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Zeno's Paradox Discussion with Garrett Mayer 

Inductica
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I discuss various topics with Garrett in mathematics, especially Zeno's paradox and Pat Corvini's solution to it.
Achilles, the Tortoise and the Objectivity of Mathematics, by Pat Corvini
estore.aynrand.org/p/194/achi...
Mathematics is About the World by Robbert Knapp:
mathematicsisabouttheworld.com/

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1 май 2020

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Комментарии : 14   
@nicolaskrusek3703
@nicolaskrusek3703 3 года назад
A fantastic discussion of mathematics. Thank you for mentioning Robert Knapp's book; I have read the first five (elementary) chapters, and found it challenging but rewarding, though I have not been so bold as to attempt the last three (advanced) chapters. Are you familiar with James Franklin's "An Aristotelian Realist Philosophy of Mathematics?" Franklin is not an Objectivist, but he and Knapp have cited each other's work, and it appears that they are thinking along broadly similar lines. My local university library has this book, and I hope to read it in the near future. I am looking for a book that gives the layperson a general overview of the field of mathematics. I started reading the celebrated "What is Mathematics?" by Robbins and Courant and got bogged down in technicalities in the first few chapters. I plan to return to it later on, but in the meantime I would appreciate any recommendations for more elementary reading on the subject. Perhaps something that takes a historical approach?
@Inductica
@Inductica 3 года назад
I'm not aware of James Franklin. As far as I know, the book you are looking for does not exist, they are all too technical or irrelevant in their details. Two authors I can generally recommend are Issac Asimov and Morris Kline. There's "Mathematical Thought from Ancient to Modern Times," by Klein, and "On Numbers," by Asimov, but neither of these are exactly what you are looking for. In physics I would also recommend "The History of Physics," by Asimov. This is by far the most inductive book on physics I have ever read and I highly recommend it above all math and physics books. It lacks the mathematical detail I would want to see, but that actually makes it perfect for your purposes.
@UFO314159
@UFO314159 4 года назад
"1984" was published in 1948; Orwell simply reversed the digits. "Atlas Shrugged" was published in 1957.
@UFO314159
@UFO314159 4 года назад
My understanding of the solution to Zeno's paradox: Any division of motion is purely cognitive. There isn't an infinite amount of steps in Achilles' or the tortoise's motion, for each there is only one continuous motion. To catch and surpass the tortoise Achilles doesn't have to complete an infinite number of steps, he only has to complete the one step of catching and then surpassing the tortoise. I'm fairly sure this isn't my original idea, but I don't remember my source for it. If you have any objections to this argument, feel free to voice them.
@UFO314159
@UFO314159 4 года назад
P.S. I just bought Pat Corvini's lecture. Perhaps it will elucidate this matter further, although from what you said about the grain of sand idea it sounds like she is returning to the discreteness of space idea.
@Inductica
@Inductica 4 года назад
@@UFO314159 No, it does not refer to the discreteness of space, it refers to the fact that our measurement will always choose some standard, that standard can be as small as you would like (like a grain of sand) but it must always be something.
@UFO314159
@UFO314159 4 года назад
@@Inductica I'll keep this in mind as I listen to the lecture.
@UFO314159
@UFO314159 4 года назад
@@Inductica I thank you for giving me the incentive to listen to Pat Corvini's lecture. Some time ago, I became aware that mathematics seemed to be based on the premise of infinitely precise measurement, which we don't have in the real world, and that because this premise disconnects mathematics from reality it would be necessary to completely rebuild the subject by taking the finite precision of measurement into account. Now that I have listened to Mrs. Corvini's lecture, I have a more enlightened understanding of the nature of mathematics, which is: mathematics is the science of establishing among quantities universal relations which do not depend on the precision of our measurements. I see now that, thankfully, no such rebuilding is necessary.
@Inductica
@Inductica 4 года назад
@@UFO314159 Awesome dude! Sounds like you got it. Do you happen to work in a math related field?
@luketerry2006
@luketerry2006 4 года назад
I have never spent any time on the paradox, but just spitballing here, isn't zenus only concrete conclusion is that the hare could never catch up to the tortoise so that they are absorbed into one entity? There is no amount of motion in relation between two objects where one object becomes the second. But the paradox is only commenting on the relationship between two objects. There is no paradox if you discuss the relationship of the two objects to some third object, I.e. this paradox goes away if you are discussing the relationship of a hare and a tortoise both traveling to a pond. Clearly the hare can outdistance the tortoise in that case. But at no point can the tortoise or the hair get so close to the pond to become the pond because of the law of existence and identity
@UFO314159
@UFO314159 4 года назад
In the infamous paradox, Achilles and the tortoise are running side by side, as in an ordinary foot race. Zeno's only concern is as to how far each runner is from the starting line, and how these distances compare to each other. The paradox still persists even if Achilles and the tortoise can't physically merge with each other (which, of course, they can't). If you haven't already done so, listen to Pat Corvini's lecture on the paradox, linked in the description box. It is quite illuminating.
@luketerry2006
@luketerry2006 4 года назад
It seems the socialist trick is that capitalism is a necessary stepping stone in human progress, but it becomes a point where it is more harmful than helpful. so every socialists argument is that now is the time where we are able to evolve past capitalism to something better
@Inductica
@Inductica 4 года назад
That isn't just a trick, that is actually an explicit part of Marx's philosophy.
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