Is 2+2=4 part of an oppressive racist system? Is math even real? And could math be evidence that God exists? Trent answers those questions as he explores recent social media debates about the nature of mathematics.
Welcome to the Counsel of Trent Podcast, a production of Catholic Answers.
Trent Horn:
Some ideas are so stupid, only an intellectual could believe them. Welcome to The Counsel of Trent Podcast. I’m your host, Catholic Answers apologist and speaker, Trent Horn. And we’re in the midst of what some people call the great awakening, a greater sense of race consciousness, of awareness of past injustices, past racial sins and crimes, as well as the perpetuating effects into the present that causes harm to minority communities. That’s all good. That’s something good to be aware of when it comes to combating social injustice. What’s not good is saying that everything under the sun is racist, everybody is racist, and every thing is racist.
Well, I’ve been noticing the chatter on social media over the past few months, and it turns out that math is racist. For example, in Seattle, of course, it’s Seattle, right? I’m sure they came up with this stuff in the Capitol Hill Occupied Zone, CHOP, You remember that? It says in this article that the curriculum in the Seattle schools is going to be modified so that it’s more race conscious. And this is all the curriculum, not just what you would expect maybe in like social studies or history class, or maybe in English, but in all of them, even in subjects that have absolutely nothing to do with race relations or ethics, or public policy. Like take math, take Algebra One, Algebra Two, you just have students who are trying to wrap their heads around difficult concepts.
I remember trying to wrap my head around these difficult concepts, and I’m not a math guy. I did great in English. I did great in history, but math, I was not able to get my head around. I remember my eighth grade Algebra One teacher, he did help me get the basics. He said, “Trent, when it comes to algebra, I know it’s confusing, but you got to balance the two sides. I know there’re Xs and Ys. It can be confusing, but you want to get both sides to balance. It’s like you have a fat man on a seesaw. Trent, you have a fat man on a seesaw. The other end goes up. You got to get another fat man on the other side of the seesaw and balance them out. So 5X equals 30, and 30 is the big fat man pushing down. How do we get the other fat man down? How many fives do we need?”
“We need six fives.” “Oh, you’re right. Yes. And then I’ve got the Seesaw balanced.” And it was the breakthrough I needed to get through Algebra One, the two fat men balancing on the seesaw. I bet nowadays that would never fly. The fat men on a seesaw, that’s sizeist, that’s ableist, and why is it a man in these discussions? Why is it two men? Why isn’t it a woman? Why is the outline, it’s a white figure in a black outline. Why is it a white figure? Why isn’t it a dark figure? It would be absurd. It would be absolutely absurd if they tried to teach me today how I was taught these subjects so many years ago. So according to the draft curriculum in Seattle, it says in math, the lessons are more theoretical.
Seattle’s recently released proposal includes questions in the math curriculum like, where does power and oppression, with capital P and capital O, where does Power and Oppression show up in our math experiences? And how is math manipulated to allow inequality and oppression to persist? So some people make the claim, people make the claim that math is racist, that it’s not even objective. And I’ll get to it shortly why this matters for us because if we believe in sharing the truth with other people, objective truth, religion is not a subjective truth. It’s not something you believe just because it works for you, or it feels good for you. It’s not like ice cream. It’s more like medicine. It objectively affects you and it’s what you need to save you from this deadly disease called sin that you have contracted, through no fault of your own, but it’s a disease you have nonetheless.
It’s something that’s objective. And some people just can’t wrap their heads around it that no, I create reality. I define who I am. If I don’t think I’m a man, I’m actually a woman. I can define who I am. I define my own reality. We cannot get people to accept that the Catholic faith is true or Christianity is true if they can’t even accept the concept of objective truth in the first place. And my go-to is always well, mathematics is objectively true. We don’t create it. It’s not a reflection of human beings. It’s distinct from us. It’s independent. We discover it. And yet you’ll hear claims from people saying that even math is racist. And of course, racism is a property of human beings. It’s a property of moral agents that commit the sin of prejudice and bigotry, and mistreating others just because of something that is morally trivial.
Not that racism is trivial, but that a property that has no moral relevance like skin color. So the idea that people say math is racist. Well, how can that be? There’s usually two different meanings when people say that math is racist, either that math is used for racist purposes, which means it’s not really racist. Or that trying to say that math is objective is a racist statement. So I’ll give you an example of the first one. This is a clip from the Fox News show, ableist’ World, or it’s a segment of it. I think Jesse Watters is the host and he’s interviewing a sociologist, someone who has a PhD in sociology who makes this claim that math is racist. And it takes like three quarters of the interview until he can get this woman to nail down the point. What does she mean when she says math is actually racist?
DeLessio-Parson:
Well, the first premise, the first starting point that we have to get on the same page on is that we live in a white supremacist racial caste system.
Jesse Watters:
Okay. I’m not willing to agree with that.
DeLessio-Parson:
Are we on the same page about that?
Jesse Watters:
No. I disagree with that.
DeLessio-Parson:
No.
Jesse Watters:
But just explain because we’re running out of time, doctor. How is two plus two equals four, how does that discriminate against black people or brown people?
DeLessio-Parson:
One stick plus two stick, humans we’re like, “Hey, here’s a stick. Here’s another,” I just did some math. That was not racist. We’re on the same page with that?
Jesse Watters:
Okay. Yeah.
DeLessio-Parson:
One plus one equals two.
Jesse Watters:
Yes.
DeLessio-Parson:
Okay. Humans have then used math and numbers, and statistics in all sorts of ways from counting black and brown bodies as they made them property and brought them over to these lands, to much more recently, scholars who said that white people were more intelligent than people of color. That’s called scientific racism, the use of statistics and tools to construct the idea that it’s like something deep in our brains. It’s hard to recognize. And that’s why it requires time, Jesse. I asked you a question-
Jesse Watters:
Wow. Just because people counted-
DeLessio-Parson:
… and it took me more than three years to get here.
Jesse Watters:
… with slavery, does it make counting racist?
Trent Horn:
So that would be an example of the first criteria that something is racist if it’s used for racist purposes. So imagine if we applied that to every subject in school, we would never actually teach subjects. We would just teach about racism all the time that math is racist because people used calculations to help determine rates in the transatlantic slave trade. In physics class, do we have to… or let’s take chemistry, is chemistry anti-Semitic because chemists developed Zyklon B to eradicate Jews and other unwanted people during the Holocaust? Are we going to do a lecture on the Holocaust during chemistry one honors or chem two AP? Or should we keep the lecture on the Holocaust in history AP, or world history where it belongs?
And so Watters makes a good point here, and you might think, oh, well, that’s just one silly example of a sociologist trying to make that point. And that’s Dr. DeLessio-Parson who’s the sociologist who makes that point. But you find in other places, another famous example of this is Matthew Desmond’s New York Times article, American Capitalism is Brutal. That was part of the 1619 project. And we read that from the New York Times trying to say, well, America is, started in 2019 saying that America was not founded in 1776. It was founded in 1619 based on the transatlantic slave trade. And so Desmond makes a similar kind of argument here that math or economics, or capitalism is racist apparently because it was used to facilitate the transatlantic slave trade.
So he writes, “Perhaps you’re reading this article at work, maybe at a multinational corporation that runs like a soft purring engine. You report to someone and someone reports to you. Everything is tracked, recorded, and analyzed via vertical reporting systems, double entry record keeping and precise quantification. Data seems to hold sway over every operation. It feels like a cutting edge approach to management, but many of these techniques that we now take for granted were developed by and for large plantations. When an accountant depreciates an asset to save on taxes, or when a mid level manager spends an afternoon filling in rows and columns on an Excel spreadsheet, they are repeating business procedures whose roots twist back to slave labor camps.”
But that is totally false. Double entry bookkeeping did not emerge in the 17th century on American plantations or through the slave trade. It was known centuries before that. In fact, Jewish merchants had been practicing double entry bookkeeping for, oh gosh, probably seven or 800 years even before that. It did not become common among non-Jewish Europeans however, until the publication of Franciscan friar, Luca Pacioli’s famous arithmetic textbook. As I wrote in my book, Why Catholics Can’t Be Socialists, or Can a Catholic Be a Socialist? I wrote there, “If you were glancing over Leonardo da Vinci’s desk as he painted the last supper, you might’ve seen this reminder in one of his notebooks. He actually wrote this, “Learn multiplication from the root from Maestro Luca.””
So da Vinci was talking about his friend who is friar Luca Pacioli, who lived from 1447 to 1517. So he died right as the Protestant reformation was just getting off the ground. So what he did, he took these methods that originally had been employed by Jewish merchants actually, cultural appropriation, but nobody talks about it there. So he took these methods and helped to explain them because Venetian merchants and mercantile capitalism had been taking off in 13th century Venice and 13th century Italy. That was the birthplace of modern capitalism 300 years before the slave trade. So these elements that were used like double entry bookkeeping, modern accounting measures, that’s where it developed.
So it’s just wrong to say that it’s something that you got from this kind of horrible evil environment. Oh, by the way, though, even if you got knowledge from a horrible evil environment, it doesn’t follow the knowledge is false or that you should never use it. For example, a lot of what we know for treating victims of hypothermia came from experiments that were performed on Jewish inmates at concentration camps. A lot of knowledge in anatomy textbooks was discovered by cadaver work that was done in concentration camps. And there have been bioethical articles published on this. What do you do with this kind of illicit knowledge? But actually that’s not the case with capitalism and modern accounting. This rather is an example of people who are trying to make everything racist. We should point out racism where it exists.
We should eradicate the evil of racism and we should change, if there are social structures that are designed to lead towards racist outcomes, we should change those structures. But it doesn’t do anybody any good to exaggerate and claim that things are racist when they’re not. So that’s number one, the view of saying math is racist. The other view is when people say, well, maybe math is not racist in that way. What they mean is that claiming math is objective, your claim that two plus two always equals four, that’s just your opinion as a white, European, heteronormative Christian male, that’s just your white European opinion. Other cultures have different ways of understanding mathematics. And so we have to respect those cultures.
I remember once I was at Arizona State University speaking to an anthropology major and I told them, “Well, there are some truths that are objective, they’re true for everyone.” He says, “I don’t believe that.” I said, “Well, obviously there’re some like that the earth is round.” And he said, “Well, there are some tribes that think that it’s flat,” and people on the internet, I did a whole episode on flat earth a long time ago. I’m going to have to revisit that topic. I said to him, “Well, does that mean it has no shape?” He says, “I can’t tell them that they’re wrong.” He couldn’t even say the shape of the earth was objective because other cultures have different ways of viewing it. So this erupted on social media over the summer. So let me give you a timeline of how it all went down.
So James Lindsay is a liberal academic, a classical liberal. So he is actually anti-religious. He’s written several articles and a book arguing against God. He’s anti-religious in that sense, but he doesn’t buy into modern PC culture, wokeness. He thinks it’s totally bunk. And so he’s actually done fake studies to, like so-called did to submit them to hyper woke liberal journals to show that it’s completely farcical. So he ended up posting this meme on his social media account. I think it was Facebook. He said, “Two plus two equals four, a perspective in white Western mathematics that marginalizes other possible values.” So it was a joke, so Lindsay is a mathematician. And so he just published as a joke.
Two plus two equals four. No, it’s a perspective in white Western mathematics that marginalizes other popular values. So he writes on his blog. “I tweeted that particular meme for the first time on June 8th of this year. And hopefully, you get the joke. It seemed humorous enough and made my point. So I was content with it as were many of my followers. What I underestimated, however, was the fact that in cutting too close to the bone, I had inadvertently introduced a conceptual virus into the woke matrix. What happened next is what led us to the present moment in the course of human history.” So then other people, including mathematicians and math teachers who have bought into total wokeness doubled down on it.
And they said, things like this on Twitter, “The idea of two plus two equaling four is cultural. And because of Western imperial colonization, we think of it as the only way of knowing.” Another person said, “Math is actually not universal, treating it as such upholds white supremacy.” So here’s the problem. What they’re trying to do. If you can crumble one foundational truth, people will think, well, I believe, I’m Catholic. I’m Christian. I believe in God. You have a way that the world makes sense. What if you can overturn the whole apple cart and say, you always thought two plus two equals four and it turns out it’s not, that’s racist. That’s just one white person’s view. Math is way more complicated and different than that.
Wow. If two plus two doesn’t always equal four, how could I be sure of anything else like God, or the church. So you see what happens here, that people try to attack faith by attacking just any fundamental ground of surety or objectivity. For example, here’s a tweet that absolutely makes that point. This person wrote, “I really do think public education is important, but the extent to which it has caused people to smugly embrace simplifications of reality like two plus two equals four, there are only two sexes, Columbus discovered America, really makes me resent it.” Now I agree the claim Columbus discovered America is ambiguous. Obviously the first people who arrived in America were indigenous peoples who crossed the Siberian Land Bridge 10,000 years ago. And Columbus wasn’t even the first European to make it to the new world.
It seemed like Erik the Red or the Vikings got here first. But Columbus was an important individual making it possible for Europeans to colonize and explore the new world. But the other two, there are only two sexes, two plus two equals four. But you see, it’s like with transgender. You say there’s man and woman, and then someone will come along and say, XXXY, did you the chromosomes, there’s also just X or XYY? There’s all these chromosomal disorders. I had no idea. If you listened to my previous episode on Bill Nye, refuting Bill Nye on abortion and sexual identity, I address that objection. But just be wary that when people will try to do this, they’ll say, “Oh, what you thought you knew, actually it’s way more complicated.” So there are no objective truths. There’s no foundation.
Now, all that means is reality is more complicated than we can just quickly summarize to someone. But that doesn’t mean there’s no objective truths about the biological nature of men and women, or the mathematical nature, or the objective mathematical truth that two plus two equals four. So he says, their third point is that narratives that have been considered hegemonic or ruling in the past or present like two plus two equals four should be regarded with extreme suspicion going forward into the future. And people who can make a claim to being oppressed by hegemonic narratives at all get to have the say on how we should think about those narratives and their specific contents, including simple matters of quantity.
The idea here is that truth is not what corresponds to reality, what these critical race theorists and other postmodernists will say is that truth is just what the powerful decide is the truth. Even if it’s something mundane, like two plus two equals four. So we have the right to challenge these truths, especially if you were weaker in society. So if you are a person of color who is LGBTQ and belongs to the math community, then you can just say, oh, well, this is used to oppress me and have white male heteronormative imperialism. Two plus two doesn’t necessarily equal four, two plus two could even equal five if we said so. Two plus two can equal five, you can arrive at these truths in different ways.
And Lindsay said no, what I think infuriated him was that other mathematicians who have a political bias towards this radical postmodernism, which is so common in university departments, university campuses. So other mathematicians went online and they tried to say to Lindsay, “Well, yeah,” and other people were saying, “Two plus two could equal five. That’s just as valid as two plus two equals four.” And he says, “What are you talking about?” And I love the reasons people tried to give, and they were just absolutely terrible. For example, imagine you have two factories and each factory has half the parts necessary to build another factory. So that’s two factories puts together with that each one has the half to build another one equals five factories. That’s not two plus two equals five. That’s 2.5 plus 2.5 equals five. So nice try.
Other people, Kareem Carr, who is a former mathematician and probably former because he says stuff like this. He would say, well, if people speak very literally, they could say one rooster and one hen makes three if I leave them alone for a few months. Or one fox and one hen make one if I leave them alone together. No, one rooster and one hen equal two animals. And then after that, another animal came into existence because they reproduced. Or one fox and one hen equals two animals, if one animal eats another animal, how many animals do you have left? You have one animal, Johnny. False. You’re a racist, Johnny. This is what it’s turning into. Here’s another one. Sometimes when you put two grams of something with another two grams of something, you get five grams.
To which Lindsay says, “Nothing in the universe actually works this way except words.” To which people tried to say similar to the factory example. Well, 2.3 plus 2.3 equals 4.6, and you can round 2.3 down to two and you can round 4.6 up to five. So therefore two plus two equals five. The mental gymnastics people have to do to try to defend their alternative hegemony, it’s really unbelievable. Here’s my favorite one. What if you wrote it as two plus two equals five, and the twos and the five are spelled out, T-W-O plus T-W-O equals F-I-V-E. And so T equals five, W equals two, O equals three, F equals one, I equals zero, V equals four, E equals six. So that the letters in the words, two plus two equals five become the numbers 523 plus 523 equals 1,046.
So here you could have the words, two plus two equals five, if you just redefine the word two to mean the number 523, and the word five to mean 1,046. And Lindsay writes, “For what it’s worth, the stunning example just above was sent to Shraddha Shirude in reply to her request to find a way to make two plus two equals five into a true statement. She is a leader in Washington State’s ethnic studies education program.” Of course, what makes all of this absurd is that math is not something that we created. Now, we did create some elements of math. We created numerals. So for example, there’s different numerals that you can use to do mathematical operations. Like we’re lucky that we use Arabic numerals, one, two, and three.
If you were to write them down, you would probably write them with Arabic numerals as opposed to things like Roman numerals, but we didn’t create the numbers themselves that the numerals represent, or these mathematical truths or sets. They exist, we discover things about them. And that’s actually very strange when you think about it. So recently there was a viral TikTok video from a young woman, her account is Gracie Ham, and she was just putting on makeup in the morning and she had these questions about math. And a lot of people ridiculed her about why she even asked these questions. But thankfully, a lot of philosophers came to her defense and said she’s actually asking really profound questions about mathematics for us to take seriously. Here’s what she said.
Gracie Ham:
And to tell you guys about how I don’t think math is real. And I know that it’s real because we all learn it in school or whatever, but who came up with this concept. And you’re going to be like, Pythagoras. But how? How did he come up with this? He was living in like the, I don’t know whenever he was living, but it was not now where you can have technology and stuff. He didn’t even have plumbing. And he was like, let me worry about y=mx+b, which first of all, how would you even figure that out? How would you start on the concept of algebra? What did you need it for? Because like I get like addition, like, hey, if I take two apples and then add three it’s five. But how would you come up with the concept of algebra? Because what would you need it for?
Trent Horn:
And some people made fun of this. And obviously she’s in high school, she doesn’t understand that the ancient Greeks actually had a fair amount of technology to work with to apply to problems. But coming up with advanced mathematics beyond just simple arithmetic or geometry, you do wonder, well, how do we come up with these things? Especially high level mathematics. So the idea is that we do develop concepts to help us to understand mathematics, but those are the tools we’re developing. These mathematical truths themselves seem to be written into the very fabric of the universe. So this is a debate actually among mathematicians about whether mathematical truths exist independently of human beings or whether they are just merely the product of human beings.
It’s called the Platonism anti-Platonism debate in mathematics. I actually wrote about this in my book, Answering Atheism. Jim Holt, who is an excellent author who talks about metaphysics and religion. He writes in the New York Times that, “Although most mathematicians are atheists, the majority of them still believe in heaven,” quote unquote. What Holt means is that most mathematicians think numbers would still exist even if people did not exist to espouse numerals to describe them. But instead of existing in the physical universe, these numbers and mathematical objects exist in an abstract heavenly realm and the detection of these real but abstract objects, you don’t use the scientific method. Instead, you have a kind of extra sensory perception.
So as Holt concludes, you might say that mathematicians are no strangers to belief in the unseen. So this idea that mathematics is universal, it is distinct from human beings, is part of the fabric of the universe, or at the very least that even if we came, like, let’s say we did come up with mathematical truths, let’s say they were fictions, things that we came up with to describe the world. It’s amazing that they apply to the world in such an amazing way. So there’s the mystery of why they exist if they’re independent, or if they don’t really exist. If there’s something that human beings came up with, how is the fact that when we come up with them, they apply so uniformly and evenly across the universe?
And so that’s led actually William Lane Craig to develop in the past year or two, another argument for the existence of God based on what’s called the applicability of mathematics. So you go back to the 19th century thinker, Leopold Kronecker. He said this very famous quote, “God made the integers, all else is the work of man.” The idea that going back to how I would tease my father-in-law, mathematics is the most fundamental foundation of reality that, I think it was Galileo that said that the book of nature is written in the language of mathematics. You see mathematical structures everywhere, you see in the shell of what, the nautilus shell, the way that it moves actually is according to the Fibonacci sequence.
When you see this and start noticing all these patterns of the way that gravity interacts, there are these consistent mathematical rules and laws, and theorems that are always applied over and over again. And so that has led Craig to put forward this argument on the applicability of mathematics to the existence of God. At his Reasonable Faith website, they have these wonderful animated videos that talk about this. So here’s the one they have on this particular argument.
Speaker 6:
Why does mathematics work? Think about it. Mathematical entities like numbers, sets, and equations are nonphysical and abstract. They can’t cause anything, yet for some reason, the physical universe operates mathematically. Mathematics enabled astronomers to pinpoint the location of a previously undiscovered planet. And James Clerk Maxwell used mathematics to predict the existence of radio waves. Albert Einstein, working with theoretical mathematics developed 50 years earlier formulated his general theory of relativity, a pillar of modern physics. In 1960, the Nobel Prize winning physicist and mathematician, Eugene Vigna, published an article that stunned the scientific community entitled The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Vigna concluded that the effectiveness of mathematics is a miracle, which we neither understand nor deserve. Why is mathematics so effective?
Trent Horn:
So there’s two separate questions when it comes to using these mathematical truths as a path to God. So one would be if you took a Platonist view and you see that these mathematical truths exist, you’d say, well, why do they exist? What’s the explanation for why they exist and why they are the way that they are. And I don’t believe Craig is not arguing that way as saying, look at all these mathematical truths, what explains their existence? Because actually, Craig, as far as I understand, he does not believe abstract objects like infinite sets, propositions, truths, he doesn’t believe that they exist. He’s concerned that if they did exist, they would exist apart from God as if God would be beholden to infinite truths beyond him or laws of logic, or mathematical truths of identity that even bind God himself.
Whereas the classical view in theism, in theistic philosophy would be that if mathematical truths existed, if the number two exists, if an infinite set exists, if it does exist, it exists conceptually in the mind. And in fact, in Ed Feser’s book, Five Proofs for the Existence of God, one of his proofs is called the Augustinian proof. That proof goes back to Saint Augustine and that argues that some truths, truth exists in the mind, some truths are necessary, they must exist like mathematical truths. In that case, these truths must reside in some kind of necessarily existing mind. So you’d say that the number two, these things exist in an objective, though conceptual way. The number two isn’t out there in some kind of platonic heaven floating around.
Like Plato said, there’s a perfect form of the chair. There’s a perfect form of the dog. And any chair or dog we see in this world is a faint shadow of that perfect form. And so the Platonic view would be that whenever we see two of something, that’s just an instantiation of that perfect two in the platonic heaven. But Christians, there has been Christian Platonism throughout history, but most people see Platonism as antithetical to Christianity because it holds that these abstract objects exist apart from God, but God is sovereign over everything. So the traditional view would be that they exist in God’s mind. And Craig has said that would be his fall back position. So in his First Things article, Keep it Simple, Ed Feser describes Craig’s view and talks about it in detail. So here’s what he says about the issue.
“In contemporary philosophy, the alternatives to Platonism that receive the most attention are variations on the medieval doctrine of nominalism which treats numbers and other purported abstract objects as mere names or linguistic constructs rather than as really existing entities. And especially influential version of this idea is fictionalism, which holds that mathematics is like a made up story, the elements of which are useful to science even though they’re not literally true. Is it correct to say Tony Stark is Iron Man and Peter Parker is not? Yeah. Since that’s the way things are in the Marvel comics and movies.” So he goes on to say, “Craig discuss…” Now of course, what that means is not literally true. It’s just true in that fictional construct.
Then he talks about how Craig discusses fictionalism and other related views to talk about how to explain mathematics, numbers, mathematical truths, that they don’t have a kind of real existence. Craig is rather an antirealist, though the classical term for that would be a nominalist, nomos meaning name, that these are just names, just like Iron Man and Peter Parker are names for fictional elements, for the numbers and shapes. These are also names as well. And so Feser goes on to say these rifts on nominalism are all antirealist in so far as they avoid Platonism by denying that mathematics certainly describes objective reality.
And while Craig does not endorse any one of these specific variations to the exclusion of the others, he strongly favors the general antirealist approach as the best way to rebut that the Platonist challenge to aseity, which is the idea that God exists independently of anything else. So Feser goes on to say, “Antirealists have trouble explaining how theories can work so well if they aren’t really true.” So it’s one thing that you come up with Tony Stark is Iron Man. That’s fictional in that fictional universe. But when we come with mathematical truths, you can apply them to a construction project across the world with people who have a different language and culture, and it will still work. This is called the indispensability argument against fictionalism or nominalism in mathematics.
So Feser says, “Craig says little in response to this problem other than to suggest that an antirealist who is a theist can explain the effectiveness of mathematics by saying that God has simply caused the world to operate in a way that reflects the mathematics we know. So the argument that Craig makes on his Reasonable Faith website and other recent publications is not that mathematical truths exist and God explains their existence. But rather that mathematical truths are nominalist, they’re antirealist. We create them. In fact, he was on recently and he was having a discussion about this with Graham Oppy, who’s like the smartest atheist in the world. I’d love to sit down and chat with him. Maybe we’ll do that in the coming months or next year here on the podcast.
And they were debating this argument. And it was so high level, this was on Capturing Christianity at Cameron Bertuzzi’s channel on YouTube, and I’ll include a link to it in the description at trenthornpodcast.com. It got so high level, Bertuzzi asked another lecturer to come in and explain to everyone what Oppy and Craig were talking about because when you talk about mathematics, and aesthetic value, and applicability, indispensability, Platonism, anti-Platonism, it gets pretty high and lofty very fast. So the five-year-old version of the argument, like if I was to explain it to a five-year-old, Craig’s argument, what this lecturer said, he described it this way.
“Math is a crazy world with all kinds of impossible ideas that humans invent for the fun of it. It would be surprising if it matched the real world. Hey, it does fit the real world. Could that be a coincidence or something more?” So that’s how Craig is a nominalist with mathematics, uses it as an argument for God and saying, even if we came up with math in this fictionalist kind of way or an antirealist way, or nominalist way, it applies so universally, how could that be? Unless God created the world so that it has this mathematical structure written into it for us to come up with and apply. And that was the essence of Eugene Vigna’s paper that was referenced in the Reasonable Faith video about saying that it’s a miracle that it corresponds in this way. There’s actually a similar argument for God for morality.
Not that morals are created by God, but rather, even if you don’t believe that, you could wonder, how is it the case that evolution set, even if there were moral facts there, because there are atheists like Erik Wielenberg who believe that moral truths are Platonic. They just exist out there like that you ought to do good and avoid evil is a truth humans cannot change. God can’t change it. It doesn’t relate to God. It’s just out there. It’s like a Platonic value. But even if that were true, the challenge to that is to say, how is it that human beings evolved with the pressures of evolution to happen to come across these specific moral truths? And there’s other moral truths that are out there. You would think there’s a moral truth like the strong can have whatever they take from the weak. That’s a moral truth.
I think it’s false, but it’s a moral truth. How is it that we stumbled across just these particular ones that happened to be true that we evolved to have a sense of being able to discover them? That’s called the evolutionary argument for morality, or the moral knowledge argument that has shown up in some more recent literature on morality and the relationship with God. So I’ll document if you want to go deeper into this argument, check out the discussion Craig and Oppy have on the Capturing Christianity channel. Maybe you should watch the lecture Bertuzzi put up later explaining it like I’m five then going and listening to the whole thing. I’m not totally sold in this argument because I’m not a nominalist, I believe in universals, I believe that numbers have existence.
Universals like colors have existence. So they are ultimately rooted in the nature of God. So I wouldn’t follow Craig in his applicability argument, but I might follow like what Feser does with the Augustinian argument in his book, Five Proofs of the Existence of God and say, and actually, I talk about this a little. I briefly reference to that I think in my cosmic skeptic debate that these things, these universals, how can we explain their existence if they are abstract? But they are conceptual in nature. They ultimately would have to be found in a necessary kind of being where concepts can reside, namely like a mind or something analogous to a mind, something like God.
Well, we rode the rollercoaster today. We hit the lows of wokeness and the heights of mathematical philosophy. I hope you really enjoyed it. I will include all the links that we talked about in the show description at trenthornpodcast.com. If you become a subscriber to trenthornpodcast.com for as little as $5 a month, you can comment, you get access to all the resources we talk about, submit ideas for episodes, questions for episodes, lots of great stuff you don’t want to miss out on. Thank you all so much. And I hope you have a very blessed day.
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