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Kurt Gödel proved a version of Statement 1:
In any formal language, there are questions that can be asked but not answered.
A perfect example of Gödel's incompleteness law can be found in math:
- Positive Integers (lengths) can subtract a larger number from a smaller number. The answer is a negative integer, leading to:
- All integers can divide and result in a fraction, leading to:
- Fractions can be used in geometry to result in real numbers, leading to:
- Real Numbers can have square roots that are imaginary, leading to:
- Complex numbers, etc...
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In a certain village, a barber shaves all those who do not shave themselves. Who shaves the barber?
"A little song, a little dance, a little seltzer down your pants"
Chuckles the clown
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The famous Russel's Paradox, from what i remember.
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Behind every paradox lies a Cretan.
Religious freedom is the freedom to say that two plus two make five.
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A rule having no exception: "death and taxes"
The difficult we do right away...
...the impossible takes slightly longer.
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I once discussed that with my religious brother-in-law. He insisted that there are exceptions to that rule. May not to the "taxes" part, though.
Religious freedom is the freedom to say that two plus two make five.
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Amarnath S wrote: Would you agree with this conclusion? If so, is there any example of a rule having no exception?
Agreeing that a proof is valid is not the same as stating that it must be true. Now claiming that it is true could suggest that one should provide the example. Or provide other discussions that would suggest it is true. Or just believe and dispense with the work.
My favorite example with this is geometry (Euclidean) where parallel lines do not intersect. I certainly believe it. And I doubt anyone can provide an example that shows they do intersect. But for that matter they cannot provide an example where they do not intersect either.
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jschell wrote: parallel lines do not intersect
Though I am not a theoretical physicist, have heard that "space is curved", whatever it means. If space is curved, will there be a possibility of parallel lines meeting? Not sure.
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The exception for statement 1 is no exception. Doh
"A little time, a little trouble, your better day"
Badfinger
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You :
does a solution to the Russel Paradox exist
ChatGPT
Yes, several solutions to the Russell Paradox exist, which emerged after Bertrand Russell presented the paradox in 1901. One common solution is to restrict the comprehension principle, which states that for any property, there exists a set of all objects that have that property. By restricting this principle, mathematicians and logicians have been able to formulate set theories, like Zermelo-Fraenkel set theory (ZF) or von Neumann-Bernays-Gödel set theory (NBG), which avoid the paradox by disallowing the formation of certain "self-referential" sets. Another approach is to distinguish between sets and classes, where classes can contain sets but not be sets themselves, thereby sidestepping the contradiction. These solutions have allowed set theory to develop into a foundational framework for mathematics without succumbing to paradoxes like Russell's.
Me : If Statement 2 is a rule it must have an exception.
Conclusions: Statement 1 has no exception. There is at least one rule which has no exception.
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Wordle 1,045 2/6
⬛⬛⬛⬛🟩
🟩🟩🟩🟩🟩
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Wordle 1,045 4/6
⬜🟨🟩⬜⬜
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🟩🟩🟩🟨⬜
🟩🟩🟩🟩🟩
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Wordle 1,045 3/6
⬜⬜🟩🟨⬜
⬜🟩🟩⬜🟩
🟩🟩🟩🟩🟩
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Wordle 1,045 4/6
🟨⬜⬜⬜⬜
⬜⬜⬜🟨🟨
⬜⬜🟩🟨🟩
🟩🟩🟩🟩🟩
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Wordle 1,045 3/6
⬛⬛🟩🟨🟩
⬛🟩🟩⬛🟩
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Jeremy Falcon
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Wordle 1,045 3/6*
🟨🟩⬜⬜⬜
🟨🟩🟩⬜⬜
🟩🟩🟩🟩🟩
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony
"Common sense is so rare these days, it should be classified as a super power" - Random T-shirt
AntiTwitter: @DalekDave is now a follower!
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Wordle 1,045 4/6*
⬜⬜🟩🟨⬜
🟨🟩🟩⬜⬜
⬜🟩🟩🟨⬜
🟩🟩🟩🟩🟩
Happiness will never come to those who fail to appreciate what they already have. -Anon
And those who were seen dancing were thought to be insane by those who could not hear the music. -Frederick Nietzsche
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🟩🟩🟩⬜⬜
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In a closed society where everybody's guilty, the only crime is getting caught. In a world of thieves, the only final sin is stupidity. - Hunter S Thompson - RIP
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Wordle 1,045 4/6
🟨⬛⬛⬛⬛
⬛🟩🟩⬛🟩
⬛🟩🟩⬛🟩
🟩🟩🟩🟩🟩
Ok, I have had my coffee, so you can all come out now!
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Wordle 1,045 3/6
🟩🟩⬛⬛🟩
🟩🟩⬛🟩🟩
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WordleBot
Skill 74/99
Luck 74/99
If you can't explain something to a six year old, you really don't understand it yourself. (Albert Einstein)
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Wordle 1,045 5/6*
🟨🟨⬛⬛⬛
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⬛🟩🟩🟨⬛
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Thunderbird has been my SMTP client for years. My problem may be Thunderbird related, but my gut feeling says that it is not ...
I have several times noticed, when fetching new mail, that the status line says: 'Retrieving message 4 of 12', or something like that. When it completes, there are far less than 12 new messages in my inbox.
Tonight, it retrieved 'x of 6 messages', but only a single new message was in my inbox. There is nothing in the Thrash (and when something goes to Thrash, a counter displays the number of new entries). If a filter had redirected the messages to some other folder, it would have been seen in new count for that folder. Anyway, I have looked through every single folder, without finding anything new.
This is a fairly new thing; I have noticed it for a few weeks. Can anyone explain what is happening? Why does Thunderbird report 6 messages and display only 1 to me? I am suspecting that someone are trying to check if my mail address is valid, possibly also to see if I am reading the mailbox, by sending messages which somehow is marked to be deleted immediately, or possibly at a specific point in time that is already past - but I wasn't aware that SMTP had such a feature.
For the sender to be notified that I have received the mail, I am aware of an SMPT option for that. Thunderbird has several times presented a dialog box telling that the sender has requested a confirmation that the message has been received, with buttons for 'Return confirmation' and 'Do not send confirmation'. I have seen nothing of this when messages are 'missing'. I wasn't aware of an SMPT option for 'silently' generating a read confirmation - does it exist? If it exists, can it be used to secretly 'ping' me, the way it appears to me now?
Is there some other possible explanation? Could it be a Thunderbird hiccup? (That is a strange hiccup!)
Religious freedom is the freedom to say that two plus two make five.
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Duplicates in 'All Mail' and Important ? I've seen that happen, but didn't pay attention to the message count.
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I do not have, nor can I remember ever having an 'All Mail' and 'Important' folder. Searching in the TB help information, it seems as if it may be related to IMAP mail servers - my connection is via pop3. Some entries about 'All Mail' also seem to relate it to gmail, but gmail is not my mail provider; I use online.no, a mail service run by the Norwegian phone company.
Any further proposals?
Religious freedom is the freedom to say that two plus two make five.
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