Dogma, in religions and other places

Most people are familiar with the dogmas promoted by powerful religious institutions such as the Roman Catholic church, evangelical protestant churches and some branches of Islam. The institutions claim they have sole possession of the truth, direct from God, and that anybody that does not agree is a heretic, someone to be avoided, and who may be punished.

Dogmatism is annoying, anti-social and causes a great deal of misery, both for people growing up under the power of the institution proclaiming the dogma and for some of those that interact with them.

It’s also pretty well recognised. One need only mention religious dogma and heads start to nod. People know what you’re talking about.

Despite the negative connotations the word has for most people, the leadership of the RC church does not object to the term and still uses it as a core part of its teachings. They invented the term, and use it without shame to describe propositions that the church says RCs are obliged to believe. When I was an RC I never thought to ask what happens if one does not believe a dogma. It seemed too impertinent. But now when I research it, the answer that appears fairly consistently across different RC sources is that it is not a sin to disbelieve the dogma, as long as you don’t say so aloud, because that might encourage somebody else to disbelieve it. That would be heresy, which is a grave sin, punishable by an eternity in hellfire. A few centuries ago, the punishment was lighter – a mere burning at the stake.

Although the RC church invented the word ‘dogma’, it is not the only institution to proclaim dogmas. There are plenty of dogmas in evangelical protestantism, and some variants of Islam are heavily dogmatic. Perhaps non-RCs would reject the application of the word ‘dogma’ to their essential beliefs, given the pejorative sense in which the word is mostly used these days. But it would be hard to argue that concepts such as ‘biblical inerrancy’ or ‘justification by faith alone’ are not dogmas for some protestant sects.
It would be a mistake to equate dogma with religion, because most religions are not dogmatic. It is just our misfortune that the three most dominant religions of our world: Roman Catholicism, Evangelical Protestantism and Islam have many adherents that assert an obligation to believe the relevant dogmas.

I am not aware of any pre-Christian religion that had obligatory beliefs. Judaism had many rules, but they were about practices, not beliefs. Even for worship, the injunction was to not worship other gods, or idols in particular. As long as you didn’t bow down or offer sacrifices to golden calves or statues of Ba’al, it didn’t matter whether, in the privacy of your own thoughts, you really believed Yahweh was the greatest god. In fact the Torah says nothing at all about obligatory beliefs, so far as I recall. Other pre-Christian religions, like Buddhism, the many variants of Hinduism, Mithraism, Zoroastrianism and the ancient Greek, Roman and Egyptian religions also appear to set no expectations about their members’ beliefs.

Dogmas appear in places other than religions. Just as some protestants, while abjuring RC dogmas like the Immaculate Conception or Trans-substantiation, insist on their own dogmas, people who are opposed to all religions – the so-called New Atheists – can be as dogmatic as those they criticise. Classic New Atheist dogmas are things like ‘it is wrong to believe anything that cannot be proven to be true’, or ‘for all questions and human challenges, science is the best means to an answer’. For some militant atheists it even seems to be an item of faith that adherence to any religious belief at all must be a sign of stupidity. I know these dogmas because for a while I was a born-again atheist and subscribed to them. I used to listen to podcasts of debates between Christians and atheists about whether God exists, cheering on my side and hoping for the unconditional surrender of the other. Looking back, it seems such an odd thing to do. Neither the debaters nor their supporters in the audience ever changed their views one iota. Each side had their dogmas and stuck steadfastly to them. They may as well have both been shouting into the wind. But really I suppose they were just playing to their supporters. I believe such debates can never get anywhere because it is impossible to prove or disprove the existence of a god, and any attempt to do either relies on presuppositions – usually unstated –  that one side will accept and the other will not.

I have not completely forsaken atheism. I am still atheist on Mondays and alternate Wednesdays. But I have forsaken the dogmatism that accompanies the more aggressive variants of atheism.

Dogmas manifest in wider circles than the theological and anti-theological. Other areas where they crop up are philosophy, politics, economics, psychology and sociology. People debate whether there is such a thing as objective morality, whether equality is more important than liberty, whether wealth really does ‘trickle down’ in a capitalist society, and whether most psychological disorders can be traced back to early childhood experience. Debates between evangelical christians and militant atheists seem mild and friendly compared to the vicious passions unleashed in a debate between a Berkeleyan Idealist and a Materialist acolyte of GE Moore about whether a tree that falls in a forest makes a noise if there is nobody there to hear it.

I’m not suggesting that none of those things matter. It matters very much what political and economic theories are adopted by governments. They affect many people’s lives. Even some sorts of philosophy have huge effects. One can trace the roots of many important social movements to the ideas raised by philosophers, such as the influence of Enlightenment philosophers on the American and French revolutions. It’s hard to see how the ‘actual existence’ or otherwise of impossibly distant galaxies could affect our lives, but other similarly meaningless topics, such as whether the Holy Ghost proceeds from the Father and the Son, or just from the Father, have led to wars, the rise and fall of empires and many burnings of people that had the misfortune of siding with the wrong opinion.

The common element of dogmatic claims is not their capacity or otherwise to affect our lives, it is their total immunity to proof, disproof, or experimental testing of any kind.

There is no dogma about the law of gravity, no dogma of quantum mechanics or a doctrine of the periodic table. A good biology teacher will not demand that her class believe that cells of mammals have a nucleus containing bundles of DNA and little packets of RNA. A good mathematics teacher will not demand that the class believe that the method being taught for long division works. The teacher is saying: “Here is a method, or an approach to understanding something. Most people find it useful in getting important things done“. The teacher could add – but generally doesn’t bother – “If you don’t like what I’m teaching and want to go and invent your own method of long division (or theory of the elements), be my guest! I’ll still be here to help you learn this method if you change your mind.

It is both ironic and predictable that the claims about which we humans get most dogmatic are those about which it is least possible to be certain. When there is a high level of certainty – as with Newton’s Laws of Motion – there is no need for dogmatism. You can take it or leave it. More fool you if you leave it. But when there is little to no certainty available, as with doctrines of neo-liberal economics (or, to be fair, Marxist economics), doctrines of the nature of the Holy Ghost, or proofs and disproofs of the existence of god(s), people generally ramp up the dogmatism and turn the volume to eleven. They use dogma and noise to make up for their lack of confidence and inability to provide any concrete evidence for the proposition.

This has led to my strongest philosophical position being anti-dogmatism. No matter what proposition somebody makes, be it about religion, ontology, economics or politics, and regardless of whether I sympathise with the belief being promoted or not, I now instinctively react against it and look to debunk it, if it is made dogmatically. That doesn’t mean I don’t hold any opinions on those topics. I have loads. Some of them – mostly the political ones – I hold very strongly and am prepared to march the streets, donate to a cause and publicly argue to try to persuade people over. But I hope I never get to the stage of believing that I am unquestionably right about something and that those who disagree are unquestionably wrong. That seems a poor way to live. I have sometimes been like that in the past, but I think I am not now and hope I won’t be again. For me, unquestioningly accepting a dogma is the coward’s excuse for not thinking for oneself.

That is my opinion, which I acknowledge may be mistaken.

Andrew Kirk

Bondi Junction, April 2019


Mastering maths monsters

‘Partial differentiation’ is an important mathematical technique which, although I have used it for decades, always confused me until a few years ago. When I finally had the blinding insight that de-confused me, I vowed to share that insight so that others could be spared the same trouble (or was it just me that was confused?). It took a while to get around to it, but here it is:

https://www.physicsforums.com/insights/partial-differentiation-without-tears/

My daughter Eleanor make a drawing for it, of a maths monster (or partial differentiation monster, to be specific) terrorising a hapless student. The picture only displays in a small frame at the linked site, so I’m reproducing it in all its glory here.

Andrew Kirk

Bondi Junction, October 2016


Acoustic ‘beats’ from mismatched frequencies

Here’s a piece I wrote explaining the mathematics behind the peculiar phenomenon of acoustic ‘beats’.

https://www.physicsforums.com/insights/acoustic-beats-mismatched-musical-frequencies/

It’s a bit maths-y. But for those that don’t love maths quite as much as I do, it also has some interesting graphics and a few rather strange sound clips.

Andrew Kirk

Bondi Junction, August 2016


Too many words!

Books are too long. People talk for too long. Academic papers are too long. Almost everything is too long.

Why? Partly, because to be concise is very difficult. Urban legend has it that Blaise Pascal once wrote at the end of a letter to a friend: ‘I’m sorry this letter is so long. I didn’t have time to write a short one’.

I struggle with conciseness. Part of the problem is that, when I am trying to explain something, I worry about whether what I have said is clear enough, so I keep on saying it over, in a slightly different way each time, in the vague hope that one of the attempts will make the connection.

I think a better strategy might be to make one brief attempt at an explanation and then wait for a response. If more is needed, I imagine my interlocutor will tell me. If they do, the particular nature of their response will better enable me to tailor my next statement to fill in the information that was missing in my first.

But that requires discipline, and nerves of steel. It is like being silent in an interview after giving a short reply to a question – forcing the interviewer (or interrogator) to make the next move. Few people can carry that off, and I suspect I am not one of them.

Academic papers can be particularly irritating, droning on about all the references and who has written what, so that by the time one gets to the bit about what the authors have done that’s actually new, one is exhausted and wants to retire for a tea break. It’s not clear to me whether this is a stylistic practice, imposed by the producers and reviewers of journals, or whether it reflects insecurity on the part of the authors, who may feel that they need to mention some minimum number of other papers in order to be taken seriously.

Arthur Schopenhauer railed against this sort of writing in a series of essays collected under the title ‘The Art of Literature’. He opens with an unrestrained broadside ‘There are, first of all, two kinds of authors: those who write for the subject’s sake, and those who write for writing’s sake.‘ Schopenhauer loved the first (and of course considered himself to be one of them) and loathed the second.

If someone really has something important to say, it usually doesn’t take very long. When Neville Chamberlain announced the grim news to the British people in 1939 that Britain had declared war on Germany, the message had been delivered by the end of the 67th word. I did a test reading just now and it took about 26 seconds, including pauses for effect.

Einstein’s legendary 1905 paper that presented his special theory of relativity to the world, ending decades of confusion amongst physicists, is only 24 pages, and the key part that resolves the paradoxes by which physics was previously beset is complete by the end of page 12! John Bell’s paper that turned the world of Quantum Mechanics upside down in 1964 is only six pages. Bell cited only five references. Einstein cited none.

In general communication, most people use too many words. I do too, but I am trying to correct that. I feel that, where possible, I would like to conduct a post-mortem on every sentence I utter and work out whether that sentence has added any new information. If it hasn’t, then it was probably a waste of everybody’s time.

Politicians exploit this deliberately. They are trained to, when asked a difficult question by a journalist, give a long-winded, emphatic speech about something only tangentially related, thereby avoiding the issue and (they hope) making the journalist despair of persisting with the question because of the pressure of time. Even better, if the politician sounds confident in their ‘answer’, the less analytic watchers will form the impression that the politician is competent and frank. The more analytic types just shrug their shoulders in disgust and turn the telly off.

A sentence can be very long and yet not reveal what information it contains until late in the sentence. Sometimes there is a key word that makes it all fall into place, The words before that one stack up like the numbers in a long calculation on a Reverse Polish calculator, impotent while they wait for release. Then the key word comes and it all falls into place. It attains a meaning. The wait for that word can sometimes be prolonged, like in this:

Though they all came from different social strata, sub-cultures and occupations, crammed together against their will in the prison cell from which they wondered if there would ever be any release, though none of them had known each other – or even known of each other – in their previous lives, though they squabbled and quarrelled over the tiniest of things, the one thing that bound them together despite the rivalries and petty jealousies, the perceived slights and reconciliations, the development, disintegration and reformation of cliques, was a single shared emotion, an emotion so powerful that they could feel it oozing out of one anothers’ pores, smell it on their breath and discern it in the tones of voice – the emotion of fear.

In some cases, the key word never comes. Perhaps the writer or speaker confuses themselves by their excessive verbiage and ends the sentence with an admission of defeat.

Books are too long as well! Novels are generally OK, as it takes time to get to know and care about the characters. But I have a strong sense that non-fiction books are often padded to reach whatever is considered a minimum page count for a book – usually at least 200. There isn’t really a strong market for writings that are halfway between essay and book length. In many cases a book really only has one idea, which could make a decent essay, but doesn’t justify a book. But essays don’t get to be put on a prominent shelf that catches your eye as you enter the bookshop, nor do they get listed on the New York Times best sellers’ list.

Nassim Taleb’s famous book ‘The Black Swan’ is like that. It really only contains one idea, which is that investors, bankers and other financiers have for decades been making crucial financial decisions based on theories in which they assume that the future will be like the past, and that all occurrences of randomness must follow the Normal Distribution (the nice friendly old ‘Bell Curve’). Decisions based on that erroneous, oversimplified assumption have repeatedly led to disasters, because events tend to be more extreme than is predicted by the Bell Curve. Taleb’s is a good insight, and definitely worth saying, but probably not worth stringing out to book length.

And then, if the book sells well, they write it again, ever so slightly differently, and pretend it’s a new book, with new ideas. Taleb did that. Self-help authors do it all the time – which raises the question ‘If your first book about how to live a better life was so incomplete that it needs to be supplemented by a second, why did I waste my time reading it?‘ I suspect Richard Dawkins may do it too. As far as I can tell he has written at least four popular explanations of evolution. I read The Blind Watchmaker and thought it was great (but too long, of course!). But I didn’t read The Selfish Gene, The Ancestors’ Tale or The Greatest Show on Earth because I couldn’t see any indicators that they would contain much substance that hadn’t already been covered in the one I had read. I imagine there is some new material in each of them, but I would guess it’s more likely to be a dozen pages’ worth rather than 200+.

Fiction authors and other creative artists do this too. Stravinsky acidly observed that Vivaldi wrote the same marvellous concerto five hundred times. Bach shamelessly reused his work (goodness knows he was paid little enough for it!) and Enid Blyton invented maybe a dozen adventure and fantasy stories, which she recycled into what seems like hundreds of similar tales (surely I’m not the only one that’s noticed the remarkable similarity between Dame Slap’s School for Bad Pixies and Mr Grim’s School for Mischievous Brownies?). And let’s not even mention Mills and Boon. But somehow I don’t mind that so much. We humans are story-telling animals, and telling the same story repeatedly, changing it just a little every time, is what we have always done. I find myself able to smile indulgently on the prolixity of Enid and Antonio and Mills (?), but alas not on that of Nassim or Richard, or Deepak Chopra.

I think I’ve ranted for long enough now about how We All (including me) need to work on being more concise with our communication. It’s time to relent a little.

Not all language is just about conveying information, so the efficiency with which the information is conveyed is not always the best test. In comforting a frightened child, information communication is not the purpose of our speech. I will restrain myself from objecting that the second half of the soothing phrase ‘There, there‘ is informationally redundant. In fact, I think I could even stretch to approving of its repetition, if its first invocation was insufficient to assuage the poor mite’s distress.

Declarations of love, expressions of support, telling jokes, goodbyes, hellos and well-wishes are all ‘speech acts’ that have important non-informational components. It seems appropriate to apply different expectations to those speech acts from those we apply to informational speech. Even there, there are limits though. Many’s the operatic love aria I’ve sat through where after a while I just feel like screaming ‘OK, you love him, we get it, can we move on with the plot now please?’ And waiting for Mimi to die in La Boheme (of consumption, what else?) in between faint protestations of her love for Rodolfo, can become a little trying on one’s patience after the first ten minutes of the death scene.

But communication of information is the purpose of much of the language we use, especially in our work lives. It is a pity that so much of it is ill-considered.

Hmmm. 1,742 words. I wonder if I could turn this into a book.

Andrew Kirk

Bondi Junction, November 2015


Metaphysics as a creative craft

In my writings I have not infrequently been dismissive of metaphysics, arguing that most metaphysical claims are meaningless, unfalsifiable, and of no consequence to people’s lives (leaving aside the unfortunate historical fact that many people have been burned at the stake for believing metaphysical claims that others disliked).

Perhaps it is time to relent a little – to give the metaphysicians a little praise. At least I will try. The basis for this attempt is a re-framing of what metaphysics is about. Instead of thinking of it as a quasi-scientific activity of trying to work out ‘what the world is like’, perhaps we could instead think of it as a creative, artistic activity, of inventing new ways of thinking and feeling about the world. Metaphysics as a craft, as delightful and uncontentious as quilting.

Why would anybody want to do that? Well I can think of a couple of reasons, and here they are (except that, like the chief weapons of Python’s Spanish Inquisitor, the number of reasons may turn out to be either more or less than two).

We know that there is a very wide range of human temperaments, longings, fears and attachments. A perspective that is inspiring to one person may be terrifying to another, and morbidly depressing to a third. For instance some people long to believe in a personal God that oversees the universe, and would feel their life to be empty and meaningless without it. Others regard the idea with horror. Some people are very attached to the idea that matter – atoms, quarks and the like – really, truly exists rather than just being a conceptual model we use to make sense of our experiences. Philosophical Idealists (more accurately referred to as Immaterialists) have no emotional need for such beliefs, and accordingly deny the existence of matter, saying that only minds and ideas are real. Indeed some, such as George Berkeley, regard belief in matter as tantamount to heresy, which is why the subtitle of his tract ‘Three dialogues between Hylas and Philonous‘, which promoted his Immaterialist hypothesis, was ‘In opposition to sceptics and atheists‘.

So the wider the range of available metaphysical hypotheses, the more chance that any given person will be able to find one that satisfies her, and hence be able to live a life of satisfaction, free of existential terror. Unless of course what they really long for is existential terror, in which case Kierkegaard may have a metaphysical hypothesis that they would love.

One might wonder – ‘why do we need metaphysical hypotheses, when we have science?‘ The plain answer to this is ‘we don’t‘. But although we do not need them, it is human nature to seek out and adopt them. That’s because, correctly considered, science tells us not ‘the way the world is‘, but rather, what we may expect from the world. A scientific theory is a model that enables us to make predictions about what we will experience in the future – for instance whether we will feel the warmth of the sun tomorrow, and whether if we drop an apple we will see it fall. Scientific theories may seem to say that the world is made of quarks, or spacetime, or wave functions, but they actually say no such thing. What they say is, if you imagine a system that behaves according to the following rules – which might be rules about subatomic particles like quarks – and you observe certain phenomena (such as my letting go of the apple), then the behaviour of that imaginary system can guide you as to what you will see next (such as the apple falling to the ground).

It’s just as well that scientific theories say nothing about ‘the way the world is’, because they get discarded every few decades and replaced by new ones. The system described by the new theory may be completely different from that described by the previous one. For instance the new one may be all about waves while the previous one was all about tiny particles like billiard balls (electrons, protons and neutrons in the Rutherford model of the atom). But most of the predictions of the two theories will be identical. Indeed, if the old theory was a good one, it will only be in very unusual conditions that it makes different predictions from those of the new theory (eg if the things being considered are very small, very heavy or very fast). So by recognising that scientific theories are descriptions of imaginary systems that allow us to make predictions, rather than statements about the way the world is, we get much greater continuity in our understanding of the world, because not much changes when a theory is replaced.

I think of metaphysics as the activity of constructing models of the world (‘worldviews’) that contain more detail and structure than there is in the models of science. We do not need the more detailed models of metaphysics for our everyday life. Science gives us everything we need to survive. But, being naturally curious creatures, we tend to want to know what lies behind the observations we make, including the observations of scientific ‘laws’. So we speculate – that the world is made of atoms like billiard balls, or strings, or (mem’)branes, or a wave function, or a squishy-wishy four-dimensional block of ‘spacetime’, or quantum foam, or ideas, or noumena, or angels, demons, djinn and deities. This speculation leads to different mental models of the world.

So metaphysics adds additional detail to our picture of the world. Some suggest that it also adds an answer to the ‘why?’ question that science ignores (focusing only on ‘how?’). I reject that suggestion. As anybody knows that has ever as a child tried to rile a parent with the ‘but why?’ game, and as anybody that has been thus riled by a child knows, any explanation at all can be questioned with a ‘but why?’ question. No matter how many layers of complexity we add to our model, each layer explaining the layer above it, we can always ask about the lowest layer – ‘but why?’ Whether that last layer is God, or quarks, or strings, or the Great Green Arkleseizure, or even Max Tegmark’s Mathematical Universe, one can still demand an explanation of that layer. By the way, my favourite answers to the ‘But why?’ question are (1) Just because, (2) Nobody knows and (3) Why not? They’re all equally valid but I like (3) the best.

Some of these mental models have strong emotional significance, despite having no physical significance. For instance strong solipsism – the belief that I am the only conscious being – tends to frighten people and make them feel lonely. So most people, including me, reject it, even though it is perfectly consistent with science. Some people get great comfort from metaphysical models containing a god. Others find metaphysical models without gods much more pleasant.

So I would say that metaphysics, while physically unnecessary, is something that most people cannot help doing to some extent, and that people often develop emotional attachments to particular metaphysical models.

Good metaphysics is a creative activity. It is the craft of inventing new models. The more models there are, the more people have to choose from. Since there are such great psychological and emotional differences between people, one needs a great variety of models if everybody that wants a model is to be able to find a model with which they can be comfortable.

Bad metaphysics (of which there is a great deal in the world of philosophy) is trying to prove that one’s model is the correct one. I call this bad because there is no reason to believe that there is such a thing as ‘the correct model’ and even if there was one, we’d have no way of finding out what it is. There can be ‘wrong’ models, in the sense that most people would consider a model wrong if it is logically inconsistent (ie generates contradictions). But there are a myriad of non-contradictory models, so there is no evidence that there is such a thing as ‘the right model’. Unfortunately, it appears that most published metaphysics is of this sort, rather than the good stuff.

It’s worth noting that speculative science is also metaphysics. By ‘speculative science’ I mean activities like string theory or interpretations of quantum mechanics. I favour Karl Popper’s test for whether a model is (non-speculative) science, which is whether it can make predictions that will falsify the model if they do not come true. A model that is metaphysical can move into the domain of science if somebody invents a way of using it to make falsifiable predictions. Metaphysical models have done this in the past. A famous example is the ‘luminiferous aether’ theory, which was finally tested and falsified in the Michelson-Morley experiment of 1887. Maybe one day string theorists will be able to develop some falsifiable predictions from the over-arching string theory modeli that will move it from the realm of metaphysics to either accepted (if the prediction succeeds) or discarded (if the prediction fails) science. However some metaphysical models seem unlikely to ever become science, as one cannot imagine how they could ever be tested. The debate of Idealism vs Materialism (George Berkeley vs GE Moore) is an example of this.

So I hereby give my applause to (some) metaphysicians. Some people look at philosophy and say it has failed because it has not whittled down worldviews to a single accepted possibility. They say that after three millenia it still has not ‘reached a conclusion’ about which is the correct worldview. I ask ‘why do you desire a conclusion?‘ My contrary position is to regard the proliferation of possibilities, the generation of countless new worldviews, as the true value of metaphysics. The more worldviews the better. Philosophy academics working in metaphysics should have their performance assessed based not on papers published but on how many new worldviews they have invented, and how evocatively they have described them to a thirsty and variety-seeking public. Theologians could get in on the act too, and some of the good ones (a minority) do. Rather than trotting out dreary, flawed proofs of the existence of God. the historicity of the resurrection, or why God really does get very cross if consenting grown-ups play with one another’s private parts, they could be generating creative, inspiring narratives about what God might be like and what our relationship to the God might be. They could manufacture a panoply of God mythologies, one to appeal to every single, unique one of us seven billion citizens of this planet. Some of us prefer a metaphysical worldview without a God, but that’s OK, because if the philosopher metaphysicians do their job properly, there will be millions of those to choose from as well. Nihilists can abstain from all worldviews, and flibbertigibbets like me can hop promiscuously from one worldview to another as the mood takes them.

We need more creative, nutty, imaginative, inspiring metaphysicians like Nietzsche, Sartre, Simone Weil and Soren Kierkegaard, not more dry, dogmatic dons that seek to evangelise their own pet worldview to the point of its becoming as ubiquitous as soccer.

Andrew Kirk

Bondi Junction, January 2015

i. Not just a prediction of one of the thousands of sub-models. Falsifying a sub-model of string theory is useless, as there will always be thousands more candidates.


What is a cause? Trying to distil clarity from a very muddy concept

Preface

Scene 1: So! – shrieked the evil monocled Gestapo officer. Eef you do not tell me ze name off ze leader off your resistance group, I vill shoot zis prisoner. Make your choice keffully! Do you vish to be ze cause off ze death off zis poor eenocent civilian?

Fade to scene 2: And now m’lud, intoned the imposing barrister, as you have just heard, if the defendant had correctly diagnosed the plaintiff’s stomach pain as a torsion of the testicle rather than prescribing antacid tablets, the testicle could have been saved by a simple operation that would have enabled the plaintiff to live the happy, fulfilled sexual life that he so richly deserves. I ask the court to award damages of five million dollars against the defendant for causing this poor man’s loss of sexual function.

Fade to scene 3: Have you found out why my car won’t start asked Jedediah. Well, I’m not sure, mister, said the mechanic, with a sarcastic look on her face, but it might have something to do with this snake that’s gotten its tail wedged in your starter motor. Mind your hands there, it looks a bit annoyed. Well golly, said Jedediah, who’d’ve thought that a little ol’ critter like that could cause so much trouble?

Three stories, three problems, three causes. Or are they?

If our heroine refuses to name the resistance leader to the Gestapo, will she have caused the civilian’s death? Or will the Gestapo officer have caused it? Or both? Or something else?

Did the doctor really cause the loss of the plaintiff’s testicle, or was it the fact that it managed to twist so as to strangulate the blood supply, or perhaps it was the plaintiff’s genes that gave them a particular anatomy that made them vulnerable to such an occurrence? If the latter then were the plaintiff’s parents the cause of the loss, or should we perhaps blame the person that introduced the parents to one another?

And was the snake really the cause of Jedediah’s car problems, or was it that he’d parked his car in the bush while camping overnight, providing an enticing warm place for any passing snakes to nestle in the warm engine?

Defining a ’cause’

The idea of cause and effect is an ingrained part of our language. We all feel that we know what the terms mean. But do we really? The above examples show how it’s not usually possible to point to one thing and say that is the cause of this. We might feel however that, with more care and thought, we will be able to precisely describe what really caused any given event.

The amazing answer is that No, actually we can’t. There is no such thing as a single cause of an event in the way it is traditionally thought of. The purpose of this essay is to examine the idea of cause (and effect) and work out what, if any, meaning we can give to this vague and rubbery, yet ubiquitous concept.

Is a cause necessary? Is it sufficient?

A natural place to start looking for a meaning seems to be to ask whether a cause is a necessary or sufficient condition, or both, for its effect to occur.

None of the suggested causes in the preface are necessary conditions. There are plenty of other ways the civilian could have died, the testicle been lost or the car failed to start. So we can dismiss necessity as a feature of causes straight away.

What about sufficiency? Neither of the suggested causes in the first two stories in the preface are sufficient conditions. The prisoner could have refused to snitch but the Gestapo officer relented and didn’t shoot the civilian. The undiagnosed twisted testicle could have untwisted by itself, or another doctor passing five minutes after the defendant misdiagnosed it could have had a look and diagnosed it correctly. The snake is another story though. Having a snake’s tail wedged in your starter motor effectively guarantees that your car will not start. So perhaps some causes are sufficient conditions for their claimed effects. We’ll come back to that later.

Cause as a difference between alternative prior scenarios

If I go to the dentist and ask why my lower right incisor aches, she may find decay in it and say “the cause of your ache is decay in the tooth”. The decay is neither a necessary nor a sufficient condition for the ache. The ache could be psychosomatic with no decay, or there could be decay but a dead nerve, in which case I’d feel no ache.

Yet I know what she means. So what is it that I, and any other dental patient, understands from the dentist’s statement?

I think it is that the situation I am experiencing while sitting in the dentist’s chair, call it situation S1, may be compared with another situation S2, that is identical to S1 in every respect except that there is no decay in the tooth. In neither case do I suffer psychosomatic hallucinations, nor is the tooth’s nerve dead. The only physical differences between the two situations is the decay. If a message takes a nanosecond to travel along a nerve from the tooth to my brain then in the situations one nanosecond later than S1 and S2, call them S1a and S2a, S1a will have me experiencing toothache and S2a will not.

Now the dentist has not explicitly mentioned an alternative situation, but that’s because it’s implied. I naturally interpret her statement as meaning “According to my observations and the biology they taught me at dental school, the key difference, in the toothy-brainy part of your body, between you and somebody very like you that does not have a toothache is that you have decay and they do not”.

We can formalise this idea of a cause with a precise definition:

‘If:

    1. S1 and S2 are descriptions of alternative possible states of a system at time t, and
    2. the difference between S1 and S2 is C, and
    3. theory T requires that event E occurs at time t+dt if the system state at time t is S1, and
    4. theory T requires that event E does not occur at time t+dt if the system state at time t is S2,

then C is the cause of E in system state S1 with respect to system state S2, according to theory T.’

Note that lines 3 and 4 use the concept of sufficiency, raised in the previous section. S1 is sufficient reason for E to occur and S2 is sufficient reason for E to not occur.

People rarely, if ever, refer to two alternative system states when saying something is a cause. Usually, as with the dentist, the natural choice for S2 is evident and need not be stated. But it is useful to remember that there is nearly always an implied comparison state S2 when we talk about causes. Whenever controversial or confusing claims are made about causality, as happens so often in litigation, politics and philosophy in particular, it can help enormously if we analyse the claim by trying to identify what the implied comparison state is.

Do we really need to say ‘according to theory T’?

The appendage to the definition – ‘according to theory T’ – might seem superfluous and annoying to some. After all, people don’t usually quote a theory when they say that pricking the balloon with a needle caused it to burst. Nevertheless, just like the comparison state, a theory is always there. In the case of the balloon, the theory is Physics, as taught at modern universities. Training in Physics up to third-year university would provide all the understanding needed to explain the pop of the balloon.

Looking at the dentist example, we see that our interpretation of her diagnosis does include reference to a theory, viz: ‘according to … the biology they taught me at dental school’.

Now we might imagine that both Physics and Biology are just parts of a Grand Theory of Everything, of which science has so far only discovered a portion. If that were so, then we could leave off the appendage to our description of a cause, and just imply that the theory we mean is the Grand Theory of Everything.

But although some might find the Grand Theory of Everything a nice idea, and wish there really were one out there, we have no reason to suppose there is. I discuss this further in my essay ‘Some random thoughts on whether the world is random’. The conclusion is that, unless we are prepared to regard an enormous list of everything that ever happens in the universe as a theory of everything (which most people wouldn’t) there is no way to decide what sort of a collection of statements could qualify as such a theory. Is there a word limit? Does the collection have to be finite? Does it have to be expressible in English? Does it have to be comprehensible by an intelligent human?

In addition, as I argue in my essay ‘Replacing Truth with Reason’, there may not even be any ultimate description of the universe. Our scientific advances may lead to increasingly more complicated theories that, while intriguing, exciting and pragmatically useful, never converge to a final, stable, ultimate theory. Perhaps the universe is too complicated to be described by any theory.

So we will have to put up with the appendage for the time being. Devout Platonists may wish to assume that there is a Grand Theory of Everything, and omit the appendage, implying that T is that Grand Theory. But that is an act of faith that I do not feel inclined to emulate.

It does however seem reasonable to omit the appendage when conversing in the vernacular, if our implication is understood to be not that T is the Grand Theory of Everything, but that it is “Science as taught at universities, in the year in which we are speaking”. I will call this Science 2013, as that is the year in which I am writing. This ties the use of ‘cause’ to a sense of what the best scientists in the world currently understand about how the world works, and that seems to me to pretty accurately reflect how the person in the street would understand the term ‘cause’.

When discoursing philosophically though, as in this essay, it will be wise to retain the appendage specifying the reference theory, in order to be clear.

Can we define cause without a comparison state?

Some scenarios in which we might like to talk of causes do not naturally suggest comparison states. We might for instance consider the Cosmic Microwave Background Radiation (CMBR) that suffuses the sky, which is left over from the ‘last scattering surface’ of the Big Bang. We want to say that the Big Bang caused the CMBR. But we are stymied by the fact that we cannot think of an alternative situation with no CMBR. That situation would have to have no Big Bang, and hence possibly no spacetime, and hence no place in which to observe the lack of CMBR.

Here is an alternative definition of ‘cause’ that solves that problem.

‘If S is a description of a physical system at time t and theory T requires that event E occurs at time t+dt if the system was in state S at time t, then we say that S is the cause of E in system state S, according to theory T.’

In most situations this definition will be useless, because it requires a full description of the system state at the prior time. In order for E to be inevitable, that will have to be something like the location, momentum, type and spin of every particle within radius c.dt of the location of E (c is the speed of light) at time t. That is way too much information for everyday use. It’s a bit like saying ‘everything’ is the cause of E. But it may be useful to have this definition available as an alternative if we want to talk about causality in relation to situations that don’t have natural comparison scenarios.

In order to distinguish our two definitions of cause we’ll call the first one the Comparative Definition and the second one the Singular Definition. If we don’t specify, we’ll mean the Comparative definition because that’s likely to be most often the one we mean.

Looking back at the snake’s tail story, we can see that that meets the definition of a Singular cause of the engine not starting, if the tail is still wedged in the starter motor when the electric current unleashed by the ignition key hits the coils in the motor. If the time the current hits the coils is t, then we can say that the configuration of a spherical region of space with radius 10cm centred at the middle of the starter motor is the cause of the engine not commencing to fire at t+3.3×10-10 seconds, and that region includes the wedged snake’s tail.

A Singular cause is always sufficient for its effect, but the price we pay for that sufficiency is that the cause either has to be a complete description of the state of an enormous volume or, as is the case with the snake’s tail, the effect must occur a very tiny interval of time after the cause (a third of a nanosecond here).

Causes must be prior to their effects

The two definitions I have suggested require a cause to be earlier than its effect, which we call being ‘temporally prior’. Sometimes people talk of causes that are not temporally prior, so we should consider whether that can make sense. There are two common ways people do this.

‘Simultaneous’ causes

Some people give examples of what they think are physical causes that are simultaneous to their physical effects. They all turn out however, to be based on a misunderstanding of physics. There is a very simple reason why one physical event cannot cause another that happens at the same time, and that is the principle of relativity, which states that physical influences cannot travel faster than the speed of light. For event E1 at time t to affect event E2, also at time t, would require the influence of E1 to travel the distance between the two locations in no time at all, that is, at an infinite speed, which would break the speed limit and irritate the Great Cosmic Traffic Cop.

Examples offered of putative simultaneous causes are

  • a ball (cause) sitting on a pillow and causing a depression (effect), or
  • pushing one end of a lever down (cause) so the other end goes up (effect).

It is not the ball’s presence at time t that causes the depression in the pillow at time t, but the ball’s presence at earlier times. We can see this by imagining the ball suddenly magically pouffing out of existence. The pillow would not instantly regain shape. Rather it would start to spring back to its original, undepressed shape. If the ball were present on the pillow up to time t and instantly then disappeared, the shape of the pillow at time t would be exactly the same as if the ball were still there. The depression would gradually disappear as the pillow started to regain its usual shape after time t. In the real, non-Harry Potter world, change takes time.

Similarly, the footpath of a bridge does not stay up because its supporting beams are there, but because those beams were there an instant earlier.

When we push down one end of a lever, the other end does not instantly lift. Rather, a shock wave travels through the lever, deforming it in such a way that, a tiny instant of time later, the other end lifts. The shock wave travels at the speed of sound in the lever, which will be very fast indeed if it is made of a stiff substance like steel, but still much slower than light. Because the wave is so fast, we cannot perceive it without specialised equipment, so the effect seems instantaneous. If we had a fast enough camera, we might even be able to film the deformation of the lever as the shock-wave passes through. But we’d need an enormous enlargement of the frames to see the lever’s deformation in the film, because the shockwave of the initial push has probably reached the other end before the end we are pushing has moved a millimetre.

Readers who are familiar with the Quantum Mechanical phenomenon of entangled particles might hope for a loophole in the cosmic speed limit via the fact that, when one member of a pair of entangled particles is measured, the wave function collapses and the other member attains a definite value of the measured quantity.

This ‘spooky action at a distance’ as Einstein called it, does not however break the speed limit, because no physical influence is being transmitted. The wave function is simply a mathematical abstraction we use in Quantum Mechanics to make predictions and its collapse has no physical significance. In particular, there is no experiment we can do to find out whether the wave function of a particle has already collapsed. It will collapse when we make the measurement in the experiment, but that cannot tell us whether it had already collapsed before that.

So in summary, there is no escape from the cosmic speed limit, and hence there is no such thing as a simultaneous physical cause.

‘Logically prior’ causes

Another way people try to escape the need for temporal priority is to talk of a cause as something ‘non-physical’ that entails its effect via the laws of logic rather than of science. They could for instance say that the rules of arithmetic are the cause of 2+2 equalling 4, or that the fact that all men are mortal and Socrates is a man is the cause of Socrates being mortal.

This could be formalised by saying that if A→B where A and B are propositions and → denotes logical entailment (if the proposition before the arrow is true then the proposition after the arrow must be true) then A is the cause of B. Let’s call it a Logical Cause to distinguish it from the Comparative and Singular definitions of causes that we discussed above. In this context only, we will refer to causes meeting those definitions as ‘physical’ causes. Defining ‘physical’ is usually a controversial mess. But here all we mean by ‘physical cause’ is a cause that satisfies our Comparative or Singular Definitions.

There’s nothing incoherent about defining logical causes this way. No contradictions or ambiguities arise. The trouble is just that it’s a completely different use of the term cause from how it is used in relation to everyday physical things, so one cannot apply any conclusions drawn about physical causes to logical causes, or vice versa.

Further, there is already a perfectly good word in use within the field of symbolic logic for a logical cause. It’s called an antecedent. And the thing coming after the arrow is called a consequent.

So all we achieve by using ‘cause’ in this context is confusion, by applying a word that has a meaning in a different, completely unrelated field (the physical) to a concept that already has a perfectly clear label in this field.

Readers should beware of arguments that try to use logical causes. Such arguments might use words like ‘now consider causes that are logically prior rather than temporally prior to their effects’. The only reason I can think of to use the word ‘cause’ for a logical antecedent is to try to smuggle in some of the properties of physical causes and apply them to logical causes, without the validity of doing that being challenged. As logical and physical causes have no relation to one another, other than in a vague, touchy-feely sort of way, it is invalid to apply any properties of physical causes to logical causes.

Sorting out which event is the cause and which is the effect

Another problem of not requiring causes to be temporally prior is that it creates ambiguity as to which of the two events is the cause and which is the effect. In the physical case, this is clearly resolved by requiring a cause to be earlier than its effect. We lose that capacity if we don’t require temporal priority.

In the logical case, if we have A→B but not B→A then we can say, if we wish, that A is a Logical Cause and B is its logical effect. But if we have both A→B and B→A then there is no basis for saying one of A and B is the cause and the other is the effect. We will see in the next section how this can lead to grief.

Examples of the use of our definitions

Let’s try out our two definitions – Comparative Cause and Singular Cause – in a few situations where the word ‘cause’ is key to the thinking processes, to see how they fare.

Causation in philosophy

More than 2000 years ago Aristotle thought and wrote about causation, in a way that has been adopted by many philosophers since then. He listed four types of cause, of which only one, the Efficient Cause, is close to the way the term is typically used now. Unfortunately, even the notion of an Efficient Cause is bound up with Aristotle’s ideas about physics which, being pre-Newtonian, are incompatible with the way we now understand the world to work.

Nevertheless, philosophers still blithely make arguments using the word ‘cause’, only rarely pausing to consider what if anything the word actually means, and whether it really belongs in their arguments. A notable exception is Bertrand Russell in his marvellous 1912 essay ‘On the notion of cause’.

Here are a couple of examples of how ‘cause’ is used in philosophical arguments, and how we can use the considerations above to understand them better.

First Cause arguments for the existence of God

There is a very old and venerable argument that there must be a being (God) that is the cause of the universe’s existence. There are a number of versions, including a popular one that has been revived recently, based on a medieval Islamic argument from the Kalam school. All versions of the argument rely on God being a Cause for the universe. An obstacle to all these arguments is that there can be no ‘before’ the universe, as time is itself a feature of the universe, not something that applies outside it. So there cannot be a cause that temporally precedes the universe. Devotees of the First Cause argument sometimes respond that God is logically prior, rather than temporally prior to the universe. That is, God→Universe.

There are two problems with this argument.

Firstly it relies on a premise that every object of a certain type must have a cause. It tries to generate support for that premise by appealing to our experience, and all the examples used are of physical causes. Hence the premise is restricted to physical causes and tells us nothing about non-physical causes, which is what the argument wishes to argue God is. This is a smuggling attempt, of the kind discussed above.

Secondly, what the argument actually does is to reason from the existence of the universe to the existence of God. That is, Universe→God.

But now we have a situation that is logically symmetrical between God and the Universe, which a logician would denote as God↔Universe. Each implies the other, so we cannot say that one is logically prior. One might be tempted to say that there was a time, before the creation of the universe, when there was only God and no Universe, which makes God prior, and hence the cause. But that route is forbidden because it relies on the existence of time, which is part of the Universe.

So the philosopher that pursues this route is committed to saying that, if there is a God, then it is caused by the Universe as much as it causes the Universe.

Such a conclusion is likely to satisfy neither theist nor atheist, and demonstrates quite nicely the futility of trying to reason about causes that do not temporally precede their effects.

The Epiphenomenal hypothesis of consciousness

Epiphenomenalism is a hypothesis that says mental events (consciousness) are caused by physical events in the brain, but have no effects upon any physical events. In other words, brain activity causes consciousness, but consciousness does not cause any brain activity.

For this to be the case, given our definition of cause, a mental event must occur after the physical (presumably brain) event to which it relates. Hence the brain event can be a cause of the mental event, but not vice versa.

Importantly, if the mental event occurs simultaneously with the related brain event then we cannot say that either causes the other, because neither precedes the other. This is a crucial observation because sometimes people talk about Epiphenomenalism as if it is a simultaneous occurrence caused by the contemporary brain activity. However, as we have seen above, for simultaneous events there is no way to identify which is cause and which is effect. So a mind-body model that involves simultaneous processes is not Epiphenomenalism.

Causation in Science

Does all science rest on the assumption that everything has a cause? It might seem so, and this claim is often made, but it’s wrong. Science doesn’t need everything to have a cause, to be useful. Science rests on the observation that there are patterns in nature, such that systems appear to evolve in regular, repeatable ways that can be described by natural laws. If we can discover such a law, by inventing theories based on experimentation, and then testing the theory’s predictions using further experiments, then we may be able to predict future events, and shape the course of those events.

So science is best described not as a search for causes, but as a search for laws that describe how physical systems evolve.

We don’t even need to believe that everything is governed by natural laws. For instance, some interpretations of Quantum Mechanics hold that there is no law determining the precise time at which a radioactive particle will decay. The apparent absence of a cause for that particular aspect of reality does not however prevent us from making very precise predictions about the behaviour of physical systems using Quantum Mechanics.

In science we don’t need to have causes for everything, or even to believe they exist. At most we need causes for the important features of the system we are evaluating.

Causation in Physics

Light cones

An important concept in physics is that of the light cone. For a given point P in spacetime, the past light cone is the set of all spacetime points from which a particle could have travelled prior to passing through P. There is also a future light cone, which is the set of all spacetime points that can be reached by a particle that first passes through P. The particles in question may be photons, which travel at the speed of light, or slower particles with mass, like electrons or cricket balls.

Physicists talk about two spacetime points as being ‘causally connected’ if one is in the other’s past light cone. This means that the later point can be affected by something that happens at the earlier point. Events at points that are not causally connected cannot affect one another. That is, changing what happens at one point will have no impact on the other. Such points are called space-like separated points.

For point P, the future light cone marks out the limits of the points P can causally influence, and the past light cone marks out the limits of what points can causally influence P. Hence the light cones are regarding as showing the limits of causality.

This usage harmonises with both our Comparative and Singular definitions. In the Singular definition, the cause (according to Science 2013) of an event E at spacetime point P, with time coordinate t, is the state of the set R of all points in P’s past light cone that have time coordinate t-h for some positive h. In the Comparative definition, if S1 and S2 are alternative possible states of R, such that E happens at P if R has state S1 but not if R has state S2, then the difference C between S1 and S2 is the cause of E in S1 with respect to S2, according to Science 2013.

It might seem that the light cone perspective adds an additional constraint to causality above the constraint in our definitions that causes must precede effects. For not only must the cause precede the effect, but it must also lie in the effect’s past light cone.

It turns out that, because of the theory of relativity, this is not an additional constraint at all. We can only say unambiguously that C precedes E if C is in E’s past light cone, because then the time of C will be earlier than that of E in every possible reference frame. If C is in E’s future light cone we can say unambiguously that E precedes C, so C cannot be a cause of E. That much is obvious. But if C is in neither the future nor the past light cone of E, it will be later than E in some reference frames and earlier than E in others. Einstein’s theory of relativity tells us that no reference frame is any more valid than any other, so C cannot be a cause of E if there is even just one reference frame in which it occurs after E (in fact if there is one such frame then there will be infinitely many).

This last consideration tells us that, if we ever discovered particles or other influences that could travel faster than light, it would destroy our notion of causality entirely. Because then we would have pairs of events that we thought were cause and effect, for instance the beginning and end of a path followed by one of these particles, but for which in some perfectly valid reference frames the effect preceded the cause. We would have to either jettison the notion of causality entirely, or develop a completely new one, that may only have very slight similarities to the existing one.

It is fortunate for us then that the superluminal neutrino speeds observed in experiments in 2011-12 turned out to be experimental errors.

Quantum indeterminacy

In both our definitions of Cause we say theory T ‘requires that’ the effect occurs after the cause. However quantum mechanics tells us that nothing is certain to happen. Things we think of as inevitable are really only very, very likely. How then can we meaningfully talk of an effect being required to occur after its cause?

One solution is to replace statements of certainty by probability statements. We could replace ‘theory T requires that’ by ‘under theory T there is a greater than 99.9% probability that’. Here T is of course Quantum Mechanics. If we make this substitution in the Comparative Definition (twice, for the two instances of ‘theory T requires’) and the Singular Definition (once) then these definitions are ship-shape and ready to be used in the Quantum Mechanical world.

We might wish to go further and call C a cause if the probability of E occurring after S1 is lower than 99.9%, say 50%, and the probability of E not occurring after S2 is still 99.9%. In that case C is a sort of enabling condition for E to occur, but it does not guarantee it. If we wanted to go down that route it would be better to give this type of relationship a slightly different name like ‘probabilistic cause’, to avoid confusion with the cases where C makes E almost certain to occur.

Correlation does not imply causation

A famous dictum that is often used in both science and social studies is ‘correlation does not imply causation’. Let’s put our Comparative Definition to the test to see if it supports this uncontroversial dictum. But because medical and social sciences are quite complex, we’ll use an example involving something simple instead – bowling alleys.

Imagine that a bowling alley has an easily depressed light switch placed in the middle of the alley, 20cm away from the central lead skittle. When depressed, the switch closes an electric circuit that illuminates a light above the skittles. After watching a few matches we notice that the light goes on for a fraction of a second and then off, immediately prior to every strike (knocking down all ten skittles). We have observed a correlation between illumination and strikes, and we wonder whether the light causes a strike.

First we compare two situations, describing the region R around the bowling alley, at the time a ball that has been bowled passes the switch. The situations S1 and S2 are identical except that in S1 the ball is on the switch and illuminating the light, while in S2 the ball is to the left of the switch, too far left for a strike to occur, and the light is not illuminated. The region R is large enough that nothing that is outside R when the ball passes the switch can change whether a strike occurs.

In S1, Science 2013 requires that a strike will shortly occur and in S2 it requires that a strike will not occur. So our definition of cause is satisfied. We can say that the difference between S1 and S2 caused the strike after S1. But what is the cause we have identified? It is everything in S1 that is different from S2.

That includes the light being on but it also includes the ball being in the middle of the lane. We could if we wish say that B caused the strike where B is ‘the light being on and the ball being in the middle of the lane’. The latter is consistent with what a lay person would think of as being the cause, so that’s a good start. It is reasonable to describe B as the cause. The bit about the light seems superfluous though. Can we get rid of it?

Yes we can, as follows. We add a new situation, S3, which is the same as S2 except that someone stands on the lane, avoiding the ball, and briefly depresses the light switch as the ball passes, if the ball does not itself roll over the switch. Now let’s compare S2 and S3. In both cases there is no strike. They are identical except for the man standing on the lane and the light being on. So it appears that the light being on is not a cause of a strike. The light illumination is correlated with, but not causative of, strikes.

This confirms that the Comparative Definition can, at least in this case, reproduce results that accord with our intuitions about causation.

Conclusion

We have developed a definition of cause – the Comparative Definition – that captures the everyday meaning of the term while removing ambiguity. The price of the additional accuracy was having to specify a comparison scenario S2 and a reference theory T.

For cases where a comparison scenario is not readily imaginable, we have an alternative definition – the Singular Definition – that still captures the commonly understood meaning. The price of this additional power is having to specify the prior scenario – the ‘cause’ – either over an enormous volume of space or a tiny period of time prior to the effect.

We have seen that an essential feature of any useful, unambiguous notion of cause is that it requires causes to precede effects in time. We observe that invocation of simultaneous causes or logical causes is usually a symptom of a flawed argument.

We have identified a way to generalise the notion of cause to handle the uncertainty that comes from Quantum Mechanics, by including probabilities in the description of a cause.

We have observed how these definitions of cause can be used in practice in a variety of fields of inquiry.

Finally, if we can take any ‘moral’ from this rather prolonged meditation, it is that in any argument that relies on notions of cause we should examine closely how the term ‘cause’ is used and what properties are ascribed to it in the argument. If this is not clearly set out, the argument may well have hidden flaws or, in some cases, be incoherent, no matter how plausible it may sound.

Andrew Kirk. Bondi Junction, 8 June 2013


Replacing Truth with Reason

“What is Truth” asked Pilate?

I’ve always been rather fond of that riposte in the New Testament. Good old Pontius sure put those scribes, priests and Pharisees – whatever they were – in their place. Is there more to it than just a great put-down though?

It sounds deep as well, although there’s always the risk that it may be faux deepness, or ‘deepity’ as Daniel Dennett would call it.

Now I’m not going to go all post-modern here, and suggest that everybody has their own version of truth. Nor am I going to suggest that Truth isn’t a useful concept. To ask Freda whether she thinks Bill is telling the truth is a meaningful and useful question. It is actually a speculation about the state of Bill’s mind. Is he telling us what his memory tells him happened, or not? No, what I’m wondering about is what is sometimes called Absolute Truth, the sort of thing exemplified by Bertrand Russell when he says ‘Edinburgh is North of London, whether anybody knows it or not.

Sometimes Truth is held up as a sort of Holy Grail, the quest for which can fill one’s life with meaning. The Search For Truth is the sort of noble thing to which holy men and scientists alike are said to be dedicated. Indeed, it’s not that long ago that it was a key component of a little motto I made up for myself in an idle moment – “Truth, Beauty and Compassion” – a more inclusive version of St Paul’s triumvirate “Faith, Hope and Love”. I vacillated for a while over whether I should add “Reason” to my motto. I mostly omitted it, because things just seem so much neater in threes, as well as because there seemed to be too much overlap with Truth. Sometimes I included it though, because there seem to be things covered by Reason that are not covered by Truth. For example, one can use Reason to devise a strategy to win the heart of one’s true love, but this has little if anything to do with Truth. Recently though, I have sometimes felt inclined to drop Truth from the motto in favour of Reason, and I blame Kurt Godel for this, as I will explain in the next couple of paragraphs.

Godel and Truth

The logician Kurt Godel is most famous for his First Incompleteness Theorem, which destroyed the most ambitious mathematical project of the early 20th century – the Hilbert Program, which was an attempt to find a way to formally prove everything that was believed to be true about arithmetic and basic mathematics. What Godel’s theorem showed was that, in any logical system that we use to write proofs, there will exist some logical statements that can neither be proved nor disproved, yet are perfectly meaningful. He did this by creating an ingenious variation of the famous ‘Liar Paradox’, which says ‘this statement is false’.

Now, in their attempt to make Godel’s discovery more interesting to a lay audience, some texts and sources claim that the theorem says that there are statements that are ‘true but not provable’. The trouble is that the ‘true’ part of this statement doesn’t have any clear meaning. The closest we can get is to observe that Godel’s theorem shows that there are statements that are unprovable in the chosen logical system, but for which we can prove, using a different logical system, something that is very similar to the original statement. So in that case the word ‘true’ doesn’t relate to some fundamental cosmic reality, but just to what can be proved in an alternative logical system. The word ‘true’ is superfluous as well as ambiguous here, as we can express everything Godel discovered using variants of the word ‘proved’ instead of true.

The realisation that ‘True’ is a useless word in this critical context made me wonder if there is any context in which it expresses something important, that cannot be more accurately described by other words. It is that question that I wish to explore here.

Science and Truth

Let’s start with science. Is that a search for truth? The task of science is to construct theories that relate past experiences (‘observations’) to one another in an ordered way and enable us to make predictions about future experiences, such as the appearance of comets or the effect of mixing hydrochloric acid with sodium hydroxide.

Are scientific theories ever true? Not many scientists or philosophers of science would claim that in any absolute sense. Any scientific theory, however useful, is eligible to be replaced by a more sophisticated one that better explains our observations. The first simple atomic theories were replaced by the Rutherford model in which a nucleus of protons and neutrons was surrounded by electrons whizzing around the outside. That was in turn replaced by Quantum Mechanics, and then we had quarks and other subatomic particles coming into the theory in the 1960s. Now physicists speculate on whether the subatomic particles in turn are just symptoms of some deeper underlying phenomenon such as vibrating strings in eleven dimensional space. It seems natural to suppose that there is some underlying final theory that tells everything, and that the theory is ‘True’ regardless of whether we eventually discover it. But that is by no means the only logical possibility. Here are two others:

  • There is an unending descending chain of theories, each more complicated than the one above it and including all its ancestors as special cases that are good approximations under restricted circumstances.
  • There are multiple theories that can explain the full range of possible experiences, all as valid as one another. The competing corpuscular and wave theories of light are crude examples of this. In the end, they both proved inadequate to explain all the experimental results obtained, but for a while they were both successful in explaining different aspects of the behaviour of light. There is no apparent reason why there could not be two or more different theories, each of which can by itself explain everything we experience.

Sometimes the Common Sense view of the world is that of course there is an underlying Truth – that quarks and electrons really exist and we just need to find out more about them. While I am passionately in favour of finding out more about quarks, I regard that as a desirable refinement of our theories, not a discovery of Truth. If we are to think in terms of common sense, I cannot help but observe that common sense tells me the table in front of me is a hard, solid, opaque object, not the strange collection of pinpricks and force-fields in empty space that quantum mechanics suggests. That is not to say I don’t ‘believe’ quantum mechanics. Quite the contrary. Rather it is to say that I don’t want to give common sense any privileged role in such a deliberation. And also, that the notion of Truth is compromised. Which is more true, my perception of the table as hard and solid, or the idea of it as an empty space with the odd tiny quark and electromagnetic force field? The practical response is that the question is meaningless. Both representations of the table have their uses, and are complementary. Table as solid object is useful if I want somewhere to put my kettle. Table as quarks is useful if I want to understand why it doesn’t collapse under the weight of the kettle (or how heavy a kettle I can put on it).

Perhaps a belief in Truth equates, in this context at least, to a Realist view of the world – that the world really is made of a specific sort of thing or things, and we just need to find out what it is. It is a belief in Reality, with a capital R.

But hold on, any moderately sane person believes in Reality don’t they? Well, it depends what one means by reality. I am sure I have been guilty of saying ‘so and so lives in a dream world – they have only a passing acquaintance with reality’. My defence is that I do not mean by this that so-and-so doesn’t believe in quarks. Rather, I mean that they do not reason about their experiences in such a way as to give a strong likelihood of their expectations of future experiences being fulfilled. Perhaps so-and-so has gone sun-bathing on the beach in the middle of a summer’s day, under the illusion that a coating of sunscreen will be enough to protect her for two hours in full sun. The ‘reality’ from which she is disconnected is that that evening she will have the experience of red, horribly painful skin, and two days after that she will have the experience of the skin peeling off in sheets. So-and-so’s delusion has nothing to do with her metaphysical opinion of quarks. It is about her inability to use reason to control the nature of her future experiences.

So it seems that when I use the word ‘reality’ in everyday intercourse, I am referring to what experiences we can expect in the future, and what we might be able to do to control those experiences.

Note that Reason, or Rationality, has stepped in here to fill the vacuum left by our jettisoning the notion of Truth.

Truth in other contexts

A belief in Truth is not limited to just quarks. At various times, people have proposed the existence of other forms of truth in the form of objects that exist independently of what people know. Moral rules, aesthetic truths and mathematics are key examples of this. A Moral Realist will claim that moral rules exist, and the purpose of moral education and ethical inquiry is to discover them. A mathematical realist will say the same thing about Pythagoras’s Theorem, or the number six. An aesthetic realist may be a rarer beast, but if I could find one, I would expect them to assert that Mozart’s Requiem is beautiful and Milli Vanilli is not.

Yet there is no more need to believe in such Truths than there is with quarks. I can develop a system of moral rules for my own use, or discover them in my own mind by reflection on my feelings. If I prefer something less subjective, I can define a moral truth to be any feeling about how to treat others that is shared by a large proportion of the human race.

With mathematics I can, if I wish, regard any mathematical concept as an invented idea that helps me arrange things in my mind and reason about what might happen next. I can take the view that everybody invents the mathematics that they use for themselves. So every toddler invents the number six, rather than discovering a pre-existing abstract object. Or perhaps they find a pre-existing pattern for the number six somewhere in their brain, placed there by evolution because of its usefulness to survival.

The more I reflect on this, the less value I see in maintaining a concept of Absolute Truth in the way one thinks about the world.

Consider the binary expansion of Pi. Let F(n) be the statement that, for any m greater than or equal to n, there are more 1s than 0s in the first m bits of that binary expansion. Let S be the statement that there is some number n for which F(n) is true. There is no way of proving or disproving S by trial and error, because we cannot try out what happens with all the infinite number of combinations of values of m and n. Perhaps there’s a clever way of proving it or disproving it that doesn’t require trying an infinite number of combinations, just as we can prove that the sum of two odd numbers is always even, without trying it on all possible pairs of odd numbers. But nobody knows of one, and it seems entirely plausible that there is no such proof.

Yet most people would say that S is either true or false, but we just can’t know which. This seems to be a problem, because there are no words to explain what we mean by true or false here. Let us explore some more.

The Liar Paradox

The Liar Paradox is a statement that generates a contradiction, however you interpret it. One of its more sophisticated versions is ‘This sentence is not true’. If we suppose it’s true then what it says must be true, so it is not true, which contradicts our supposition that it’s true. If we suppose it’s false then what it says cannot be true, so it can’t be true that the sentence is not true, so the sentence must be true, which contradicts our supposition that it’s false. The third possibility is that the sentence is meaningless. But if it’s meaningless then it’s not true, which is exactly what the statement says is the case, so the statement is true, so it’s not meaningless, which contradicts our supposition that it is meaningless.

There are a number of ways to resolve this paradox. Most of them involve questioning what we mean by truth in this context. One possible meaning is provable – we say that something is true if and only if it can be proved. This has shades of Godel’s Theorem. If we take this approach then the paradox disappears because ‘This statement is not provable’ is not paradoxical if we require our proofs to be strictly logical (although one has to have at least a partial understanding of Godel’s theorem to see why that is so).

Another possible meaning is that a sentence is true if it accurately reflects our perception of reality (or just our perception, if we want to avoid the equally troublesome word ‘reality’), false if the opposite of the statement reflects that perception, and meaningless otherwise. This is a popular interpretation of ‘Truth’, which is called the ‘Correspondence Theory of Truth’. With that meaning, it is ‘true’ to say a soccer ball is round because, when we look at it, it looks round. With this meaning, we can resolve the paradox by observing that the sentence is meaningless because it doesn’t say anything about our perception of reality. All it does is talk about itself.

In both these resolutions, we have only been able to make sense out of the sentence by getting rid of the vague, undefined word ‘true’ and replacing it with a clear, pragmatic definition.

This realisation strengthens my feeling that the word True is a troublemaker, that sows confusion wherever it is used. Perhaps we really should dispense with it, except in causal, imprecise, everyday slang. But if so, what should we replace it with?

What can we replace Truth with?

The words ‘true’ and ‘truth’ are so much a part of everyday language that, if we were to discard them, replacement would be required on a large scale. For someone that subscribes to the Correspondence Theory, mentioned above, that theory provides a satisfactory way of defining the terms, and hence justifying their retention. The price that must be paid for that though, is believing that there is such a thing as Ultimate Reality – a unique description of the way things are, to which any other descriptions are only approximations. Furthermore, that description must exist regardless of whether anybody knows it.

Most people seem to hold that belief, and for them the dilemma ends there. But, for the reasons given above, I am skeptical, and certainly see no justification for such a belief in terms of other, more fundamental and intuitive concepts. All we can say with confidence is that we have experiences, and that there are models available – called scientific theories – to connect these experiences together in a patterned way and make predictions about what we may experience in future.

For someone that suffers this same ‘skeptical disability’ as me, the Correspondence Theory is not an option. So what, if anything, can we use instead?

My proposal is to replace it by ‘consistency with experience’. We will call a statement ‘true’ if it is consistent with both actual and potential future experience. By ‘consistent’ we mean there is no possible rational deduction from actual or potential experience that contradicts any part of the statement. So if June tells us that she has not eaten the last biscuit, that is not true if, upon inspecting the biscuit barrel, we would see that there are no biscuits left in there and, if we used an endoscope to inspect her stomach contents, we would find traces of that type of biscuit therein. It would also fail to be true if June’s statement was inconsistent with her own experience – that is, if she has had the experience of taking and eating the last biscuit. It would even fail to be true if June were a sleepwalker who has been known in the past to sleepwalk to the kitchen, take a snack and return to her bed without waking, and she woke this morning with a rash of a kind that she has only ever had before after eating that type of biscuit. In this latter case, June has not experienced eating the biscuit, but she can rationally deduce from her experience of the rash that she has probably eaten it in her sleep.

So that’s my suggested replacement for Truth – consistency with experience. And since the key ingredient for assessing this consistency is Reason, I will adopt that as the third leg of my little motto: Compassion, Beauty and Reason!

Note that we haven’t really got rid of the word Truth. All we’ve done is redefine it. Or rather, defined it because, unless one subscribes to the Correspondence Theory, it was never properly defined in the first place.

This definition has some interesting implications.

Interesting Implications

Remember the above example of the statement S about the number pi? With this definition we have to conclude that, unless a proof one way or the other exists, S is neither true nor false, because there is no potential experience we could have that would confirm or deny it. In the mathematical context, true means the same thing as ‘provable’.

Further, even if there is a proof or disproof of S that we just haven’t found yet, Godel’s Theorem tells us there will be other statements that can be neither proven nor disproven. So we are now committed to saying that those things are neither true nor false.

On the other hand, we are empowered to say very clearly that provable statements like 2+2=4 are true, because we can easily go through the experience of proving them. Strictly, what we need to say is that ‘In Peano Arithmetic, 2+2=4’, because one could easily invent another system of arithmetic in which 2+2 equalled something else. So the statement is actually about the consistency of what we are saying with the rules of the system – in this case the axioms of Peano Arithmetic.

Here’s another one: ‘The universe will expand forever’. The current state of cosmological knowledge is that we do not know whether that will happen or whether the expansion will eventually slow and then reverse, ending in a Big Crunch. The Big Crunch will happen if the Cosmological Constant is positive, but not if it’s zero or negative. If the constant is positive or negative, we may one day be able to demonstrate that. But if it’s zero, we’ll never be able to demonstrate that, because there’s always the chance thet it’s a positive or negative value too small for us to detect. So if the cosmological constant is zero then the universe will expand forever but we can never know that that’s what it’s going to do. Under our new interpretation of ‘true’, we would have to say that this cosmological statement may be neither true nor false, as there can be no experience that can confirm or deny it. In fact so is the statement ‘The Cosmological Constant is zero’.

If this seems disconcerting, we can comfort ourselves with the idea that, for all the common , everyday uses of the word True, the definition gives us exactly the interpretation that we want:

  • “are you telling the Truth” means ‘is what you are telling me now consistent with your own experience of what you are talking about?’
  • “I feel cold” is true if the person saying it is currently having the experience of feeling cold.

So we can preserve a role for the word ‘True’ in our everyday language. What I think we can’t do without having to make unfounded assumptions about the existence and nature of Ultimate Reality, is elevate the concept to some universal principle that guides our understanding of the universe. “Reason” does a much better, and more practical, job.

Andrew Kirk, Bondi Junction, February 2012

Postscript

It occurred to me a few days after finishing the above essay that, if somebody nevertheless wishes to retain a notion of Absolute Truth in their worldview, perhaps for aesthetic reasons, or just because it fits with long-accustomed habit, one way to do so is to incorporate an omniscient conscious entity in the worldview. That way, Absolute Truth can simply be defined as what it is that this entity knows. This is entirely consistent with the above suggestion of defining truth in terms of experience because, as the entity is omniscient, it experiences every object or event.

This entity may sound a bit like what some people call God. But I should note that other attributes ascribed to God by the most popular Middle-Eastern religions of Christianity and Islam, such as omnipotence and being a creator, law maker and law enforcer, are not necessary in order to take this route to believing in Absolute Truth. Nor does this approach necessitate that there be only one omniscient entity.

If the entity is infinite then it could even know the truth status of the mathematical proposition S above. Knowing the truth status of S requires knowing an infinite amount of information but perhaps that would not be a problem for an infinite entity.

This approach has echoes of the way that George Berkeley completed his Idealist theory of existence. Berkeley’s theory says that only ideas exist, not matter, and he addressed the problem of whether objects exist when nobody is looking at or thinking of them by saying that they still exist as ideas in God’s mind.

Personally, I like the idea of a universe without Absolute Truth and have no need or wish to hypothesise such an entity. But it may be of comfort to those who do like the notion of Absolute Truth to know that there is a rational basis on which they can do so.