# Difference between revisions of "User talk:Aschlafly"

(Set theory is a different style of reasoning. Otherwise there would not have been such intense, hostile opposition to it. But its power and logic ultimately prevailed over the opposition. And Georg Cantor is properly given all the credit.) |
m (→So the last will be first, and the first last: Fix obvious slip. Are you using a touch screen, by any chance? Touch screens can do an amazing amount of damage at the slightest touch.) |
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I for one am not baffled by it at all. Jesus was not making a statement about set theory or measure theory. He was making a moral/ethical statement about pay scales. One can disagree with Him (and some of the workers did), but His statement was very clear. The "first" and "last" referred to the wages of the workers and the time when they had joined the work crew. Jesus's statement was clear in Biblical times and is clear now. | I for one am not baffled by it at all. Jesus was not making a statement about set theory or measure theory. He was making a moral/ethical statement about pay scales. One can disagree with Him (and some of the workers did), but His statement was very clear. The "first" and "last" referred to the wages of the workers and the time when they had joined the work crew. Jesus's statement was clear in Biblical times and is clear now. | ||

− | One can't just say "I have invented a new field of mathematics, and I am calling it 'set theory'". One needs to provide various theorems and results showing that it is a fruitful new area of mathematics, Cantor, and others, did just that. There are the various theorems about cardinality and measure theory. There's the Baire Category Theorem (which provides another proof, independent of diagonalization, that the cardinality of the reals is strictly greater than the cardinality of the rationals). There's the Cantor set, which is a uncountable set of measure zero, a seemingly paradoxical result. There's the Cantor function, which has derivative equal to zero everywhere except on a set of measure zero, but has f(0)=0 and f(1)=1, also seemingly paradoxical. And there are other theorems, like the Heine-Borel theorem and the Bolzano-Weierstrass | + | One can't just say "I have invented a new field of mathematics, and I am calling it 'set theory'". One needs to provide various theorems and results showing that it is a fruitful new area of mathematics, Cantor, and others, did just that. There are the various theorems about cardinality and measure theory. There's the Baire Category Theorem (which provides another proof, independent of diagonalization, that the cardinality of the reals is strictly greater than the cardinality of the rationals). There's the Cantor set, which is a uncountable set of measure zero, a seemingly paradoxical result. There's the Cantor function, which has derivative equal to zero everywhere except on a set of measure zero, but has f(0)=0 and f(1)=1, also seemingly paradoxical. And there are other theorems, like the Heine-Borel theorem and the Bolzano-Weierstrass theorem. And Zorn's Lemma. And, of course, all of analysis and topology. |

You can't just treat set theory like some simple monolithic thing invented by Georg Cantor. The notion that the field could have been worked out by an open-minded reading of Matthew 20:16 is rather far-fetched. [[User:SamHB|SamHB]] ([[User talk:SamHB|talk]]) 00:27, 19 June 2019 (EDT) | You can't just treat set theory like some simple monolithic thing invented by Georg Cantor. The notion that the field could have been worked out by an open-minded reading of Matthew 20:16 is rather far-fetched. [[User:SamHB|SamHB]] ([[User talk:SamHB|talk]]) 00:27, 19 June 2019 (EDT) | ||

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:Workers at the time of Jesus disagreed with him, as many do today, when he observed paradoxically that the "last shall be first, and the first last." But when viewed as a set theorist does, there is not paradoxical about it at all.--[[User:Aschlafly|Andy Schlafly]] ([[User talk:Aschlafly|talk]]) 00:34, 19 June 2019 (EDT) | :Workers at the time of Jesus disagreed with him, as many do today, when he observed paradoxically that the "last shall be first, and the first last." But when viewed as a set theorist does, there is not paradoxical about it at all.--[[User:Aschlafly|Andy Schlafly]] ([[User talk:Aschlafly|talk]]) 00:34, 19 June 2019 (EDT) | ||

+ | |||

== MPR deletion == | == MPR deletion == | ||

## Revision as of 09:35, 19 June 2019

## Contents

## Deletion request

Hello Andy, would you please delete these two redirects: [1][2] They give way too much recognition to a leftist website created to vandalize CP and which slanders CP editors. --1990'sguy (talk) 08:29, 16 April 2019 (EDT)

- Done as requested!--Andy Schlafly (
**talk**) 09:15, 16 April 2019 (EDT)

## Miley Cyrus photo

Hello Andy, do you think it's inappropriate to include this photo on the Miley Cyrus page? File:Miley Cyrus.jpg I don't have much of a problem with it, but DouglasA disagrees. --1990'sguy (talk)

- I'm OK with it.--Andy Schlafly (
**talk**) 14:23, 19 April 2019 (EDT)

## MPR suggestion

This struck me as a very Conservapedia type of story: "'In God We Trust' will remain on US currency as Supreme Court declines atheist challenge." PeterKa (talk) 20:54, 10 June 2019 (EDT)

## So the last will be first, and the first last

Could you please explain this concept in the language of set theory? What *is* the paradox, and how is it resolved by set theory? Thanks. --AugustO (talk) 10:45, 13 June 2019 (EDT)

- The paradox is obvious. In number theory and virtually every other system of logic, the last cannot be the first. But in set theory it can.--Andy Schlafly (
**talk**) 18:31, 15 June 2019 (EDT)- I take the bait: how can the last be the first in set theory? --AugustO (talk) 19:40, 15 June 2019 (EDT)
- Thanks for archiving. Enumeration of elements of a set is up to the intelligent designer. This is how Georg Cantor proved that the set of real numbers is larger than the infinite set of rational numbers. But you're in good company if you resist his way of looking at things. Many great mathematicians of his time thought (incorrectly) that he was some kind of charlatan.--Andy Schlafly (
**talk**) 20:44, 15 June 2019 (EDT)

- Thanks for archiving. Enumeration of elements of a set is up to the intelligent designer. This is how Georg Cantor proved that the set of real numbers is larger than the infinite set of rational numbers. But you're in good company if you resist his way of looking at things. Many great mathematicians of his time thought (incorrectly) that he was some kind of charlatan.--Andy Schlafly (

- I take the bait: how can the last be the first in set theory? --AugustO (talk) 19:40, 15 June 2019 (EDT)

Georg Cantor's great breakthrough ("Cantor diagonalization") was not in showing that the rationals are countable—that is a fairly straightforward construction—but in using that fact to show that the reals are not countable. There are many ways to specify the correspondence between a given denumerable (countable) set and the natural numbers. In fact, there are a uncountably infinite number of ways to set up the correspondence. Whether any of these constitute "intelligent design" is not for me to say, except that I think that term gets overused in certain quarters.

Then there's the matter of a "well ordering". A "well order" on a set is an order such that any subset has a least element. So a set with a "well order" is sort of like the positive integers—any subset of the positive integers, even an infinite subset, has a least element. (Note that the full set of integers, or the rationals, or the reals, are *not* well-ordered by their normal arithmetical order.) But it is a theorem of ZFC logic that any set has a well-order.

Does the well-ordering theorem constitute intelligent design? That's not for me to say. Does it disprove the Cantor diagonalization theorem? No. The well-order on the reals necessarily uses the Axiom of Choice, and cannot be constructed. Cantor diagonalization *can* be constructed.

Getting back down to Earth, sets can have different orders—the natural numbers from 1 to 100 can have an increasing order and a decreasing order (and 100 factorial other orders too.) With that notion, "the last" under one order "will be first" under the other order. But this is completely obvious under any system of logic, including set theory. But claiming that it's true for the *same* set with the *same* order is simply nonsensical.

- But I'm in good company if I resist your way of looking at things in this manner. I'm sure AugustO is also.

SamHB (talk) 00:39, 17 June 2019 (EDT)

- "sets can have different orders" - precisely. But the number line does not. What Jesus taught was nonsensical to logicians and philosophers of his time, but perfectly logical once Georg Cantor overcame intense opposition and developed the breakthrough of set theory. If Cantor's opponents had recognized the Bible as a book of logic with an open mind, then they would not have mistakenly opposed Cantor so much. Ditto for Thomas Paine.--Andy Schlafly (
**talk**) 00:47, 17 June 2019 (EDT)

- "sets can have different orders" - precisely. But the number line does not. What Jesus taught was nonsensical to logicians and philosophers of his time, but perfectly logical once Georg Cantor overcame intense opposition and developed the breakthrough of set theory. If Cantor's opponents had recognized the Bible as a book of logic with an open mind, then they would not have mistakenly opposed Cantor so much. Ditto for Thomas Paine.--Andy Schlafly (

- The real line, like all sets of more than one element, most definitely
*can*have multiple different orderings. Here's an alternative ordering off the top of my head. Let SWAP(X) be result of swapping the 1^{st}and 2^{nd}decimal digits, the 3^{rd}and 4^{th}digits, and so on. Then we can define an ordering on the reals that has X < Y in this ordering if SWAP(X) < SWAP(Y) in the usual numerical ordering. While this may sound weird and contrived, this sort of thing happens all the time in set theory and measure theory, and is actually very close to what goes on in Cantor diagonalization.

- The real line, like all sets of more than one element, most definitely

- Many people were criticized or vilified at some point in their lives. Georg Cantor, Thomas Paine, Galileo Galilei, Louis Pasteur, and Oliver Heaviside come to mind. I don't think it is fruitful to analyze these cases in detail here, and I don't think you have established that the criticism of Cantor arose from an insufficiently open-minded reading of Matthew 20:16. SamHB (talk) 00:27, 19 June 2019 (EDT)

Could you please quote one philosopher or logician of His time who was baffled be Matthew 20:16 (or Mark 10:31 or Luke 13:30)? Especially as Matthew writes ἔσονται οἱ ἔσχατοι πρῶτοι and not εἰσιν οἱ ἔσχατοι πρῶτο? --AugustO (talk) 13:02, 17 June 2019 (EDT)

- Many critics of the Bible were probably baffled by it. Don't have quotes handy, but perhaps some can be found on atheist websites.--Andy Schlafly (
**talk**) 15:03, 17 June 2019 (EDT)

- So your claim that "
*what Jesus taught was nonsensical to logicians and philosophers of his time*" wasjust made up. --AugustO (talk) 18:53, 17 June 2019 (EDT)**probably**- My statement was self-evident. When I have more time I can research it further, but the reality is that writings of Jesus and his followers survived to a far greater extent than those of his detractors, so the thinking of non-believers is not always easy to find.--Andy Schlafly (
**talk**) 23:30, 18 June 2019 (EDT)

- My statement was self-evident. When I have more time I can research it further, but the reality is that writings of Jesus and his followers survived to a far greater extent than those of his detractors, so the thinking of non-believers is not always easy to find.--Andy Schlafly (

- So your claim that "

I for one am not baffled by it at all. Jesus was not making a statement about set theory or measure theory. He was making a moral/ethical statement about pay scales. One can disagree with Him (and some of the workers did), but His statement was very clear. The "first" and "last" referred to the wages of the workers and the time when they had joined the work crew. Jesus's statement was clear in Biblical times and is clear now.

One can't just say "I have invented a new field of mathematics, and I am calling it 'set theory'". One needs to provide various theorems and results showing that it is a fruitful new area of mathematics, Cantor, and others, did just that. There are the various theorems about cardinality and measure theory. There's the Baire Category Theorem (which provides another proof, independent of diagonalization, that the cardinality of the reals is strictly greater than the cardinality of the rationals). There's the Cantor set, which is a uncountable set of measure zero, a seemingly paradoxical result. There's the Cantor function, which has derivative equal to zero everywhere except on a set of measure zero, but has f(0)=0 and f(1)=1, also seemingly paradoxical. And there are other theorems, like the Heine-Borel theorem and the Bolzano-Weierstrass theorem. And Zorn's Lemma. And, of course, all of analysis and topology.

You can't just treat set theory like some simple monolithic thing invented by Georg Cantor. The notion that the field could have been worked out by an open-minded reading of Matthew 20:16 is rather far-fetched. SamHB (talk) 00:27, 19 June 2019 (EDT)

- Set theory is a different style of reasoning. Otherwise there would not have been such intense, hostile opposition to it. But its power and logic ultimately prevailed over the opposition. And Georg Cantor is properly given all the credit.

- Workers at the time of Jesus disagreed with him, as many do today, when he observed paradoxically that the "last shall be first, and the first last." But when viewed as a set theorist does, there is not paradoxical about it at all.--Andy Schlafly (
**talk**) 00:34, 19 June 2019 (EDT)

## MPR deletion

Hello Andy, would you please restore the massive amount of information accidentally deleted in this edit on Template:Mainpageright? (scroll down a bit): [3] I also sent you an email about this. --1990'sguy (talk) 17:27, 15 June 2019 (EDT)

- Thanks, I thought I restored it already. It seems to have the proper link at the bottom.--Andy Schlafly (
**talk**) 18:30, 15 June 2019 (EDT)