Re: A Guide for Cantor Cranks

Article View: sci.logic

Article #763

#763

From: James Burns
Date: Tue, 29 Mar 2011 21:33

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Transfer Principle wrote:
> On Mar 27, 10:49 am, Jim Burns <burns...@osu.edu> wrote:
>>On 3/27/2011 7:46 AM, Albrecht wrote:
>>>On 27 Mrz., 05:45, Barb Knox<s...@sig.below> wrote:

>>>>Whatever he does next, he will be sure that
>>>>it is correct.
>>>>Your exposition is helpful and to the point,
>>>>but it will not get through.
>>
>>[ Piggyback to Barb Knox:
>>   Thank you for your kind words.
>>   Whether or not it gets through,
>>   I think I understand the reals
>>   a bit better every time I explain them.
>>]
>>
>>>You must be a sybil. You love this job?
>>
>>How could she not, what with the high pay and perks?
>>How does declaring the naturals, integers,
>>rationals and reals to form proper classes
>>instead of sets get rid of any silliness?
>>Isn't the proper class of naturals still
>>larger than the proper class of reals?
>
> Most proper class theories have a "Limitation of Size"
> axiom, thereby guaranteeing that all proper classes
> have the same size. So the answer should be "no."

< Limitation of Size:
< For any class C, a set x such that x=C exists
< if and only if there is no bijection between C
< and the class V of all sets.
http://en.wikipedia.org/wiki/NBG_set_theory#Axiomatizating_NBG

It doesn't look like it works the way you seem
to think it does.

It looks to me as though, if you were to declare R
a proper class and it DID NOT biject with V, the
proof that R did NOT biject with V would not disappear,
it's just that you now also have a proof that R
DOES biject with V. All you would get is an
inconsistent system for your trouble.

So, the answer would be either "yes" or anything you want,
including "Colorless green ideas sleep furiously".

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<40e69d0c-eb77-4308-996e-c7dfc1a0ec1e@j13g2000pro.googlegroups.com> <92a4e0aa-6497-4357-8a6b-ecc706fa10f5@d26g2000prn.googlegroups.com> <5d2c87a8-5926-4b27-a445-3bc3ab5c98d0@u3g2000vbe.googlegroups.com> <35760f05-df0e-4c29-85c0-08f98cf10a42@s18g2000prg.googlegroups.com> <521e5cfe-5269-4d9a-ab45-5e8cf597b2d1@y31g2000vbp.googlegroups.com> <971970b6-b722-4f38-96cb-4aef5f17e96e@b22g2000prb.googlegroups.com> <d9d86644-ea52-4f53-ba2f-42d2718630c0@k7g2000yqj.googlegroups.com> <b05355b2-d80e-47ec-9c3b-43e7bc40ab32@22g2000prx.googlegroups.com> <4D8B5041.9060702@osu.edu> <936fb9f1-da8e-4533-93a1-15cf5d060cc5@k7g2000yqj.googlegroups.com> <iml34b$k08$1@charm.magnus.acs.ohio-state.edu> <see-A72772.16452927032011@mx01.eternal-september.org> <6423234e-e533-49f4-a8de-3d474d056299@x8g2000prh.googlegroups.com> <imntb9$8ll$1@charm.magnus.acs.ohio-state.edu> <03695b17-fbd4-4862-9238-d5ffc639d84b@18g2000prd.googlegroups.com>

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From: James Burns <burns.87@osu.edu>
Newsgroups: sci.logic,sci.math,comp.theory,sci.physics,aus.science
Subject: Re: A Guide for Cantor Cranks
Date: Tue, 29 Mar 2011 17:33:00 -0400
Organization: Ohio State University
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References: <40e69d0c-eb77-4308-996e-c7dfc1a0ec1e@j13g2000pro.googlegroups.com> <92a4e0aa-6497-4357-8a6b-ecc706fa10f5@d26g2000prn.googlegroups.com> <5d2c87a8-5926-4b27-a445-3bc3ab5c98d0@u3g2000vbe.googlegroups.com> <35760f05-df0e-4c29-85c0-08f98cf10a42@s18g2000prg.googlegroups.com> <521e5cfe-5269-4d9a-ab45-5e8cf597b2d1@y31g2000vbp.googlegroups.com> <971970b6-b722-4f38-96cb-4aef5f17e96e@b22g2000prb.googlegroups.com> <d9d86644-ea52-4f53-ba2f-42d2718630c0@k7g2000yqj.googlegroups.com> <b05355b2-d80e-47ec-9c3b-43e7bc40ab32@22g2000prx.googlegroups.com> <4D8B5041.9060702@osu.edu> <936fb9f1-da8e-4533-93a1-15cf5d060cc5@k7g2000yqj.googlegroups.com> <iml34b$k08$1@charm.magnus.acs.ohio-state.edu> <see-A72772.16452927032011@mx01.eternal-september.org> <6423234e-e533-49f4-a8de-3d474d056299@x8g2000prh.googlegroups.com> <imntb9$8ll$1@charm.magnus.acs.ohio-state.edu> <03695b17-fbd4-4862-9238-d5ffc639d84b@18g2000prd.googlegroups.com>
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