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tech / sci.math / Some axioms of similar scientific value as the axiom of choice:

SubjectAuthor
* Some axioms of similar scientific value as the axiom of choice:WM
+* Re: Some axioms of similar scientific value as the axiom of choice:Mostowski Collapse
|`* Re: Some axioms of similar scientific value as the axiom of choice:FromTheRafters
| `- Re: Some axioms of similar scientific value as the axiom of choice:Timothy Golden
`- Re: Some axioms of similar scientific value as the axiom of choice:Serg io

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Some axioms of similar scientific value as the axiom of choice:

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Subject: Some axioms of similar scientific value as the axiom of choice:
From: wolfgang...@hs-augsburg.de (WM)
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 by: WM - Sat, 25 Dec 2021 10:45 UTC

 Axiom of two even primes: There are two even prime numbers. (But provably it is impossible to determine whether the second one is less or larger than 2.)
 Axiom of prime number triples: There is a second triple of prime numbers, besides (3, 5, 7). (But provably this second triple is not arithmetically definable.)
 Axiom of meagre sum: There is a set of n different positive natural numbers with sum n^2/2. (This axiom is not constructive. Provably no such set can be constructed.)
 Axiom of ultimate mathematical simplification: All mathematical problems are solved by whatever is declared as their solutions. (This axiom is guaranteed not less useful than the axiom of choice in considerably shortening proofs about uncountable sets.)
 Axiom of well-ordering: Every set can be well-ordered. (This axiom is not constructive. In most cases provably no set theoretic definition of a well-order can be found.)

How obvious a contradiction has to result from an additional axiom in order to reject it?

Regards, WM

Re: Some axioms of similar scientific value as the axiom of choice:

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Subject: Re: Some axioms of similar scientific value as the axiom of choice:
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Sat, 25 Dec 2021 12:01 UTC

- axiom of shit for brains: WMs envy of mathematics is so high,
he now thinks there are dark numbers

WM schrieb am Samstag, 25. Dezember 2021 um 11:45:15 UTC+1:
>  Axiom of two even primes: There are two even prime numbers. (But provably it is impossible to determine whether the second one is less or larger than 2.)
>  Axiom of prime number triples: There is a second triple of prime numbers, besides (3, 5, 7). (But provably this second triple is not arithmetically definable.)
>  Axiom of meagre sum: There is a set of n different positive natural numbers with sum n^2/2. (This axiom is not constructive. Provably no such set can be constructed.)
>  Axiom of ultimate mathematical simplification: All mathematical problems are solved by whatever is declared as their solutions. (This axiom is guaranteed not less useful than the axiom of choice in considerably shortening proofs about uncountable sets.)
>  Axiom of well-ordering: Every set can be well-ordered. (This axiom is not constructive. In most cases provably no set theoretic definition of a well-order can be found.)
>
> How obvious a contradiction has to result from an additional axiom in order to reject it?
>
> Regards, WM

Re: Some axioms of similar scientific value as the axiom of choice:

<sq747k$3kb$1@dont-email.me>

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From: erra...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Some axioms of similar scientific value as the axiom of choice:
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 by: FromTheRafters - Sat, 25 Dec 2021 12:52 UTC

Mostowski Collapse formulated on Saturday :
> - axiom of shit for brains: WMs envy of mathematics is so high,
> he now thinks there are dark numbers

Muckymath's 'Axiom of Because I Said So' is so powerful that he needs
no other axioms.

Re: Some axioms of similar scientific value as the axiom of choice:

<sq7k8d$eg4$1@gioia.aioe.org>

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From: inva...@invalid.com (Serg io)
Newsgroups: sci.math
Subject: Re: Some axioms of similar scientific value as the axiom of choice:
Date: Sat, 25 Dec 2021 11:26:36 -0600
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 by: Serg io - Sat, 25 Dec 2021 17:26 UTC

On 12/25/2021 4:45 AM, WM wrote:
>  Axiom of two even primes: There are two even prime numbers. (But provably it is impossible to determine whether the second one is less or larger than 2.)
>  Axiom of prime number triples: There is a second triple of prime numbers, besides (3, 5, 7). (But provably this second triple is not arithmetically definable.)
>  Axiom of meagre sum: There is a set of n different positive natural numbers with sum n^2/2. (This axiom is not constructive. Provably no such set can be constructed.)
>  Axiom of ultimate mathematical simplification: All mathematical problems are solved by whatever is declared as their solutions. (This axiom is guaranteed not less useful than the axiom of choice in considerably shortening proofs about uncountable sets.)
>  Axiom of well-ordering: Every set can be well-ordered. (This axiom is not constructive. In most cases provably no set theoretic definition of a well-order can be found.)
>
> How obvious a contradiction has to result from an additional axiom in order to reject it?
>
> Regards, WM

Those are your Axioms, you fix them. You have to eat what you cook.

Re: Some axioms of similar scientific value as the axiom of choice:

<2f54b2c3-f26e-4c6e-b177-90609cfc86c4n@googlegroups.com>

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Subject: Re: Some axioms of similar scientific value as the axiom of choice:
From: timbandt...@gmail.com (Timothy Golden)
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 by: Timothy Golden - Sun, 26 Dec 2021 00:01 UTC

On Saturday, December 25, 2021 at 7:53:18 AM UTC-5, FromTheRafters wrote:
> Mostowski Collapse formulated on Saturday :
> > - axiom of shit for brains: WMs envy of mathematics is so high,
> > he now thinks there are dark numbers
> Muckymath's 'Axiom of Because I Said So' is so powerful that he needs
> no other axioms.

That is pretty much how axioms go, sir. They are grants. If they are unbelievable then they will not be believed. Propagation under threat of failure however is an entirely effective mechanism.

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