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Hello, let me state what my views are on Russell's Paradox:
I think Russell was correct to redefine some of the language. If one understands the true meaning of a "set" as a collection of elements that has no specific existence in and of itself, that is, it's not a predicate, then one can easily dissolve the dilemma in my opinion.
This would make R not a member of itself because the definition itself is arbitrary (i.e. not "real"), just like the definition of a set itself. However, R would also be a member of itself because of the definition of what goes under R. This is a contradiction only because I think one fails to differentiate between what actually exists and what is being defined. For example if I have a blue car, then I can say accurately that "I drive a blue car." However, if I had to break my car down into individual atoms, then I'd be driving something that's neither blue nor a car (something similar to Sorites' Paradox or Theseus' Ship).
So the "barber who shaves all men who don't shave themselves" example can best be understood by acknowledging that one hasn't defined the relationship between customer and barber properly. This might seems contradictory, but just like our "blue car" example, it's ultimately an example of the fallacy of language: such a barber does not "exist," just like sets don't "exist" in and of themselves.
So if any of these ideas of mine have a possible grain of understanding, I was wondering how they might relate to the vacuous truth (R has a property that it doesn't have because it doesn't "exist"), Godel's Incompleteness Theorems (which if I understand correctly, imply that one cannot fully prove anything to be what it is without making some assumptions), and Kant's idea that "existence," isn't a predicate (which I think relates to the 'possible worlds' of philosophers). -- Cornelius ( talk) 03:05, 29 October 2016 (UTC)
I've been reading List of countries by length of coastline, and understand how the coastline of Britain is fractal and varies as the measuring stick used changes. I am puzzled by the coastline of GB being stated as 28000km (what is the superscript 1.43?) yet the table list the bigger UK as only 12429km.
Anyway that apart, how does the Hausdorff measure work? I've read the article and don't understand a word of it. Could someone summarize how it works in English rather than in Maths please. One (semi-random) idea inspired by the superscript number is that in some fashion the coastline length remains stable with changing measure stick at some particular fractional dimension. (Or not ...) -- SGBailey ( talk) 08:17, 29 October 2016 (UTC)
HOTmag ( talk) 21:26, 29 October 2016 (UTC)
Mathematics desk | ||
---|---|---|
< October 28 | << Sep | October | Nov >> | October 30 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Hello, let me state what my views are on Russell's Paradox:
I think Russell was correct to redefine some of the language. If one understands the true meaning of a "set" as a collection of elements that has no specific existence in and of itself, that is, it's not a predicate, then one can easily dissolve the dilemma in my opinion.
This would make R not a member of itself because the definition itself is arbitrary (i.e. not "real"), just like the definition of a set itself. However, R would also be a member of itself because of the definition of what goes under R. This is a contradiction only because I think one fails to differentiate between what actually exists and what is being defined. For example if I have a blue car, then I can say accurately that "I drive a blue car." However, if I had to break my car down into individual atoms, then I'd be driving something that's neither blue nor a car (something similar to Sorites' Paradox or Theseus' Ship).
So the "barber who shaves all men who don't shave themselves" example can best be understood by acknowledging that one hasn't defined the relationship between customer and barber properly. This might seems contradictory, but just like our "blue car" example, it's ultimately an example of the fallacy of language: such a barber does not "exist," just like sets don't "exist" in and of themselves.
So if any of these ideas of mine have a possible grain of understanding, I was wondering how they might relate to the vacuous truth (R has a property that it doesn't have because it doesn't "exist"), Godel's Incompleteness Theorems (which if I understand correctly, imply that one cannot fully prove anything to be what it is without making some assumptions), and Kant's idea that "existence," isn't a predicate (which I think relates to the 'possible worlds' of philosophers). -- Cornelius ( talk) 03:05, 29 October 2016 (UTC)
I've been reading List of countries by length of coastline, and understand how the coastline of Britain is fractal and varies as the measuring stick used changes. I am puzzled by the coastline of GB being stated as 28000km (what is the superscript 1.43?) yet the table list the bigger UK as only 12429km.
Anyway that apart, how does the Hausdorff measure work? I've read the article and don't understand a word of it. Could someone summarize how it works in English rather than in Maths please. One (semi-random) idea inspired by the superscript number is that in some fashion the coastline length remains stable with changing measure stick at some particular fractional dimension. (Or not ...) -- SGBailey ( talk) 08:17, 29 October 2016 (UTC)
HOTmag ( talk) 21:26, 29 October 2016 (UTC)