Zeno’s paradoxes

Zeno’s paradoxes are amongst the most venerable and to many impenetrable of all philosophical puzzles. There have been many attempts to explain Achilles and the tortoise, the arrow paradox and the so-called dichotomy paradox, often illustrated by 'proving' the impossibility of a frog ever managing to hop its way out of a pond. Apparently there were about 40 in all, and were originally created by Zeno of Elea to illustrate Parmenides’ conception of the world as logically changeless by showing that much of what we believed we witnessed in the world simply could not be happening.

This view has undergone a lot of humorous parody and satire, from Zeno’s contemporaries to Terry Pratchett’s occasional sketches of ‘Ephebian’ (i.e., Greek) philosophers deducing all sorts of wonderful things. All in all it tends to remind one of the wonderful line in Monty Python and the Holy Grail, ‘and that, my lord, is how we know that the earth is banana-shaped’.

There have been plenty of attempts to refute Zeno too, involving ideas like infinitesimals (roughly speaking Aristotle’s answer), which works quite well. For we have known since Archimedes that the sum of an infinite number of progressively smaller amounts will add up to a finite total. Or rather, it will tend towards a finite result, which is a problem, since it is not obvious that this is not actually simply a mathematical way of simply restating the original paradox, because this reasoning does not, in itself, conclude that the frog ever actually reaches the side of the pond.

Another use of the infinitesimals inherent in Zeno’s original paradoxes is to reject them. If it simply isn’t true that there is always a point lying between two other points, no matter how close together, to which the frog/ arrow/ Achilles/ whatever can move next, then it must make definite progress and eventually Achilles will be the winner. You can also reject the idea that things are anywhere definite or finite at any given point in time, but I think it’s a bit much to have to rely on relativity or the uncertainty principle to beat up classical philosophers!

I have never quite understood why these paradoxes seem to attract solutions like this. Perhaps I am missing something, but hasn’t Zeno actually defined the problem in such as way that it cannot be solved? He describes all these events in terms of them never being concluded. For example, if Achilles’ movements are defined in terms of reaching where the tortoise was last – a place from which it must have moved on – then plainly he can never overtake it in this framework. But that is only to day you can define a problem in terms of failure, which is what Zeno has done. If at each step Achilles' motion is defined as reaching only to where the tortoise last was, he cannot have reached where it is now. So the problem is actually stated in terms that permit only failure. In other words, failure is not a paradoxical result of this overall situation but a simple deduction from its definition.

There is no need to appeal to any fancy mathematics. All you have to do is to realise that this is not a paradox at all, but rather the description of an activity in negative terms that cannot be shaken off without seeming to disregard the original problem. Zeno’s paradoxes strike me as valid but uninteresting – except for what they tell us about how philosophers and mathematicians reason.

Free will and determinism

A rather long theoretical speculation.

Free will and determinism are generally treated as polar opposites. Here is a hypothesis that starts from that position and concludes with them being identical.

Human free will is difficult to establish. The concept itself is extremely evasive and analysing consciousness and decision-making (which I take to be among the more intractable issues for free will) is fraught with contradictions and infinite regressions. In addition, many of the material determinants of human action and experience are clearly external to the human individual, either as social or as natural entities. As such most social and natural conditions would necessarily limit our material freedom, even if free will were in principle possible. Unlike writers for whom the conceptual analysis of free will and practical constraints on freedom are to be studied separately, I would argue that the reason why the concept of free will is too hard to pin down is the same as the reason we are not, in practice, free.

Essentially, we lack freedom either because of the relative immaturity of the subjective intelligence through which we exist in the world or because of the limitations (gaps, mistakes, conflicts and contradictions) of the objective systems and relationships by which our worlds are actually composed. That is, we are prevented from achieving what we set out to achieve because the structures on which our actions and experience are based stop us from succeeding. It is not simply a matter of weakness: defeat of one kind or another (including subversion, diversion, distraction, disablement and frustration as well as outright defeat) is often built into the very systems and processes through which we act.

For example, even within our world of formal social freedoms (citizenship, equality before the law, and so on), the contradictions that beset our relationships with bureaucracy, representative democracy, economic activity and the law are too well known to need elaborating here. And once again, these are contradictions, not just misfortunes: the problems are built in. Others, created by inhabiting a world made up increasingly of money, commodities and roles, are less obvious, though they are often yet more fatal.

Furthermore, because these structures are contradictory, they prevent us from experiencing the world (or even our own experience) in a coherent manner. This in turn stops us coming up with any way of fully or accurately describing or analysing that experience without working through a huge range of social and historical systems, and so of formulating our goals and intentions adequately in the first place. Furthermore, the vast scale and complex yet ambiguous structure of our social systems makes it unlikely that many people will have the necessary knowledge, or any idea of how to acquire it, or any idea that it is needed.

For example, a capitalist society creates a basic individualism that prevents us from seeing straight away that our problems are social and historical rather than psychological. For most people, the response to bureaucracy, injustice and the general malaise of everyday life is personal frustration, resignation and depression, not social analysis, organisation and action. We divide our efforts between work and consumption, and even these supremely social activities are experienced in terms of a narrow individualism or, at best, instrumental social groupings (office, shopping mall, public transport) to which we commit little of ourselves. This perverse structuring of action and experience both creates innumerable illusions about how the world really works and effectively undermines every attempt to do something about it.

For example, in work we are typically isolated as individuals and functional groupings, and the knowledge we have of the larger systems and relationships we need to do our jobs is generally very narrow. There are timetables, duties, targets, techniques, but little meaning outside the group or the even the task. And in consumerism, we exist solely as isolated individuals, in families and other small, specialised and isolated groups.

So by and large, the only knowledge we need to operate within society is at the level of simple, formally prescribed facts (a great deal of which is anything but correct at any profound level). The massive social and economic processes whereby we ended up there at the supermarket are treated as a combination of the trivially obvious, too dull and difficult for non-specialists to bother with, and none of our business.

At the same time, we are constantly bombarded by complacent and unimaginative politicians, newspaper editors and pundits, and endless other spokespeople for the status quo telling us that we are all already free – or, with one of those small, resigned twists in which modern ideology excels – we are as free as we should try to be.

Even for professionals who specialise in such questions, social life is not exactly training for solving problems of free will and determinism! In fact, the disciplines of history, philosophy and the social sciences seem to be almost as confounded by these assumptions about how our lives work (if that is the word) as everyone else. I doubt that one sociologist in a hundred could explain the idea of alienation.

The basics of the real processes through which all this takes place should be all too familiar to need explaining, though they certainly are not, even for those with a background in the social sciences. Or perhaps they should be anything but familiar. After all, why would any social system regard a theory that that system does not make sense as a tool for making sense of itself? It would be a confession of failure and futility and an invitation to do something about it.

On the other hand, if the ways we understand our relationships to the world and to one another and the systems and structures through which we actually live are so closely interconnected, creating a world of freedom and conceiving of free will properly ought to be mutually fruitful enterprises. If we could do something about these endemic contradictions that constantly frustrate freedom we would be able to grasp the concept of free will, and the more thoroughly we work through the conceptual contradictions (including their social and historical aspects), we more clearly we will know how to go about creating a world in which genuine liberty is the norm.

So what is the general model of freedom I am arguing for? In brief, freedom is lacking whenever the structures that determine either our intentions or the means to realise them are outside our control. If everything that controlled both how we grasped the world and what we wanted, expected, needed (and so on) was (in some sense) a part of ourselves, then we could say that the ways we conceived of our existence in the world and the structures that through which that existence was enacted were one and the same, both with one another and with ourselves. In other words, the structures that determined and realised our will would all be part of ourselves. It would thus be free will, yet wholly determined, yet subject to no material constraints or limitations from beyond itself. Conversely, if we could internalise within ourselves over all the structures needed to materialise those intentions and desires in the external world of practical reality, there would be no constraints on the exercise of our free will either. In other words, our free will would be exercised in freedom.

But what are the structures that need to be created to freedom to be achieved? And, given that the structures that impinge on the exercise of our will might be found anywhere in the entire universe, in what sense could they possibly be internalised? I have tried to describe in detail the historical and phenomenal processes through which truth and freedom (for truth and freedom come down to the same thing) can be reconciled with determinism in my The History of Human Reason. But in the most general terms, this argument entails that a) such a reconciliation is possible, and b) it is susceptible to scientific investigation in all its aspects, with no sneaky corners of irreducible indeterminacy.

Isn’t philosophy fun?

Negative reality

A small contribution to science fiction rather than science, I suspect.

There is no such thing as a vacuum. Quantum theory tells us that, even if a vacuum existed, it would soon find itself being populated with particles caused by inherent quantum fluctuations. Once they come into existence these particles are normal enough, but a moment ago they simply weren’t here. So where were they? Nowhere. They just emerged out of a quantum flux.

And then there are negative numbers. I can have one apple, two bananas, three protons, four quantum physicists – but not -1 of anything. Why not? Isn’t that a bit of a paradox? No – as Piaget tells me, negative numbers represent not things but actions – taking away. So positing one apple is literally positing – putting into position. And by the same token, negating is simply taking away. Of course, when you get to zero, you can still hypothesise a lot of taking away – hence the negative numbers. Well...

Actually that sounds like a lot of sense to me. But I can’t help speculating in slightly more empiricist vein anyway (probably because I’m British). Is there a possible connection between these quantum fluctuations and negative numbers? How about this? There is a positive universe to which we have access, and a negative universe to which we don’t. That’s not to say that there is nothing there – it just exists on a plane we cannot touch or interfere with. On such an account, nothing/zero refers not to an absolute limit but to a transition point. Being creatures of the positive universe, we cannot make that transition, but that does not mean that matter as a whole is limited to our half of these cosmic Siamese twins. Indeed, that is exactly what the quantum fluctuations in the vacuum – the closest we have to physical nothing – signify – particles shifting between positive and negative universes.

Now, what would happen if we could fish in the vacuum and pull something a little more substantial through from the negative universe? I feel a sci-fi story coming on...

Theory of Everything? No, actually...

So on September 10 CERN switch on the Large Hadron Collider – the biggest scientific experiment of all time. Will it simply create a black hole that will suck the Earth into oblivion? I think I can say with absolute certainty that, No, it won’t. Of course, the only reason I am so confident is that if I am right then I can crow about it afterwards, but if I am wrong, exactly who is going to tell me so?

Another thing I often hear about these experiments is that they will move us a little – or maybe a lot - towards the scientific grail – the Theory Of Everything – which, rather inelegantly for a holy object, is often referred to by lazy typists like me as just plain TOE.

This ‘Theory of Everything’ stuff impresses me though. A Theory of Everything, eh? So it will explain the weather? The nature of beauty? Why feudalism gave way to capitalism? Whether or not we will deal with climate change? Why I talk to my cat? The nature of consciousness? Why I think Eddie Izzard is funny? How about something a lot simpler, like the nature of life? Or are such things, as people who cannot handle complicated things (like reality) like to say, unreal, epiphenomena, or secondary (whatever that could possibly mean)?

I’m not sure that anyone is claiming that TOE will explain anything like this. So what is the problem? Qualitative change – which necessarily cannot be explained in mathematical terms – is perfectly real. Not in the sense that something magical suddenly appears, but in the sense that novel structure of the kind that the first consciousness, the first life and the first atom were all derived from not only stabilises existing patterns of activity but also reveals new patterns. That is after all why we have not only physical action but also chemical reactions, life and natural intelligence.

So why is it that scientists like to repeat that this really will lead to a genuine Theory of Everything? It may well tell us really important things about the physical world – though even that is likely to be limited to a certain level - but ’everything’? Absolutely not.

(Incidentally, the BBC’s webpage on the day poses the fascinating question ‘Is particle physics the new rock n’ roll?’ I think I can reply with some authority on this one: No. And please don’t say anything so silly again.)

Making sense of human nature

I have spent a great deal of my life studying psychology in various ways. Most of the time I have been looking for clues as to what it is that differentiates intelligent life from its non-intelligent cousins and precursors. I have written quite a lot about this (e.g., my History of Human Reason and yet-to-be-published Birth of Reason), but I often feel that I have missed the point.

Quite a lot of human existence is readily captured by the conventional notion of intelligence. We are almost uniquely conscious and historical beings. The only other species that exhibit consciousness are our primate cousins and a few very smart birds and dolphins, and none at all has a history. So far as we tell at the moment (animals are difficult to study in direct proportion to their evolutionary distance from Homo sapiens), these species are all characterised by essentially the same kinds of intelligence as ourselves. Or at least, they can be tested for the same aptitudes and abilities.

Yet I don’t spend my personal life dwelling on the sorts of things that are normally associated with testing intelligence. I don’t sit about doing mathematical puzzles or organising objects into classes and sequences. Right now, I am writing this blog, listening to Muddy Waters and feeling pretty pleased that I have finally coaxed my cat to want to sit on my lap after literally years of trying. Last night I watched Shakespeare’s Two Gentlemen of Verona and thought about my life. What all that has to do with intelligence as conceived of by science I have no idea. Nor, I think, has science.

Yet I am quite sure that that is where the explanation lies. The problem is that, like everything else about the science of human nature, the study of intelligence seems to take in everything about human beings apart from what makes them so peculiarly human. As so often, science studies what it can readily comprehend and already knows how to research, and everything that does not fit that model is left by the wayside. Later, once it has established a massive body of empirical findings, it announces that this is what humanity is, and all the rest is illusion, epiphenomenal, trivia.

But then, isn’t that where we are now? With all those modules and genes-for and all that – where is anyone asking, ‘So what has all this got to do with human beings?’ The truth is, you can’t get there from here.

So let me suggest a list of things any would-be science of human nature should take as its central problems:

• Love
• Music
• Laughter
• Beauty

I know that there are some studies of some of these things, but precious little. Even when they are studied, there is something strangely mechanical about the way we go about it. How can a checklist or an ECG reading capture anything of significance? No, they aren’t a ‘starting point’ or ‘building blocks’ for a full theory, or anything else of any value, any more than a scientific study of the properties of bricks tells us anything about Westminster Cathedral – or, indeed, a multi-storey car park.

Does intelligence evolve?

Human beings and human intelligence are indisputably the products of evolution. But that does not mean that human intelligence will itself evolve further. In fact it won’t.

Well, if that doesn’t sound like special pleading, I don’t know what does. But then human intelligence is special. Or rather natural intelligence as a whole is special. Not magical or blessed or the product of a special creation, but rather so placed by evolution itself that it can undo the knots and straighten out the hidden connections that driven evolution itself, and so take charge of the process.

Yet if natural intelligence is special on every level, it is only in the same sense that organic structures and processes are ‘special’ from the point of view of physical of chemical systems. Just as life introduces a whole raft of new structures such as ecosystems, reproduction and natural selection, and yet is the product of prior physical, chemical and generally material process, so natural intelligence introduces a whole new range of elements – not least history, consciousness and individuality – that have analogues, but not equals, among organisms.

The consequence of all this is that although intelligence assumes a biological substrate and platform and could neither have evolved nor developed without the pre-existence of life, once it exists it does so on terms that are very different from those of evolution. So if evolution continues to be a factor intelligence must continue to deal with – which it certainly does – that does not mean that it is determined by evolution. After all, a cat has to deal with gravity, but you would be hard pressed to explain a cat’s startling acrobatics through the equations of physics.

So in what sense is intelligence immune to evolution? As I have argued elsewhere, it is a long story, perhaps stretching back to eh origins of life, but the basic case is quite easily explained. It is a story in three chapters, to be told in no particular order, about the most basic structures of human existence: objects, subjects and the world.

What are you doing?

Let me start with a very abstract claim (don’t worry, it only lasts a paragraph). Everything human beings do consists of constructing objects. You know something when you can grasp it on its own terms – which is to say, objectively. You know you have succeeded in doing something when the reality you were trying to achieve endures without you continually having to shore it up - which is to say, as an object in its own right. You know you are acting rationally when you can say what goal you are trying to achieve or what value you are trying to realise, plus explain how you are going to get there without introducing prejudices and assumptions you cannot defend – which is to say, as objects on their own terms. And so on.

Leaving out the philosophical problem of whether objectivity can ever be complete – personally I have no doubt that it can, but the present argument doesn’t rely on this fact – how does this make intelligence any different from any other kind of organic structure, and what difference does it make to evolution?

In short, one of the most striking yet unregarded facts about human beings is that we know what we are doing. There is, unless we deliberately adopt the method of trial and error, no place for random variation or natural selection in intelligent activity. But neither are we limited to executing pre-programmed instructions, even if we allow for the qualifications of learning, memory, facultative adaptations, and so on. Unlike any non-intelligent organism, human beings are capable of saying and justifying in advance what they are trying to do, devising and justifying a plan for doing it, executing and justifying that plan in an orderly manner, and continually monitoring and justifying whether we are fulfilling our purpose.

Piaget had a useful term for this ability – he called it 'object permanence'. By this he meant that our intelligence lets us recognise that things exist independently of our consciousness of them. Even from consciousness’s own point of view, object permanence means that we can look at things in a detached manner, and see not only objects themselves but also the relationships between them, the relationships between these relationships, and so on. As a result, the simple ability to recognise that things exist in themselves soon allows us also to recognise the rules, systems and laws that determine how they exist and the kinds of things our objects can, must and will – or will not - do.

Nor is this talent limited to consciousness as such. Because of our insight into what makes our objects what they are, we not only know that a house we build still exists when we are not aware of it (which is radical enough) but we made it that way precisely so that it would exist – and act - as it does, independently of our own actions. We made it with walls and roof and doors and windows and rooms and systems and furniture and all the rest so that these things would do things for us without us continually having to do them for ourselves.

In short, the object permanence that intelligence gives us also gives us technology. Of course, many organisms use small parts of their environment in an analogous manner, especially (for example) nesting creatures. But nest-building does not seem to be based on any genuine insight into the nature of the situation its maker is in, the nature of the materials they are using or the purpose for which they are used. In human beings not only is this insight there but this talent seems to be generalisable to absolutely any situation, from architecture to global communications systems to evolutionary theory.

So what difference does all this make to evolution? In a nutshell, if we can grasp that things exist independently of our consciousness of them, this is as true of the biological forces by which we are surrounded as of anything else. In other words, we can recognise evolution itself, how it works and what it is doing – and might do – to us. We can recognise, anticipate and deal with sources of variation and selection and decide for ourselves whether we want to allow, evade, forestall or reverse them. Unlike any non-intelligent organism, we can understand what is happening to us and take action if it is not what we want. Of course, we don’t always succeed, but that is a different matter. Meanwhile, through our objective grasp of the structures whereby life operates, we can invent our own selective forces, or intervene still more directly. At the moment we are just beginning to discover genetic engineering; who knows what we will know a century from now.

Who are you?

One of the most basic rules of evolution is that organisms in different lineages never throw up quite the same structure. The bodies of shark, ichthyosaur and dolphin may be streamlined in broadly similar ways, and the eye may have evolved over and over again, but never did this process result in the same structure showing up in more than one place. The possible ways of solving the same functional problem are so many and starting points and conditions so varied that the odds are simply too long.

Except, it turns out, in the case of intelligence. The evidence is thin on the ground, but at present it looks like, when organisms as diverse as human beings, chimpanzees, birds and dolphins start to develop intelligence, what they produce is not just a set of functionally equivalent structures – the equivalent of the fish and whale body-shapes – but exactly the same intelligence, over and over again.

It’s very hard to prove, especially as non-human intelligence is generally so limited and so hard to interpret, but there are at least two features of all natural forms of intelligence that strongly suggest that the same structure has popped up repeatedly. Firstly, the developmental process seems to be the same for all forms of natural intelligence. Intelligence develops through the same sequence of stages no matter what the starting point. If human and bird intelligence were not structurally the same, this would be quite absurd. Secondly, when human beings and dolphins of equivalent levels of intelligence make mistakes because of their lack of maturity, the mistakes they make are of the same kind. Again, if the underlying structure were not the same this would be impossible to explain.

From an evolutionary point of view, this is just about as odd as can be. Just consider the evolutionary distance and biological differences between human beings, birds and dolphins. It is more than two hundred million years since we last shared a common ancestor with African grey parrots. None of our brains are very similar either, especially not in the areas human intelligence relies on.

Why does all this matter to evolution? Because the internal structure of natural intelligence – which is what the above was all about – is what is also known as the subject. As an intelligent being, it is the framework that defines your every experience, shapes your every desire, allows you to make sense of the world and organises how you act. It is, at the most abstract level, who you are.

It’s also another thing that takes you out of evolution. Because if all intelligence shares the same structure internally, then the evolution of intelligence can only conclude in one result. There is no variation around it, and no possibility of selection between variants, because there aren’t any. The structure of intelligence seems to be completely invariable. So unless evolution is able to take intelligence away as well as give it – and I think that the other sections of this essay make it clear that that is not likely – once you have intelligence, evolution has lost its power. Once you are a subject, you have escaped from evolution.

Where are you?

You live in the world. Which is odd, because no non-intelligent creature does. It may – must – inhabit a niche, to which it responds and which it may even change in various ways. But in the absence of a stable subjectivity and a capacity for grasp things objectively, a niche is a pretty unstable, fragmented place. After all, if the organism has no idea that things exist objectively then it can have no sense of the niche itself – which is to say, of whole within which it lives. Still less can it have any idea how it works. On the other hand, if the organism itself has no consistent or stable internal structure then there is no one there for whom the niche could exist.

Hence the oddity of living in a world. It is a single whole, which no niche is. But that is only the first oddity about the world. For a world can’t even be properly compared with an entire environment. Hence its second oddity. For while the organism’s niche includes (one might say) only that subset of its environment that directly affects or supports its activity, even its environment includes only that subset of the universe that might impinge on its niche.

For example, the tulips in my back garden already inhabit quite a large niche, given that they are directly affected not only by the soil they grow in, the garden fences that protect them from the wind and the occasional watering they get from us but also the entire UK weather system. As for its environment, current global warming means that their effective environment also includes Chinese factories, the machinations of New York stock market investors and the land management policies of the Brazilian government. But leaving aside the possibility of a rematch with the meteorite that put paid to the dinosaurs, I think it’s safe to say that their environment does not include much outside the Earth and nothing at all from outside the solar system.

Which cannot be said of the world of intelligent beings. That doesn’t seem to have any limitations at all - its ultimate universe is the universe. Quanta, quasars – they’re all there. How is that possible? Back to objects. For if we recognise objects exist independently of our consciousness of them, then we can’t help also recognising that they themselves exist in relationships with one another (and quite possibly with things we are not even aware of), whose existence is immediately implied by our recognising that the objects we are directly interested in exist. But if that is the case, then our limits in things is not limited to the parts and aspects of the universe that might us in more practical (e.g., adaptive) reasons. In fact we have a name for the study of things, regardless of whether we have any practical interest in them. It is called science.

Hence our ability – again - to transcend evolution. We inhabit a world that itself transcends any adaptive interest. Object permanence also gives us a practical grasp of that world that allows us to change it – make it more in our own image, perhaps. As a result, from generation to generation we have created a world that is increasingly defined by human concerns, human purposes, human desires, and human systems. This has now reached the point where, for better or (as now seems likely) for worse, human beings are now the biggest factor in the lives of many of the world’s species. It is likely that we will have killed off a third of the world’s species some time soon, and if the research Mark Lynas cites in his terrifying Six Degrees is anything like correct, we will soon have wrought so much damage that no species – and certainly no ecosystem – can be considered safe. But from a purely evolutionary point of view, this complete reversal of the relationship between organism and evolution means that the essential question is now whether evolution is controlled by intelligence rather than the reverse. Plainly, I would say, the answer is Yes.

How is this possible?

Finally, how is all this possible from an evolutionary point of view? How can evolution throw up a structure that breaks all the rules of evolution? It has nothing to do with the usual villains, such as ‘Intelligent Design’ (was any theory ever more absurdly named?), some of whose more blatant absurdities are catalogued here. The truth is a long but really quite simple story, which I have tried to piece together in my Birth of Reason, of which you can download a free copy here. And if you would like to read a more detailed version of the present argument, try here.