A Thoroughgoing form of Empiricism about Arithmetic

If that description doesn't light up your heart, you may not be the right reader for this new book.

Some of the logical empiricists defended the claim that the basic mathematical axioms are definitions and that the theorems of mathematics are consequently analytic. This position has subsequently fallen out of favor. Critics have alleged that the position was refuted by Gödel’s Incompleteness Theorems, that it is obscure what “analytic” and “definition” are supposed to mean, that there are no “analytic” truths, or that the axioms cannot be definitions. True by Definition revisits this debate. It introduces the distinction between analytic and synthetic truths and explains the controversy around the distinction in the philosophy of mathematics and beyond. The book also defends a radical new position. It is argued that, in certain contexts, the axioms of arithmetic have the status of definitions; however...

I don't want to spoil the suspense. I am of course immediately suspicious of the impulse to introduce the synthetic/analytic distinction. 

The author is a guy I know; he and his wife are both quality philosophers. Some of you might be into a work of philosophy of math.

Colby Acuff

I was a little surprised to learn that this young man apparently has no relation to Roy Acuff, the very famous Grand Ole Opry performer ("For drawing power in the South, it was Roy Acuff, then God"). Young Colby is not bad, and not traveling on a family name. About halfway into one of his standards, he transitions into a Hoyt Axton song that Elvis and Waylon Jennings covered as well. 

Nice to see a young man keeping up traditions. 

Search for the Real Killers

Since this just came up recently, the claim caught my eye. I don't know what AI was used in that claim that is going around on social media, but I ran it through Claude as follows: "Help me check this statistic that is going around: Women since the 191h Amendment have aborted 5-10 times as many babies as all the men have killed in all the wars and murders over the same time. Leaving aside all the ways in which the comparison is problematic,* does the statistic hold water as a bare factual claim?"

Claude has a more nuanced response than this one: 

Short answer: no. Not because it's too aggressive, but because it isn't a number that falls out of any consistent scoping. Depending on how you define the denominator, the true ratio is either three to six times *larger* than claimed, or less than 1.

**The numerator.** Cumulative U.S. abortions since Roe are reasonably well documented: roughly 66.1 million from 1973 through 2025, built from CDC surveillance and Guttmacher provider censuses. The widely circulated 63,459,781 figure comes from National Right to Life tracking the same two sources, current to about 2021. The 1920–1972 portion is the weak leg: the standard 1955 estimate of 200,000–1,200,000 illegal abortions per year rested on qualitative assumptions, and a range that wide over five decades means the pre-Roe addition could be anywhere from ~5 million to ~40 million. Call the full-period total 66–100 million with genuine uncertainty in the upper half.

**The denominator, U.S.-scoped.** Since the 19th Amendment is a U.S. fact, the natural like-for-like comparison is U.S. war deaths plus U.S. homicides:

| | Deaths |

|---|---|

| WWII | 405,399 |

| Korea | 36,574 |

| Vietnam | 58,220 |

| Gulf War | 382 |

| Iraq + Afghanistan + GWOT | ~7,100 |

| **All U.S. war deaths since 1920** | **~508,000** |

| U.S. homicides, 1920–2025 (est.) | ~1.5 million |

| **Total** | **~2.0 million** |

The homicide figure is mine, built from decade-average rates against decade-average population — roughly 9 per 100,000 in the Prohibition years, near 4.5–5.0 in the 1950s, a peak of 10.2 in 1980 and 9.8 in 1991, and 5–7 since. It's good to maybe ±15%, which doesn't matter at this scale.

That gives a ratio of about **32 to 1**, not 5–10 to 1. On its own terms the claim substantially understates itself.

**The other scoping.** If "all the wars" means all wars everywhere, the denominator explodes. WWII alone killed an estimated 70–85 million, and one aggregate estimate puts 20th-century war deaths near 110 million, with others running to 130–142 million including civilians. Add global homicides (~440,000/year currently, so tens of millions cumulative) and you're at roughly 120–160 million. Against 66 million U.S. abortions, abortions are the *smaller* number — ratio about 0.5. The claim fails in the opposite direction.

Global-versus-global lands back in the same neighborhood as the U.S. comparison: global induced abortions currently run about 73 million a year, so the cumulative figure is in the billions and the ratio is again in the tens.

**Verdict.** The "5–10x" is the one answer no consistent pairing produces. It reads like a hedge — someone with a sense that the number was very large, picking a multiplier that sounded defensible. If you want to use the underlying comparison, the U.S.-vs-U.S. version is the only internally coherent one, and the honest figure is roughly 30-to-1, with a caveat that the pre-1973 leg is an estimate resting on 1950s guesswork rather than data.

One measurement note that isn't just framing: homicide totals count victims, not male perpetrators. Since men commit roughly 88% of U.S. homicides, correcting for that shrinks the denominator slightly rather than growing it — it doesn't rescue the ratio.

Emphasis added. O.J. had nothing on this.

* There are many of these ways in which the comparison is problematic. In addition, the comparison leaves out justification entirely: some homicides are clearly justified and even proper, and some wars can be, and some abortions are on most ethical schema if they are necessary to save the life of the mother in a case where both the mother and child will otherwise die. (The exception is the Catholic standard of 'never actively choose and perform an evil action,' where the killing of an innocent is always evil; the Church argues that it is morally better not to take on performing the evil action even though it results in letting both die instead of saving the one who can be saved. I dissent from that teaching.) 

Still, here as elsewhere sorting out the problematic issues with the comparison doesn't save abortion's bacon. Even in an unjust war, the enemy one might have killed was probably trying to kill you; even in gang violence, the other gang likely was. The abortions not only happen on a vaster scale, they always target the morally innocent. 

A Return Home

From Mount Pisgah, NC.

Homemade ice cream at the Harley shop’s Labor Day weekend party. 

UPDATE:

I love American biker culture. I just got caught in a huge rainstorm. I found some shelter and soon enough was joined by another group of bikers. They were busily making fun of their group leader for steering them into the storm, and he was making fun back, and one of them handed me an airplane-sized bottle of Kentucky bourbon whiskey without asking or introduction.

Had to stand there for an hour waiting for the storm to pass anyway, so there was no reason not to warm the blood a bit until the rain went over. 

UPDATE:

I saw a healthy adult black bear running across the road in front of me on my ride today. It looked like a male, though I only saw it for a moment. It always makes me feel happy to see a bear in the wild, being free. 

Matria Potestas

In ancient Rome, the father who headed a household had extreme power over it -- a genuine patriarchy led by a patriarch, or in Latin, paterfamilias. In his legal powers he was patria potestas, which included the right to kill his sons (or sell them into slavery) even into adulthood. Willingness to kill a son who refused military orders was seen as a proof of the honor of the father and the family, as it placed the needs of the society over the needs of the family or the individual. Such sacrifices for the common good were taken as an exercise in virtue. 

Two years ago, a writer in the New Oxford Review proposed that modern women are insisting on a similar power over their children, mater potestas. 

Roe created an adversarial model of the mother-child relationship, one that the elite or mainstream culture imbibed and prizes, perhaps without even consciously examining its implications.

Its implications, however, are profound: Maternity has been turned into the matria potestas, a 21st century American version of legal rights over offspring, not just to give them a name but even an acknowledged existence. Berg and Wiseman claim that one-third of women in the prime years of becoming mothers insist they must have a matria potestas, the power of life or death, over their offspring. Let’s also be honest about the slavery part: a mother can sell her offspring (though prices might be regulated) to another person through surrogacy, a trafficking-in-persons most recently legalized in Michigan.

What I think is missing there is the scale, which is captured in the X post linked under the screenshot of the post. The scale of the killing is very hard for people to grasp: if unborn Americans count as Americans, then abortion is the leading cause of death of Americans. It's not close: even omitting at-home 'Plan B' style abortions for lack of information, it's on the order of a quarter million a year more than the next leading cause.

I don't think we can easily grapple, either, with the point about the moral harm to the fabric of our society of having blood-guilt spread that widely. Societies have had large-scale populations of killers before; in The Tigers of Baluchistan, an anthropological survey of that ancient people, Sylvia A. Matheson pointed out that no Balochi man could hope to marry until he had killed another man. Like the Romans, the equally-ancient Balochi believed that this demonstration of a willingness and ability to kill was a proof of personal virtue. 

What does it mean to have so many of our women bearing this guilt? And not openly as the Balochi or the Romans would: they bear it without admitting it, so many of them preaching loudly about empathy while neither conceiving nor granting empathy to all the innocent dead children? What do we get from so many women preaching so often about the violence of men, and convinced of how much better society would be with more women in power? If 25% of men were killers, let alone killers of children, it would be a very different world. 

Road Dog

A new truck-driving song, which is a genre we occasionally like to host around here. 

Coming Right At Us

South Park anticipated, as they occasionally do, this line of retreat being posed by a Georgia police department that shot a baby donkey in its own field. 

A Cedartown police officer has been placed on administrative leave while the department investigates the shooting death of a baby donkey.

Hannah Israel, whose family owns Elsberry Riding & Farm in Rockmart, said officers shot and killed HeeHaw, a bottle-raised donkey, early Sunday.

Israel said the officers claimed they were in danger after HeeHaw ran toward them while braying. The officers used a Taser on the donkey before shooting him, she alleged in a Facebook post Sunday morning.

"HeeHaw was raised in the house and did petting zoos. He never knew a stranger and was shot and killed in his own pasture for doing what donkeys do, alerting to a stranger," Israel wrote. "There is no way this is legal!"

Sadly, that is not true. It will prove to be perfectly legal to murder your farm animals on your own land, just as cops tend to shoot our dogs with abandon.  

Comments Issue

Blogger comments seem to be down, both here and at other Blogger-hosted sites I visit. This is a Google problem, not a local problem that I can fix; standby and hopefully they'll come back soon.

UPDATE: This seems to be fixed. Feel free to test in the comments to this post.

An Airport in Taiwan

Tom Tugendhat is the new Shadow Foreign Secretary of the United Kingdom; I met him on the Taiwan trip because he happened to be there too. Cool guy, with a military intelligence and special operations career and a veteran of both Iraq and Afghanistan. 

He has an article (W.Post original, but paywalled) on a concern in Taiwan around an airport on an island that, while currently under Taiwan's jurisdiction, is physically quite close to the mainland by comparison to the Isle of Formosa that is Taiwan's main island.

It's somewhat inside-baseball for most Americans, but it's an aspect of the conflict that I'm fairly confident Hall readers haven't heard about. 

A Prophet Without Honor in Her Own Country

It is unsurprising to see disparaging remarks about the late Gloria Steinem on the political right, nor especially the political wing with Christian ideas about abortion's immorality. What is perhaps more surprising is to see how strong the reaction against her at the hour of her death happens to be on the political left, which views her as a CIA-funded effort in mind control, and her version of feminism as an attempt to suborn and subjugate genuine liberation movements in the name of American/Israeli hegemony. 

The CIA connection is not a conspiracy theory in the usual sense of the term; it is well-documented, including by the CIA. 

Was at least her feminism, or a strain aligned with it, a CIA project to destabilize traditional societies? It's not a ridiculous idea. We know that USAID -- often said to be a CIA funding/action arm -- supported similar transgender movements globally. The aim seems to have been to build out and identify networks of people with deep, existential grievances against their own society and its mores -- an ideal recruiting base for agents who would act against their own governments. The CIA also funded modern art as a psychological warfare approach against traditional societies. 

In a way, such efforts were at once revolutionary and counter-revolutionary. The disruption being wrought by left-leaning movements to traditional societies is inherent in Marxism, which aspires to revolutions against agricultural/feudal societies towards capitalist/industrial ones and, then, against capitalist ones towards communist/socialist ones. Marxism always advocated for the equality of women as a liberation from traditional roles, even though women who joined Marxist and Maoist movements rarely found themselves in positions of power once the revolutions carried the day. Trying to find a way to suborn and redirect this feminist thrust to support the position of America and its allies was an insight that made a lot of sense to the American elites who ran both State and the Agency.

De mortuis nil nisi bonum. I merely note the controversy; may she rest in peace. 

A Classical Lesson from Football

Louisiana being itself, the judge in the state-level case is reportedly a season-ticket holder for LSU football, who appears here with the LSU coach giving the LSU football hand sign; the lawyer representing LSU had endorsed the judge's wife in her election campaign; the Louisiana Attorney General began her remarks on the case with "Geaux Tigers!"; and the ruling was compared to 'a cup of cold gumbo.'

The South collectively having been subject to many rounds of legal and judicial interference in its culture and laws, the SEC knew not even to wait for the state-court ruling before filing its own case in Federal Court so the state court can be overridden. Southern football rivalries being what they are, it filed this suit in a Federal court not in Louisiana but in Alabama. 

This is a very nice illustration of Aristotle's point in the Rhetoric about why you can't trust judges in matters of justice. 

Now, it is of great moment that well-drawn laws should themselves define all the points they possibly can and leave as few as may be to the decision of the judges; and this for several reasons. First, to find one man, or a few men, who are sensible persons and capable of legislating and administering justice is easier than to find a large number. Next, laws are made after long consideration, whereas decisions in the courts are given at short notice, which makes it hard for those who try the case to satisfy the claims of justice and expediency. The weightiest reason of all is that the decision of the lawgiver is not particular but prospective and general, whereas members of the assembly and the jury find it their duty to decide on definite cases brought before them. They will often have allowed themselves to be so much influenced by feelings of friendship or hatred or self-interest that they lose any clear vision of the truth and have their judgement obscured by considerations of personal pleasure or pain. In general, then, the judge should, we say, be allowed to decide as few things as possible. But questions as to whether something has happened or has not happened, will be or will not be, is or is not, must of necessity be left to the judge, since the lawgiver cannot foresee them.

Emphasis added.

Wheels Down

My last flight has landed at Asheville. No more flying for a while! I’ve crossed the international date line twice in a week and spent long days working in time zones 12 hours off of each other. I’m glad to be back to my mountains. 

My Second Favorite* Anglican Priest Gets Interviewed by My Favorite** Orthodox Iconographer

The Rev. Dr. Malcolm Guite has just published the first volume of an "Arthuriad," a projected 4-volume ballad that retells the Arthurian stories. It's made a bit of a splash.

If you're interested in Arthur, Tolkein, CS Lewis, poetry, fiction, history, the role of imagination in modern life, Christianity, or just hearing two interesting people talk about storytelling, you might enjoy this interview.

* My favorite Anglican priest will always be Fr. Terry, who was a kind and generous pastor when I was asking whether Christianity might be the right path or not.

** To be fair, he's the only iconographer I can name of any denomination, so it's not as impressive as I've made it sound in the title. His Symbolic World podcast / YouTube channel is what he's famous for, but "... Interviewed by a Podcaster" was a less-interesting title.

Back in the USA

I did hear a David Allan Coe song in a bar in Taipei, but this still feels more like home. I won’t actually be home until late tomorrow night. 

Rest in Peace, Wendell Berry

Wendell Berry passed away yesterday.

Some advice he gave to himself, but which seems to profit others as well:

How to Be a Poet
(To remind myself)

i
Make a place to sit down.
Sit down. Be quiet.
You must depend upon
affection, reading, knowledge,
skill -- more of each
than you have -- inspiration,
work, growing older, patience,
for patience joins time
to eternity. Any readers
who like your poems,
doubt their judgment.

ii
Breathe with unconditional breath
the unconditioned air.
Shun electric wire.
Communicate slowly. Live
a three-dimensioned life;
stay away from screens.
Stay away from anything
that obscures the place it is in.
There are no unsacred places;
there are only sacred places
and desecrated places.

iii
Accept what comes from silence.
Make the best you can of it.
Of the little words that come
out of the silence, like prayers
prayed back to the one who prays,
make a poem that does not disturb
the silence from which it came.

Taipei

Downtown, with Taipei 101 on the skyline

Closer to 101.

An unexpected angel. It’s mostly Buddhist here; I saw many Buddhist monks and a few nuns, but no other signs of Christianity except that in the hotel room there was both a New Testament and a Teachings of the Buddha.

The Formosan Bear is, unofficially, the national animal of Taiwan (of old called Formosa Isle).

Taipei Main Station. I caught the High Speed Railway from here. Recommended.

The Most Important Store. Only very recently is it legal to buy a Harley in Taiwan. Until late, large displacement motorcycles were banned by law.

Kind of a rainy afternoon on the first of September, and my last day in country. 

Tetraphobia

A lot of American skyscrapers don’t have a 13th floor, in the sense of a floor with that designation, because the number was thought to be bad luck. 

In East Asia, the number omitted is four. The word for four and the word for death are the same syllable with only a slightly different pronunciation. 

Fare Thee Well, Dolly

Dolly Parton and Carol Burnett

Dolly Parton giving an impromptu performance in Paídi Ó Sé's Pub

(I've started this video just a bit before she starts singing, skipping over several minutes of people milling about, a t-shirt being given, mic testing and so forth.)

Merle Haggard talks about falling in love with Dolly

Probably my favorite of her songs, recorded with Chet Atkins

What a joy she was. 

No Pictures Today

All day exercises from before dawn until well into the dark today. Tomorrow we resume early again, but will end a little earlier. Perhaps I’ll have time for something I can post then. 

Our Taiwanese allies are very enthusiastic, disciplined, and intelligent. I won’t say more about it, but you should have a warm place in your heart for Taiwan.