Piglets of Infinite Regress

I was quite young, I think, when I first noticed an anomaly in my toy collection. A truck had roughly the same dimensions as its associated cars. But, from experience, I knew that trucks are generally many times larger than cars. Something was wrong. I felt the need to get rid of the toy truck and before long I’d learnt that the problem was one of scale. After a bit of searching, I happened upon a toy car-transporter truck, which seemed to be roughly in proportion to my assortment of toy cars. I’d also gleaned from my father or brother that scale could be expressed in numerical form – either as a fraction or as a ratio. I scrutinised the boxes of various toys, and sure enough, some displayed a scale. The most concise, in this regard, being the components of model railways. My attention moved to model railways therefore, out of respect for their shared scaling concerns. For a while I spent my pocket money on building up the stock of model railway items that were consistent with the best items in the existing collection. Around this time, an incident took place that has stayed with me ever since. A local grocery shop had installed a new window display. It was to promote a certain brand of tinned, processed meat. Said brand used a cartoon of a piglet in its advertising logo. The piglet sat reclining on one front trotter, whilst in its other front trotter it holds up a tin of the meat. There were several disturbing things about this logo already. For one thing, the creature had the proportion of a piglet but the expression of an adult. And then, it seemed to me that no real pig or piglet could adopt the reclining position that the animal had assumed. And of course, no real piglet could grasp a tin – or anything else, for that matter – in one of its trotters. And anyway, why would a piglet look so gleeful about displaying a tin containing the chopped remains of other pigs? But, whilst all this had been disturbing enough already, the shop display had only re-doubled the horrors. Centre-stage of the display was a model of the offending piglet clasping a REAL tin of the meat. The most disturbing thing about the whole wanton apparition was the sense of vertigo it induced in me. Because – well, think about it. On that tin of meat was the logo, showing a picture of the piglet with a smaller tin in its trotter. And on that smaller tin of meat was a yet-smaller logo, with an even smaller piglet and an even smaller tin of meat. It was dizzying! I remember staring agog in front of the grocery window, wondering how it is that grown-ups could commit such atrocities of existential anxiety without, apparently, any sense of responsibility, or indeed, any sense of shame. The name for this – I later learned – is an infinite regress. The infinite regress is familiar to children and their parents in another form – namely, questions that lead to further questions, that lead to further questions, that lead to… Why, Mum? Why, Dad? And the embattled parents will try to give an answer or otherwise resort to threats or distractions to avoid further interrogations. For my part, I usually managed around five why-questions of my mother, but only around three with my Dad. The infinite regress is one of three ways in which truth manifests itself to us – according to Aristotle – the other ways being through circularity or through brute facts. This is Aristotle, who, when asked if he was the most intelligent man in the world, argued that it was only because he knew one thing. But the one thing he knew was that he knew nothing. So, we might not hold out much hope of getting to any truth by the routes that Aristotle suggested. But nonetheless, it is worth digging a little deeper, because what all three of Aristotle’s suggestions offer us is an understanding of a certain fundamental paradox in the universe. Let’s go back to the piglets and their tins of meat. Perhaps what induced that vertigo in me as a child was the sense that the regress could go on forever, with ever-smaller piglets and tins. In reality, of course, there would come a point where the logo is going to be just too small for the next-smallest piglet to be recognisable. And so the regress stops. It reaches a practical limit, despite its theoretical infinity. But what if we made that initial piglet as big as could be fitted into the universe? And, let’s say, initially, that the universe is finite – say 30 billion light years in diameter – for the sake of argument. It seems at least theoretically possible to make that first giant piglet. (I know this would be a horrible universe, especially for vegetarians, but bear with me.) Well, more piglets and more tins, but same conclusion. Eventually, within a finite number of times, the regression has to stop. Here though is where the real bite of the infinite regress takes place. What if the universe is infinite and we start our piglet and tin regress with an infinitely large reclining piglet? Then, surely, the regress would be truly infinite. The real rub though is that, whilst we can conceive this thought experiment, we would probably all agree that, in practical terms, it would not be possible. Wqe could generalise this a bit, and say – as an initial conjecture – that there are ‘perfections’ in the world that we can imagine and which can be realised. No problem with this. But, there may be perfections in the world that can be imagined, but which can never be realised. That’s why this infinite regress has such bite, and why it disturbs so much, as I’ve tried to show with the piglets in this example. Well, dear reader, you may, at this point, be thinking that I have gone with an especially absurd example, just to demonstrate some obscure and irrelevant point. But, I would counter, these imagined perfections that are nonetheless unachievable actually surround us at every turn. Take, for example, the Fibonacci ratio – otherwise known as the Golden mean. It’s a simple fraction and is, in this sense, mathematically perfect. It occurs frequently in nature, but here the perfection is never quite reached. There has, instead, to be a series of whole numbers – the Fibonacci sequence – which tends towards perfection, but could only reach it through an infinite number of iterations. Seashells –and for that matter, drawings of Fibonacci spirals – are somewhere between this. The curve is theoretically perfect, like its associated ration, but the practicality of creating the spiral can never be perfectly achieved. We have to turn to Plato to drill down further into this. Plato is best remembered for his world of perfect forms (the Realm of Being), which exists quite separately from our everyday, familiar world (the Realm of Becoming). The usual interpretation of this is to say that Plato thought our world to be a poor shadow of the world of forms – that Earthly things are shoddy representations of their eternal and perfect form. But it seems that there are perfect forms that can be explained and understood, but could never, by definition, be realised. This is a puzzling conclusion. I don’t have an answer to it except to say that I think it is a fundamental paradox of the universe. There are perfections, but the world in which we live is flawed. Perhaps it helps here to invoke one of Aristotle’s other categories of truth – the brute fact. Let’s start by going back to the toy cars. The problem here, you’ll remember, was scale. To be a proper model car, it needs to match up – more or less – with the real car. In philosophy this is referred to as correspondence. Apart from scale though, the toy cars are quite a good match. They’re made of similar materials and their make and model are at least recognisable. By analogy, physicists hope that the universe turns out to have similar correspondence to their models. If there’s a good enough match between what theory predicts and what is actually our there then that suggests a successful model. If we had sufficient observations then maybe we could find a theory that fits them all. That’s the dream of science. But maybe we won’t be able to collect enough facts. Or maybe we won’t find a theory. Or, perhaps worse, maybe we find more than one theory and cannot decide which is best. Well, there’s another probability that is perhaps even more disturbing. Perhaps there will be a failure of correspondence. At the moment, we simply assume dead matter, in particular arrangements, is what makes up the entire universe. But what if there are other ‘relations’ between things that are important, besides just physical relations between things in space? What if consciousness matters, or agency – or life itself? We have a glimmer of this with quantum entanglement, which so far, of course, is unexplained. What would a theory of science have to be like in order to tackle these more complex relations? The chances of successfully finding such a theory are perhaps not zero, but right now they surely seem very small indeed. And hence, the brute fact! Some things we just seem forced to accept, even although they cannot be proven. The circular argument is one that – rather than heading off into an infinite regress – instead returns to a brute fact. Mum and Dad say, ‘just BECAUSE!’ Science, at least in its official version, recognises the contingency of all its discoveries. It will wait, perhaps for centuries, for new thoughts to arise and new evidence to come in. But what of us? Well, for the most part, we are not too keen on things that are vague or incomplete. So we have stories – filling in the gaps where knowledge fails us. And, of course, there are a lot of contenders. Our different truths lead to different meanings – different meanings to different values – different values to different ethics and moralities. In short, we see the world in different ways. For what it’s worth, I prefer just to wonder at the paradox that our discoveries has unearthed. Somehow there is knowledge of perfection, yet somehow the universe falls short, or is ‘asymmetrical’ or flawed. But maybe it needs to be flawed in order to exist at all? Even this stance of mine though – what you might call, sitting on the fence – is still a world view of sorts. It leads, perhaps, to those liberal values of tolerance and acceptance. Which, in turn, lead perhaps to the morality of a liberal society. We tolerate everything except the intolerant. But, let’s face it, I wonder still about the different groups of folk all shaking their fists at each other. So much anger from those who hold desperately to at they take to be the ABSOLUTE TRUTH. Gets us in a lot of trouble. I’m not pretending to answer this question. But let’s at least look for some common ground. We can ask – what is it that you will do with your truth? I don’t mean, what kind of rules or morality you might devise. I mean, what will you, personally, do, when faced with some big question in your life? Because, if we face such questions together, then that way we can talk as people – both having, I’d dare to suggest – inadequate knowledge and limited powers of discernment and judgement. We meet then, outside the bounds of truth and falsehood, right and wrong. The other area of common ground goes back to what I was saying above about perfection and imperfection. Perhaps this can, in fact, be solved, and perhaps that would give us answers. The story is taken up in another essay – ‘The View from the Mountaintop’.