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.
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.
The trouble with free will is not that there is no such thing, but rather that nobody has yet managed to say what sort of a thing it would hypothetically be, in a way that satisfies those that wish to believe in it.
One of the best-known definitions of free will is David Hume’s, which runs as follows (from ‘An enquiry concerning human understanding’. Section 8, part 1):
By liberty, then we can only mean a power of acting or not acting, according to the determinations of the will; that is, if we choose to remain at rest, we may; if we choose to move, we also may. Now this hypothetical liberty is universally allowed to belong to every one who is not a prisoner and in chains.
Ardent believers in free will (‘Libertarians’) reject this because it depicts us as purely at the mercy of the determinations of our will, rather than suggesting, as they would wish, that we are in some indefinable way in control of what we determine – that we control our will rather than our will controlling us.
A Libertarian typically wishes to say, in contradiction of Determinists, that the decisions we make are not even theoretically predictable based on a full description of the prior states of our brain, body and environment. But neither do they wish to say that those decisions are random, which would destroy any notion of responsibility for our actions. They wish the actions to be somehow caused, yet also uncaused. They wish it to be the case that the person ‘could have acted differently’.
This idea is hopelessly vague. First, it rests on the notion of cause, which is very difficult, yet tractable, as covered in my essay “What is a cause?”. But then we have the additional problems of deciding what is meant by ‘could have’ and ‘random’. ‘Random’ is a perennial difficulty. Nobody has yet come up with a satisfactory non-epistemological definition of randomness, as discussed in my essay “Some random thoughts on whether the world is random”.
The idea of ‘could have acted differently’ is also a major problem. Unless we are prepared to describe the action as one of a number of different possible random outcomes, the closest we can come to explaining this phrase is to say it means we can imagine the person having acted differently. But we can imagine many things that we know are impossible, so it is hard to see how imagination is helpful in this context.
I suspect that there is no possible definition of free will that would satisfy the Libertarians.
I further suspect that what determines our actions is the combination of our nature (genes) and our environment. There is no spooky metaphysical third factor that represents the act of ‘choice’. That opinion would make me a Determinist, except that Determinists have to deny that the world contains randomness and, since I deny that randomness is well-defined, I cannot say whether the world contains it.
But does such an opinion require me to believe that we don’t make choices in this world? That would seem an absurd conclusion, as we feel very strongly that we do make choices, all the time. Fortunately, it doesn’t require that.
Choosing is the process of discovering, through considering alternatives, what course of action you are going to follow. A Libertarian would say that the outcome of the process is neither predictable in advance, nor is it random. A Determinist would say that choosing is the process of discovering your destiny.
What happens when we choose an action is typically this. We think about all the alternative possible actions. We think about their consequences, and perhaps enumerate the good and bad consequences for each possible action. We consider how we feel about those consequences. Then we do the action that scores best against the values that are dominating our consciousness at that time. Hence, in short, we can say that:
Choosing is just the process of thinking about several alternative actions and then doing one of them.
The fact that the course of action may have been predetermined (as a Determinist would say it was) does not entail that the process of choosing – considering alternatives – was pointless. I considered the alternatives, and in the way that I did, because I am the type of person I am, because of my nature. And I chose the action I did because of my nature too. If I had not considered the alternatives I did then my nature would have been different, and my decision would likely have been different too.
Say I have a test at school that I very much want to pass. I will probably choose to study for the test. That choosing will involve considering the consequences of studying and of not studying, and comparing them. If I choose to study then I will probably pass. A Determinist would say that I was always going to pass, but that the reason I was always going to pass is that I was always going to study, and I was always going to do that because my brain is so constructed as to place a more positive assessment on the likely consequences of studying than on those of not studying. The ‘choosing’ to study, including the deliberation that precedes the choice, was an inevitable and necessary part of the process. So says the Determinist. But regardless of whether I agree with her on that, we can still both agree that I chose to study, in that I thought about the consequences of studying or not studying, and then studied.
Another example is being persuaded by an argument. Say I have been persuaded, by an ethical argument put to me by another, to become vegetarian. My choosing to become vegetarian is simply the process of my listening to the argument, considering it, especially the consequences of becoming or not becoming vegetarian, and then ceasing to eat meat.
While I was listening to the argument I was probably not aware which way I would choose. I may even have thought that I would remain omnivorous. A moment will come though, either while listening to the argument or in my subsequent reflection on it, when I realise that I will no longer eat meat. I realise that I have decided. That is the way it works for me (I can’t speak for others). My decisions are realisations. I just become aware that the decision is made. I do not decide to decide. If I did that I would have an infinite regress, because before I could do that I would need to decide to decide to decide, and before I could do that I would need to decide to decide to decide to decide, and so on.
The important feature of this example of a persuasive argument is that it counters the suggestion that there’s no point trying to persuade anybody of anything, because everything is predetermined. If it is predetermined (as Determinists would suggest) then every decision is a consequence of the genes and environment of the person deciding, and putting a persuasive argument to that person is a significant element of that environment. Perhaps it was predetermined that I would make that argument, and that I would persuade the person. But I can imagine an alternative world in which the argument was not made – perhaps because I was not there – and the decision was different.
So I conclude that, regardless of whether a satisfactory definition of free will is possible, regardless of whether our minds work according to that definition, and regardless of whether everything is predetermined, we still make choices.
Perhaps that is ‘Compatibilism’, or perhaps there is more to Compatibilism than that. I don’t place much stock in categorising ideas by ‘isms’ so I’m never sure whether any of my ideas fall into any of them.
A brief coda: Another satellite of the free will idea, to which many people are attached, like the notion of ‘choosing’, is that of reasons. What is the reason that I chose a certain action?
This is trickier than ‘choosing’, because we rarely seem to have a single reason for choosing anything. Often there is a network of interconnected reasons that are clearly visible in the choosing process. But even in the simplest decisions, where there seems to be only one reason, there are actually more. Think of any simple decision you’ve made, and your ostensible reason for choosing it. Now consider whether you would still have chosen it if it was guaranteed to make you suffer a prolonged, agonising death within one year. Probably not! So do you not need to include, as an additional reason for choosing it, the fact that you had no reason to believe that it would make you suffer a prolonged, agonising death within one year? We could find countless other such reasons for any choice, however simple.
A reason for an action is in many ways like a cause, and we need to be very precise about our definitions if we want to speak completely unambiguously about our reasons for choosing an action. I would say that the full reason for a voluntary action is the complete set of our expectations regarding the consequences of the action. Looked at another way, I choose an action because it accords more strongly than any of the alternatives, with the values that are uppermost in my mind at the moment of deciding.
Many of the considerations in my “What is a cause” essay will apply. In practice though, one reason may stand out as particularly noteworthy and we may just mention that (“the reason I am fining you is that you were driving at twice the speed limit; and I won’t mention the additional reason that you weren’t in a fire engine racing to put out a fire, as I think we all know that”).
Given that there is so much vagueness about the reason for any action, I think it is reasonable to adopt the following approach, which I like because it is broadly consistent with the way minds work (or maybe just my mind. I don’t know about yours), and because it reflects the idea that we realise we have decided, rather than deciding to decide. It’s vague, erratic and anomalous, but no more so than any other notion of a single reason for a decision:
The ‘reason’ why I did a particular action is the last thing I thought about before I first realised that I was going to do it.
Andrew Kirk. Bondi Junction, 24 August 2013
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?
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.
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.
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:
- S1 and S2 are descriptions of alternative possible states of a system at time t, and
- the difference between S1 and S2 is C, and
- theory T requires that event E occurs at time t+dt if the system state at time t is S1, and
- 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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
I find that in the majority of cases when someone poses a philosophical question that appears deep and difficult, my first response is to zoom in on a key term in the question and wonder ‘what do you mean by that?’. An uncharitable observer might suggest that is just a stalling tactic to mask my confusion. But I suspect it is not. It seems to me that most of the paradoxes, dilemmas and confusions we find ourselves in are really a consequence of being insufficiently clear about meaning. Equivocation is a classic example – where a single word is used in different parts of the argument with different meanings, and then the meanings are implicitly equated under the cover of the fact that they are denoted by the same word. A folksy example of this is:
Premise 1: Dry bread to eat is better than nothing
Premise 2: Nothing is better than chocolate cake
Conclusion: Dry bread is better than chocolate cake
Here ‘nothing’ in Premise 1 means ‘not having anything to eat’ but in Premise 2 it means ‘There is no other food that…’. These are different meanings so they cannot be equated to reach the conclusion.
A more philosophical example is the old classic ‘Nothing comes from nothing’ (ex nihilo, nihilo fit). It seems plausible, because the same word occurs twice, so it just seems to say that you get out what you put in. But the two nothings are very different. The first one means ‘It is not the case that any thing…’. The second one means ‘a state in which no thing exists, including no vacuum, no time and no space’. The first of these is completely understandable, and makes perfect sense when attached to a remainder of the sentence such as ‘..heavier than 1kg remains in a cereal box from which all the cereal has just been removed’. But the second one is inconceivable to most humans, and subject to considerable debate about whether the words mean anything at all. So the sentence as a whole, despite its superficial plausibility, has an unclear, and quite possibly nonexistent, meaning.
‘Free will’ is another good one. Questions about whether free will exists seem impenetrable until one starts to seriously question whether we really understand what we mean by ‘free’. David Hume’s resolution, to say that ‘free will’ is the ability to do what you want to do, is dismissed by free will libertarians as being too weak because it supposes no control over what it is that you want, but they are unable to propose a stronger formulation that is clear and understandable. What they are searching for is a concept of not just choosing what you do but also choosing what you want to do, but attempts to express that clearly seem to me to always end up in a confusion of circularity (Can you choose to want to want to want to do what you want to want to want to want to do? How many ‘wants’ do we have to put in here to describe true Libertarian Free Will? No matter how many we put in, we always seem to need one more!).
The absolute, objective existence of unobserved things is a concept that raises particular ire. Scientific Materialistsi argue passionately that the cup they just put in the cupboard is still there even though the door is closed and we cannot see it. I say I agree, in the sense that, yes my mental model of the universe includes a cup object in the cupboard too, and if we were to open the door we would experience seeing the cup. They then peevishly retort that they are not just talking about a mental model, or what would happen if we looked, but the fact that the cup really exists, all the time, whether being observed or not. My reply is that I don’t know what such a statement means, unless interpreted in terms of a mental model, or potential observations. I can neither affirm nor deny that the cup exists when unobserved, because I can make no sense of either claim other than in relation to components of a mental model. I don’t know what ‘exist’ means when my two clear interpretations (component of a mental model; potential or actual observation) have been thus disallowed.
Now sometimes when we ask ‘what do you mean by that?’, it is possible to arrive at a shared understanding via further discussion. Even if the first definition leads to a request for further definitions (of words used in that definition), it may be that, after the fourth or fifth round of definitions, we arrive at concepts for which we have a shared understanding. If so, everybody is happy and we can proceed with discussion, and in learning from one another. That is always my hope when I ask ‘what do you mean’, and I think it is fulfilled more often than it is thwarted.
But there are some concepts that elude definition, and things like free will and unobserved existence are paramount examples of that. An attempted definition of one elusive term rests crucially on another equally elusive one, then another, and so on. We never get to a point where the meaning is clear. At worst, a discussion of those topics can end with the accusation ‘You know perfectly well what I mean! You’re just pretending that you don’t’, or the old classic ‘You’re just playing with words!’.
If a Scientific Materialist was so annoyed with my failure to understand her that she wanted to derail my thinking at any cost, she could take the tactic of saying ‘You say you don’t know what I mean by “exist”. Well what do you mean by “experience”?’ I could try to explain ‘experience’ but she could then pick another word in my explanation and say ‘but what do you mean by that?’. And so on. The game of ‘what do you mean by that?’ can be played interminably and, if you play it long enough, you will end up in a circle of definitions.
So is it just a silly game, or ‘playing with words’ to object that I don’t know what somebody means by something?
I was perplexed by this for quite a long time. I felt that my objections about the lack of clarity of concepts like ‘free will’, ‘a state of nothing’ or ‘absolute, unobserved existence’ were valid, but I felt that I would be unable to defend myself if those with whom I was discussing turned to me with a question about what I meant by one of my key terms, which usually revolve around concepts like ‘experience’, ‘observation’, ‘meaning’, ‘understanding’ or ‘feeling’, and then met all my attempted explanations with requests for further definitions.
This seemed such an obvious avenue for fruitful counter-attack that I found it strange that nobody used it. Now I think I know why they don’t. I think it’s because those terms are meaningful to them. Most people have a firm understanding of terms that are directly connected to first-person experience, perhaps because that’s where we all start in learning to speak. We see, we point, we name, we imitate.
If somebody did ask me what I meant by ‘experience’ for instance, I would try to describe what an experience was to me. I have a strong feeling that they would understand what I meant. Of course we can never know what it is like to be somebody else. But we make the working assumption that it is pretty similar for them to what it is for us. And that assumption seems to work, in the sense that communication is frequently effective, that we often get along, cooperate and achieve things together. It’s like how I assume that red looks the same to you as it does to me. It may not, but that doesn’t seem to matter. When we talk about red together, say buying a red cardigan, we seem to agree that the outcome of the discussions is what we expected.
What would I do then, if somebody claimed not to know what experience means, and met all attempted definitions with requests for further definitions? The only time someone ever did this to me it was not an annoyed Scientific Materialist but one of my children, who spotted an opportunity to confound their father and exploited it for all it was worth, for the sheer joy of it. Bless them! My patriarchal heart swells with pride at their ingenuity.
I have come to the realisation that the best response to such a line is simply to point out that we seem to have insufficient common vocabulary for a constructive discussion. That is neither a declaration of victory nor an admission of defeat. It is just an acknowledgement that for discussion and argument to achieve anything, there must be a certain minimum amount of shared language, and if that is not present there is no point.
Does it seem a little asymmetrical and unfair for me to demand a definition of ‘existence’ but not offer one for ‘experience’? The asymmetry comes from the fact that my interlocutor has not asked for a definition of ‘experience’, so it’s fair in the sense that I have attempted to provide definitions wherever requested. But in any case, this is not a poker game, where the winner takes all. For me, scientific, mathematical or philosophical discussion is a collaborative enterprise, the fruits of which are an improved understanding and acceptance of the world for both parties. Discussions where we start with opposing views can be especially useful, because they exposes one’s own views to critical analysis, both at the hands of the interlocutor, and in one’s own attempts to explain them clearly. My views have often changed as a result of such discussions, I hope usually in the direction of increased sophistication.
Discussions with a fervent advocate of Scientific Materialism or Libertarian Free Will usually end up with a realisation that we simply cannot reach a common understanding of what the key term – say ‘absolute, unobserved existence’ – means. In the first several such discussions I probably left with a somewhat smug feeling that the concept they were upholding had no meaning, but they were unable to realise that. Now I’m not so sure though. It is certainly possible that they are just mistaken, muddling themselves up with words that they think mean something but in fact don’t. But it is also possible that there is some real idea, feeling or concept of which they have an elusive sense, but which they are simply unable to put into words. After all, the ability to express something in words is a hopeless arbiter of what is real and meaningful to us. I cannot express Beethoven’s Fifth Symphony or the colour of a sunset in words, but those are both powerful experiences.
So perhaps the best way to resolve a frustrating discussion of this sort is for the party that has asked for an explanation of a key term to say to the party that is unable to supply one:
“It sounds like you feel very strongly that there is an important, real concept of x (say ‘absolute, unobserved existence’). Unfortunately there doesn’t seem to be any way to express the concept in words clear enough to allow us to consider it logically. Although I feel as though there may be no such concept, you may be right that there is one, just hiding beyond the limits of our language’s ability to describe it adequately. It’s also possible that you may have fruitful discussions about it with others that share your sense of the existence of such a concept. Unfortunately, you and I don’t appear to have any such shared sense, so we will have to discuss something else. So tell me, what do you think is the future of Capitalism?”Andrew Kirk Bondi Junction, January 2013
iScientific Materialism is a philosophical position in ontology that has absolutely no relation to how much one understands, believes or relies on science. So please don’t conclude from the fact that I am not a Scientific Materialist that I am anti-science. That would be the complete opposite of my real view.
Does the physical world exist, or are ideas all that there is?
This old philosophical question can never be proven one way or another, despite the best efforts of Berkeley to argue one side and Russell arguing the other. In fact, not only can it not be proven, but the question cannot even be interpreted in a way that has any meaning. What does it mean to exist? Is existence a predicate?
It can be frustrating that questions that we feel ought to have both a meaning and an answer appear to have neither. After some irritable chawing away at the discomfort this causes me, I have come up with a solution. I call it the ‘what then?’ test. This goes as follows:
For any given question with which we are faced, we should first ask: ‘if the answer is yes, what then?’ If the answer is ‘nothing of consequence’ then it probably means the question is unimportant, and quite likely also meaningless.
Some questions have obvious significant consequences, for example:
- Is that a gun in your pocket?
- What time shall I meet you?
- Is it right for me to eat meat?
Others have significant consequences that only become apparent after some consideration, for example:
- are animals conscious?
- Is there a god that is a person and who is all-powerful?
- Is Cartesian dualism true?
The first has important consequences because whether animals are conscious, and hence capable of suffering, is critical to our assessing the ethics of how we treat them.
The second has important consequences because, if there is an all-powerful, all-knowing being with opinions, desires and an interest in humans, we may be able to obtain advantage by pleasing it, or at least avoid punishment by not displeasing it.
The third has the important consequence that, if the answer is yes, it opens the possibility that the mind could survive without the body, and thereby that a continuation of conscious life after death may be possible.
But for some questions, one cannot find any consequences for our lives. Here are some examples:
- Do propositions about the future have a truth value?
- If there were no humans or other sentient beings, would moral values still exist?
- Is Idealism true?
- Do objects exist about which nobody can ever have any information?
- Is there a world of Platonic forms?
- If a tree falls in the forest and there is nobody there to hear it, does it make a sound?
I just cannot see any way that the answers to these questions have any consequences for us, one way or the other. In the light of that, it seems that these questions are useless to us, and not worthy of consideration.
But I think we can make a stronger statement than that. I think we might actually be able to say that questions that have no consequences have no meaning. How can one define a meaning for a concept that does not in some way touch upon our experience? I can’t say for sure that one cannot. But when I look at the concepts for which there are clear meanings, they all derive ultimately from simpler concepts based on past or potential future experience.
Take something very abstruse and seemingly far removed from everyday reality – the wave functions of quantum mechanics. These are elements of infinite-dimensional Hilbert spaces. What relevance could such a complex and abstract thing have to my life? The answer is that analysis of the mathematics of those wave functions allows predictions to be made about what I will experience in future, and that is part of my real life. When I press a button on my MP3 player, it plays the track I expect because of the quantum mechanics that govern the tiny electronics inside it.
Now take a question that appears to be very simple, but which has no impact on my everyday life. ‘Do things exist of which neither I nor anybody else will ever be aware?’ The naive physical answer to this is ‘of course’: there are rocks buried deep in the Earth that no creature has ever seen. There are stars in distant galaxies, from which no light has ever reached the Earth.
‘Yes’, says the sceptical philosopher, ‘but how do you know they are really there? How do you know that anything that is not currently being immediately sensed by you exists?’
The answer is that I don’t. The model of the universe in my brain says that there are rocks deep underground that I will never see, but I cannot categorically state that they exist.
Does this create a state of confused scepticism? No, because, if I was particularly concerned about what sort of rock lies five metres beneath my feet I could dig down and have a look. If I want to know whether the universe still exists outside my field of vision I can turn around. Of course it’s possible that the evil demon whose job it is to trick me quickly conjures up that part of the world just before I turn around. But then my special question comes into play: ‘what then?’ What difference does it make whether the world existed while I wasn’t looking? The only way that it makes any difference is if, at some future time, the demon will leap out in front of me and shout ‘April Fool!’ But that’s not the scenario Descartes had in mind when he imagined this demon. He imagined the demon would always be there, always maintaining the illusion of a complete physical universe. If so, then it is of no consequence to me whether the universe is real or a demonic illusion, as it will never have any impact on me or anybody else, one way or another.
Further, there is no real meaning to the question of whether the demon is there. What do I mean by a demon being there? The only meaning that can be ascribed to it is that there is a creature behind me that I or somebody else could see if we looked quickly enough. But by definition we cannot look quickly enough, so that meaning does not work. We cannot say that the demon is there and mean anything by it. Every statement we make about the existence or otherwise of objects, and the properties and relationships they may have, is based on the object, its properties or its relationships with other objects being able to be perceived through our senses, either directly, or indirectly through circumstantial evidence.
I conclude that any proposition whose truth or falsity cannot be ascertained now or at some time in the indefinite future by one or more sentient beings is meaningless. That probably accounts for at least half of metaphysics (but not all of it).
An uncomfortable apparent corollary of this conclusion is that perhaps even the question of whether we have free will is inconsequential and probably meaningless. It is hard to imagine any test that would irrefutably determine whether we have free will, so does that just make it an empty question like the others above? I think the answer is that it does as far as my own free will goes. I will never be able to be sure whether or not I have free will, so I should stop thinking about it. However it is important in relation to what I think about other people’s free will. Given the strong doubt about whether free will exists, or even means anything, I should avoid blaming others for their moral choices or seeking retribution against them, except where I think that would serve some socially beneficial purpose.
An old philosophical question is whether a prediction, by which I here mean a statement about the future such as
P: ‘it will rain on Sydney Town Hall at 1pm tomorrow’
is true or false at the time it is made, or whether it is neither, and only becomes true or false when the event to which it refers occurs, or fails to occur by the predicted time.
I think whether you accept that a prediction currently has a truth value depends on whether you subscribe to an A or B theory of time.
The ‘A theory of time’ holds that the future does not exist but is in the process of being created. Under this interpretation most predictions have no truth value. There will be some exceptions, which are things that have to be true, such as: “at 1pm AEST on 1 Jan 2013 it will either be raining on Sydney Town Hall or it won’t”. But I don’t think they’ll be very interesting. This one about rain in a given spacetime location is just a particular instance of a logical rule of inference – the ‘law of excluded middle’. It is true even though the events to which it refers have not yet happened because, no matter how the future unfolds, the prediction will be true.
The A theory does not seem to me to be compatible with a belief in absolute determinism – that is, that there is only one possible future, which will inevitably unfold under entirely deterministic laws of nature – the ‘clockwork world’. Under the most widely-accepted interpretations of quantum mechanics there is an irreducible randomness at the quantum level that makes determinism impossible. There is a minority view held by some physicists that future discoveries will be made that dissolve the apparent quantum randomness by revealing underlying deterministic processes. A-theorists would have to eschew such a view though, as a future that is completely determined by the present state of the world seems as real as the past.
Under the B theory of time, all of spacetime exists as a four-dimensional block in which separate events may be earlier, later or contemporaneous with one another (under Einstein’s Theory of Relativity, the ordering of events is not uniquely determined. For two events u and v, u may be earlier than v in one reference frame and later than v in another), and the passing of time is just our subjective experience, as the trajectory of our life is embedded in that block. Under this theory, every proposition about events in the spacetime has a truth value, seen from a timeless framework that transcends the block, including propositions about spacetime events later than the time the proposition is stated. The passing of time only changes our ability to know the truth value, not its existence.
The rest of this essay considers the question in the context of the A theory.
A common argument from those that hold predictions do have a truth value is that a prediction is just a proposition about the future, and propositions are either true or false. If one accepts this then there is nothing more to say. But whether we accept it depends crucially on the definition of proposition. For a start, one would have to disallow as propositions all statements that are incoherent, such as “nibble, squawk, omnipotence“, “the colour of my aura is five” or “one of Jim’s legs is both the same“. But doesn’t coherent simply mean that the statement has a truth value (that is certainly the problem with these three examples)? If so, it becomes far from obvious that a prediction is a proposition, because it is incoherent unless it has a truth value. So one has to suppose the conclusion – that the prediction has a truth value at the time it is made – in order to prove it.
Alternatively, if we do not require that all propositions are coherent then the second part of the argument fails: a prediction being a proposition does not entail that it has a truth value.
One can argue that a prediction does not have a truth value by asserting that the statement ‘it will rain tomorrow’ has no meaning – it is as incoherent as “nibble squawk omnipotence” This seems a very strong and surprising claim, but it is not easy to see a rebuttal. It is hard to explain what the meaning of the statement is without simply restating it, at best substituting some synonyms for the words therein.
Why do people so often say things like ‘it will rain tomorrow’ then, if they have no meaning? I think the answer is that people generally don’t, or if they do they don’t mean what they say. What they do say, if they’re careful about their words, is:
P1: “I believe that it will rain on Sydney Town Hall at 1pm tomorrow“
The crucial difference from P is that P1 is a statement about the present not the future. It is describing a current state of the speaker’s mind, saying that it holds a certain belief. This doesn’t help much with the dilemma though, because we can ask ‘but what is it that the speaker believes?’ We can rewrite P1 as:
P2: “I believe that P“
and it looks like we’re back where we started.
P3: ‘Most of the possible states to which I believe the planet Earth can evolve at 1pm tomorrow, starting from its current state, include rain falling on Sydney Town Hall‘
P3 is a statement about the present, as it is a statement about the now-existing set of solutions to a set of mathematical equations that represent:
- the current state of the world, and
- the laws of nature under which states can evolve, as the speaker understands them
- quantum randomness, and
- the speaker’s necessarily incomplete understanding of the laws of nature
We can sidestep the second of these sources of uncertainty by considering the statement:
P4: ‘Most of the possible states to which the planet Earth can evolve at 1pm tomorrow, starting from its current state, include rain falling on Sydney Town Hall‘
In contrast to P3, P4 may well be false if the speaker has an erroneous understanding of the laws of nature, or the current state of the world. That is because P4 is a statement about the laws of nature and the current state of the world, rather than about the speaker’s beliefs about those things.
Finally, the residual (quantum) uncertainty can be removed from P4 only if the laws of nature are, contrary to current mainstream scientific opinion, deterministic. Only then can the following statement be coherent:
P5: ‘The state to which the planet Earth will evolve at 1pm tomorrow, starting from its current state, includes rain falling on Sydney Town Hall‘
As noted earlier though, determinism appears incompatible with the A theory, so this statement only makes sense within a B theory, under which statements about the future are generally regarded as having a truth value.
Let’s summarise. What do A and B theorists make of the following statements, made at spacetime location (x,t)?
- Event E happens at spacetime location (x’,t’).
For a B-theorist this statement has a truth value, which is determined solely by whether E happens at (x’,t’), regardless of the value of t. For an A-theorist the statement does not have a truth value if t<t’.
- I believe that event E happens at spacetime location (x’,t’).
This has a truth value for both A and B theorists, but in both cases the truth value depends solely on the speaker’s beliefs at time t, not on whether E happens at (x’,t’).
- Given the state of the spacetime in the spatial neighbourhood of (x,t), event E probably happens at spacetime location (x’,t’).
This has a truth value for both A and B theorists, which is determined by the states to which the state of the world can evolve starting at (x,t) under the non-deterministic laws of nature. This is a purely mathematical statement, not about reality. For a B-theorist, this statement can be true even if E does not happen at (x’t’).
Theologian William Lane Craig, in his resuscitation of the Kalam Cosmological Argument, relies on a proposition that ‘an actual infinite cannot exist’. His primary argument in favour of this proposition is a reference to Hilbert’s Hotel and the apparent paradoxes it creates.
Hilbert’s hotel is a thought experiment devised by the early 20th century German mathematician David Hilbert. It is a hotel with an infinite number of rooms, all of which are full. A new guest arrives wanting to stay and is told all the rooms are full. But the hotel manager makes room for the new guest by moving the guest in room N to room N+1, for N=1 to infinity, and putting the new guest in room 1. Craig adduces the apparent absurdity of this as a compelling reason why an actual infinite, by which we presume he means an infinite set of objects each comprised of a finite, nonzero amount of matter, cannot exist.
But why is the outcome absurd? It is unusual, but there are many things in the universe that are strange and unusual. Is the sticking point that an empty room appears to have been created where none previously existed? If so then that problem is resolvable, by considering the process of transition to the state in which all the guests, including the newcomer, are accommodated. To do so we need to consider the process by which the hotel manager effects the transition, bearing in mind that we are dealing with a hypothetical physical situation here, so the laws of physics must be obeyed.
One possible such process is as follows: the manager writes an order, addressed to all guests, stating that, on receipt of the written order, each guest should:
- pack up and move out of their room
- go to the room numbered one greater than theirs and deliver the letter to the guest in that room
- when the guest in that next room has moved out, move into that room.
In this scenario, there will always be one guest without a room, as they wait for the next guest to vacate. This situation persists forever because the manager’s message only proceeds at a finite – indeed a very slow – pace. So it would appear that no extra room has been created: we had one person without a room as soon as the new guest arrived, and we still do, in perpetuity. It’s just that the person without a room changes every few minutes.
OK then, but what if the manager asks all guests to move at the same time – does that remove the need for all this infinite waiting outside rooms? Maybe. Let’s see.
How can the manager ask all the guests to move at the same time, bearing in mind that this is a physical hotel in a physical world, and hence must obey the laws of physics? Well, he could transmit his order by email so that it flashes up on a large electronic screen prominently situated in each hotel room. Let us assume the message is transmitted at the speed of light – physics dictates that it cannot travel any faster – from the manager’s office adjacent to room 1. The message says ‘To all guests: on receipt of this message please immediately pack up and move to the room with number one greater than yours. The occupant of that room has been instructed to move to another room. Thank you for your cooperation. By order of the manager.’ Seeing the message, all the guests start packing up and moving. On arriving at the next room, they have to wait while it is vacated. The waiting time, including the time taken for the guest to travel form the door of her room to the door of the next room, will be a minimum of d/c where d is the distance between rooms and c is the speed of light. It will be longer if the guest in the next room is out, or if they weren’t paying attention to the screen and so did not see the message at the earliest possible moment. If the guest’s walking speed is v (which must be less than c) then the guest will spend time of at least d/v outside a room, longer if they have to wait to be admitted to the next room.
As in the previous scenario, the room shuffle will never be completed, as there will always be an infinite number of rooms at which the manager’s message – travelling at the fast but finite speed c – has not yet arrived. At any point in time there will be a very large number of people outside their rooms as they walk from one room to the next. As the typical time taken to move from one room to the next is d/v and the delay from one room receiving the message to the next room’s receiving it is d/c, there will typically be (d/v)/(d/c) = c/v people in the corridor at any time after the first few minutes. Based on a typical walking pace of 1m/s this means there will always be about 300,000,000 people in the corridor. Clearly this situation is much worse than with the hand-written message.
In fact, however you try to arrange the transition, it will always involve at least one person being without a room for an infinite amount of time.
Although it is possible for all the existing guests plus the newcomer to be accommodated in the hotel without having to create new rooms, the transition from the existing state to a new state where all are accommodated involves an infinite amount of homelessness. This seems unsurprising, given the hotel was full to start with. So, when we take account of the process of transition, there are no miraculous or absurd consequences that cause us to conclude that an actual infinity cannot exist.
Hilbert’s thought experiment can be extended to allow an infinite number of new guests to arrive, or even an infinite number of coaches each carrying an infinite number of new guests. As with the single new guest, these new guests can be accommodated in the existing set of rooms together with the existing guests. But, as in the above scenario, the transition will still involve an infinite amount of homelessness.
A further twist on the hotel ‘paradox’ is the situation where a guest leaves. In this case all the guests move down a room, thereby moving towards a state in which all the rooms are occupied again, despite the departure. This version is easily understood by inverting the logic above and thinking of a room without a guest in the same way as we previously thought about a guest without a room. Hence the transition will involve one or more rooms being empty for an infinite amount of time.
Craig’s assertion that an ‘actual infinity’ is impossible relies on being able to deduce an absurdity from the existence of such an actual infinity. That absurdity must be something other than our scepticism that a hotel with an infinite number of rooms could exist, otherwise the argument becomes circular: ‘an actual infinity cannot exist because I consider the existence of an actual infinity to be absurd.’ If, when the new guest arrived, the manager were able to wave a wand and make all the guests instantaneously and simultaneously teleport, with all their luggage, into the next room, then we would have an apparent absurdity via the immediate accommodation of the newcomer despite all the rooms being full (that is the absurdity adduced by Craig as proof that an actual infinity cannot exist). Such an action can be contemplated in mathematics, but Craig has no objection to mathematical infinities (‘potential infinities’). It is actual, physical infinities that he claims are impossible. But by considering the problem of transition, which only exists for physical infinities, we see that it is precisely the constraints imposed by physics that prevent the absurdity from arising.
One might object that this is a nitpicking point about transition and that, after the transition is complete – i.e. after an infinite period of time has passed – everyone including the newcomer will be accommodated and we will have a physical absurdity. This objection is easily dismissed on the grounds that:
- we will never get to the point when an infinite amount of time has passed
- after a finite period of time all the guests will have died (or disintegrated by slow radioactive decay even if the guests are androids and hence not vulnerable to death); and
- after an infinite period of time, nothing should surprise us – think monkeys typing Shakespeare
The conclusion is that, whatever arguments might be made against the possibility of an actual infinite, Hilbert’s Hotel cannot be one of them.