GUEST ESSAY: The hare overtaking the tortoise is no illusion: What Zeno’s paradoxes can tell us about the hard problem of consciousness

By Stephen Davies

(This is a guest essay submitted to the Metaphysical Speculations Discussion Forum, where it was extensively reviewed and critically commented on by forum members. The opinions expressed in it are those of its author.)

One of the paradoxes of the pre-Socratic philosopher Zeno, involves a race between a hare and a tortoise. Here is a different version of that paradox: I challenge world-record-holder Usain Bolt to a 100 metre race. My only condition is that he gives me a 10 metre start. He accepts. I’ll now explain why he cannot possibly beat me.

The race begins. To overtake me, Bolt must first reach my starting point at the 10 metre mark. This will take him some time, let’s say roughly one second. In that second I will have moved forward from the 10 metre mark, let’s say 5 metres. 

So now, after one second of the race has passed, Bolt is at the 10 metre point and must reach my new position at the 15 metre point. This will take him about a half of one second, but in that time I will have moved forward again a short distance.

There is no end to this process; however quickly Bolt catches up to where I was, I will have used that time, however short, to move ahead, albeit by a shorter distance each time. However small the time and distances get, Bolt can never catch me, I will always be ahead.

So the paradox is that it is impossible for Bolt to overtake me in a 100 metre race. Because we know that this isn’t true, the paradox is telling us something is wrong in the process that got us to that conclusion. 

What goes wrong with the hare and the tortoise paradox is that the endless series of points that, in my example, Bolt would have to pass through, are not actual points. They are abstractions. The points aren’t there, marked in the ground, they are part of a theory. Bolt does not have to run past an infinite number of actual things, just an infinite number of ideas, an infinite number of abstractions.

It doesn’t seem so impossible now, does it, to run past an abstract idea of endless points. And better still, as each abstract point is a dimensionless point with no length, even if they did exist, how long does it take to run past something that has no length? However many points of zero length you have, zeros don’t add up to anything.

Another paradox of Zeno states arrows cannot fly. The argument here is that at any particular moment of the flight, the arrow is not moving; at any instant of time, the arrow will be stationary at that particular point. Imagine taking a video of the flight of the arrow and then looking at every frame of the video: in each and every frame the arrow is not moving.

Again, we know arrows do fly through the air, so this paradox must be telling us there is something wrong with the thought process, not with the flying arrow.

Zeno has made the same mistake here with time as he made with distance with the hare and the tortoise; he has assumed that the actual is made up of the abstract, that time is made up of frozen instants. In the same way as an infinitesimal point on a line has no length and so the line cannot be made up of points, a frozen instant in time has no duration and so a period of time (the flight of the arrow) cannot be made up of duration-less instants.

(Zeno’s paradoxes have also been solved by mathematics using sums of infinite series tending to a limit. Infinite series as described by Zeno can in fact be calculated within a finite limit, so there is a point that can be calculated when Bolt will overtake me. Assuming time and space are discrete—that they have a shortest non-zero length—is also a way of solving the paradoxes. There are no instants of time; there is a smallest duration of time and the arrow will be moving within that.)

The materialists are making the same type of error as with the Zeno paradoxes of time and distance; they are assuming that an experience we know does happen, is made up of abstractions we can use to describe that experience.

Let us now turn our attention away from distance and time, away from hares and arrows, and look at consciousness. I will attempt to formulate a new Zeno-type paradox for consciousness and see what light that sheds on the hard problem of consciousness.

Before formulating this new paradox, we need to briefly explore what the hard problem of consciousness is, and to do that we need to look at the metaphysical philosophy of materialism. Simply stated, this asserts that everything is made of matter, of physical stuff. You may wonder why such a seemingly obvious and self-explanatory statement requires the title of a metaphysical philosophy. The reason is that materialism isn’t just saying that there are physical things, it is saying everything is physical. Materialism is saying that the thoughts you are having now are physical; it is saying that the curious and unique mix of emotions you are subjectively experiencing at this very moment are purely and solely physical material things. And it is saying that the awareness that witnesses all these subjective feelings is physical. This no longer seems so obvious, does it?

Not only does it perhaps seem a little strange to assume that all our mental, emotional and spiritual experiences, and the subjective experiencer, are actually objective, external and physical, materialists have absolutely no idea, even in principle, how matter could possibly create our rich inner life of conscious awareness and experience. This is what is referred to as the hard problem of consciousness.

This is why materialism is a metaphysical philosophy. It is a theory with an assumption that attempts to account for all things. It has not done well at all when it comes to accounting for your continuous and immediate experience of everything. There are other theories that, arguably, do a better job of this. We will look at one later.

But what of science? Isn’t the indisputable and phenomenal success of science and technology proof that materialism is an extremely successful theory? No. Science is agnostic on metaphysical philosophy. The scientific method and all the advances and technological breakthroughs that follow, work perfectly well regardless of your philosophical beliefs. That is, in fact, its strength: it relies on empirical data, not belief. 

The connection between the scientific method and the philosophy of materialism is no more than the fact that most scientists tend to also be materialists. That’s it. There are scientists who are not materialists; their science is no less valid. The success of science comes from following the scientific method, not from the philosophical beliefs of the scientist.

Materialism then, posits that consciousness—if it is anything at all—must be physical; it must be so because everything is. All your subjective experiences are simply properties of material arrangements, just like the other physical properties of mass, charge, spin etc.

Any subjective conscious experience, according to the materialist, must, therefore, be describable in purely measurable and physical terms. Just as we can describe the mass and charge of particles in numbers and their interactions with equations, the materialist must account for all conscious experiences in the same way; a materialist must treat consciousness the same as matter because, for them, it is matter; because everything is matter.

To be a materialist, you have a difficult choice to make: choose the fundamentalist path of denying undeniable reality; or take on the burden of Sisyphus, endlessly rolling the rock of matter towards consciousness, doomed for it to forever roll back to the beginning of your false assumption.

Scientists find many correlations between conscious experience and brain states, and brain states can be described mathematically. This seems promising for the materialist project. Because neuroscientists are mostly philosophical materialists, they tend to assume that this correlation is evidence of causation; that is, that each and every conscious experience is reducible to a specific brain state. This would mean they could describe consciousness with numbers and equations, as your conscious experiences would be nothing more than physical properties of precise neural arrangements in your brain.

But remember the hard problem. No scientist, and no materialist, has a clue how that could be possible. There is simply no testable hypothesis as to how subjective conscious experiences arise as properties of neurons in your brain. The correlations are science, but the idea that brains cause consciousness, that remains firmly metaphysical.

The metaphysical theory that everything is matter is a philosophy, not a scientific fact. But we can go further and say that even the assumption that there is any matter at all, is equally a theory and a philosophical assumption, not a scientific fact. The idea that there is physical matter outside of our conscious experience is just that, an idea. We only know for sure that we have subjective experience; we cannot know for sure what constitutes that experience. The only thing we know for sure is our immediate experience of being subjectively aware. Everything we can ever possibly know can only be known by us within and via the medium of our subjective experience.

The scientific method successfully explores the behaviour of the contents of our subjective experience and gives us technology as a result, but the scientific method hasn’t discovered the essence or the true nature of the contents of our conscious experience. It can describe and predict and mimic what happens; it doesn’t tell us what it is.

The most successful theory of physics, by far, is quantum field theory. It states that what we think of as matter is best understood and predicted by an equation of probabilities. Some recent experiments in quantum mechanics lead Bernardo Kastrup and others to the conclusion that the idea of there being an objective and external physical world is all but untenable. The verified results point very strongly to the conclusion that each observer is experiencing their own world, just like in a multi-player computer game where each player gets their own view of the game-world that they interact with.

This quantum description of our experience of the world sounds eminently compatible with our earlier description of the one thing we can know for sure—that we are each having a subjective experience—and it actually coherently argues against the materialist assumption of an external and objective physical world outside of consciousness. It seems that what the world is, as described by the best science we have, fits perfectly with what we know with certainty: our subjective experience. 

A consistent interpretation of the experiments of quantum mechanics even goes so far as to say that the ‘material’ experience we each have, only exists when there is a measurement or observation. Without that, matter remains as nothing more than a possibility, a calculable probability of existence.

These experimental results, despite arising out of a materialist desire to explore the presumed physical and material nature of reality, have led us to a description of a world that is not an external and objective physical world at all; it has described separate worlds that appear to each subjective experiencer and are—prior to a measurement or observation taking place—nothing more than probabilities.

In light of this, it is not such a great leap of imagination, to then posit a non-materialist philosophy—namely the metaphysical idea of idealism—that states that it is actually consciousness that is fundamental; not just epistemologically (i.e. what is known), but also ontologically (i.e. what exists).

Idealism not only accounts for your immediate subjective experiences—something materialism has completely failed to accomplish—it also seems that idealism fits rather nicely with our best empirical science, which provides evidence that consciousness may be instrumental in the creation of our world. We can simply posit that the quantum probabilities of what might happen—from which, it is agreed, all matter arises—are mental in nature. This gives us consciousness as the foundation of the ‘material’ world, as well as of our inner life.

Conjuring up possibilities of what might happen is something we are all very familiar with as something our conscious minds can do quite easily, so idealism posits that the shared and consistent nature of the quantum world we all experience is due to the fact that we are all within an overarching foundational consciousness that generates the quantum probabilities. Upon our observation, these probabilities become the world each of us experiences.

In contrast to this idealist view of the world, a materialist philosophy posits an external and objective physical world that is not directly knowable. Our only experience of such a world, if it exists at all, is through our subjective experiences. The idea that there is such an objective external physical world is an abstraction thought up by consciousness. And it is an abstract theory that is becoming less and less supported by the results of our best scientific experiments in quantum mechanics.

Ironically, then, despite the close association between scientists and materialist philosophers, the best science, far from providing evidence that the essential nature of our experience is objective and external physicality, actually lends itself much less problematically to a non-materialist philosophy such as idealism, where it is consciousness that is the ground of all experience, not matter; the one thing we can know for sure, is the one thing within which all our experiences occur.

So what has this to do with Zeno’s paradoxes where, as we've seen, assuming that experiences of movement are made up of abstractions (dimensionless points on a line and frozen instants of time) led to the paradox that movement and motion are impossible?

Materialists have fallen foul of this same type of paradox. Where Zeno questioned how motion could be possible, materialists have started to question how consciousness can be possible. Where Zeno posited abstract points and instants, materialists posit an objective and external physical world outside of consciousness. Where Zeno assumed distance and duration are made of abstract points and instants, the materialist assumes that our subjective experiences are made of their abstract formulation of an objective external physical world. Just as Zeno found that a paradox followed if distance and duration were made up of his abstractions, materialists are struggling to figure out how conscious experiences can be made up of their abstractions and measurements: they have hit the hard problem of consciousness.

Hares overtake tortoises, arrows fly through the air, we have conscious experiences. The fact that it is possible to describe and measure various abstractions associated with all these phenomena, does not mean that these phenomena are made of those abstractions, and it certainly does not mean that those phenomena are impossible or illusory.

If we take any phenomenal experience—for example, feeling the existential dread of having to return to the office on a dark and cold Monday morning in mid-winter when the alarm goes off—we could capture the entire physical picture of that moment. In particular, let’s say we have a complete scan of exactly what is going on in our brains at that time of feeling dread.

The paradox is then, that (under a materialist assumption) all conscious experiences are describable in terms of, and nothing more than properties of, brain states. But the hard problem of consciousness says there is nothing about any of the physical properties of matter, of that particular brain state, that could account for a phenomenal experience of consciousness, of existential dread. The punch-line of the paradox is that the experience can’t be happening, and yet we know that it is.

The materialists are making the same type of error as with the Zeno paradoxes of time and distance; they are assuming that an experience we know does happen, is made up of abstractions we can use to describe that experience.

The Hare paradox created an abstraction of infinitesimal points to describe a distance, and then assumed actual distances were made up of those points, of those abstractions. The Arrow paradox created an abstraction of timeless instants to describe the flight of the arrow, and then assumed actual periods of time were made up of timeless instants. Materialists have created the abstraction of physical matter and then assumed consciousness is made up of the associated measurements of brain states. They assume the actual experience is made up of these abstract measurements of an abstract material world.

Unfortunately, the materialist doesn’t stop there. A further error is then made: they do not use the obvious falseness of the conclusion (that the conscious experience can’t happen) to look at what has gone wrong with their thinking; materialists don’t question their assumption (that their physicalist abstractions create consciousnesses) and instead question the reality of conscious experiences.

The materialist-illusionist insists upon a paradoxical conclusion and states that conscious experience is impossible; it must be some sort of illusion. The illusionist is saying the equivalent of ‘Bolt actually cannot overtake you in a 100 metre race. The fact that he appears to cross the line first is an illusion’. In denying conscious experience, the illusionist is saying the equivalent of ‘Arrows cannot fly. That arrow in your chest is an illusion.’ But most bizarrely of all, the illusionist is literally, not metaphorically, saying we cannot have conscious experiences. 

(Strange as it may seem, Illusionists really do exist. I haven’t made them up to make an abstract point. More worryingly, they are taken seriously.)

The illusionist believes that their materialist equivalents of dimensionless points and timeless instants are ontologically real; they believe their physical abstractions and descriptions of matter are ontologically real. Even more incredible than believing Zeno’s conclusion that lengths and durations—movement and motion—are impossible and illusory, the materialist-illusionist actually believes that the subjective experience you are having right now, and that they themselves are all having every moment, is impossible and therefore some sort of abstract illusion and not real. They believe their abstractions are actual and actuality is an abstraction.

To believe such a paradoxical conclusion must only be possible if someone is so attached to their abstract processes and mistaken assumptions that got them there, that they are more willing to deny their own immediate experience than to question their philosophical belief. This is the mindset of a fundamentalist; so wedded to their philosophical belief, they will question any reality that doesn’t fit, even the one and only reality that is undeniable, the fact that we are having a subjective experience.

Non-illusionist materialists make a different error to the illusionist. They realise, to their credit, that the metaphorical hares do overtake tortoises, that people can be shot by arrows; that is, they do believe we have conscious experiences. But again, they do not want to question their assumption that their abstractions have an ontology, that their abstract measurements actually create the thing they are measuring.

Instead of illusionism, the materialist who accepts conscious experiences is engaged in the equivalent of the impossible task of finding out just how dimensionless points do make up a line; just how many timeless instants do make up a duration of time; that is, just exactly how do brain states create conscious experience. This attempt—equivalent to trying to count infinite infinitesimals—continues, with no hope of reaching an end.

To be a materialist, you have a difficult choice to make: choose the fundamentalist path of denying undeniable reality; or take on the burden of Sisyphus, endlessly rolling the rock of matter towards consciousness, doomed for it to forever roll back to the beginning of your false assumption.

Instead we can choose a simpler and less abstract route, and take the epistemological certainty of consciousness as our ontological foundation in the form of an overarching foundational consciousness that we are all a part of. With this as our philosophy, we can continue to progress with empirical scientific methods, quantum mechanics and technology, and seek to better understand all aspects of our existence, including our inner life, as well as our experience of our shared world.

Hares overtake tortoises, arrows fly through the air, we have conscious experiences. The fact that it is possible to describe and measure various abstractions associated with all these phenomena, does not mean that these phenomena are made of those abstractions, and it certainly does not mean that those phenomena are impossible or illusory.

Let us learn from Zeno and start from the premise that consciousness is real and any seeming paradoxes suggesting it isn’t, are the results of mistaken assumptions. As Bernardo Kastrup says, there is no hard problem of consciousness, it is simply an artifact of wrong thinking. 

Let us put aside our mistaken assumption that consciousness is made of matter, that matter somehow creates consciousness; let us stop categorising abstractions as actuality. Let us start with what is actual and knowable, our immediate conscious experience, and explore within that foundation, the patterns and dynamics of all of our experience.

Copyright © 2020 by Stephen Davies. Published with permission.


  1. I enjoyed this, Stephen -- it's a novel way for me to think of what it is that materialists get wrong, if not exactly why. I'd hazard a guess that the "why" has something to do with the fact that they are conscious beings with a tendency, the same as everyone else, to construct a world view to which, for whatever reason, they become attached. Maybe they find the idea of the universe having a telos preposterous or threatening, or maybe they've just been conditioned and accept materialism unquestioningly.

    I myself went through a materialistic phase. Mostly, it was conditioning through secondary school (despite it being a Roman Catholic establishment) and university education in science, particularly biology. I just went with it unthinkingly. I can't put my finger on when or why I began to be sceptical about materialism; it just kind of grew like Topsy.

    Maybe scepticism about neo-Darwinism was one signally important factor. Evolution? Sure. Plenty of empirical evidence for it. But by random mutation and natural selection? Not so much. When I first heard about the Cambrian (and other organismal) "explosions", and realised how those contradicted the idea of gradualism, the rot set in, though to be fair I've always been a bit of a contrarian by nature.

    One thing led to another and now I see the idea of materialism as an enormous con job which has seemingly befuddled the minds of some otherwise highly intelligent people, certainly many of them more intelligent than I am. I secretly find it gratifying that increasingly, it's becoming untenable and wonder when the dam's finally going to break.

    Soon, I hope.

    1. I find your reference to a Roman Catholic establishment remarkable. I used to be a materialist myself, and an atheist.

      Finding both positions untenable, but not both for the same reason, I certainly did not embrace Christianity, which has kept materialism alive more than almost every other ideology. Resurrection in the flesh, the transubstantiation, go far beyond what most materialists are ready to contemplate.

      With the transubstantiation, Jesus managed to get people to quarrel over trivial details without realizing that they are in agreement over a much bigger issue, and equally wrong about it: The atheistic research chemist will go on and on about the wine of your observation being and remaining fundamentally unknowable 'real' material wine, while the priest he is arguing with maintains that the unknowable 'real' material wine turns into unknowable 'real' material blood, with only the appearance (the one actual knowable fact) remaining the same.

      Both are misled into ignoring that the wine experience is all they can ever get and that the supposed underlying matter is an untestable fantasy.

      As for the fundamentalist materialist's denial of the reality of consciousness, this is the same phenomenon as the 'strong AI' assertion that we are just running an algorithm. AI fanatics don't even need an ontological commitment to hardware to misdescribe the software we are!

  2. I must say I am sympathetic to the argument but I have a several naive questions:
    Are you implying that reality would cease to exist without the existence of human beings?
    Did humans always have consciousness?
    Did reality not exist prior to human Origin?
    Did the Universe not exist prior to our existence and will cease to exist upon our demise?

    The quantum term “observation” has always seemed recursive. How can biological beings which are derived from chemical processes which in turn are derived from physical interactions “observe” a quantum event? We are part of the experiment.
    I am not engaging in refutation but merely trying to grasp the ideas.

    1. You raise a very good point as the answer to your question isn’t covered in this essay but is required to make sense of the whole picture.

      Before conscious humans existed the overarching consciousness, that is the foundation of everything in Idealism, still existed. The world as we experience it arises from our interaction with this overarching and foundational consciousness. So without our interaction, the physical world as we perceive it doesn’t exist.

      It’s like a multi-player computer game where the image on your screen of the world of the computer game, only appears when you are playing the game. When you are not playing, the program that generates that image when you interact with it still remains.

      It is the observation, made by an individual consciousness, of the overarching consciousness, that creates the perception of the world. The world is what foundational consciousness looks like from the point of view of a localised consciousness. The body is what a localised consciousness looks like.

      Consciousness generates physical experience, biology doesn’t generate consciousness. Your computer avatar doesn’t generate the player, the avatar is how the player appears within the world of the computer game.

  3. Wow and Bravo...!! And a small thing, though what is being said is perhaps clear enough, the first sentence in the eighth paragraph from the bottom could use some grammatical tweaking...? I will be passing this on to some folks... _/\_

  4. Long before the hard problem of consciousness came front and center, materialist science had faced another fundamental challenge to its presuppositions. I've recently plunged into the forgotten work of the British Society For Psychical Research (and its American counterpart) and the findings of the eminent group of scientists and scholars who undertook decades of painstaking, highly-controlled research, initially designed to debunk the spiritualism craze which arose in the mid-19th Century and continued to roughly the end of the First World War. Like the estimable William James, who was intimately involved in this research, my materialist-conditioned mind was blown by the exploration of this repressed/suppressed scientific investigation. It would have shocked me just a year ago, as it will likely now shock many readers of this excellent blog, when I make the unequivocal statement that any intelligent, open-minded person who takes the time to do this homework will come to similar conclusions: that the human personality survives bodily death, and that our consensual reality, however it may be formed, is encompassed within a larger, more complex "spiritual" world. Thus I've come to understand that the knee-jerk reaction of materialist scientists to the contemporary hard problem of consciousness is but a replay of what happened over a hundred years ago. Maybe this time around, with the determined work of Bernardo and others, and contributions such as this clear and cogent essay by Stephen Davies, the stone wall of materialist science will finally be breached to the immeasurable benefit of us all.

    1. More recent Near-Death-Experience research is also very compelling. Idealism can easily accommodate and make sense of such ‘paranormal’ phenomena.

  5. Excellent essay...and I have already expressed that on the forum, so just to comment on Newton's comment: yes, what you say is absolutely correct. I too. for many years now, have delved deeply into that canon of research recorded by those two Psychical Societies (and beyond). The public has no idea about how compelling and voluminous the evidence is for the survival of human consciousness after way past the point where it is reasonable to deny it. That does indeed kill materialism dead, all by itself. However, because of the, sadly, brilliant job done by the materialist system to discredit ALL such research (by hand waving of course), it is simply less hassle to focus on the hard problem of consciousness as our leading argument against materialism.

    1. The hard problem of consciousness, joined by ongoing research into the NDE, have certainly taken the place of the earlier evidence obtained through mediums, and perhaps now deserve to be our leading argument. But Chris Carter, in his excellent trilogy on the paranormal, came to the same conclusion I did; namely, that this earlier evidence developed by the SPR and the ASPR yields the strongest and clearest demonstration of post-death human survival. After all, the hard consciousness problem is largely theoretical/philosophical, and no one who had an NDE actually died at the time. IMHO, it is only the established fact that individual personalities repeatedly manifested and communicated after death, manifested and communicated with all of their individual inclinations and idiosyncracies, which prove not only that human beings are eternal, but also that what is eternal about them is essentially personal. Who would care about surviving death if it were only as drop of water dissolving into an ocean? How would that substantially differ from oblivion?

  6. Consciousness of our material or mental experience is 'personal'. We feel it, think it, and think we observe it. Individuated consciousness produces an illusion of ‘personality’ constructed through observation. Personality is an irrelevance, scientifically and spiritually, in either materialist or idealist observational alleys. Those who have made the journey from personality (individuated 'self’) to universality (unity of consciousness) are not concerned with death. There can be no death of consciousness save that of the mental 'personality' separating the individual from the universal. There is no hard problem. Just hard heads burrowing for immortality in a wormhole.

  7. Well done, Stephen! Essay champ of the world of Idealism!

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  9. Thanks Stephen for a very interesting essay.

    I must admit though to struggle with a fundamental point. You state, "In the same way as an infinitesimal point on a line has no length and so the line cannot be made up of points, a frozen instant in time has no duration and so a period of time (the flight of the arrow) cannot be made up of duration-less instants."

    But the Bolt paradox doesn't rely on points with no length, it is all about intervals with length. Both you and Bolt are traversing across intervals, not abstract points.

    What am I missing?

    1. Thanks Perry. That’s a good point. A slightly different version of the paradox illustrates the infinite point idea better: To travel any distance you have to reach the halfway point; to get halfway you have to get halfway to the halfway point; etc etc. So to travel any distance you have to pass through an infinite number of (halfway) points.

    2. Although I guess your point still stands with this version, you can still describe it as an infinite number of intervals rather than points, so the arrow paradox is probably the better analogy. The main point though is that descriptions of the world are abstract and the world isn’t made of those abstract descriptions.

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  12. Hmm. If assume that there is a solid material arrow that flies through the air, regardless of whether or not it is perceived, then to me it seems Zeno's paradox proves the solid material arrow cannot fly. Since arrows DO fly, that, I think, shows arrows are not solid physical objects.