The Last Superstition: Reasoning With Aquinas

Chapter 3: Aquinas’s logical reasoning

Eventually, Feser settles down to tell us a bit about Aquinas. In particular, his method of reasoning:

What Aquinas is doing can be understood by comparison with the sort of reasoning familiar from geometry and mathematics in general. Take the Pythagorean theorem, for example. Once you understand the axiomatic method, the definition of triangularity, and so forth, and then reason through a particular proof of the theorem, you can see that the theorem must be true, and necessarily so. It is not a “hypothesis” “postulated” to “explain” certain “evidence,” and it is not merely “probable.” [p.81]

Metaphysical arguments of the sort Aquinas is interested in combine elements of both these other forms of reasoning: they take obvious, though empirical, starting points, and try to show that from these starting points, together with certain conceptual premises, certain metaphysical conclusions follow necessarily. [p.83]

In other words, Aquinas is trying to prove God the way you’d prove a mathematical theorem, through logic and reason, and most emphatically not through observation. You could sum this up as “it stands to reason”.

There are a few problems with this approach: while mathematics is undeniably useful, it also describes a lot of things that don’t actually exist. For instance, Wikipedia defines a Hilbert space as a generalization of Euclidean space, one that can have thousands, or even an infinite number of dimensions, instead of our paltry three or four or twenty-some.

More trivially, mathematics tells us that if you put six quadrillion apples into a basket, and add another eight quadrillion apples, you’ll have fourteen quadrillion apples in your basket. This is obviously false because there aren’t that many apples on the planet, and no basket that can hold them all. In this case, the math describes a world with fourteen quadrillion apples, which is not the world we live in.

The point of this isn’t that mathematics is broken, but rather that it’s important to make sure that you’ve picked the sort of mathematics that describes the world you’re living in, and specifically the problem you’re studying. Don’t go beyond its area of applicability: Euclidean geometry might work on the scale of a town, but not that of a continent, where you have to take the earth’s curvature into account, lest you get wrong answers.

Furthermore, the longer a demonstration goes on, the greater the odds that it’ll contain some error in reasoning, perhaps a subtle one. When Andrew Wiles presented his proof of Fermat’s last theorem, several reviewers went over it looking for errors (and found some). That’s why, when you’re drawing conclusions about the real world, it’s important to have a reality check from time to time to make sure you haven’t gone off the rails. But Feser sees no need for this.

In a criticism of “scientism”, Feser says that science makes certain metaphysical assumptions:

Of its very nature, scientific investigation takes for granted such assumptions as that: there is a physical world existing independently of our minds; this world is characterized by various objective patterns and regularities; our senses are at least partially reliable sources of information about this world; there are objective laws of logic and mathematics that apply to the objective world outside our minds; our cognitive powers – of concept-formation, reasoning from premises to a conclusion, and so forth – afford us a grasp of these laws and can reliably take us from evidence derived from the senses to conclusions about the physical world; the language we use can adequately express truths about these laws and about the external world; and so on and on. [p. 84]

Maybe a scientist or philosopher of science will correct me, but this doesn’t seem quite right:

there is a physical world existing independently of our minds
I think this is a working assumption, one that could be proved wrong.

this world is characterized by various objective patterns and regularities
I’d call this a discovery, not an assumption. Things could conceivably have been otherwise; Greg Egan explores this possibility in his novel Schild’s Ladder in which there is a region of space where there don’t seem to be any consistent laws of physics; every experiment gives inconsistent results. My point is that if such a zone existed, we’d know it. So it seems reasonable to assume regularity, at least until there’s reason to think otherwise.

our senses are at least partially reliable sources of information about this world
there are objective laws of logic and mathematics that apply to the objective world outside our minds
our cognitive powers – of concept-formation, reasoning from premises to a conclusion, and so forth – afford us a grasp of these laws and can reliably take us from evidence derived from the senses to conclusions about the physical world
These all seem to be conclusions, or at worst working assumptions.

the language we use can adequately express truths about these laws and about the external world
But natural languages like English and Greek are often not up to the task of describing reality. That’s why the language of science is math, and why Newton and Leibnitz had to invent calculus. And of course every discipline invents its own jargon, to describe the objects and ideas specific to that discipline, as well as mathematical techniques for those areas.

It’s true that some of these may be basic assumptions, or at least working assumptions. In fact, Feser could just as easily have listed “God is not messing around with my experiment” as a working assumption. But most of them seem at least potentially falsifiable, like in the movie The Matrix, where Neo, the main character, did find out that he was a brain in a vat. I also like this article that uses supernova SN1987A to show that the speed of light was the same 300,000 years ago as it is today, using trigonometry, astronomical observations, and the decay rate of cobalt to cross-check each other.

This cross-checking and verification are things that make science so robust and reliable, and they’re things that I don’t see in Feser’s presentation. And given that he seems to be basing his reasoning on what a medieval monk thought was obvious, I think there’s good reason to be skeptical of his conclusions.

Series: The Last Superstition

The Meaning of Christmas, a Quantitative Analysis

I’ve often heard atheists say that the things people associate with Christmas are mostly secular, and so in a real sense Christmas has stopped being a religious holiday, if it was. But I’ve never seen anyone try to quantify that. Aha! A lacuna that I can fill!

Originally, I was going to google “What Christmas means to me”, see what people come up with, and sort that into “Religious”, “Secular”, and “Mixed” (or “could go either way, depending”). But then What Christmas Means to Me turned out to be a Stevie Wonder song, and I couldn’t be bothered to find the posts that didn’t refer to that song.


But what the hell. In the spirit of Christmas, let’s see what Stevie lists, and whether it’s religious:

  Rel Mix Sec
Candles burnin’ low    
Lots of mistletoe    
Lots of snow and ice    
Choirs singin’ carols    
little cards you give me    
runnin’ wild, as anxious as a little child    
Greet you neath the mistletoe    
Wish you a Merry Christmas baby    
happiness in the comin’ year    
deck the halls with holly    
Sing sweet silent night    
Fill the tree with angel hair[1]    
pretty, pretty lights    
Christmas bells are ringin’    

[1] A note says that “angel hair” means tinsel, so I’m counting it as secular.


After that, I googled “What I like about Christmas”.

Rozario Fernandes, Express Tribune, 8 Things I Love About Christmas:

  Rel Mix Sec
Listening to Christmas carols    
Fairy lights and pretty decorations    
Buying gifts for your loved ones    
Keeping a secret stash of holiday sweets    
Another reason to stay out late    
Family get-togethers    
Vacation time    
Attending the midnight prayer service    


Next on the list was a Yahoo! Answers entry, which I didn’t pick because honestly, it’s a discussion thread, so it’s not clear where it ends, or how the entries were chosen.


What Do You Like About Christmas by Carey Kinsolving is an explicitly-religious piece, a list of children’s answers to the titular question interspersed with Bible verses. The site was down when I tried accessing it, so I had to rely on Google’s cache. But let’s see how it fares:

  Rel Mix Sec
giving people presents    
celebrating Christmas[2]    
donees’ faces lighting up with joy    
celebrating Christ’s birth    
the lights, because of the light in the sky when Jesus was born    
spending time with family    
share Christ’s love    

[2] Could be either secular, religious, or a mixture, depending how the person celebrates.


Aprille Rose at allwomenstalk writes 7 Things I Love About Christmas:

  Rel Mix Sec
The smells of Christmas[3]    
Seasonal flavors    
Christmas movies and cartoons[3]    
Christmas songs on the radio    
Stringing up lights around the house    
Decorating the tree    
Baking cookies    

[3] All the examples listed are secular.


The 25 Greatest Things About Christmas by Belinda Moreira at Arts.Mic:

  Rel Mix Sec
Christmas trees    
Chance of snow    
Vacation time    
Hot chocolate    
Christmas parties    
Ugly Christmas sweaters    
Ice skating    
Carols and music[3]    
Christmas sales    
Gingerbread houses and men    
Time of giving    
Time with friends and family    
Classic Christmas movies    
Holiday cheer    
The chance to feel like a kid again    


I skipped this page at Amazon’s Askville, for the same reasons as the Yahoo! Answers one.


Jesse Carey at Relevant Magazine lists 7 Reasons Why We Still Love Christmas:

  Rel Mix Sec
Spending time with friends and family    
opening gifts    
getting away from work    
Celebrating the birth of our Savior    
Inflatable lawn ornaments[4]    
Christmas sweaters    
Claymation specials    
Family Christmas cards    
Advent calendars    
Christmas carols    
Office gift exchanges    

[4] I’m counting this as secular because I have yet to see an inflatable Jesus.


I count 6 religious, 11 mixed, and 56 secular things to love about Christmas. I think we can confidently say that you can give up religion without giving up the things that make Christmas special. Numbers don’t lie.

Criminally Incompetent Teachers

Over at Kent Hovind’s Whinery, I ran across this comment:

I am a high school science teacher. So far I have been able to teach creation science a couple years without being stopped by administration. I spend as much time if not more teaching creation science as I do going thru the textbook they make me use. Of course, I skip all the chapters with evolution. I use Dr. Hovind’s seminar notebook and his book Are You Being Brainwashed. In a couple weeks I will be going at it again. I pray I can continue to do the same as I have been.

Hopefully, this guy is just lying, and has made the whole thing up. Because if not, that means he’s not just failing to teach the kids science, he’s teaching them antiscience, filling their heads with nonsense that has to be unlearned before they can be properly taught. He’s skipping important parts of the curriculum. He’s bringing in “teaching” materials by a wackjob so far out there that even other young-earth creationists have asked him to stop. And if this has really been going on for years, we have to consider the possibility that the school administration knows about his activities, but is turning a blind eye to them.

How would one go about subpoenaing’s httpd logs to see where this clown posted from, to see whether any of it is true?