The hierarchy of propositional truths

The following message was given by me on Sunday 24th July at St Mary’s Café Church in Portreath.

In my professional training I am a mathematician at the University of Exeter and I have a wider interest in quantum physics, the universe and evolutionary biology.  Music is an incredibly important part of my life and I am fortunate enough to be the worship leader for Dawlish Christian Fellowship, which is my church back home in Devon.  Through my professional training, I have had to learn what constitutes proof and make professional judgements about what constitutes appropriate evidence to demonstrate any given statement.  This is an analytical approach that I seek to bring to my understanding of the Christian faith also and I will talk more about this later.

If you were here last year when I spoke, then you may recall that we discussed at length science and religion, the nature of “knowledge” and what constitutes “evidence” to determine the truth of any given statement.  For example:

  • If I want to know why the sky is blue, then I will find more suitable evidence by appealing to science, than to creation mythology;
  • If I want to know how you feel, or what you received for your last birthday, then I am better off asking you than plugging electrodes into your brain;
  • If I want to know what a historical person such as Jesus did and who he is, then I am better off looking at historical documents detailing his life and impact on those around him than appealing to the result of one or other scientific experiment.

In short, the question you ask may give you a clue as to what is an appropriate methodology for answering it.  Of course, it is not always simple and straightforward … the question “Does God exist?” might admit evidence from scientific methods, historical methods, sociological methods, philosophical methods and perhaps many other areas.

What I want to talk to you about today is what I will call the “hierarchy of propositional truths” and I will try to explain what I mean by that.  As a mathematician, part of what I study is logic and in particular I am interested in the following questions:

  1. If I have a collection of statements I assume to be true (my premises) what new statements can I derive from them that must also be true (my conclusions)?
  2. If I change my premises, how do my conclusions need to change?
  3. If I am interested in a particular conclusion, what is the smallest collection of premises for which that conclusion is true?

Let me try to illustrate this with an example.  A prime number is a number that is divisible perfectly only by itself and 1; if a number isn’t prime it is called composite.  So 2 is prime, 3 is prime, 4 is composite because you can divide it by 2, 5 is prime, 6 is composite (you can divide it by 2 and 3), 7 is prime, 8 is composite (divisible by 2 and 4), 9 is composite (divisible by 3), 10 is composite.  Primes get rarer the further you go along the number line (there are more things that you can be divisible by), but I can prove that there are infinitely many primes (if you are interested in the proof, then ask me afterwards).  We know that every composite number can be written as a product of primes in a unique way, so 4 = 2 x 2, and 6 = 2 x 3, and 8 = 2 x 2 x 2, and 9 = 3 x 3, and 10 = 2 x 5.  This is called the Fundamental Theorem of Arithmetic.  Now the interesting question is not just why is this true, but what properties of arithmetic does it depend on.  For example, it clearly doesn’t depend on whether or not the sky is blue.  More interestingly, it also doesn’t depend on using fractions – you need to know how to multiply, and add, and subtract, but you don’t need to know how to divide.

Now the Fundamental Theorem of Arithmetic is an interesting conclusion if you start with the rules of arithmetic as your premises, and you can even purge the rules for division from your premises and the Fundamental Theorem of Arithmetic remains true.  Not all conclusions are interesting however … for example, if I take the Fundamental Theorem of Arithmetic as my premise, then the conclusion that 6 is a unique product of primes is not really interesting, because it is now a particular example of something more general.  If all numbers are a unique product of primes, the statement that some numbers are a unique product of primes is simply not interesting.

Now proving the Fundamental Theorem of Arithmetic is a little like climbing Everest.  You have to tackle it in stages, setting intermediate goals instead of heading straight for the summit.  Each of these intermediate goals is a conclusion (endpoint) in its own right, and then becomes the premise (starting point) for the next stage.  This is the “hierarchy of propositional truths” – given a set of premises, certain new statements are arrived at in a certain order.  It’s a bit like, if I fly to Nepal, then certain things have to happen along the way and there are constraints on how they are arranged:

  • So I have to leave Cornwall;
  • And I have to leave the UK;
  • And I have to get on a plane;
  • And I have to travel over the sea;
  • And I have to leave Europe …

There is a certain hierarchy to those statements, but they are not strictly linear (I don’t have to board the plane in the UK, for example).  With any given set of premises, there is a tangled hierarchy of conclusions that can result from them and part of the job of the mathematician is to understand how all the bits depend on each other.

Now, how does this relate to Christianity?  I think this has a really interesting parallel with the Christian journey and by extension how Christians can evangelise effectively.

If I can speak to the mature Christians here, I hope we all feel that the upper slopes are exhilarating, as we see the summit more clearly and ever closer.  But I think we forget quite a lot of detail about what it was like taking those first steps in the foothills of Mount Everest.  In fact, we may have spent so much time figuratively above the clouds, that we’ve forgotten quite a lot about what the terrain of the foothills looks like.  We’ve forgotten perhaps that there are lots of routes up the mountain, some very different to the ones we explored.  Perhaps we spend a lot of our time now with like-minded explorers dissecting obscure passages from the bible, forgetting just how much of the knowledge and experience we’ve built up over the years this depends on.

Reciprocally, to those earlier in their journey ambling in the foothills, that’s exciting too.  Your fellow Christians are here to help you to navigate your way further up the mountain, but be patient with your guides – they have forgotten a lot since they did the journey themselves.  It may feel that they were just parachuted in somewhere higher up the mountain when they tell you to use a foothold that looks 10 metres higher than you can reach, but that’s because they’ve forgotten the route or took a different path to you.

Coming back to the language I used earlier, most of us (myself included) don’t have a good understanding of the hierarchy of propositional truths relating to Christianity – that tangled web that tells us how various statements about the faith relate to each other and in particular, which are “basic” truths and which sit much higher up the hierarchy.  And it is a difficult web to untangle: where, for example, does the question “Who is Jesus?” sit in relation to the question “Does God exist?”.  Does one sit higher than the other?  Or is there something more complicated going on e.g. a resonance whereby as you explore one, you find more evidence for the other until you can establish both are true simultaneously?

Paul in his first letter to the Corinthians describes this a different way: feeding babies milk, until they are mature enough to eat meat.  That’s not meant to be patronising or to say that the big challenging theological questions aren’t the ones to start with, but it recognises simply that there is an order of precedence, or a hierarchy to the questions one wishes to explore.

As a concrete example, one issue that many Christians misplace in this hierarchy is their statement of faith about the bible itself.  My church belongs to a tradition whose profession of faith in the bible declares that it is “the inspired and inerrant self-revelation of God”.  Now we can argue about what that means and I have deliberately not said whether or not I believe that personally.  What we can perhaps agree on is that this statement sits very high up in the hierarchy.

To be more specific, if you start with the premise “everything the bible says is true”, then the conclusion that “Jesus is God incarnate” is not very interesting, because that conclusion is simply one of the many statements that the bible makes.  What is much more interesting is the question, how little do we have to believe about the bible in order that the conclusion that “Jesus is God incarnate” is a valid inference.  Because no-one seeking to understand the Christian faith is going to accept “everything the bible says is true” as a starting point, and why should they?  But they might be prepared to start from the place of asking what historical documents exist from around the time of Jesus’ life and death, and whether or not these are credible sources.

If one were to try to establish that the bible is the “inspired and inerrant self-revelation of God”, then there are possible routes that one could take, but they are boot-strapping arguments, whereby you have to start with something much less ambitious.  For example:

1)      we might start from the point of view that the gospels are interesting historical documents that have something to tell us about Jesus;

2)      we might conclude that they provide convincing evidence that Jesus is God;

3)      we might ask what Jesus’ views were on scripture and how he used it;

4)      we might conclude because of how Jesus, who is God, viewed scripture that it is indeed more than a collection of interesting historical documents and perhaps we will find sufficient evidence to declare the bible the “inspired and inerrant self-revelation of God”.

Notice however that the crux of this, and in fact just about every other matter in the Christian faith, is the question Jesus poses to his disciples: “Who do you say that I am?”  And to answer that we need to appeal to historical documents about Jesus, questioning why we should accept them as a credible witness and identifying what evidence they can provide to answer that question.  That’s digging (or trekking) that everyone has to do for themselves, with help as necessary, but it is not a question you can answer without having given it serious consideration and research.  C.S. Lewis’ key observation on the question of “Who is Jesus?” is given on the handout:

A man who was merely a man and said the sort of things Jesus said would not be a great moral teacher. He would either be a lunatic — on the level with the man who says he is a poached egg — or else he would be the Devil of Hell. You must make your choice. Either this man was, and is, the Son of God, or else a madman or something worse. You can shut him up for a fool, you can spit at him and kill him as a demon or you can fall at his feet and call him Lord and God, but let us not come with any patronizing nonsense about his being a great human teacher. He has not left that open to us. He did not intend to.

Dorothy Sayers, in her essay “The greatest drama ever staged” (pp 4-5), writes the following about our tendency to domesticate Jesus, rather than digging deeper to find out who he really is:

We have very efficiently pared the claws of the Lion of Judah, certified him “meek and mild,” and recommended him as a fitting household pet for curates and pious old ladies.  To those who knew him, however, he in no way suggests a milk-and-water person; they objected to him as a dangerous firebrand.  True, he was tender to the unfortunate, patient with honest inquirers, and humble before heaven; but he insulted respectable clergymen by calling them hypocrites.  He referred to King Herod as “that fox”; he went to parties in disreputable company and was looked upon as a “gluttonous man and a winebibber, a friend of publicans and sinners”; he assaulted indignant tradesmen and threw them and their belongings out of the temple; he drove a coach-and-horses through a number of sacrosanct and hoary regulations; he cured diseases by any means that came handy, with a shocking casualness in the matter of other people’s pigs and property; he showed no proper deference for wealth or social position; when confronted with neat dialectical traps, he displayed a paradoxical humour that affronted serious-minded people, and he retorted by asking disagreeably searching questions that could not be answered by rule of thumb.  He was emphatically not a dull man in his human lifetime, and if he was God, there can be nothing dull about God either.

It all depends on who this man is … and we have an obligation to pose the question, so that others can seek the answer in their turn.

In evangelising, we can only be effective evangelists for Jesus, however, if we are prepared to meet people where they are on their Christian journey, not where we are.  Otherwise, we are simply advising the traveller who is asking for directions, “Ooh, well I wouldn’t start from here”.

The Apostle Paul understood this well as he travelled the Roman Empire preaching about Jesus’ life, death and resurrection.  In the book of Acts (17:22-31), Paul comes to Athens and sees that they are deeply spiritual people who have an altar inscribed “To an unknown God”.  So he proceeds to use this as the starting point to tell them the Good News about Jesus.  Paul writes in his first letter to the Corinthians, “I have become all things to all men, that I may by all means save some.”  By this he doesn’t mean that he has become unscrupulous in the way he preached Christ on the cross, but that he met people where they were.  If someone was a Jew, then he could discuss where their religion was pointing; if someone was seeking spiritually, he was able to engage them in explaining why they felt the need for something more and where to find it; if someone was poor or ill, he comforted and healed them, discussing the hope they have in Jesus.

We have to do the same, engaging people where they are and getting to know them in order that we can help them on their faith journey more effectively.  And lest I give the impression that the intellectual route is the only path up the mountain, we should be clear that it is not the most effective witness for everyone.  Some people want to hear the stories of lives transformed; some people want to see Christians stepping out and doing good works in the community; for some people it is prayer, or music, or art that draws them closer to Christ.

And recognising that I’m going to finish by presenting the gospel message in song.  Many of these words are drawn from Isaiah 53, which was written approximately 600-700 years before Jesus’ birth and we have manuscript copies from about 200 years before his birth.  It is called “Immanuel”, which means “God with us”.

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