Alright, final week with On the Babylonian Captivity of the Church. I’m about halfway through On the Freedom of a Christian, which is the third one of the 1520 publications, and I don’t currently have anything to say about it, so we might end up skipping it altogether. It’s not bad, just nothing is jumping out at me that’s particularly worth me talking about. After that, you might be interested to know that I’ve got Montaigne’s essays, so that’s going to be our next endeavour after Luther. For what may be the last time, then, let’s talk about Luther. I think he’s got something to say about math.

So Luther is complaining that the Catholic church has made up a bunch of random rules that weren’t actually in the Bible, which, you know, yeah. His perspective is that the church isn’t allowed to make up random shit: “the promises of God make the church, not the church the promise of God.” As far as he’s concerned, the church is only responsible for one thing: “it can distinguish the Word of God from the words of men.” This is actually a really crucial point if you want to crack Luther open – he ultimately still validates the church as being able to discern the Word of God. We know that Luther sets up the Bible as the highest form of authority within Christianity; that’s sola scriptura, the Bible alone. But which Bible, we might ask. The Protestants knocked the canon down to 66 books, while the Catholics have 73. Both groups are pretty sure that they’re correctly discerning the Word of God – so who’s right? You can’t appeal to the Bible, because the shape of the Bible is the thing that’s under question. And that’s the problem with sola scriptura; the text is always indebted to the community that holds it up as authoritative.

Anyway, Luther is trying to justify his unjustifiable argument, and he starts a little ramble about how truth works. He’s trying to preserve the priority of the Bible over the church – that is, if the church can say what is and isn’t the Bible, that implies that the church is hierarchically sort of above the Bible. Luther points out that by that logic, the church is above God, because we also say things about who God is. No, he says, really it’s the other way round: “The truth itself lays hold on the soul and thus renders it able to judge most certainly of all things.” We’re not saying this stuff because we’re in charge of who God is, we’re saying it because we have been struck by divine revelation. We are vessels of truth, rather than dictators; the truth has laid hold to our souls.

As an example of the sort of thing he’s talking about, Luther makes an unusual reference to math. “For example, our reason declares with unerring certainty that three and seven are ten, and yet it cannot give a reason why this is true, although it cannot deny that it is true.” That’s what we’re here for today. Seven and three are obviously ten, right, but if you ask someone why, they might squint at you a bit. They might say, ‘There is no why, it just is.’ We can’t imagine things being any other way. That’s what Luther is saying: we cannot give any reasons why it’s true, but we can’t deny it either. It just is. We have been taken captive by mathematical truth. Sacred doctrine works in the same way: “she [the church] is unable to prove it, and yet is most certain of having it.” It just is. Of course, all the problems from above still apply – when you treat sacred doctrine as true but not provable, you end up with a bunch of different denominations all declaring that they’ve got the proper truth and everybody else is just mishearing. That’s the attitude that the Catholics and the Orthodox take: they talk about concentric circles of Christianity, the true core versus those on the fringes, who have a partial, impeded revelation. In that instance, the Bible essentially becomes a casualty of war. When the most important thing is establishing who has the truest revelation, you can’t use the revelation itself as evidence. Imagine – ‘our revelation is the true one because it says that it’s the true one.’ Very unconvincing.

I want to turn back to the math example for a second, because it’s an interesting point of reference. We all know that seven and three are ten, but – like, not to be a first year philosophy major, but why? Why should seven and three make ten? It’s a weird question, because we can’t imagine it being any other way – and that’s sort of the point. Why can’t we imagine anything else? Is that really Just How It Works, or is it a failure of imagination on our part? Is there something in our brains that makes us conceptualise math in this very specific way? What we’re reaching towards is the philosophy of math. Now, we could argue that addition has to work like it does because it corresponds to our real world experiences. If you have one brick, and then introduce another brick, you have two bricks. And you can use different names for ‘one’ and ‘two’ – you can call them tahi and rua – but conceptually it’s still the same thing. You still mean ‘an individual object’ and ‘an individual object with another’. There’s no other way of bringing objects together. And yeah, we could take that kind of experiential approach, but it’s not something that holds up for all areas of math. It works well enough for addition and subtraction, because we have those very concrete examples. But what about imaginary numbers? If you’re not familiar, imaginary numbers are what you get when you look for the square root of a negative. Look, uh –

Normally, a square is when you multiply a number by itself.

5 x 5 = 25

We can also write it as 5². That still has a real-world equivalent – it’s just a different way of writing multiplication. But under that system, you can’t ever have a square root of a negative number. When you multiply a negative by a negative, it becomes a positive:

-5 x -5 = 25

The only way to get to a negative number would be to multiply a negative by a positive, which isn’t a true square:

-5 x 5 = -25

However, what they have in math is this concept of imaginary numbers, which is what you get when you look for the square root of a negative. The square root of -25 is 5i, where ‘i’ stands for the imaginary number.

5i x 5i = -25

i² = -1

It’s an idea that does useful work in calculus, but how do you derive an imaginary number from bricks? Even if you do manage to cram this weird-ass idea into some useful practical outcome, there’s a whole bunch of interlaced conceptual stuff involved. It’s not as simple as one-brick-two-brick. There’s a host of other similar issues in the broader stable of mathematical ideas. I’m not educated enough to go much further into them, but even with this one example it should be clear what’s at stake. Mathematical ideas aren’t just putting two bricks next to each other and going ‘look, it has to work like this.’

So when Luther says that we are taken captive by truth, and uses the example of seven and three being ten, he’s accidentally invoking some broader questions about the philosophy of math. Sure, we could say that our minds are captured by the truth of addition – or we could ask some deeper questions about what math is, and why our minds conceptualise mathematical systems in the way that they do. And then we could go back to Luther and ask further questions about why he thinks what he thinks, and whether he’s really been captured by the truth, or whether something else might be going on there too.