of stuff, has no potentiality, is not made of parts (is “simple” in a technical sense). He has no extraneous properties. Let’s continue to flesh out, as it were, more of God. We’ll skip a little quickly through these two chapters, because they’re easier and non-controversial (everything here follows simply if you accept what came before). The reader is encouraged (do it!) to go to the original chapters for the complete story.

Chapter 24: That the divine being cannot be specified by the addition of any substantial difference

2 …Whatever needs something added to it, in order to exist, is in potentiality to that thing. But the divine substance is not in potentiality in any way, as proved above:[3] and God’s substance is His being. Therefore His being cannot receive essential specification from something added to it.i

3 Moreover. Whatever makes a thing to be in act, and is intrinsic to that thing, is either the whole essence thereof or part of its essence. Now that which specifies a thing by an essential specification, makes a thing to be in act, and is intrinsic to the thing specified: otherwise the latter could not be specified essentially thereby.ii Therefore it must be either the very essence or part of the essence of that thing. But if something be added to the divine being, it cannot be the whole essence of God, for it has already been proved[4] that God’s existence is not distinct from His essence. Therefore it follows that it is a part of the divine essence: and thus God would be composed of essential parts, the contrary of which was proved above.[5]…

Chapter 25: That God is not in any genus

1 HENCE it follows of necessity that God is not in any genus.iii For whatever is in a genus, has in itself something whereby its generic nature is specified: for nothing is in a genus without being in some one of its species. But in God this is impossible, as shown above.[1′] Therefore it is impossible that God be in any genus…

3 Again. Whatever is in a genus differs as to being from the other things contained in the same genus: otherwise a genus would not be predicated of several things. Now all things that are contained in one same genus, must agree in the whatness of the genus, because the genus is predicated of all in respect of what a thing is. Therefore the being of anything contained in a genus is beside the whatness of the genus. But this is impossible in God.[4′] Therefore God is not in a genus.

4 Further. A thing is placed in a genus by the nature of its whatnessiv, for genus is predicated of what a thing is. But the whatness of God is His very being.[5′] Now a thing is not placed in a genus according to its being, because then being would be a genus signifying being itself.v It remains therefore that God is not in a genus.

5 That being cannot be a genus is proved by the Philosopher as follows.[6′] If being were a genus, it would be necessary to find a difference in order to contract it to a species. Now no difference participates in the genus, so that, to wit, the genus be contained in the notion of the difference, for thus the genus would be placed twice in the definition of the species: but the difference must be something besides that which is contained in the notion of the genus.vi Now there can be nothing besides that which is understood by being, if being belong to the notion of those things of which it is predicated. And thus by no difference can being be contracted. It remains, therefore, that being is not a genus: wherefore it follows of necessity that God is not in a genus.


iIf you need food, then you’re potentially fed. (Something actual must bring this about.) But if you need something that you don’t have, you’re not complete. And God is complete, and has no potentiality (and no parts).

iiThis two sentences are, after a moment’s thought, obvious. But look how well they’re put. Succinct city! It’s also good to reflect. That which causing something to be actual is what makes up that thing’s essence. Causality (act) and essence are linked. This applies everywhere, of course. Not just to God.

iiiFor Aristotle and Aquinas, there are two levels, species and genus, the latter being a collection (if you like) of species. Genus is higher up in the taxonomic order. If something is in a genus, it must then be in one of the species of that genus. But God is sui generis. There is nothing like Him.

ivQuiddity, essence.

vEvery being has being; rather, everything that is in existence, so that it exists does not a genera make.

viThe key phrase is “the difference must be something besides that which is contained in the notion of the genus.” You cannot use the definition of genus as a genus. It is to be real differences which make up a genus. The rest is like the previous argument.

[3] Ch. xvi.
[4] Ch. xxii.
[5] Ch. xviii.

[1′] Ch. xxiv.
[4′] Ch. xxiv.
[5′] Ch. xxii.
[6′] Metaph. iii. 8.

BBC: Why Is There Something Rather Than Nothing? BBC: Because Something

Something (which can be observed) rather than nothing (which cannot).

Something (which can be observed) rather than nothing (which cannot).

Opens the BBC’s campaign:

Some physicists think they can explain why the universe first formed. If they are right, our entire cosmos may have sprung out of nothing at all.

People have wrestled with the mystery of why the universe exists for thousands of years. Pretty much every ancient culture came up with its own creation story – most of them leaving the matter in the hands of the gods – and philosophers have written reams on the subject. But science has had little to say about this ultimate question.

Philosophers indeed have written reams on this subject and science little for the simple obvious inescapable reason that science must forever remain mute when discussing what isn’t science.

Place a can of tomato soup on the table in front of you. Question: is there something on the table or nothing? A philosopher will answer “Something.” But a scientist of the stripe of, say, Lawrence Krauss or Alexander Vilenkin might say “Nothing.”

Why this affront to commonsense? Let’s see.

Scientists like Krauss are running around claiming the universe was created from nothing. Now nothing is a very simple concept. It means the complete absence of anything, where anything means something. To thus insist nothing is equivalent to something is to exhibit a mild form of lunacy.

The Beeb: “Quantum mechanics tells us that there is no such thing as empty space. Even the most perfect vacuum is actually filled by a roiling cloud of particles and antiparticles, which flare into existence and almost instantaneously fade back into nothingness.”

I read that as admitting a “perfect” vacuum is filled with something and not nothing. You? That means “perfect”, where perfect evidently means imperfect, vacuums cannot be candidates for creation from nothing.

Stephen Hawking, the creature, is quoted saying “In quantum physics, if something is not forbidden, it necessarily happens.”

Dude. Necessarily is one of philosophy’s strongest words, second in importance, maybe, to Truth itself. If something necessarily happens then it will happen no matter what. Something which necessarily happens cannot be contingent on any state of the universe. Whatever this necessary thing is, we are doomed to face it.

Not forbidden by quantum mechanics is you turning into a wave and entering your house simultaneously by your garage and front doors (and reappearing inside intact). If Hawking is right, this necessarily must happen. Good party trick.

“Look here Briggs, Hawking didn’t say when. Given enough opportunities, it will eventually happen.”

Ah, the frequentist fallacy, wherein probabilities are somehow imbued with causative powers. Bunk. Whenever any quantum mechanical event happens, such as you splitting in two or when “virtual” particles appear in a “vacuum”, something causes the event to occur. It is impossible that nothing causes quantum mechanical events.

It is possible, and seems to be true, that we cannot know these causes. But because we cannot know them does not mean they do not exist. Nothing cannot be a cause. How could it? It is nothing.

In other words, little bubbles of space and time can form spontaneously. “If space and time are quantized, they can fluctuate,” says Lawrence Krauss at Arizona State University in Tempe. “So you can create virtual space-times just as you can create virtual particles.”

Accept this. In accepting this we are forced to admit “little bubbles of space and time” are something. They are not nothing. Yet notice Krauss’s use of “spontaneously”, here a synonym for “from nothing” or “uncaused.” Krauss is thus assuming what he wishes to prove. And assuming the impossible at that.

Krauss believes in magic. If what he says is true, only magic could account for why quantum mechanical events occur. Magic, unfortunately, is still not nothing.

The BBC quotes him as concluding, “The laws of physics as we understand them make it eminently plausible that our universe arose from nothing – no space, no time, no particles, nothing that we now know of.”

Are the laws of physics nothing? From whence did they arrive? Why these laws and not others? No matter how you answer, you end up at something and not nothing.

Before you can catch onto his trick, Krauss and another physicist named Linde distract you with multiverses, breathlessly reporting, “There could be a mind-boggling smorgasbord of universes”. Fine, let there be. But in this scenario another universe somehow created ours. Is another universe nothing or something? And where did all those other universes come from? It can’t be nothing. Pushing the “problem” back one level does not make it disappear.

I’m no expert in multiverses, but I did read in Gell-Mann’s The Quark and Jaguar of his exasperation with fellow physicists who confuse probability, which is a measure of information, with reality, which is real. When we flip a coin, probability-as-measure-of-ignorance informs what might happen; it’s not that the coin splits and becomes both head and tails in separate universes.

An Introduction To Uncertainty: Probability, Statistics, and Modeling of All Kinds

Spencer Tracy is trying to fit round pegs into square holes.

Spencer Tracy is trying to fit round pegs into square holes.

This is a teaser, the first part of a 3,200-word narrative outline for the book that I’ve started to shop around. The current title is in the headline. Regular readers know it has undergone many changes, thus it is rational to conclude it might change again.

Why is this rotten thing taking so long? It took me forever to realize what I could leave out—which is a lot. I wanted to introduce to people not used to it to Aristotelian epistemology, and what this fine and true subject meant for the practical understanding and communication of uncertainty. But there’s no way to be complete about this without going on and on, at book length, by which time the reader, anxious to get to the “good stuff”, will have been put to sleep.

So out goes everything except the bare necessities. Besides, if readers are into that sort of thing, there’s plenty of other books to read. What’s left is an explanation of what probability is, what it means to “do” modeling, how to communicate results properly, and how to purge the magical thinking from our midsts.

I sent the outline to one well known publisher, who that very same day wrote back and called my bluff. The editor labeled the proposal “intriguing” and said that it “raises a lot of important points” but then asked me to immediately ship off two chapters. Sure. As if these were ready, and that, even if they were, I could pick the right two.

Finishing these chapters so that they are at least not embarrassing is what I’ll be doing for the next week.

Incidentally, the “Why?” which follows, suitably fleshed out, will become either the Preface or Chapter 1.


Fellow users of probability, statistics, and computer “learning” algorithms; physics and social science modelers; big data handlers; spreadsheet mavens; other respected citizens. We’re doing it wrong.

Not completely wrong: not everywhere: not all the time: but far more pervasively, far more often, and in far more places than you’d imagine.

What are we doing wrong? Probability, induction, statistics, the nature of causality, modeling, communicating results, expressing uncertainty. In short: everything.

Your natural reaction will be (this is a prediction based on observation and induction), “Harumph.” I can’t and shouldn’t put a probability measure to this guess, though. That would lead to over-certainty, which I will prove to you is already at pandemic levels.

You may well say “Harumph”, but consider: there are people who think statistical models are causal, that no probability can known with certainty until at the close of the universe, that probabilities can be read from mood rings, that induction is a “problem”, that randomness is a magical cause, that parameters exist, that computers learn, that models are realer than observations, that model fit is more important than model performance.

And that is only a sampling of the oddities which beset our field. How did we get this way? Best answer is that it is well known that the human race is insane.

More practically, our training lacks a proper foundation, a philosophical grounding. Introductory books plunge the student into data and never look back. The philosophical concepts which are necessarily present aren’t discussed well or openly. This is rectified once, and if, the student progresses to the highest levels, but by that time his interest has been turned either to mathematics or to solving specific problems. And when the student finally and inevitably weighs in on, say, “What models really are”, he lacks depth. Points are missed. Falsity is embraced.

So here is a philosophical introduction to uncertainty and the practice of probability, statistics, and modeling of all kinds. The approach is Aristotelian, even Thomistic. Truth exists, we can know it, and we can sometimes but not always measure its uncertainty, and there are good and bad ways of doing it.

This isn’t a recipe book. Except for simple (but common: regression, “binomial”) examples, this book does not contain lists of algorithms. Rather, this is a guide on how to create such recipes and lists. It is thus ideal for students and researchers looking for problems upon which to work. The mathematical requirements are modest: this is not a math book.

Do I have everything right? Well, I’m as certain I do as you were that you had everything right before you read this introduction. One thing which is certain is that we’re not done.

Sex With 21 (Not 20) Women Lowers Risk Of Prostate Cancer. It’s Science!

Not too pretty.

Not too pretty.

Today’s headline was modified from the Telegraph, one of the least lurid and sensationalistic of those generated by the peer-reviewed paper “Sexual partners, sexually transmitted infections, and prostate cancer risk” by Andrea Spence, Marie-Claude Rousseau, and Marie-Élise Parent in Cancer Epidemiology.

The Telegraph reported, “The University of Montreal has found that men who had sex with more than 20 women lower their prostate cancer risk.” Twenty wouldn’t do it; neither 19. Had to be more than 20. But what, you ask, about sodomy?

In contrast, men who slept with 20 men doubled their risk of developing prostate cancer compared with men who have never had sex with another man.

That level of specificity can only arise via models, neighbors and friends, statistical models. Let’s see what happened.

Some 3,208 Canadian men, half with and half without cancer, were asked in-person personal questions. Now since these were extremely intimate questions about highly sensitive topics (sexual “orientation”, STDs, etc.), it is assured, academically speaking, that everybody told the truth. Right? Right?

Turns out that men who reported having had only 1 sexual partner over their lifetime, 25% of men in each group, half had cancer. The same thing was found for people who had 2-3 partners (about 16% of men; cancer rate about 50%). Those who reported 4-7, 19% of men with cancer and 16% of men without, 54% had cancer. Oho! Another similarity for those reporting 8-20 partners (about 20% of men, cancer rate about 50%). Only 25 men claimed celibacy, 15 with cancer and 10 without: too few to say anything about (though this didn’t stop anybody).

Say, how did we jump from just 1, then 2-3, then 4-7, then 8-20? Hey! That was peer reviewed. So don’t ask. These divisions may seem arbitrary to us, but not to scientists.

Finally, those men who reported having greater than 21 partners, 14% versus 16% of men, the cancer rate was 47%. A wee p-value confirmed that this was “statistically significant”, meaning…what, exactly? We’ll come to that. First, it’s interesting that of those who refused to tell how many “partners” they had, 5% of the men with cancer and 7% without, the cancer rate was only 40%!

That’s just “partners” so far, mind. Not man on woman, but man on anything. So the clever authors split the data to count just those who admitted having had female “partners”—which was all but 10 of the people surveyed. Since this was nearly everybody, the overall results are scarcely different. Yet they are reported as being a whole new separate part of the study, especially in the media.

Stay with me.

The authors then split the cancer cases into those with high and low Gleason scores. A Gleason score is a subjective rating (2 to 10) about how ugly the prostate cancer tissue looks under a microscope. The authors chose 7 as the demarcation point because why not?

According to the hypothesis tests, no “significant” differences between the groups in any “partner” category except the greater than 21 “partners”, and only for those with Gleason scores less than 7. Say, that’s a lot of testing! Any adjustment of p-values? Nope.

The authors then broke the data out by those who admitted having committed sodomy. This was 141 men. Of these, 55% had cancer. 22% of those 141 who admitted having 21+ “partners” had cancer and 11% did not, for a rate of 68%.

Question: was it sexual activity, or its lack, that caused these differences in prostrate cancer rates? Wasn’t that the point of the study? To show what caused observed differences? If activity is causal, then having sex with 4-7 women causes more cancers and having sex with 21+ causes fewer, at the same rates. (This may be why men notch belts: so that they don’t lose count. We already knew sodomy is destructive to health.)

Parent told the Telegraph, “It is possible that having many female sexual partners results in a higher frequency of ejaculations”, so she certainly thought the statistics demonstrate causality. Sort of.

But when asked whether public health authorities should recommend men to sleep with many women in their lives Dr Parent added: “We’re not there yet.”

However, the authors in the paper say, “ours is the first study to report a protective effect of having several female sexual partners over the lifetime.” That’s cause-and-effect language, sisters and brothers. Except for a guessed-at more frequent emptying of seminal fluids (any why can’t that happen inside a marriage?), they know not how this cause works. But they’re sure it’s there.

Yet the authors had no awareness that people could have lied—misremembered, maybe, but not lied. The arbitrary cuts were never acknowledged as arbitrary. The huge number of tests hunting for wee p-values were not mentioned. They did admit that only 63% of those without cancer agreed to participate, but 86% of those with cancer did. And since we’re talking about differences between these groups, this large difference might be meaningful.

And they never realized that statistical models aren’t causal.


Thanks to reader and contributer Bob Kurland for bringing this paper to our attention.

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