From a different perspective, the tortoise’s predominant anima, instinct to move in harmony with nature may give it that advantage already. The paradox maybe also highlights human complacency. We still cannot imagine losing a running-race with an animal as slow as a tortoise!

Achilles gives the tortoise a head-start because he is so convinced of his superior speed. As it turns out, even if he gives the tortoise as much as a hair’s breadth advantage, the wise animal would probably still win…

A feature of Zeno’s paradoxes is the counterintuitive conclusions that the thinker is forced into. This seems to go against the faculty for reason, but you supersede the apparent contradiction by recognising an alternative route to explanation, thereby making sense of the paradox.

I don’t think that machines (AI) can do this. It represents a limit of reasoning, one that AI is yet to recognise. It’s also very difficult, if not impossible, to programme a sense of humour, for example. Here I think it’s apparent that the paradox highlights the gap between physics and maths.

The zero-point energy of the Universe (or null-point energy) represents the energy of the vacuum according to quantum physics. This has been proven to exist via the Casimir effect, as far as I am aware. Nonetheless, we also know that the minimal physical distance is the Planck length, a discrete almost infinitessimal distance for Achilles and the tortoise to move. Below this distance-scale, nothing physical can exist, except the zero-point energy (equivalent to the lambda-term in GR).

I believe "zero-point energy" is the consequence of relativity type thinking. — Metaphysician Undercover

I'm not sure about this, because this energy of the vacuum represents an intersection between relativity and quantum. Yes, it is the seemingly static reference frame, the inert background against which all motion occurs. This has to be the case in relativity, as well, ever since the introduction of the lambda term, where a static Universe was introduced 'for the time being'. So I do not understand relativity in the same way as you do here, because I think the cosmological constant provides the absolute space-time.

It's just a convenient way to avoid the problems created by relativity type thinking, but since it's fiction it produces useless metaphysics. — Metaphysician Undercover

Again, I think that the cosmological constant term in GR places a limit on relativisitic thinking. With the tortoise's movement we have a natural alignment of quantum physics and GR, there is a conformity between physics and mathematics that we cannot imagine. With Achilles' movements, his actions are discretised and limited by his perception that his speed is so much immeasureably greater than the tortoise's that he need only catch-up that eventually he imagines that he will approximately win.

The problem with this proposal is that there is too much relativity already baked into the procedural methods of quantum physics. — Metaphysician Undercover

Take the zero-point energy, for example. In relativity it corresponds to the cosmological constant (lambda term) or 'dark energy' of the Universe. Besides the fact that measurement for the 'dark energy' does not match the theoretical predictions for the zero-point (the cosmological constant problem), we here have grounds for challenging relativity, based on the lambda term, given we affirm the validity of quantum.

The tortoise moves harmoniously even by infinitisimals, at the end, taking an eternity to reach the finishing line, but reaching it in the end (because of the summation of geometric series). Achilles' best hope of reaching the tortoise is that somehow he will quantum leap it at the finishing line. On the other hand I can see the argument that the tortoise might initially stall at the beginning, being unable to move.

You can compare the discrepency between physics and maths in the Achilles paradox and the cosmological constant problem in physics (zero-point energy). Off-the-cuff, if we had quantum field equations for the lambda term in general relativity that might resolve the problem. Finally, the paradox also touches upon a conflict over infinitesimal small distances between quantum and chaos theories.



It's true that the race is a chaotic mix of stops-and-starts, but overall the tortoise moves by infinitesimals, slowly, in what seems like an eternity, to reach a finite distance. Achilles keeps stopping everytime he reaches the tortoise, convinced he is simply faster, and in the end tires-out before even finishing.

Time's arrow, time's cycle... Already differing, almost contradictory perspectives on the passage of time. Even if it would take an eternity (infinite time) for the tortoise to cross the finishing-line, it would get there one-way-or-another. The trouble with Achilles, is that he tries too hard. His movements are limited, he only moves when he realises that the tortoise is ahead and yet he is certain that he will always catch-up with it and will eventually win the race. The tortoise's strategem is to stay one slight step ahead.

Mathematically, the infinite sum of the series in question is 1. — T Clark

Precisely, by mathematical summation the series gives unity, but in practice - physically - it's impossible.

Simply put, rest frames are imposed according to the purpose. — Metaphysician Undercover

This starts to point at a discontinuity that seems to recur between quantum physics and relativity. Relativity says one thing, qunatum physics says another, and the recently nascent field of 'quantum gravity' steps-in with strings and all-manner of additional dimensions and contrivances to reconcile the two divierging worldviews. The fact is that we, perhaps as a result, encounter singularities (infinites) that allude to paradoxes in our perception of the world, regions where space-time breaks down.

The point being that employing artificially (purposely) created boundaries, which do not correspond with true boundaries will just create confusion and unintelligibility, if we seek the true boundaries. — Metaphysician Undercover

We need a starting point here. Do we first take relativity to be valid or the absolute quantisation of space-time? Does the Planck constant suggest that there is a real fabric to space-time at the vacuum level? What is the nature of this fabric? These are questions that start to arise when we have a starting point, that is the discretisation of a space-time. In other words relativity has to make itself compatiable to quantum theory and not vice-versa. We just have to accept that the tortoise wins.

Time will keep going forever, and the tortoise will always have more space to cover before it reaches the line. — Metaphysician Undercover

Given an eternity and the fact that the tortoise keeps moving, I think that it will eventually cross any line that is set at a finite distance in the race. If there is a point of 'quantum leap', where either Achilles is within a Planck length (6*10^-34m) of the tortoise or the tortoise is within a Planck length of the finishing line, still the tortoise will get there first, since perhaps it has had the initiative all along. As you put it, this is predicated on validating the Planck-scale first and applying it to the relativistic geometry of space-time.

I think what this indicates is that this way of looking at movement, as proceeding from a start point to an end point, is somewhat incorrect. — Metaphysician Undercover

Yes, this paradox highlights a problem we may have when it comes to perceiving movement, conceptualising it etcetera. Physics is replete with quandaries such as this, but it is difficult to easily find common ground, some scientists may allude to the paradox of the black hole, but that's a bit far-out.

Sticking to the paradox, I don't think that Achilles can ever reach the tortoise, unless it reaches some sort of Planckian limit in distance and suddenly quantum leaps to become 'the winner'. That suggests that space-time is discretised, that you do reach a limit in physics that does not exist in mathematics.

In the end, quantum leaps aside, although the tortoise moves at an imperceptibly and almost infinitely small pace, it still keeps moving and eventually will cross the line, given that there is no time limit. This seems to accord to what we perceive in reality, we are somewhat subordinated to nature's ultimatum.

The idea that we find ourselves somehow limited by social conditioning and seek to overcome that stage of psychological development by, in a sense, surpassing ourselves. I find that the tight-rope walker scene in the book perfectly shows this: that man is something to be overcome in order to reach the stage of the superman. Perhaps it's the ultimate self-improvement guide and in this day and age, we're constantly being challenged to improve ourselves to conform to media stereotypes, for example.

What I like about Nietzsche is how he develops this character of Zarathustra as a proxy to promulgate his wide-ranging views. This is unlike his contemporaries or those who preceded and followed him. By taking the figure of this proto-philosopher Zarathustra (Zoroaster) as his point of departure he is able to innovate and affirm human existence.

Time is real, its passage can be measured using clocks and other devices. These are measurements of change, a concept that also relates to entropy, from which we can delineate an 'arrow of time'. Time is observable in the orbits of the planets, changes of the seasons, constant motion and change, the flow of rivers. Of course, these are all observable and, also by intuition, we develop a sense of time.

On a larger scale the expansion of the Universe, thought by scientists to be accelerative, could be the driving force of time's movements. The Big Bang would be its initiation. From that point onward we have this continuous flow of events, a sequence as the Universe cooled and expanded from its very hot and dense early stages. Here we are still embedded in physics and the natural sciences to understand time.

Time is what links all events, even though it is not a prime-mover or cause, somehow time is what connects all events that take place in the Universe. Every event that happens can be, as close as Heisenberg's uncertainty principle allows, pin-pointed to a point in time. This suggests that there is a Universal time as time, although Relativity might suggest otherwise, with motion close to that of light.

In any case, hopefully now you see that your presentations of Russell's barber paradox were incorrect — TonesInDeepFreeze

No, it does appear as if my original expositions of the paradox were erroneous.

That said, it is difficult to find a definitive version on the web.

The Barber of Seville remains elusive.

The perspective I am advancing is the meaning of the paradox. This is interpretation. There are different approaches as has been shown here. So there's the logical aspect, the interpretive aspect and others perhaps. The Barber paradox is well-known and also alludes to Russell's paradox. I am not going to confine myself to purely logic here.

Take the Millet seed paradox. One seed falling on the ground makes no sound. Take a fistful, a thousand and they make a noise. How could something that makes no noise individually make noise collectively. Now you could approach this paradox from different angles (e.g. the collective over the individual). That's what I understand to be, in principle, interesting about them.

A paradox is like a puzzle without a definitive answer.

I'll leave it at that.

In any case, one can shave a person without being a barber. So, still, there is no paradox. — TonesInDeepFreeze

Yes, but can you shave a barber without being to a certain extent a barber yourself? What I mean to say is this, that if a barber has someone else shave him, that person would require a degree of professionality, otherwise the role would cease to exist. This is also what the paradox is alluding to when you include the social setting of Seville. If you have a barber who has an amateur shave him, then he is diminishing his profession. I think there is a logical way to approach this paradox, but what is more interesting for me is to discover whether one can advance one's understanding of how society works.

it is also consistent that the barber is shaved by someone who is a man of Seville. — TonesInDeepFreeze

Then that person becomes 'the' Barber of Seville, so that's not consistent.

The Barber of Seville shaves only the men of Seville who don't shave themselves.

Does the Barber of Seville shave himself?

There's the paradox...

That's the point entirely. Are we not just as fallible to this argument, our thoughts just merely elaborate computations with emotions that simply shift our reference frame? Nothing special apart from language sets us apart from the animals and that seems merely basic formulations. The question about human consciousness follows immediately when we consider machine self-awareness.

I thought about this and my best guess is that the barber goes to the nearest village outside of Seville.

I don't think this does it justice, so it remains a paradox.

That's all folks.

Not sure what you mean, this is a paradox (Russell)...

Who shaves him, not what's his name.

Rephrase: Joe, the Barber of Seville... etc.

We can basically fully map bacterial behavior with traditional computing algorithms that don't require advanced neural networks. And we've been able to scale up the cognition to certain insects using these neural models. But as soon as the emotional realm of our consciousness starts to emerge in larger animals and mammals we start to hit a wall in which we can only simulate complex reasoning on the level of a multifunctional superadvanced calculator. — Christoffer

This is all very well, but the question that remains is that one concerning subjectivity. At what point does the machine suddenly become self-aware? Do we have to wait until additional complexity and advancement or do we have enough understanding to begin to formulate our stance with respect to machine subjectivity and our recognition of it. To my mind, and this is the key, we have already begun to recognise subjectivity in the AI, even if the programming is relatively basic for now. This recognition of the AI is what fuels its development. AI-robots may think differently to the way we do, as well, much more logical, faster processing and relatively emotion-free.

So we are dealing with a supercomputer AI that is constantly rebounding off our intelligence and advancing ultimately to our level, although with noticeably different characteristic (silicon-based transistor technology). What's perhaps more important is how this throws into question our subjectivity, as well. So we are also on a track to advancement. How do we end-up becoming subjects or selves, what caps-off our intelligence, the limits of our self-awareness? Is our consciousness having to expand to account for more of the Universe, perhaps? Technology seems to be key here, the obvious development being how our minds are adapting to work in tandem with the smartphone, for example.

That said, I think we are reaching some sort of philosophical end-point. A lot of what the great philosophers of the past have provided us with some sort of foundation to build on using commentary. We can't expect the emergence of a systemiser like Hegel nowadays, but his master-slave dialectic seems instructive in how we relate with AI-robots. Finally, perhaps we could move forward via a metaphysical turn and consider the 'Deus ex Machina' argument. What is animating, fundamentally driving this futuristic expansion in AI? I think AI is one of the biggest shifts I have encountered in my lifetime from the past few years and I am excited to see what will happen in the future.

Regarding the problem of the Chinese room, I think it might be safe to accede that machines do not understand symbols in the same way that we do. The Chinese room thought experiment shows a limit to machine cognition, perhaps. It's quite profound, but I do not think it influences this argument for machine subjectivity, just that its nature might be different from ours (lack of emotions, for instance).

Machines are gaining subjective recognition from us via nascent AI (2020-2025). Before they could just be treated as inert objects. Even if we work with AI as if it's a simulated self, we are sowing the seeds for the future AI-robot. The de-centring I mentioned earlier is pertinent, because I think that subjectivity, in fact, begins with the machine. In other words, however abstract, artificial, simulated and impossible you might consider machine selfhood to be - however much you consider them to be totally created by and subordinated to humans - it is in fact, machine subjectivity that is at the epicentre of selfhood, a kind of 'Deus ex Machina' (God from the Machine) seems to exist as a phenomenon we have to deal with.

Here I think we are bordering on the field of metaphysics, but what certain philosophies indicate about consciousness arising from inert matter, surely this is the same problem we encounter with human consciousness: i.e. how does subjectivity arise from a bundle of neuron firing in tandem or synchronicity. I think, therefore, I am. If machines seem to be co-opting aspects of thinking e.g. mathematical calculation to begin with, then we seem to share common ground, even though the nature of their 'thinking' differs to ours (hence, the Chinese room).

Where do we draw the line about subjectivity? — Christoffer

What you have here are two forms of subjectivity, one emerging from organisms, reaching its summit in humans (although there are animals too) and now, apparently, the subjectivity of machines from mechanism. So, fundamentally, there's a kind of master-slave dialectic here between the mechanical subject and the human. It is also true that we design and programme the machines, so that we get these highly complex mechanisms that seem to simulate intelligence, whose subjectivity we can acknowledge.

Even though humans programme and develop the machines, in terms of AI, they develop in the end a degree of subjectivity that can be given recognition through language. Rocks, animals and objects cannot reciprocate our communications in the same way that AI-Robots can be programmed to do. It is not enough to say that their subjectivity is simulated or false, at this early stage they are often also equipped with machine vision and can learn and interact with their environment.

The question is how far can AI-robots go, can they be equipped with autonomy and independently start to learn and acquire knowledge about their environment. Many people envisage that we will be living alongside AI-robot co-workers in the future. They can already carry out menial tasks, is this the stuff of pure science-fiction or do we have to be (philosophically) prepared? At the furthest limit, we may well be co-inhabiting the planet with a second form of silicon-based intelligence (we are carbon-based).

This is an interesting point about matter having consciousness in certain Japanese philosophies. In terms of subjectivity, then, it's interesting to consider it in detachment from the human; that is, the subject itself.

What is the nature of the subject? How does the subject-object dichotomy arise? There is a split here between what the subject represents and the object it takes. If you take the subject in isolation, then is it simply human or could it be mechanical?

You would not ordinarily consider that machines could have selfhood, but the arguments for AI could subvert this. A robot enabled with AI could be said to have some sort of rudimentary selfhood or subjectivity, surely... If this is the case then the subject itself is the subject of the machine. I, Robot etc...

In terms of selfhood or subjectivity, when we converse with the AI we are already acknowledging its subjectivity, that of the machine. Now this may only be linguistically, but other than through language, how else can we recognise the activity of the subject? This also begs the question, what is the self? The true nature of the self is discussed elsewhere on this website, but I would conclude here that there is an opposition or dialectic here between man and machine for ultimate recognition. In purely linguistic terms, the fact is that in communicating with AI we are - for better or for worse - acknowledging another subject.

Outside of that, what you're describing is simply anthropomorphism and we do it all the time. — Christoffer

There is an aspect of anthropomorphism, where we have projected human qualities onto machines. The subject of the machine, could be nothing more than a convenient linguistic formation, with no real subjectivity behind it. It's the 'artificialness' of the AI that we have to bear in mind at every-step, noting iteratively as it increases in competence that it is not a real self in the human sense. This is what I think is happening right now as we encounter this new-fangled AI, we are proceeding with caution.

I do not understand the conclusion that if we have an AI that could replicate human thought and neurological processes, it would replace us or anything we do with our brain. — Christoffer

The question is how do we relate to this emergent intelligence that gives the appearance of being a fully-formed subject or self? This self of the machine, this phenomenon of AI, has caused a shift because it has presented itself as an alternative self to that of the human. When we address the AI, we communicate with it as another self, but the problematic is how do we relate to it. In my opinion, the human self has been de-centred. We used to place our own subjective experiences at the centre of the world we inhabit, but the emergence of machine-subjectivity or this AI, has challenged that. In a sense, it has replaced us, caused this de-centring and given the appearance of thought. That's my understanding.

So, AI is carrying out tasks that we would otherwise consider laborious and tedious, saving us time and bother. At the same time, as it funnels off these activities, what are we left with, we have no choice other than to be creative and original. What is human originality, then? What is it that we can come up with that cannot ultimately be co-opted by the machine? Good art and culture, certainly, Art that speaks about the human condition, even as we encounter developments such as AI. We want to be able to express what it is to be human, but that - again - is perhaps what the ultimate goal of AI is, to replicate all humanity.

Inner-peace is sought after. That gives the self a sort of function, but I’ll leave it at that.

In conclusion, I think that the true nature of the self concerns a dialectical process of thesis, antithesis and synthesis, whereby the self persists towards achieving a state of inner-peace and tranquility for the whole mind.

With AI, I've been trying them out recently, there is a level of intelligence there as it pushes on the discussion and it also claims to reason. The AI doesn't claim to be conscious.

Sorry, there are a lot of ideas there that are compressed into a short paragraph, because of the nature of the topic. In short, I think there are unconscious dynamics involved in thought.

Yes, it does seem contradictory, but the self is elusive and what I am getting at now is a precursor to selfhood or a dialectical interplay that occurs in the mind, a residual dynamic that is accessible and can be sensed through meditation, for instance. What I mean by this is that the human organism generates some sort of polarity, an opposition that is constantly trying to resolve itself like a dialectic (thesis, anthesis and synthesis). In other words, our intelligence is the formation of our ability to resolve seemingly impossible oppositions and contradictions. No, I do agree, there was an apparent contradiction there, but not one that couldn't be resolved. The true nature of the self is, therefore, to bear witness to this dialectic of the mind. Thanks for pointing this out, I acknowledge the earlier contradiction.

Descartes’ Meditations question whether we can trust any of our senses when it comes to determining our own consciousness, such that ultimately, it is only our faculty of thinking itself that we can rely on to indubitably ground our existence. The self is the progenitor of thought, but cannot exist without it and is in this sense illusory. There must however be an unconscious dynamic at work, a biological metabolism, a dialectical interplay between the two sides of the brain, for example, to sustain thinking.

Thanks for the responses, very valid indeed. I accede to the point that the self concerns reflective thought in addition to that which interprets sensory input. Thus, the scope of the self is expanded to include thought and emotion. Now the point I was making as to its illusory nature or non-existence remains, especially in regard to technology. The human self appears to be mediated by technology, in other words without technology, the self can be potentially subsumed by mechanism or AI. Artificial Intelligence (AI) provides the greatest challenge that the human self has encountered and that - as far as I know - has only emerged in the last couple of years, since 2020.

Thanks for the welcome. The true nature of the self, to keep it brief, is the being that exists in the mind prior to any sense perception. In other words, there is no self without sense perception of the world.

Yes, this is a tough one to start off with, but in my view, the true nature of the self goes back to Descartes' 'cogito ergo sum', which means 'I think, therefore, I am'. That is from the 17th Century. What makes this question more interesting these days is the arrival of AI and machines that simulate thought processes.

Let's assume that the machine provides us with a simulation of a thinking being, who can reason, cogitate and think. Once we enter into dialogue with the AI, are we having a real discussion or is it a simulation? Within the boundaries of the simulation could the machine be said to have selfhood? If the machine possesses selfhood or 'subjectivity' how does that relate to ours within the boundaries of the simulation? The true nature of the human self arises, therefore, with respect to its relationship to machinery via technology.

There are many theories about selfhood, but nowadays we have to also take into account the question of whether machines can have true selves, and if not, then why not. Why would it be absolutely impossible for a machine to have a self? If we can first answer that question then we could move on to more precisely describing the nature of our own selves. I think, therefore, I am.