The Nature of Truth?

9th June 2023
BY Dr John Cullerne, Surmaster Academic
Dr Cullerne is Head of Faith Circles, which meets on Sundays when everyone else meets for Chapel services. The discussions are pupil-led and the following is a transcript of the talk he gave in Chapel on 9 June, prompted by a pupil, Gerald's talk, entitled 'Blind Faith'.

In a previous series of talks, Faith Circles had discussed the extraordinary idea that the behaviour and origins of the universe can be characterised by just six numbers, and even more surprisingly, those six numbers appear to be very finely tuned; that is, it turns out that if some of them differed by just a fraction of their value, there would not be the conditions for the evolution of intelligent life to contemplate any of this at all!

In my earlier life as a physicist I had become quite familiar with two of those six numbers. So, I was in fact in quite a good position to be able to talk about those. However, Gerald’s talk on Blind Faith made the point that I was certainly not an expert in the other four, and since neither I nor anyone else in FC had looked into them in any great detail, we were in fact reliant on what other “experts” tell us is true, and generally, in situations like this, we make little or no effort to verify any of it.

I had a favourite slide in Gerald’s presentation: A cartoon of a white-coated “scientist” on a pedestal, with masses of kneeling worshippers at their feet – I reused his slide by adding two extra captions: an arrow pointing to the scientist figure labelled “Just six numbers”, and an arrow pointing to the worshippers labelled Faith Circles! Okay, maybe that’s a bit much, but this does start you thinking about the nature of Truth, and what we take to be true when we are told something by authority figures.

Now, the word Proof also crops up a lot in such discussions, though in the context of Science it is often used incorrectly. You actually have a better chance of using it correctly in the context of Maths, but believe it or not, even in this context we must be wary of the word Proof.

I must now ask for your forbearance both to those who are aware of the work of a young mathematician called Gödel and those of you who have never heard of any of it. I think it would be useful just to discuss a little of what Gödel did and I hope I do it justice: that is, simplify it enough for all to take on, but not simplify it to the point that it loses its salient features. You see, what Gödel manages to discover is that within any system of logic there will always be statements that are true, but cannot be proved within that system.

What Gödel does is to assign a number to every mathematical symbol and entity known, which we now call their Gödel numbers. He then cleverly finds a way of combining these numbers so that any mathematical statement constructed out of them has its own unique Gödel number. In one particular scheme 0 is assigned 6 and the “equals” sign is 5. Then the trivial statement, 0 = 0 has its own unique Gödel number: 243, 000, 000.

So what does Gödel do with this? Well, in a perverse step of self-referencing he manages to construct the mathematical statement with Gödel number, say G, which says, “There is no proof for the statement with Gödel number G.”

Now, you might think that you could posit an extra axiom to prove G, which you could, but then it turns out that there will be always be a new G, say G’ that can’t be proved in your new system! In striving to complete your mathematical system, you find you can never catch your tail.

Let me try and have a go at explaining why this matters: To think, we generally use language, and even though everyday language is much less precise, it is nevertheless based on the logical systems that Gödel manages to define uniquely. Crucially, our attempt to conceptualise the World in everyday language necessarily requires us to arbitrarily decide how to break the Universe up into manageable bits. But the Universe is actually an undivided whole, so when we come up with self-referencing paradoxes and the like, they are not limitations of the Universe, they are limitations of the way we have decided to think in terms of language.

Sir, he’s broken Maths, I hear you say! Far from it, what Gödel manages to demonstrate is that Truth is literally richer than you can possibly imagine. The way we think has its limitations, and Gödel lays this bare.

So what’s all this got to do with Faith and indeed Faith Circles?

Well, it may be that actions convey better than words. Richard Feynman, the Nobel Prize winner, and in my opinion the best teacher of physics ever, says this:

“Religion is a culture of Faith. Science is a culture of Doubt.”

As I have said, our talks in Faith Circles are generally pupil led, so at the beginning of each session, I leave the pupil speaker in Science Lecture Theatre to set up. In the meantime, I like to be out in the corridor to welcome pupils as they arrive, and I greet them with eye contact, a smile and a, “how are you?” and take their chapel tickets. Now, this way of doing things leaves me very vulnerable: one or two pupils, who think I’m unaware, give me their chapel ticket, go into Science Lecture Theatre, and then try to leave via the back exit to go back up to house and presumably to their beds!

Okay, this is a silly example of the importance of vulnerability in a culture of Faith. You see how vulnerable this makes me: my colleagues are all probably thinking, “What kind of show are you running Cullerne?”

But, what’s the alternative? And NO, I can’t lock the back doors, they’re fire exits! So, is it the case that wanting to greet pupils in the corridor is a bit of a flaw? Might it not be better to maybe have one tutor from each house present to tick names off as pupils arrive? Oh, and to do this, pupils from each house will need to sit in designated areas. Sounding familiar?

Cultures of Faith and Cultures of Doubt have very different vibes to them when it comes to human relationships.

Mr Douglas told us last term: this is especially true of the most intense relationships between human beings: LOVE, for example. Mr Douglas told us: to love is to be vulnerable. Put another way, unless you are prepared to make yourself vulnerable, you can never really love!

I’m asked this a lot by pupils: “Why is Chapel compulsory?”

I usually answer with a question: “Why is Maths compulsory?”

I usually get a confused look at this point. You’ll say, “but, in Maths we do err… Maths.”

Yes, and if you do enough of it you may one day meet Gödel’s incompleteness theorem and, even without that experience, you will discover as you grow up that I cannot teach you just Maths and also hope to prepare you properly for life outside of these protective walls.

Actions may convey truth better than words.

So let me ask you a question:

How vulnerable must you be prepared to make yourself for the deepest most all-encompassing love?

The answer, I think, is on the Crucifix behind me. Whether you are Christian or not, you cannot escape the Truth of that.  

Related Stories