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.