Zeno’s Paradox

[Simon Adams]

I didn’t want to divert the thread by raising it there, but I noticed Cleric mentioned Zeno’s Paradox as a “real paradox”. I’ve always been completely mystified why anyone thinks this is a genuine paradox, so am wondering whether I am missing something.

Essentially Zeno chooses to count the distance between two points in a way that is never going to end, and then thinks it’s significant that it doesn’t end. Why?

If there was some suggestion that nature ‘counted’ in this way, then it would make sense as a paradox, but we have no reason at all to think it does. Yet there seems to be no end of discussion on this from many of our greatest philosophers. So what am I missing??

[Cleric K]

I don't think you're missing anything. That was exactly my point. It only becomes a paradox if the intellect imposes its linear chaining of thoughts as something fundamental to reality. It's just another of the symptoms that contemporary man is still unaware of how his cognition operates. It's of the same nature as the hard problem and the Kantian divide. Philosophers are often preoccupied with the 'end-user' perspective of thinking, without realizing that implicit (and often unconscious) ideas shape the framework of their thoughts. The overcoming of these unconscious formatting forces of thinking can be approached through the Philosophy of Freedom.

[Simon Adams]

Thank you for the sanity check. It’s weird because you’ve helped me realise that this is an example of treating the abstraction as the thing, which I thought was a purely post Descartes phenomena. Clearly not!

[Eugene I]

Right. One of such implicit ideas that humans developed and implicitly extrapolate onto reality is the idea of an actual infinity. Zeno paradox arises only if we assume that there is an actual uncountable infinity of intermediate points between two points in the "actual" space in the "actual" real world. The idea of actual infinity is only an abstraction, it was explored in mathematics with mixed results - some of them turned our to be practically useful, others led to paradoxes and inconsistencies. But regardless of the math, we have no evidence whatsoever that our idea of actual infinity has any relevance to reality.

[Simon Adams]

Yes agreed, although infinity does crop up all over the place in things like physics. It’s difficult to know whether all of those are ‘consequences of abstraction’ or pointing to something more fundamental. There are of course natural examples that have some level of ‘reality’, from circles to Mandelbrot sets...

I’ve always had a problem with Cantor’s different infinities, but mathematicians seem convinced there is a real distinction between them. They don’t call it a distinction of “size” but of “order”, but they talk as if some are bigger than others which takes the concept to another order of crazy.

[Cleric K]

One of such implicit ideas that humans developed and implicitly extrapolate onto reality is the idea of an actual infinity.

What about the possible states that Consciousness can experience? Are they a finite set?

[Ben Iscatus]

Check out the well-received guest essay by Stephen Davies on Bernardo's blog last year all about Zeno's paradoxes:
https://www.bernardokastrup.com/2020/08 ... is-no.html

[Eugene I]

What about the possible states that Consciousness can experience? Are they a finite set?

We (at least I) have no experience of an infinite set of phenomena or states of consciousness. All we actually experience (so far) is only a temporal sequence of various finite states. On the other hand, we seem to find (or at least can infer) no limits to the possible states that Consciousness can experience, so we develop an idea of "unlimited potentiality": Consciousness can in principle experience any state with no seeming limits. Now, if we apply thinking further, we can infer an idea of an "actual infinity" of the set of all possible ideas and states existing "out of time", or at least the "actual infinity" of all possible ideas and states potentially existing "out of time". Yet, to my knowledge, humans never experienced such actual infinity, so we have no experiential evidence for the existence of such reality whatsoever.

I think the idea of infinity has developed as an extrapolation to the "end result" of an unlimited process. Humans discovered that if they put a heap of rocks together, they can always add one more to it with no limitation on that process of addition. So they would naturally be puzzled - what would be an "end result" of such limitless addition? And by applying their faculty of abstract thinking, they came up with an idea of the infinity as an "end result" of the unlimited process. But when we refer to the facts of the actual experience, we can only find the "unlimited process" of never-ending addition, but never the "end result" of it.

[Cleric K]

Thank you for the sanity check. It’s weird because you’ve helped me realise that this is an example of treating the abstraction as the thing, which I thought was a purely post Descartes phenomena. Clearly not!

There's still a difference. The Greeks still experienced thoughts as legitimate part of reality. The psyche (soul) was completely real for them. Even the atomism of Democritus was not yet the lifeless atomic theory of our near centuries. He had fire atoms which were responsible for the psyche. So it was abstract, yes, but in a different way. The thoughts that the Greek experienced were for him the real substance of the psyche in the same sense that the elements were the substance of the outer world. These were intermingled together in the unified World.

After Descartes and Kant thinking becomes truly abstract - it is now taken to be only a representation, a mental image of the thing in itself. And now if these representations are taken for reality the illusion is even greater. Democritus at least thought that through the thoughts he is really feeling the structure of reality - including the atomic structure of the psyche. Now we at the same time believe that thoughts are only representations and also that the thing in itself is real, which makes the whole situation even more convoluted because the by definition it's impossible to have any direct experience of the thing in itself. Then how do we know that it exists? We make a picture of it and believe that it's real! We imagine a box, enter into the imaginary box and declare that now the interior of the box is only mental image of the true reality outside the box.

[Cleric K]

We (at least I) have no experience of an infinite set of phenomena or states of consciousness. All we actually experience (so far) is only a temporal sequence of various finite states. On the other hand, we seem to find (or at least can infer) no limits to the possible states that Consciousness can experience, so we develop an idea of "unlimited potentiality": Consciousness can in principle experience any state with no seeming limits. Now, if we apply thinking further, we can infer an idea of an "actual infinity" of the set of all possible ideas and states existing "out of time", or at least the "actual infinity" of all possible ideas and states potentially existing "out of time". Yet, to my knowledge, humans never experienced such actual infinity, so we have no experiential evidence for the existence of such reality whatsoever.

I think the idea of infinity has developed as an extrapolation to the "end result" of an unlimited process. Humans discovered that if they put a heap of rocks together, they can always add one more to it with no limitation on that process of addition. So they would naturally be puzzled - what would be an "end result" of such limitless addition? And by applying their faculty of abstract thinking, they came up with an idea of the infinity as an "end result" of the unlimited process. But when we refer to the facts of the actual experience, we can only find the "unlimited process" of never-ending addition, but never the "end result" of it.

Right. In my thinking, the positive treatment of infinity is not by trying to encompass infinitely many elements but to realize that there are things for which there's no justification to place any limits. For example, we can argue that the heap of rocks can not be infinite because we'll exhaust the rock matter of the Earth or something like that. But in relation to the possible states of consciousness there's nothing that forces us to accept that there are finite number of possible states. In fact, through thought experiments we can imagine that finite set of states would lead to strange results. At any point we can experience a new state which encompasses the previous. If in this way we exhaust all the finite states it will follow that at the last state we are no longer able to encompass the previous but will have to repeat some state that we've already went through. If I'm not mistaken Nietzsche thought that there're finite states of being and as such existence is bound to repeat itself.