wandelaar

Are Zeno's paradoxes indeed already solved by modern science? My thesis is that they are indeed solved although the solution requires one to delve into some mathematical and logical subtleties that escaped the ancient philosophers. I hope this bold position will create enough controversy for an entertaining topic. We (including myself!) might even learn something by participating.

It must still be possible to remove the spoiler by editing your post. I will show it: Do you see the spoiler?

Why not read the relevant part of the book to see whether he is right about Walt Whitman? And concerning the spoiler, you can always edit your posts afterwards...

No - I read the book myself many years ago, and your description reminded me of cosmic consciousness as it is described in the book. Bucke's book is an early classic in the psychological study of mystical experiences. There are more up to date books on the topic today. But first it would be interesting to see whether your experience indeed falls in the category described by Bucke. If you feel that that is so, then you know what to look for when searching for more information on the internet and in books and articles. That's why I posted the link. Not to disqualify your experience in any way, far from it!

Congratulations! I haven't experienced it myself, but I have read about it for instance in: https://archive.org/details/cosmconscious The experience isn't specific to any one religion or path, but the interpretation of the experience is. Particularly interesting are the many examples Bucke gives of persons who had the experience of cosmic consciousness.

This is not my opinion but how the paradox is constructed. Zeno reasoned that what doesn't increase something when added and does not diminish something when subtracted cannot be something. Now a point does not add to the length of an interval when added, and does not subtract from the length of an interval when subtracted, so he (falsely) concluded that a point has to be nothing or non-existent. It took some time before a rigorous theory of the continuum was invented. But the problem can and has been solved. See for a book-size treatment of Zeno's paradoxes from the viewpoint of modern science: https://books.google.nl/books/about/Modern_Science_and_Zeno_s_Paradoxes.html?id=eSpDAAAAIAAJ&redir_esc=y

Sure enough! And modern philosophical logic is a very creative discipline with lots of exotic approaches to choose from.

Thanks! I had to quite with this topic in a way that wouldn't add to my and others irritation, and in this way it worked.

That was probably not the intent of Zeno, because the option that the constituents are nothing is considered as absurd. See: https://www.iep.utm.edu/zeno-par/#SSH3biv

@ OldDog We had a topic about this some time ago. There is a form of logic promoted by Graham Priest that claims that true contradictions (or paradoxes) exist, and that investigates how to logically reason with them. A good candidate is this one: This sentence is not true. Is the above sentence true?

Ironic rant to blow off steam. (Better not read it!)

Well - that is a whole new perspective on what the words "rational" and "logical" are supposed to mean. Given your interpretation you might as well consider my comment as not being written.

@ Zen Pig The subject of "rational and logical thinking" would deserve a separate topic for serious discussion. I propose the following: let the topic starter explain what "rational and logical thinking" is supposed to be? Maybe his answer will be so good that no further discussion is necessary. But if not, you can still decide if you like to discuss "rational and logical thinking" or not. That might indeed not be a good idea, as it will involve all kinds of hard problems from the philosophy of science. But even if we could agree on what is at stake than there would still be several positions one could reasonably take and defend. In all likelihood only a few Bums would still be reading the topic at the point where we would be ready to draw some conclusions.

Really? How much rational and logical thinking is found in the world today? Hardly any! You will probably have to go to a research institute or university to find it. What is the probability that a random gathering of people will start reasoning in a rationally and logically sound way? Close to zero! More likely than not one will be told to shut up. You don't have to imagine that, because it's our current reality. See Trump, the social media, fake news, all kinds of bizarre conspiracy theories, pseudoscience, postmodernism, etc. No - the problem is not too much but too little rational and logical thinking.

Not saying that there really is such a process, but when there is something to win then there usually is also something to loose. Why should there be only two possibilities: a good effect and no effect, and not the possibility of a bad effect?

Have you looked in the Neiye? Maybe there is something about it there?

He did refute the opposition with his paradoxes, or at least he thought he did. The opposition were those philosophers who thought that motion is real and that there are more than one things in the world. Zeno's teacher Parmenides claimed that there is actually only one changeless being, and that all else is illusion. See: https://en.wikipedia.org/wiki/Parmenides#Thought

Is it so bad? Take a rest then...

I never said that science gives us an absolutely accurate picture of reality, and no modern scientist would dare to claim that either.

You are drifting off into empty speculation. That's a very old joke. And indeed - I cannot proof that all kind of exotic ideas like we are living in a simulation, the world is a dream, we are continually fooled by devils, etc. are not true. But the only reasonable conclusion one can draw from that is that we cannot be absolutely sure about the world or even about ourselves. The old sceptics hundreds of years before Christ already knew that. But your life goes on, and apparently you keep using your computer as if there actually exists people who appear as Bums on this forum, so in practice you don't even take your own illusion-speculation seriously yourself. And that's OK because there is no reasonable way to take those speculations serious, except that is as warnings against pretensions of absolute knowledge.

If you don't like to walk you may also look at this picture: https://www.britannica.com/science/geometric-series/media/229825/19629 Not at all! No reason to suppose that.

Walk from one side to the other side of your room. Now to do that you first have to traverse half of the distance, then half of the remaining distance, then half of the still remaining distance, etc. Nevertheless you will doubtlessly succeed because the time necessary for the subsequent acts of traversing the subsequent half's of the remaining distance are continually getting shorter sufficiently fast. And in fact all of those times fit into the time that it takes you to walk from one side of your room to the other.

The method of exhaustion isn't problematic as far as I know. But there is a logical error in Zeno's reasoning and as soon as one sees it, the paradox is solved. Or mathematically speaking: an interval of finite length can indeed contain infinitely many intervals of finite lengths without thereby becoming infinitely long itself. That is all one needs to know, and then the reasoning of Zeno falls apart.

Good! The fact that it seems impossible to accomplish infinitely many acts within finite time is exactly what makes Zeno's paradoxes hard to solve ... until you see that there actually are infinite collections of acts that can be completed in finite time.

I don't see what watching the tortoise has to do with it, as long as they move with same velocity as before they may look at whatever they like...