Views : 6,722,645
Genre: Education
Date of upload: Sep 8, 2022 ^^
Rating : 4.771 (6,326/104,144 LTDR)
RYD date created : 2024-05-05T00:56:52.599946Z
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Top Comments of this video!! :3
Unlike many of your commenters, I don't have anything pithy to say about your presentation. I had never heard of Russell's Paradox or anyone else's Paradox. All I can do is tell you how much I appreciate how you described it. I did have to go back and review a couple of sections near the end, but I got it!
You are passionate about sharing your knowledge with everyone who cares to learn. Even, and perhaps especially, people incarcerated in prisons. You are a gifted teacher, so thank you for sharing your knowledge with ALL of us.
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On the predicate paradox: The main issue you seem to be grappling with on this is functionally comparable to the old, simpler paradox: "This sentence is false." If it's false, it's true; if it's true, it's false. So which could it be?
The most descriptively accurate answer I can think of is that it is neither, because it has no constant referential point upon which to base its definition. What can the sentence even proffer within it as "false"? What truth is it trying to debunk? None, because no such truth was extrapolated. Its only point of reference is itself, but it ipso facto eliminates that point by labeling it false, thus leaving it a useless self-contradictory abstraction, vacuous of point, logic, sense or reason.
And keep in mind that for definitions literary or otherwise, constant referential points are not to be underestimated in their essentiality. Without them, the means to describe them become variable and generalized to the point of uselessness. Consider, for example, the set that contains all sets, [X]. Okay- does that set include itself, [X] + [X+1]? Does it include that set, as well, [X] + [X + 1] + [X+2]? You'd have to keep on reiterating the addition of the set within itself ad infinitum, but doing so leaves you with an infinitely escalating value - and if your set contains an infinite value, can you really say you have a definition for it, considering the whole point of these sets was as a means to define whole numbers and now you have to find a single whole number for a sigma function?
This doesn't mean that math is broken, it only means that generalized categorizations give naive (heh) interpretations of mathematics that don't hold up without much greater scrutiny. If Zeno can be wrong about his ideas on motion being an illusion and Euclid can be wrong on his ideas of geometry, so can some professors be wrong about their ideas on sets. Nobody ever said this math stuff was easy, unless they did, in which case they can file under [set x: x contains all people who are shameless liars.]
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At my age (77), I am not going to wade through 18,643 comments to check if someone else has made the same comment as I am making here! I apologise in advance, however, if that is, in fact, the case.
When I first came across Russell's Paradox, more than 50 years ago, I explained it to myself as follows: if A is a set, then A is not the same thing as {A}, the set containing A. A set, in short, cannot be a member of itself, and the Paradox arises because the erroneous assumption is being made that a set can be a member of itself - your Rule 11.
On the few occasions in the last 50 years when I have thought about this again, I have come to the same conclusion.
I concur with the other comments about the quality of your presentation. Well done!
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For a 57 year old man who cannot even recite his times tables (my head just doesn't do maths), I'm stunned I actually followed that, I really did!!
That speaks volumes about this guys ability to convey information. I applaud you Sir, especially for the ability to hold my attention for the entire video. I quite enjoyed that!! I've no idea what use it is to me personally, but it was fascinating!
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As a child I spent weeks writing "S, P, AO, Agent" and whatever else, under words for a language class (this was in a different country so abbreviations may not carry over) - its been 2 decades since, and today is the first time I have seen it used to explain something. It saved me 60, or maybe 90 seconds. Time well spent!
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As more of a physicist than a mathematician I have always held that there are no exceptions to a rule. If an exception is encountered then the 'rule' is not a rule and the 'rule' requires modification such that the exception no longer exists under the modified rule. Set theory rule #11 is at fault. Think of it spatially - set A has a boundary as it 'contains', and the set that 'contains' set A has a second boundary around Set A and is spatially different from Set A - therefore a set cannot contain itself.
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@nyc-exile
1 year ago
My teacher told me that "all rules have exceptions" and I told her that that meant that there are rules that don't have exceptions. Because if "all rules have exceptions" is a rule then it must have an exception that contradicts it.
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